PHOTOELECTRONICS

MINISTRY OF EDUCATION AND SCIENCE OF UKRAINE
Odessa I. I. Mechnikov National University
PHOTOELECTRONICS
INTER-UNIVERSITIES SCIENTIFIC ARTICLES
Founded in 1986
Number 18
Odessa
«Astroprint»
2009

UDC 621.315.592:621.383.51:537.221
The results of theoretical and experimental studies in problems of optoelectronics, solar power
and semiconductor material science for photoconductive materials are adduced in this collection.
The prospective directions for photoelectronics are observed.
The collection is introduction into the List of special editions of Ukrainian Higher Certification
Comission in physics-mathematics and tehnical sciences.
For lecturers, scientists, post-graduates and students.
Ó çá³ðíèêó íàâåäåí³ ðåçóëüòàòè òåîðåòè÷íèõ ³ åêñïåðèìåíòàëüíèõ äîñë³äæåíü ç ïèòàíü
îïòîåëåêòðîí³êè, ñîíÿ÷íî¿ åíåðãåòèêè ³ íàï³âïðîâ³äíèêîâîãî ìàòåð³àëîçíàâñòâà ôîòî -
ïðîâ³äíèõ ìàòåð³àë³â. Ðîçãëÿíóòî ïåðñïåêòèâí³ íàïðÿìêè ðîçâè òêó ôîòîåëåêòðîí³êè.
Çá³ðíèê âêëþ÷åíî äî Ñïèñêó ñïåö³àëüíèõ âèäàíü ÂÀÊ Óêðà¿íè ç ô³çèêî-ìàòåìàòè÷íèõ
òà òåõí³÷íèõ íàóê.
Äëÿ âèêëàäà÷³â, íàóêîâèõ ïðàö³âíèê³â, àñï³ðàíò³â, ñòóäåíò³â.
Editorial board of “Photoelectronics”:
Editor-in-Chief Smyntyna V. A.
Kutalova M. I. (Odessa, Ukraine, responsible editor),
Vaxman Yu. F. (Odessa, Ukraine),
Litovchenko V. G. (Kiev, Ukraine),
Gulyaev Yu. V. (Moscow, Russia),
D’Amiko A. (Rome, Italy),
Mokrickiy V. A. (Odessa, Ukraine),
Neizvestny I. G. (Novosibirsk, Russia),
Starodub N. F. (Kiev, Ukraine),
Viculin I. M. (Odessa, Ukraine)
Address of editorial board:
Odessa I. I. Mechnikov National University 42, Pasteur str, Odessa, 65026, Ukraine
e-mail: wadz@mail.ru, tel.: +38-0482-7266356.
Information is on the site: http://www.photoelectronics.onu.edu.ua
© Odessa I. I. Mechnikov National
University, 2009

TABLE OF CONTENT
R. V. VITER, V. A. SMYNTYNA, I. P. KONUP, YU. A. NITSUK, V. A. IVANITSA
Conductivity mechanism in thin nanocryctalline tin oxide films .................................................................................................. 4
G. S. FELINSKYI
Noise measurements of the backward pumped distributed fiber raman amplifier .......................................................................... 9
T. A. FLORKO, O. YU. KHETSELIUS, YU. V. DUBROVSKAYA, D. E. SUKHAREV
Bremsstrahlung and X-ray spectra for kaonic and pionic hydrogen and nitrogen ........................................................................ 16
M. V. KIRICHENKO, V. R. KOPACH, R. V. ZAITSEV, S. A. BONDARENKO
Sensitivity of silicon photo-voltaic converters to the light incidence angle .................................................................................. 20
L. S. MAXIMENKO, I. E. MATYASH, S. P. RUDENKO, B. K. SERDEGA, V. S. GRINEVICH, V. A. SMYNTYNA,
L. N. FILEVSKAYA
Spectroscopy of polarised and modulated light for nanosized tindioxide films investigation ........................................................ 24
O. O. PTASHCHENKO, F. O. PTASHCHENKO, O. V. YEMETS
Effect of ambient atmosphere on the surface current in silicon p-n junctions ............................................................................. 28
V. A. BORSCHAK, M. I. KUTALOVA, N. P. ZATOVSKAYA, A. P. BALABAN, V. A. SMYNTYNA
Dependence of space-charge region conductivity of nonideal heterojunction from photoexcitation conditions .......................... 33
V. KH. KORBAN, G. P. PREPELITSA, YU. BUNYAKOVA, L. DEGTYAREVA, A. KARPENKO, S. SEREDENKO
Photokinetics of the ir laser radiation effect on mixture of the CO -N -H O gases: advanced atmospheric model ....................... 36
2 2 2
D. À. ÊUDIY, N. P. ÊLOCHKO, G. S. KHRYPUNOV, N. À. ÊÎVTUN, K. Y. ÊRIKUN, Y. K. BELONOGOV
Elaboration of cadmium sulphide film layers for economical solar cells ...................................................................................... 39
I. K. DOYCHO, S. A. GEVELYUK, O. O. PTASHCHENKO, E. RYSIAKIEWICZ-PASEK, S. O. ZHUKOV
Porous glasses with CdS inclusions Luminescence kinetics peculiarities ..................................................................................... 43
N.V. MUDRAYA
Density functional approach to atomic autoionization in an external electric field: new relativistic scheme ................................ 48
V. A. SMYNTYNA, O. V. SVIRIDOVA
Influence of impurities and dislocations on the value of threshold stresses and plastic deformations in silicon ............................. 52
O. YU. KHETSELIUS
Advanced multiconfiguration model of decay of the multipole giant resonances in the nuclei ..................................................... 57
YU. F. VAKSMAN, YU. A. NITSUK, V. V. YATSUN, YU. N. PURTOV, A. S. NASIBOV, P. V. SHAPKIN
Optical Properties of ZnSe:Mn Crystals .................................................................................................................................... 61
A. V. GLUSHKOV
Quasiparticle energy functional for finite temperatures and effective bose-condensate dynamics: theory and some
illustrations ............................................................................................................................................................................... 65
R. M. BALABAY, P. V. MERZLIKIN
Electronic structure of heterogeneous composite: organic molecule on silicon thin film surface ................................................. 70
A. A. SVINARENKO, A. V. LOBODA, N. G. SERBOV
Modeling and diagnostics of interaction of the non-linear vibrational systems on the basis of temporal series
(Application to semiconductor quantum generators) ................................................................................................................. 76
YE. V. BRYTAVSKYI, YU. N. KARAKIS, M. I. KUTALOVA, G. G. CHEMERESYUK
Effects connected with interaction of charge carriers and r-centers basic and exited states .......................................................... 84
I. N. SERGA
Electron internal conversion in the 125,127Ba isotopes .................................................................................................................. 88
L. N. VILINSKAYA, G. M. BURLAK
Sensors on the basis of aluminium metal-oxide films ................................................................................................................. 92
O. O. PTASHCHENKO, F. O. PTASHCHENKO, V. V. SHUGAROVA
Tunnel surface current in GaAs–AlGaAs p-n junctions, due to ammonia molecules adsorption ................................................. 95
SH. D. KURMASHEV, T. M. BUGAEVA, T. I. LAVRENOVA, N. N. SADOVA
Influence of the glass phase structure on the resistance of the layers in system “glass-RuO ” ....................................................... 99
2
A. V. IGNATENKO, A. A. SVINARENKO, G. P. PREPELITSA, T. B. PERELYGINA, V. V. BUYADZHI
Optical bi-stability effect for multi-photon absorption in atomic ensembles in a strong laser field ..............................................103
L. V. MYKHAYLOVSKA, A. S. MYKHAYLOVSKA
Influence of the step ionization processes on the electronic temperature in thin gas-discharge tubes ..........................................106
E. V. MISCHENKO
Quantum measure of frequency and sensing the collisional shift and broadening of Rb hyperfine lines in medium
of helium gas ...........................................................................................................................................................................112
O. O. PTASHCHENKO, F. O. PTASHCHENKO, N. V. MASLEYEVA, O, V. BOGDAN
Surface current in GaAs p-n junctions, passivated by sulphur atoms .........................................................................................115
A. V. GLUSHKOV, YA. I. LEPIKH, A. P. FEDCHUK, A. V. LOBODA
The green’s functions and density functional approach to vibrational structure in the photoelectron spectra of molecules ..........119
A. V. TYURIN, A. YU. POPOV, S. A. ZHUKOV, YU. N. BERCOV
Mechanism of spectral sensitizing of the emulsion containing heterophase “core –shell” microsystems ....................................128
V. V. KOVALCHUK, O. V. AFANAS’EVA, O. I. LESHCHENKO, O. O. LESHCHENKO
Size distributions of clusters on photoluminescence from ensembles of Si-clusters ....................................................................133
I. M. VIKULIN, SH. D. KURMASHEV, P. YU. MARKOLENKO, P. P. GECHEV
Radiation immunity of the planar n-p-n-transistors .................................................................................................................136
K. V. AVDONIN
Build-up of wave functions of the particle in the modelling periodic field ..................................................................................140
V. A. ZAVADSKY, G. S. POPIK
Modification of parameters IR-fotodetectors by high-energy particles ......................................................................................147
Information for contributors of “Photoelectronics” articles ............................................................................................................151
²íôîðìàö³ÿ äëÿ àâòîð³â çá³ðíèêà “Ôîòîåëåêòðîí³êà” ...............................................................................................................151
Èíôîðìàöèÿ äëÿ àâòîðîâ ñáîðíèêà “Ôîòîýëåêòðîíèêà” .........................................................................................................152
3

4
UDC 621.315.592
R. V. VITER 1 , V. A. SMYNTYNA 1 , I. P. KONUP 2 , YU. A. NITSUK 1 , V. A. IVANITSA 2
1 Department of Experimental Physics, Odessa National University, 42, Pastera str., 65026, Odessa, Ukraine,
viter_r@mail.ru; phone +38-0676639327, fax:+380-48-7233515.
2 Department of Mycrobiology, Odessa National University, 2, Shampansky lane, 65000, Odessa, Ukraine,
phone +38-0482-68-79-64.
CONDUCTIVITY MECHANISM IN THIN NANOCRYCTALLINE
TIN OXIDE FILMS
Structural properties of tin oxide nanocryastalline films have been investigated by means of atomic
force microscopy (AFM) and X-ray diffraction (XRD) methods. Surface morphology, roughness,
crystalline size and lattice strain have been estimated. Current-voltage characteristics (I-V) have been
measured at different temperatures. Temperature dependence of current has been studied. Activation
energies have been evaluated and conductivity mechanism has been proposed.
1. INTRODUCTION
Tin oxide SnO 2 is well known as material for gas
sensors [1-8]. The most important reasons of tin oxide
use in sensor applications are chemical stability
to different aggressive chemical pollutants and high
temperature treatment [1]. Those advantages allow
fabricating different types sensors, based on tin oxide
to different gases [2]. Another application of tin oxide
thin films is optics where they have been successfully
used as transparent conducting electrodes in optical
devises [2-7]. Tin oxide thin films have been successfully
used for measurements in liquids to detect ammonia
in water [2].
It was published that tin oxide films consisting of
nanoparticles showed different properties from typical
polycrystalline films [3-8]. The optical characterization
of the films was performed in [4]. The thickness
and refractive index have been calculated. The crystalline
size was estimated by means of optical methods
using the absorption spectra [4]. It was observed blue
shift of optical absorption spectra in comparison with
polycrystalline samples [4]. The value of band gap estimated
from optical absorption spectra was 0,2-0,6
eV bigger, than to tin oxide single crystal (E g =3,6 eV).
Electrical characterization of nanocrystalline tin
oxide films has been performed in [3, 4]. No Shotky
barriers have been observed and non ohmic behavior
was verified [3]. However, the correct explanation of
charge transfer in tin oxide tin oxide nanocrystalline
films has not been performed.
In this work experimental results of investigation
of electrical properties are reported. Current-voltage
and temperature dependence of current have been
performed. Results of structural properties of the films
have been reported. Activation energies were determined.
Conductivity mechanism in tin oxide nanocrystalline
films has been proposed.
2. EXPERIMENTAL
Tin oxide thin films were deposited with electrostatic
spray pyrolysis technique, described in [1-3].
For deposition, tin chloride (IV) ethanol solution was
used [2]. Tin chloride concentration of sprayed solution
and sprayed solution volume were kept constant
and equaled c=0,01 mol/l and v=10 ml, correspondently.
Glass substrates, with pretreatment in ethanol
and ultrasonic bath, were used for films’ fabrication.
Applied static voltage between capillary and glass substrate
was 17 kV. After deposition, the obtained samples
have been annealed at 793 K during 1 hour.
I-V characterization was measured in the range
of 0-200 V under different temperatures 293-393 K.
Temperature dependence of current was performed at
the same temperature range and with applied voltage
kept constant 60 V.
Atomic Force Microscopy (AFM) has been performed
on the deposited SnO 2 layers in order to investigate
the surface morphology of the films.
XRD measurements have been performed with
Philips X’Pert-MPD (CuK α , λ=0,15418 nm) difractometer
to identify the nature of deposited material
and determine crystalline size.
Fig. 1. AFM image of tin oxide film.
© R. V. Viter, V. A. Smyntyna, I. P. Konup, Yu. A. Nitsuk, V. A. Ivanitsa, 2009

3. RESULTS AND DISCUSSION
The thickness of obtained films, estimated by
means of profilometer Tencor P7, was 310 nm. AFM
images of tin oxide nanocrystalline films are presented
in figures 1, 2. The images refer to 5x5 μm 2 and 800x800
nm 2 areas of tin oxide surface. The one can see that
the film had polycrystalline structure with well shaped
grains. Wiskers of 200-250 nm height were observed on
the surface of the film. It points to high concentration
of point defect on the surface of thin films [2]. Surface
roughness (Rms) of the films was 26,2 nm, what seems
to be suitable for sensor application.
XRD data is presented in figure 3. The one can see
peaks at 2θ: 26,5 , 34,5, 37,8 , 51,4, corresponding to
tetragonal crystalline phase of tin oxide and one peak
at 2θ=65,2, which represents orthorhombic phase of
tin oxide [7,8].
Crystalline size and lattice strain have been determined
in figure 4, according to equation [7, 8]:
() 0,9 ()
β⋅cos θ ε⋅sin θ
= +
λ d λ
Fig. 2. 2-DAFM image of surface of tin oxide films.
(1)
Previously [4], the crystalline size of tin oxide, deposited
at the same conditions, determined from optical
absorption spectra was 5,2 nm. However analysis of
the AFM data showed surface agglomerates with average
size of about 20 nm (fig. 2). On the other hand,
crystalline size value, determined by XRD method,
was compatible with optical absorption data. Similar
behavior has been observed in [7], when electron
microscopy images gave crystalline size of 100 nm
whereas XRD analysis showed particles with 10 nm
size. This phenomenon can be explained by formation
of agglomerates by low size crystallites.
I-V characteristics are presented in fig.5. In order
to analyze charge transfer mechanism they have
been plotted in different scales (fig.6, 7). At low voltages
(U

I, mkA
ln(J/AT 2 )
6
25
20
15
10
5
y
20 o C
40 o C
60 o C
80 o C
100 o C
120 o C
0
0 20 40 60 80 100 120 140 160 180 200
-16
-17
-18
-19
-20
-21
-22
-23
U, V
Fig. 5. I-V plots of tin oxide thin films.
U 1/2 , V 1/2
T=293 K
T=313 K
T=333 K
T=353 K
T=373 K
T=393 K
2 4 6 8 10 12 14 16
Fig. 6. I-V plots, rebuilt in Frenkel’s-Pool scale.
With increase of applied voltage (U>50 V) measured
I-V data showed Ohmic behavior. Only at T>353
K nonlinear part was observed.
Temperature dependence of current, measured
under constant value of applied voltage U=60 V, was
1
plotted in ln I ~ scale and two linear parts were
T
found (fig.8). Activation energy values were 0,16 eV
and 0,24 eV for low and high temperature regions
correspondently. The activation energies E =0,16 eV
1
and E =0,24 eV correspond to double ionized oxygen
2
vacancies and defect states [8]. The one can see good
correlation between energy values determined from
I-V measurements and temperature dependences of
current. In both cases the same surface states have
been observed.
ln I (mkA)
3
2
1
0
-1
-2
-3
-4
ln U (V)
1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0 5,5
Fig. 7. I-V plots, rebuilt in double logarithm scale.
CONCLUSION
293 K
313 K
333 K
353 K
373 K
393 K
Electrical and structural properties of tin oxide
nanocrystalline films have been investigated. AFM
analysis showed that the obtained films had polycrystalline
nature with rough surface and wiskers,
what makes these films attractive for sensor applications.
XRD measurements showed peaks, typical for tin
oxide. Crystalline size, determined from XRD measurements,
was 5,54 nm. T
I-V data showed two main charge transfer mechanisms.
Under applied voltages U50 V the Ohm’s mechanism dominates.
The temperature dependence of current had two
linear parts in Arrenius scale. The activation energies
E 1 =0,16 eV and E 2 =0,24 eV concerned with oxygen
vacancies and surface state defects.

ln(I), mkA
-12
-13
-14
0,0026 0,0028 0,0030 0,0032 0,0034
1/T, K -1
Fig. 8. Temperature dependence of current of tin oxide nanocrystalline
films.
UDC 621.315.592
R. V. Viter, V. A. Smyntyna, I. P. Konup, Yu. A. Nitsuk, V. A. Ivanitsa
CONDUCTIVITY MECHANISM IN THIN NANOCRYCTALLINE TIN OXIDE FILMS
References
1. Viter R., Smyntyna V., Evtushenko N., Structural properties
of nanocrystalline tin dioxide films deposited by electrostatic,
spray pyrolisis method // Photoelectronics. — 2005. —
Vol. 15. — p.54-57
2. M. Pisco, M. Consales, R. Viter, V. Smyntyna, S. Campopiano,
M. Giordano, A. Cusano, A.Cutolo, Novel SnO based
2
optical sensor for detection of low ammonia concentrations
in water at room temperatures // Intern. Sc. J. Semiconductor
Physics, Quantum Electronics and Optoelectronics. —
2005. — Vol. 8. — p.95-99
3. A. N. Banerjee, R. Maity, S. Kundoo, and K. K. Chattopadhyay,
Poole–Frenkel effect in nanocrystalline SnO :F thin
2
films prepared by a sol–gel dip-coating technique// phys.
stat. sol. (a) -2004. — Vol. 204. — No. 5. — p. 983–989
4. R.V. Viter, V.A. Smyntyna, Yu. A. Nitsuk, Optical, electrical
and structural characterization of thin nanocryctalline SnO2 films for optical fiber sensors application // Proceedings of
Test sensor conference 2007, Nuremberg, Germany. — May
2007. — pp. 1252-1257
5. Feng Gu, Shu Fen Wang, Meng kai Lu, Guang Jun Zhuo,
Dong Xu and Duo Rong Yuan, Photoluminescence properties
of SnO nanoparticles synthesized by sol-gel method// J.
2
Phys. Chem. B. — 2004. — Vol. 108. — p. 8119-8123
6. Shanthi S., Subramanian C., Ramasamy P., Preperation and
properties of sprayed undoped and fluorine doped tin oxide
films// Materials Science and engineering, B. — 1999. —
Vol. 57. — p. 127-134
7. Yuji Matsui, Michio Mitsuhashi , Yoshio Goto, Early stage
of tin oxide film growth in chemical vapor deposition // Surface
and Coatings Technology. — 2003. — Vol.169 –170. —
p. 549–552
8. A.K. Mukhopadhyay, P. Mitra, A.P. Chatterjee, H.S. Maiti,
Tin dioxide thin flm gas sensor// Ceramics International. —
2000. — Vol. 26. — p. 123-132
Abstract
Structural properties of tin oxide nanocryastalline films have been investigated by means of atomic force microscopy (AFM) and
X-ray diffraction (XRD) methods. Surface morphology, roughness, crystalline size and lattice strain have been estimated. Current-voltage
characteristics (I-V) have been measured at different temperatures. Temperature dependence of current has been studied. Activation
energies have been evaluated and conductivity mechanism has been proposed.
Key words: tin oxide, nanocrystalline films, I-V characterization, XRD, AFM.
ÓÄÊ 621.315.592
Ð. Â. Âèòåð, Â. À. Ñìûíòûíà, È. Ï. Êîíóï, Þ. À. Íèöóê, Â. À. Èâàíèöà
ÌÅÕÀÍÈÇÌ ÏÐÎÂÎÄÈÌÎÑÒÈ Â ÒÎÍÊÈÕ ÍÀÍÎÊÐÈÑÒÀËËÈ×ÅÑÊÈÕ Ï˨ÍÊÀÕ ÎÊÑÈÄÀ ÎËÎÂÀ
Ðåçþìå
Ñòðóêòóðíûå ñâîéñòâà íàíîêðèñòàëëè÷åñêèõ ïë¸íîê îêñèäà îëîâà áûëè èçó÷åíû ïðè ïîìîùè ìåòîäîâ àòîìíîé ñèëîâîé
ìèêðîñêîïèè è äèôðàêöèè ðåíòãåíîâñêîãî èçëó÷åíèÿ. Áûëè îïðåäåëåíû ìîðôîëîãèÿ ïîâåðõíîñòè, âåëè÷èíû åå øåðîõîâàòîñòè,
ðàçìåðîâ êðèñòàëëèòîâ è ìåõàíè÷åñêîãî íàïðÿæåíèÿ êðèñòàëëè÷åñêîé ðåøåòêè. Âîëüò-àìïåðíûå õàðàêòåðèñòèêè
îáðàçöîâ áûëè èçó÷åíû ïðè ðàçíûõ òåìïåðàòóðàõ. Òåìïåðàòóðíàÿ çàâèñèìîñòü òåìíîâîãî òîêà áûëà èçó÷åíà. Ýíåðãèè àêòèâàöèè
ïðîâîäèìîñòè áûëè îïðåäåëåíû.
Êëþ÷åâûå ñëîâà: îêñèä îëîâà, âîëüò-àìïåðíûå õàðàêòåðèñòèêè, àòîìíàÿ ñèëîâàÿ ìèêðîñêîïèÿ è äèôðàêöèÿ ðåíòãåíîâñêîãî
èçëó÷åíèÿ.
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ÓÄÊ 621.315.592
Ð. Â. ³òåð, Â. À. Ñìèíòèíà, ². Ï. Êîíóï, Þ. À. ͳöóê, Â. Î. ²âàíèöÿ
ÌÅÕÀͲÇÌ ÏÐβÄÍÎÑÒ²  ÒÎÍÊÈÕ ÍÀÍÎÊÐÈÑÒÀ˲×ÍÈÕ Ï˲ÂÊÀÕ ÎÊÑÈÄÓ ÎËÎÂÀ
Ðåçþìå
Ñòðóêòóðí³ âëàñòèâîñò³ íàíîêðèñòàë³÷íèõ ïë³âîê îêñèäó îëîâà áóëî äîñë³äæåíî çà äîïîìîãîþ ìåòîä³â àòîìíî¿ ñèëîâî¿
ì³êðîñêîﳿ òà äèôðàêö³¿ ðåíòãåí³âñüêîãî âèïðîì³íþâàííÿ. Áóëî âèçíà÷åíî ìîðôîëîã³ÿ ïîâåðõí³, âåëè÷èíè ¿¿ íåîäíîð³äíîñò³,
ðîçì³ð³â êðèñòàë³ò³â òà ìåõàí³÷íîãî íàïðóæåííÿ êðèñòàë³÷íî¿ ãðàòêè. Âîëüò-àìïåðí³ õàðàêòåðèñòèêè çðàçê³â áóëî äîñë³äæåíî
ïðè ð³çíèõ òåìïåðàòóðàõ. Òåìïåðàòóðíó çàëåæí³ñòü òåìíîâîãî ñòðóìó áóëî ïîáóäîâàíî. Åíåð㳿 àêòèâàö³¿ ïðîâ³äíîñò³
áóëè âèçíà÷åí³.
Êëþ÷îâ³ ñëîâà: îêñèä îëîâà, âîëüò-àìïåðí³ õàðàêòåðèñòèêè, àòîìíà ñèëîâà ì³êðîñêîï³ÿ òà äèôðàêö³ÿ ðåíòãåí³âñüêîãî
âèïðîì³íþâàííÿ.

UDC 535.361:621.391.822
G. S. FELINSKYI
Radiophysics Faculty, Kyiv Taras Shevchenko National University,
Glushkova Prospect, 2, 03127 Kyiv, Ukraine, Phone: +380-44-526-0570,
Fax: +380-44-526-0531, E-mail: felinskyi@yahoo.com
NOISE MEASUREMENTS OF THE BACKWARD PUMPED DISTRIBUTED
FIBER RAMAN AMPLIFIER
INTRODUCTION
Creation of light amplifiers based on stimulated
Raman scattering (SRS) in singlemode fibers is legally
refer to the most powerful practical achievements [1]
arisen as a result of long time fundamental researches
in nonlinear optics. At first practical applications of
fiber Raman amplifiers (FRA) with several pumping
sources at the end of the last century [2] high-quality
amplification of optical signals with a bandwidth
close to limiting for silica fibers about 13 THz has been
shown. Due to improvement of operational characteristics
now FRA gradually supersede other types of
optical amplifiers from the ultra wide band communication
systems and they already became the first nonlinear
optics device which has received wide practical
application in long-distance optical fiber communication
with terabit capacity.
Such amplifiers are widely applied despite of the
actual interdiction imposed by the theory. Really
modern theory [3-5] predicts that the noise figure of
any optical amplifier should be higher than the minimal
quantum limit of 3 dB. It means that the signal to
noise ratio (SNR) after the amplifier should decrease
at least in 2 times. The bit error rate (BER) in turn directly
depends on the signal to noise ratio. In addition
the noise statistics is those that the SNR level above 6
dB each decibel increasing or reducing this ratio creates
reduction or accordingly increases the BER at the
order on value. Hence each optical amplifier, including
FRA, theoretically should appreciably increase the
BER during the digital information transfer. However
there is an obvious contradiction between theoretical
performances about optical amplifiers noise and real
practice of their application in the optical fiber systems.
In particular, standard optical communication
scheme of linear signal regeneration using of sequential
application of optical amplifiers becomes theoretically
impossible without full signal restoration from
noise, in view of fast error accumulation with growth
of amplifiers amount. Even more ten years ago it has
been marked [5], that the physical phenomena which
© G. S. Felinskyi, 2009
Noise parameters of fiber Raman amplifiers are appeared in practice essentially better top theoretical
limits and the amplifier noise performance is the subject of intensive investigations now. the
experimental results on the amplified spontaneous emission (ASE) observation in the single mode
fiber span using the backward pumped distributed FRA are presented in the report. Our measurements
and quantity analysis show that physical principles of formation of the FRA optical noise with the
counter pumping lead to very small gain coefficients and it almost correspond to spontaneous Raman
properties in the silica fibers. Raman gain nonlinearity is the reason to reduce the real FRA noise figure
much below the established 3 dB limit. Our analysis of experimental data on ASE measurements
in silica fibers allows us to get the information about the nature of formation mechanism of the noise
parameters in the practical FRA.
result in extraordinary rare occurrence of mistakes in
digital optical communication systems till now yet
have not received unequivocal interpretation. Now the
same remarks can be related to the noise performance
of practical FRA.
The experimental results of the amplified spontaneous
emission (ASE) research using distributed FRA
in singlrmode fiber with the counter pumping are presented
in this work.
FRA APPLICATION PROBLEMS AND MOTIVATION TO EX-
PERIMENTS
Technical specifications of optical signal amplifiers
in telecommunication systems essentially influence
on design strategy of modern fiber optic highways
for an information exchange. The generalized quality
parameter of any digital communication system is the
bit error rate B er which is unequivocally determined by
the signal to noise ratio Q [6]:
1
Ber = erfc( Q/
2) , (1)
2
where erfc(x) is error function. Therefore to increase
of signal transfer distance in the communication
link one must not so much try to restore the
power losses of a signal due to attenuation in a link,
but mainly the maintenance of necessary value Q,
for example not less than 6 dB, that corresponds
B =10 er -9 .
Two linear regeneration schemes of the signal in
long optical fiber communication links are shown
on Fig. 1. The scheme on Fig. 1à using the linear repeaters
with full regeneration of a signal (Fig. 1b) is
the standard application in microwave multichannel
communication. Such scheme have no alternative
for the microwave systems of multichannel communication
because of restrictions on receiver sensitivity
by own noise at its input. The cascade amplification
scheme using broadband optical amplifiers (Fig. 1â) is
extremely simple due to huge reduction of the equipment
amount and it becomes dominating for modern
high-speed optical links but this design is not theoreti-
9

cally possible if the noise figure of optical amplifier, in
particular FRA, considerably exceeds unit.
10
(a) Repeaters
(Rp)
Tx
N×λn
(b)
In
N×λn
Demultiplexer
N×λn
Rp Rp Rp
Repeater Block Diagram
Rx 1
Rx 2
Rx 3
...
Rx N
Electronic
Signal
Restoration
Tx 1
Tx 2
Tx 3
...
Tx N
Multiplexer
N×λn
Rx
N×λn
Out
N×λn
appears above permissible maximum and it is create
the contradiction with the resulted theoretical performances
about optical amplifier noise. Last circumstance
practically specifies illegitimacy of direct carry
the models developed for electronic amplifiers on such
nonlinear photon system as FRA. As the our purpose
to solve the problem about the FRA optical noise have
been established, the analysis of Raman gain features
in silica fibers and experimental results on amplified
spontaneous emission is resulted in the present work.
The noise analysis of optical Raman gain may
be relieved of restrictions of traditional methods of
equivalent circuits by direct experimental noise measurements
of amplified spontaneous emission (ASE)
in commercial FRA model with the multiwave pumping
and using the theory of Raman interaction physics
as nonlinear optical process.
THEORETICAL BASIS OF RAMAN GAIN
ANALYSIS
(c) Optical amplifiers (OA)
Physical source of the Raman scattering radiation
is nonlinear polarization P
Tx
N×λn
OA OA OA
Rx
N×λn
Fig. 1. Optical signal transmission based on: a) set of recovery
repeaters, for which is shown the block diagram (b) of group signal
restoration equipment with wavelength division multiplexing; â)
set of wideband optical amplifiers.
Really amplifiers quality can be characterized by
noise figure of amplifier F=Q /Q . Parameter F n in out n
shows how times the input SNR Q is changed by the
in
amplifier due to own internal noise in relation to output
SNR Q . Noise figure of the fiber amplifiers based
out
on inversion of population densities in laser transition
is
Fn = 2 nsp( G−1)/ G ≈ 2nsp
, (2)
where nsp = N2 / ( N2 − N1)
is so called the spontaneous
emission factor or population inversion factor, N1 and N are the population density of the bottom and
2
top levels for laser transition, accordingly, G is the gain
coefficient. The equation (2) shows that at big G SNR
for amplified signal is degrades by a factor 2 (or 3 äÁ)
even for an ideal amplifier, for which n = 1. The prac-
sp
tical amplifier with n > 1 should have F ≥ 2, and the
sp n
minimal value of 2 (3 dB) in the modern theory [3-5]
is considered a quantum limit. However the physics of
processes in FRA is not deals with the population inversion
of electronic energy levels. Fundamental FRA
basis is the nonlinear optics and description of amplifier
noise performance is required not only other theoretical
approaches, but also additional experimental
researches.
Today FRA application practice has revealed some
problems, at least, two of which have fundamental
character. First, extreme simplicity of FRA technical
realization is accompanied by complexity of physical
processes of a nonlinear energy exchange between
several pumping sources and hundreds information
channels and it essentially complicates modeling and
designing of devices. Second, signal quality after FRA
NL induced by electric field
Ep of the pumping wave. Relative power of scattered
radiation on Stokes frequency ω due to the pump ac-
s
tion of the frequency ω is quantitatively described by
p
differential Raman cross section [7]:
2
d σ
dΩdωs 3 2 NL 2
ωω s pnV s < | P | > ωs
=
,
2 2 4 p
2
16πε0cnp
E
(3)
where V is the volume of scattering, ε is the dielec-
0
tric constant, dΩ is a solid angle element, n , n are the
s p
refractive indexes on frequencies ω and ω . Angular
s p
brackets designate the time averaging.
Generally the i-th component of the induced polarization
in isotropic media of fiber core irrespective
from the frequency of nonlinear interaction products
may be written using the third order susceptibility ten-
(3)
sor χ as:
NL
(3)
P =ε
i 0 ∑ χijkl
EjEkEl. (4)
jkl , ,
If our consideration will be limited to the most
general fiber types which have the weak waveguide
properties it is possible to divide the electric field both
the Stokes wave (s), and the pumping wave (p) into
transverse part Ri 2 2
(r), (where i = s, p, and r = x + y )
and on the function from z: E (z). In particular the
i
polarization of mode on the frequency ω is arisen at
s
nonlinear mixing of electric fields as:
ω s P
i
= 6 ε0 p
2
s (3) p p * s
R R ∑ χijkl
Ej( Ek) El
jkl , ,
(5)
with complex conjugation on frequency − ω . Accord-
s
ingly the equation for third order susceptibility tensor
(3)
χ is:
*
(3) N 1 ∂αij ⎛∂α ⎞ kl
χ ijkl = ⋅ 2 2 ∑ ⎜ ⎟ , (6)
12mε0V ωv−ω + 2iωγ
n ∂qn ⎝ ∂qn
⎠
where N is the oscillator quantity in the volume of interaction
V, m is the oscillator mass, ω and ω are res-
v

onant and current frequencies of molecular vibration
with attenuation γ, ij k q ∂α ∂ is the differential polarizability
(Raman tensor), q r is the displacement vector
for molecular vibration.
It is well known that the Raman active vibration q r
should be not active in infrared (IR) absorption as it
is not accompanied by the local dipole momentum at
a molecular level in this case isotropic media with the
inversion center. It means that thermal fluctuations of
radiation in a fiber cannot influence directly changes
phonon density of the Raman active vibrations. There
is the blocking of the thermal IR noise influence on
Raman scattering process in the fibers in contrast with
any other material having the inversion center in its
molecules.
The vector q r depends on E r as a corresponding
combination of the pumping and Stokes wave fields
in the case of the stimulated Raman scattering which
creates synchronous external force and it causes resonant
behavior of the given vibration. Thus there is an
amplification of power of a Stokes wave in fiber and
the gain coefficient g looks as
R
g
(3) (3)
3ω
Im[ χ iiii +χijji
]
s
R =− 2
ps
ε0cnn
p s 2Aeff
, (7)
ps
where A eff is the effective area of the pump and signal
overlapping region. The gain frequency profile g (ω) R
defines the dynamics of Raman amplification. Interaction
between Stokes intensity I (z, ω) and mono-
s
chromatic pumping I (z) in arbitrary fiber coordinate
s
z is described by the coupled equations [6]:
dIs (, z ω )
= gR( ω) Ip( z) Is( z, ω) −αs Is( z,
ω ) , (8)
dz
dI p( z)
ωp
= gR( ω) Ip( z) Is( z, ω) −αpIp(
z)
, (9)
dz ωs
The classical equations (8) and (9) were almost
exclusively used for the distributed FRA description.
Unfortunately, analytical solutions of these equations
are known only in the limited special cases even
when interaction only of two waves is considered.
Such special case is the approximation with no pump
depletion. This approach [8] allows obtaining the analytical
expressions for gain coefficients of the Stokes
signal and ASE. However these equations cannot be
applied to direct calculations of the amplifier noise
figure as such essential nonlinear Raman features
as an amplification threshold and a nonlinear mode
concurrence are remained behind of the made restriction
frameworks.
The quantum dynamical equation for the photon
number η (z) on the unit length z for Stokes photons
s
ω = ω – ω is [9]:
s p v
dη
ωω
s
p s
= C ρ( hω
f ) ×
dz
ωv
× { η ( η + 1) η −η η η −η η + ( η + 1) η } , (10)
s v p s v p s v v p
=∂αij ∂
2
k ( π
2
) (4
2
εε s p ) h
where C q h V Nm v , = h 2π
is Plank’s constant, ε , ε are dielectric constants for
s p
pumping and Stokes waves, respectively, v is phase velocity
of Stokes wave.
Rate equation (10) for the Stokes scattered photons
consists of four terms. At the quantum analysis first two
terms are often referred to as stimulated emission and
stimulated absorption. Last two terms are the spontaneous
absorption, and spontaneous emission, respectively.
Since the phonons are assumed to be in equilibrium
at temperature T, the occupation number
η (ω) is the thermal equilibrium number
v
( ) kT
ηv( ω v) = ⎡⎣exp h ωv B −1⎤⎦
, where k is Boltzmann’s
B
constant. It should be noted that the spontaneous emission
terms are proportional to n +1 for Stokes photon
v
and thus depends on the temperature of the fiber.
The equation (10) shows that the difference in
stimulated emission and absorption terms does not
depend on the phonon number η and therefore is
v
temperature-independent. In fact, the frequency profile
g (ν) may be expressed by the spontaneous Raman
R
cross section at zero temperature σ (ν) as [10]:
0
−1
λ
g v =σ v ⋅ , (11)
R () 0 ()
3
s
2 ps 2
chAeff np
where ν =ω/2πñ is the wave number, c is speed of light,
and weak frequency dependence of a pumping wave
refractive index n in the Stokes shifted area can be ne-
p
glected. The spontaneous Raman cross section σ (v) Ò
at temperature Ò is related to zero Kelvin cross section
σ (ν) as:
0
σ0 ( ν ) =σT( ν)/[ ηv( ν , T ) + 1] , (12)
The spontaneous Raman spectrum and Raman
gain profile for standard silica fiber is shown on
Fig. 2. The essential difference between spontaneous
Raman spectrum and Raman gain profile according
to (11) — (12) and the data on Fig. 2 should be
observed in the frequency region of Stokes shift less
than 6 THz=200 cm-1 where the thermal density factor
of phonon numbers essentially exceeds the unit. In
more high-frequency area the thermal density factor
of Stokes phonon numbers (> 200 cm-1 ) lose its frequency
dependence, practically not differing from
unit and consequently spontaneous Raman spectrum
coincides with the Raman gain profile.
Normalized Intensity,
1.0
0.5
0
Raman Scattering
Spontaneous
Stimulated
0 200 400
Raman shift, cm
600
-1
Fig. 2. Spontaneous Raman spectrum (solid line) and Raman
gain profile (doted line) in Stokes shifted frequency area from 0 to
21 THz (700 cm-1 ) for standard silica fiber.
Earlier we have studied [10, 11] ASE spectra in
comparison to experimental data of measurements of
11

the effective noise figure in the multi wavelength Raman
amplifier [12]. On the preliminary simulation data
the FRA noise is mainly formed in the fiber part near to
the pumping source where the pump power is maximal.
During the distribution on a fiber full pumping power
fades, the pumping gradually starts to be exhausted and
its powers not enough for effective ASE generation.
Such modeling [13] allows obtaining the information
on the noise properties formation in the real fiber optical
amplifiers. These preliminary conclusions prove to
be true our experimental ASE measurements.
12
EXPERIMENTAL SETUP AND
MEASUREMENT METODS
Experimental observations of ASE were made at
the output from singlemode fibers in the backward
direction to the pumping generated by an industrial
sample of the pumping source [11] containing four
semi-conductor laser diodes (LD). The LD’s wavelengths
are 1426, 1436, 1456 and 1466 nm. Every LD
had the maximal output power of 300 mW. The experimental
set up is schematically shown on Fig. 3.
Output pump power from each LD through the pump
combiner and circulator is directed to the 50 km span
of standard single mode fiber in this set up. Pumping
source allows independently fix the output power of
each LD in the range from 0 mW to 300 mW using
digital control unit. Output ASE power from the fiber
after circulator is registered by optical spectrum
analyzer (OSA). Spectral resolution of OSA was set
to 1 nm (~ 4 cm -1 ) for all ASE measurements. Only
one LD remained active (the others LDs are switched
off) at each registration of spectra with the fixed set of
power levels: 100, 150, 200, 250 and 300 mW for every
wavelength of the pumping LD.
ASE spectral density, nW/nm
ASE spectral density, nW/nm
20
15
10
λp=1426 nm
5
4
3
2
1
0
20
1450 1500 1550 1600
15
10
5
λp=1436 nm
5
0
1450
1
1500 1550 1600
Wavelength, nm
2
5
4
3
20
15
10
5
20
15
10
SMF 50 km
4λ pump
Circulator
Pump combiner
ASE
1426 nm 1436 nm 1456 nm 1466 nm
Pumping Source
OSA
Fig. 3. Experimental set up for ASE measurements with four
LD in commercial FRA pumping source.
EXPERIMENTAL RESULTS AND
DISCUSSION
The typical example of registered ASE spectra is
shown on Fig. 4. Presented ASE measurements show, that
the absolute power cross section of Stokes radiation for
each of four pumping wavelengths changes from (2,75 ±
0,08)⋅10 -6 at LD input pumping power of 100 mW up to
(4,3 ± 0.2)⋅10 -6 for pumping power of 300 mW. The received
numerical values for ASE cross section as of the
order size ~10 -6 and thus, whole Stokes power is approximately
-60 äÁ related to input pumping power. It
correspond to quantum efficiency more likely to spontaneous
Raman scattering, but it does not SRS because
it quantum output should be higher on about 4–5 orders.
The absolute ASE cross section was experimentally
determined as relation of total power of Stokes
spectrum, integrated on shifted frequencies diapason
from 10 cm -1 up to 1400 cm -1 , to input pump power.
5
λp=1456 nm
5
4
3
2
1
1500 1550 1600
λp=1466 nm
2
1
3
5
4
1500 1550 1600
Wavelength, nm
Fig. 4. Stokes ASE power generated with separate pumping LD.
Pp, mW
1- 100
2- 150
3- 200
4- 250
5- 300
1650
1650

The general view of the spectra submitted on fig.
5a in qualitative interpretation unequivocally specifies
features of a known spectrum of the spontaneous Raman
light scattering in silica fibers. There is obvious
similarity to a non-uniform continuum in the range of
Stokes shifted frequencies from 0 cm -1 up to 900 cm -1 .
The main distinction of the spontaneous Raman spectrum
from spectral profile of Raman gain (see fig. 2)
is shown in the raised intensity small Stokes shifted
frequency components is approximately down to 200
cm -1 . Distinction between the spontaneous and stimulated
Raman spectra directly follows from the quantum
dynamic equation (10). The terms corresponding to
spontaneous Raman scattering in this equation should
contains a phonon density factor of a kind η B (ω) +1
[14]. The Bose factor at T=300K considerably exceeds
unit in the frequency interval from 0 up to 200 cm -1 ,
and it rises to infinity when frequency aspires to zero.
AbsoluteASE power density, (nW/nm)
(a)
20
15
10
5
SMF 50 km
λp=1466 nm
Av. resol. ~ 4 cm -1
70 cm -1
5
4
6
Frequency, (THz)
12 18
440 cm -1
601 cm -1
24
Pp (mW)
1 – 100
2 – 150
3 – 200
4 – 250
5 – 300
Raman shift, (cm -1 3
2
1
0
0 200 400 600 800
)
Normalized ASE power
The Raman gain profile should be formed by SRS
process as zero Kelvin cross section scattering which
is shown by a dotted line in the Fig. 5b. In contrast to
spontaneous Raman scattering SRS does not depend
on phonon density states and, accordingly, does not
depend on temperature. It is the reason of distinction
between the observable Raman gain spectrum and the
measured spontaneous Raman spectrum and it explains
the obvious tendency of ASE distribution to the
structure of the Raman gain profile at pumping power
is increased as one can see in Fig. 5b [15].
Other feature of a spontaneous Raman scattering
is by the nature the linear process and thereby it does
not depend on pumping intensity. As result the spontaneous
Raman cross section remains the constant for
any studied material and the dashed lines in Fig. 6 correspond
to the power of spontaneous Stokes radiation
as function of pumping power.
1.0
0.8
0.6
0.4
0.2
0
(b)
1
2
3
Zero Kelvin
(Raman gain profile)
0 200 400 600 800
Raman shift, (cm -1 )
Pp (mW)
1 – 100
2 – 200
3 – 300
Fig. 5. Absolute (a) and normalized (b) Stokes ASE power distributions generated by separate LD λ p =1466 nm in backward pumped
FRA with terahetz bandwidth. Normalized curves (b) show the trend of ASE distribution to Raman gain profile (dotted line) when the
pump power is increased [15].
Power amplification of spontaneous optical noise
in singlemode silica fiber as one can see in Fig. 6, is in
enough small limits. Quantum efficiency of the Raman
grows no more than by ~40 %, and it corresponds
on\off amplification approximately on 1.9 dB when
the pumping power increases in 3 times, that is from
100 mW up to 300 mW.
It is possible to explain such situation from the
physical point of view as follows. Rather weak ASE
generation in the studied pump power range is resulted
from no coherence of the Stokes photons arising at not
elastic scattering of pump photons on huge amount of
molecular phonon vibrations with different frequencies.
Therefore Stokes radiation in addition to its random
phase distribution appears as distributed in a very
wide frequency diapason. Both these circumstances
obstruct to automatic establish the phase matching
conditions necessary for coherent accumulation of
Stokes radiation which would give Raman gain. In
other words Raman interaction in the core of the silica
based optical fiber results to “spreading” of pump
power along the wide spectrum of Stokes frequencies.
As the creation probability of the in phase Stokes photons
with equal frequencies inversely depends on Raman
radiation bandwidth as it appears available pump
power insufficiently for effective Raman noise generation.
In result spectral power distribution of ASE observable
by us looks more likely spontaneous Raman
scattering, instead of SRS.
It should be noted the presented results are received
with no optical signals in the studied single
mode fiber piece. At signal presence its coherent power
with the spectral density considerably higher than
the Stokes noise density starts the concurrence for
possession of the pump power during the SRS process.
The expending of the pump power for 20-30 dB signal
13

amplification causes the accelerated pump depletion
in the propagation process along the fiber, simultaneously
reducing effective length of power accumulation
of Stokes noise. Therefore the ASE gain coefficients
measured by us in the single mode silica fiber have the
greatest possible quantities and noise power of real
FRA cannot exceed the absolute values resulted on
Fig. 4.
Stokes ASE Power, (nW)
14
15
10
5
SMF 50 km
λp=1466 nm
- Gain
- Spontaneous scatt.
- Spont. Levels
0
0 100 200 300
Pump Power, (mW)
440 cm -1
70 cm -1
601 cm -1
Fig. 6. Stokes ASE power as function of pump power for
several peaks in experimental spectra on Fig.5a (solid dots). Right
hand diagram show that the Raman gain values are only decimal
parts in comparison with spontaneous scattering peaks [15].
The data resulted in a Fig. 6 is illustrated than the
pure ASE amplification essentially depends on peak
power in noise distribution which is defined by frequency
position of the given maximum in the spectrum.
The ASE gain coefficients appreciably grow in
the spectrum points having the big intensity as a result
of Raman nonlinearity. Simultaneously maximal
noise amplification remains many times smaller in
comparison with nonlinear amplification of the coherent
signal. The output SNR after Raman amplifier
becomes big in comparison with the case of FRA
absence, therefore there is an improvement (even to
F

UDC 535.361:621.391.822
G. S. Felinskyi
NOISE MEASUREMENTS OF THE BACKWARD PUMPED DISTRIBUTED FIBER RAMAN AMPLIFIER
Abstract
Noise parameters of fiber Raman amplifiers are appeared in practice essentially better top theoretical limits and the amplifier
noise performance is the subject of intensive investigations now. the experimental results on the amplified spontaneous emission (ASE)
observation in the single mode fiber span using the backward pumped distributed FRA are presented in the report. Our measurements
and quantity analysis show that physical principles of formation of the FRA optical noise with the counter pumping lead to very small
gain coefficients and it almost correspond to spontaneous Raman properties in the silica fibers. Raman gain nonlinearity is the reason
to reduce the real FRA noise figure much below the established 3 dB limit. Our analysis of experimental data on ASE measurements in
silica fibers allows us to get the information about the nature of formation mechanism of the noise parameters in the practical FRA.
Key words: fiber Raman amplifiers, optical fiber communications, amplified spontaneous emission.
ÓÄÊ 535.361:621.391.822
Ã. Ñ. Ôåëèíñêèé
ÈÇÌÅÐÅÍÈß ØÓÌÀ  ÐÀÑÏÐÅÄÅËÅÍÍÎÌ ÂÊÐ ÓÑÈËÈÒÅËÅ ÑÎ ÂÑÒÐÅ×ÍÎÉ ÍÀÊÀ×ÊÎÉ
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Øóìîâûå ïàðàìåòðû ðåàëüíûõ âîëîêîííûõ ÊÐ óñèëèòåëåé íà ïðàêòèêå îêàçûâàþòñÿ çíà÷èòåëüíî ëó÷øå óñòàíîâëåííûõ
òåîðåòè÷åñêèõ ïðåäåëîâ, è øóìû óñèëèòåëÿ ñåé÷àñ ÿâëÿþòñÿ ïðåäìåòîì èíòåíñèâíûõ èññëåäîâàíèé.  ðàáîòå ïðåäñòàâëåíû
ýêñïåðèìåíòàëüíûå ðåçóëüòàòû èññëåäîâàíèÿ óñèëåííîãî ñïîíòàííîãî èçëó÷åíèÿ (ÓÑÈ), êîòîðîå íàáëþäàëîñü â îäíîìîäîâîì
âîëîêíå ïðè èñïîëüçîâàíèè ðàñïðåäåëåííîãî âîëîêîííîãî ÊÐ óñèëèòåëÿ ñî âñòðå÷íîé íàêà÷êîé. Íàøè èçìåðåíèÿ è èõ
êîëè÷åñòâåííûé àíàëèç ïîêàçûâàþò, ÷òî ôèçè÷åñêèå ïðèíöèïû ôîðìèðîâàíèÿ îïòè÷åñêîãî øóìà â óñèëèòåëÿõ ñî âñòðå÷íîé
íàêà÷êîé ïðèâîäÿò ê î÷åíü ìàëåíüêèì êîýôôèöèåíòàì åãî óñèëåíèÿ, à ñàì øóì ïî÷òè ñîîòâåòñòâóåò ñâîéñòâàì ñïîíòàííîãî
ÊÐ â êâàðöåâûõ âîëîêíàõ. Íåëèíåéíîñòü óñèëåíèÿ ÊÐ ÿâëÿåòñÿ ãëàâíîé ïðè÷èíîé ñíèæåíèÿ ðåàëüíîãî êîýôôèöèåíòà
øóìà çíà÷èòåëüíî íèæå óñòàíîâëåííîãî ïðåäåëà â 3 äÁ. Ïðåäñòàâëåííûé àíàëèç ýêñïåðèìåíòàëüíûõ äàííûõ èçìåðåíèé
ÓÑÈ â êâàðöåâûõ âîëîêíàõ ïîçâîëÿåò ïîëó÷èòü èíôîðìàöèþ î ïðèðîäå ìåõàíèçìîâ ôîðìèðîâàíèÿ øóìîâûõ ïàðàìåòðîâ â
ðåàëüíûõ óñèëèòåëÿõ.
Êëþ÷åâûå ñëîâà: âîëîêîííûå ÊÐ-óñèëèòåëè, óñèëèòåëü ñî âñòðå÷íîé íàêà÷êîé, îïòè÷åñêèå âîëîêíà.
ÓÄÊ 535.361:621.391.822
Ã. Ñ. Ôåë³íñüêèé
ÂÈ̲ÐÞÂÀÍÍß ØÓÌÓ Â ÐÎÇÏÎIJËÅÍÎÌÓ ÂÊРϲÄÑÈËÞÂÀײ ²Ç ÇÓÑÒв×ÍÈÌ ÍÀÊÀ×ÓÂÀÍÍßÌ
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Íåë³í³éí³ñòü ï³äñèëåííÿ ÊÐ º ãîëîâíîþ ïðè÷èíîþ çíèæåííÿ ðåàëüíîãî êîåô³ö³ºíòà øóìó çíà÷íî íèæ÷å âñòàíîâëåíî¿ ìåæ³ â
3 äÁ. Íàäàíî àíàë³ç åêñïåðèìåíòàëüíèõ äàíèõ âèì³ðþâàíü ÏÑ ó êâàðöîâèõ âîëîêíàõ, ÿêèé äîçâîëÿº îòðèìàòè ³íôîðìàö³þ
ïðî ïðèðîäó ìåõàí³çì³â ôîðìóâàííÿ øóìîâèõ ïàðàìåòð³â ó ðåàëüíèõ ï³äñèëþâà÷àõ.
Êëþ÷îâ³ ñëîâà: âîëîêîíí³ ÊÐ-ï³äñèëþâà÷³, ï³äñèëþâà÷ ç³ çóñòð³÷íèì íàêà÷óâàííÿì, îïòè÷í³ âîëîêíà.
15

16
UDÑ 539.192
T. A. FLORKO, O. YU. KHETSELIUS, YU. V. DUBROVSKAYA, D. E. SUKHAREV
Odessa National Polytechnical University, Odessa
Odessa State Environmental University, Odessa
I. I. Mechnikov Odessa National University, Odessa
BREMSSTRAHLUNG AND X-RAY SPECTRA FOR KAONIC AND PIONIC
HYDROGEN AND NITROGEN
The level energies, energy shifts and transition rates are estimated for pionic and kaonic atoms of
hydrogen and nitrogen on the basis of the relativistic perturbation theory with an account of nuclear
and radiative effects. New data about spectra of the exotic atomic systems can be considered as a new
tool for sensing the nuclear structure and creation of new X-ray sources too.
1. INTRODUCTION
At present time, the light hadronic (pionic, kaonic
etc.) atomic systems are intensively studied and can
be considered as a candidate to create the new lowenergy
X-ray standards [1-12]. In the last few years
transition energies in pionic [1] and kaonic atoms [2]
have been measured with an unprecedented precision.
Besides, an important aim is to evaluate the pion mass
using high accuracy X-ray spectroscopy [1-10]. Similar
endeavour are in progress with kaonic atoms. It is
easily to understand that the spectroscopy of pionic
and kaonic hydrogen gives unprecedented possibilities
to study the strong (nuclear) interaction at low energies
[5-8] by measuring the energy and natural width
of the ground level with a precision of few meV. Naturally,
studying the hadronic atomic systems is of a great
interest for further development of atomic and nuclear
theories as well as new tools for sensing the nuclear
structure and fundamental interactions, including the
Standard model [1-15]. The collaborators of the E570
experiment [7,8] measured X-ray energy of a kaonic
hydrogen atom, which is an atom consisting of a kaon
(a negatively charged heavy particle) and a hydrogen
nucleus (proton). The kaonic hydrogen X-rays were
detected by large-area Silicon Drift Detectors, which
readout system was developed by SMI (see [1,8]). It is
known that the shifts and widths due to the strong interaction
can be systematically understood using phenomenological
optical potential models. Nevertheless,
one could mention a large discrepancy between
the theories and experiments on the kaonic atoms
states. (for example, well known puzzle with helium
2p state). A large repulsive shift (about -40 eV) has
been measured by three experimental groups in the
1970’s and 80’s, while a very small shift (< 1 eV) was
obtained by the optical models calculated from the
kaonic atom X-ray data with Z>2 (look [1]). This significant
disagreement (a difference of over 5 standard
deviations) between the experimental results and the
theoretical calculations is known as the “kaonic helium
puzzle”. A possible large shift has been predicted
using the model assuming the existence of the deeply
bound kaonic nuclear states. However, even using this
model, the large shift of 40 eV measured in the experiments
cannot be explained. A re-measurement of the
shift of the kaonic helium X-rays is one of the top pri-
orities in the experimental research activities. In the
last papers (look, for example, [5,6] and [10] too) this
problem is physically reasonably solved. In the theory
of the kaonic and pionic atoms there is an important
task, connected with a direct calculation of the radiative
transition energies within consistent relativistic
quantum mechanical and QED methods (c.f.[13-
15]). The multi-configuration Dirac-Fock (MCDF)
approximation is the most reliable approach for multielectron
systems with a large nuclear charge; in this
approach one- and two-particle relativistic effects are
taken into account practically precisely. The next important
step is an adequate inclusion of the radiative
corrections. This topic has been a subject of intensive
theoretical and experimental interest (see [13]). Nevertheless,
the problem remains quite far from its final
solution. It is of a great interest to study and treat these
effects in the pionic and kaonic systems (for example,
hydrogen, nitrogen, oxygen etc.). In this paper the hyperfine
structure (HFS) level energies, energy shifts,
transition rates are estimated for the pionic and kaonic
atoms of hydrogen and nitrogen. New data about spectra
of the hadronic systems can be considered as a new
tool for sensing nuclear structure and creation of new
X-ray sources. Our method is based on the relativistic
perturbation theory (PT) [10,15,16,] with an accurate
account of the nuclear and radiative effects. The Lamb
shift polarization part is described in the Uehling-Serber
approximation; the Lamb shift self-energy part is
considered effectively within the advanced scheme.
2. METHOD OF RELATIVISTIC
PERTURBATION THEORY
Let us describe the key moments of our scheme
to relativistic calculation of the spectra for exotic
atomic systems with an account of relativistic, correlation,
nuclear, radiative effects (more details can
be found for example, in ref. [15]; see also [10]). In
general, the one-particle wave functions are found
from solution of the Klein-Gordon equation with
potential, which includes the self-consistent V 0 potential
(including electric, polarization potentials of
nucleus):
{1/c2 [E +eV (r)] 0 0 2 + 2
h∇ -m2c2 }Ψ( r)=0
© T. A. Florko, O. Yu. Khetselius, Yu. V. Dubrovskaya, D. E. Sukharev, 2009

where E 0 is the total energy of the system (sum of the
mass energy mc 2 and the binding energy ε 0 ). To describe
the nuclear finite size effect the smooth Gaussian
function of the charge distribution in a nucleus is
used. With regard to normalization we have:
32 2
( rR) ( 4 ) exp(
r)
ρ = γ π −γ (1)
2
where γ= 4 π R , R is the effective nucleus radius.
The Coulomb potential for the spherically symmetric
density ρ( r ) is:
nucl
( ) (
r
∞
' '2 ' ' ' '
( 1 ) ( ) ( )
∫ ∫ (2)
V r R =− r drr ρ r R + drrρr R
0
It is determined by the following system of differential
equations:
r
' 2 ' '2 ' 2
( , ) = ( 1 ) ρ( , ) ≡(
1 ) ( , )
V nucl r R r ∫ dr r r R r y r R (3)
0
2 ( ) ( )
y' r, R = r ρ r, R
(4)
52 2
( rR) r ( r)
ρ ' , = −8γ πexp −γ =
8r
=−2 γrρ ( r, R) =− ρ 2 ( r, R)
(5)
πr
with the corresponding boundary conditions. The
pion (kaon ) charge distribution is also included in the
strict accordance to the scheme [2,7]. Further, one
can write the Klein-Gordon type equations for oneor
multi-particle system. In general, formally they fall
into one-particle equations with potential, which includes
the self-consistent potential, electric, polarization
potentials of a nucleus. Procedure for an account
of the radiative corrections is given in detail in refs.
[15]. Regarding the vacuum polarization (Vac.Pol.)
effect let us note that this effect is usually taken into
account in the first PT order by means of the Uehling
potential:
∞
2α
U () r =− dt exp( −2rt α Z ) ×
3πr
∫
× +
1
2
t
2
1 2
≡ −
3π
2 − α
( 1 1 2 t ) C() g , (6)
t r
where g=r/αZ. In our calculation we usually use more
exact approach. The Uehling potential, determined as
a quadrature (6), is approximated with high precision
by a simple analytical function. The use of new approximation
of the Uehling potential [15] permits one
to decrease the calculation errors for this term down to
~0.5%. Besides, using such a simple function form for
the Uehling potential allows its easy inclusion to the
general system of differential equations. It is very important
to underline that the scheme used includes automatically
high-order vacuum polarization contributions,
including, the well known Wichman-Kroll and
Källen-Sabry ones. A scheme for estimating the selfenergy
part of the Lamb shift is based on the method
[22-24]. In an atomic system the radiative shift and
relativistic part of the energy are, in principle, defined
by one and the same physical field. It may be supposed
that there exists some universal function that connects
r
a self-energy correction and relativistic energy. The
self-energy correction for states of a hydrogen-like ion
is presented by Mohr [18,19]. In ref. [22-24] this result
is modified for the corresponding states of the multiparticle
atomic system. Further let us note that so
called relativistic recoil contribution is not calculated
by us and its value is taken from refs [4,7]. The transition
probabilities between the HFS sublevels are defined
by the standard energy approach formula. Other
details of the method used (and Superatom code) can
be found in refs. [15,16].
3. DATA FOR HADRONIC ATOMS AND
DISCUSION
We studied the X-ray spectra for the hadronic hydrogen
and nitrogen. In figure 1 the experimental kaonic
hydrogen X-ray energy spectra is presented [7,8].
In table 1 we present the measured and theoretical Xray
energies of kaonic hydrogen atom for the 2-1 transition
(in keV). In figure 1 this transition is clearly identified.
The notations are related to the initial (n i ) and
final (n f ) quantum numbers. The calculated value of
transition energy is compared with available measured
(E m ) and other calculated (E c ) values [1,3,9,10].
Fig. 1. The experimental kaonic hydrogen X-ray energy spectrum
[7,8].
Transition
Calculated (E c ) and measured (E m ) kaonic H atom
X-ray energies (in keV)
E c ,
this work
E c
[10]
E c
[3]
2-1 6.420 6.65 6.48
E c
[9]
6.480
6,482
E m
Table 1
E m
[1,7] [1,8]
6,44(8) 6.675(60)
6,96 (9)
In tables 2-4 we present the data on energy (in eV)
contribution for selected levels (transitions 8k-7i and
8i-7h), hyperfine transition energies and transition
rates in kaonic nitrogen. The radiative effects contributions
are indicated separately. For comparison, the
estimating data from [3,9] are given too.
In tables 5-7 we present theoretical data on energy
(in eV) contribution for the selected levels (transitions
5g-4f and 5f-4d), hyperfine transition energies and
transition rates in the pionic nitrogen. The radiative
corrections are separately indicated. For comparison,
the estimating data from refs. [4,9] are given too. The
detailed analysis of theoretical and separated experi-
17

mental data shows that indeed there is a physically
reasonable agreement between the cited data. But, obviously,
there may take a place the exception too as it is
shown on example of the kaonic uranium in ref. [10].
Table 2
Energy (in eV) contribution for the selected levels in kaonic nitrogen.
The first error takes into account neglected next order radiative
corrections. The second is due to the accuracy of the kaon mass
(±32 ppm)
Contributions 8k-7i [9]
8k-7i
This work
8i-7h
This work
Coulomb 2968.4565 2968.4492 2968.5344
Vac. Pol. 1.1789 1.1778 1.8758
Relativistic Recoil 0.0025 0.0025 0.0025
HFS Shift -0.0006 -0.0007 -0.0009
Total 2969.6373 2969.6288 2970.4118
Error 0.0005 0.0004 0.0004
Error due to the kaon mass 0.096 0.096 0.096
18
Transition
Table 3
Hyperfine transition (8k-7i) energies in kaonic nitrogen
F-
F’
Trans. E
(eV)
[3]
Trans. E
(eV)
This work
Trans. rate
(s-1 )
[3]
Trans.
rate (s -1 )
This work
8k-7i 8-7 2969.6365 2969.6289 1.54 × 10 13 1.51 × 10 13
7-6 2969.6383 2969.6298 1.33 × 10 13 1.32 × 10 13
7-7 2969.6347 2969.6264 1.31 × 10 13 1.29 × 10 13
6-5 2969.6398 2969.6345 1.15 × 10 13 1.12 × 10 13
6-6 2969.6367 2969.6284 0.03 × 10 13 0.02 × 10 13
6-7 2969.6332 2969.6248 0.00 × 10 13 0.00 × 10 13
Table 4
Hyperfine transition (8i-7h) energies in kaonic nitrogen (this work)
Transition F-F’ Trans. E (eV) Trans. rate (s -1 )
8i — 7h 7-6 2970.4107 1.16 × 10 13
6-5 2970.4135 0.99 × 10 13
6-6 2970.4086 0.96 × 10 13
5-4 2970.4193 0.81 × 10 13
5-5 2970.4114 0.02 × 10 13
5-6 2970.4073 0.00 × 10 13
Table 5
Energy (in eV) contribution for the selected levels in pionic nitrogen.
The first error takes into account neglected next order radiative
corrections. The second is due to the accuracy of the pion mass
(±2.5 ppm)
Contributions 5g-4f [4]
5g-4f This
work
5f-4d This
work
Coulomb 4054.1180 4054.1146 4054.7152
Self Energy -0.0001 -0.0002 -0.0004
Vac. Pol. 1.2602 1.2599 2.9711
Relativistic Recoil 0.0028 0.0028 0.0028
HFS Shift -0.0008 -0.0009 -0.0030
Total 4055.3801 4055.3762 4057.6857
Error ±0.0011 ±0.0007 ±0.0009
Error due to the pion mass ±0.010 ±0.010 ±0.010
We mean the agreement between theoretical estimating
data and experimental results. One should
keep in mind the following important moment. In a
case of good agreement between theoretical and experimental
data, the corresponding levels are less sensitive
to strong nuclear interaction. In the opposite
case one could point to a strong-interaction effect
in the exception cited (as example, some transitions
in the hadronic U) [10]. In a whole, to understand
further information on the low-energy kaon-nuclear
(pion-nuclear) interaction, new experiments to define
the shift and width of kaonic H/deuterium are now in
preparation in J-Parc and in LNF (c.f. [2,6,8]). Finally,
let us turn attention at the new possibilities, which
are opened with X-ray, γ -lasers (raser, graser) action
on hadronic system. Namely, speech is about a set of
the possible new nuclear quantum-optical effects in
the kaonic and pionic systems [25-27].
Table 6
Hyperfine transition (5g -4f) energies and transition rates in pionic
nitrogen
Transition
F-F’
Trans. E
(eV)
[3]
Trans. E
(eV)
This work
Trans. rate
(s-1 )
[3]
Trans. rate
(s -1 )
This work
5g -4f 5-4 4055.3779 4055.3744 7.13 × 10 13 7.10 × 10 13
4-3 4055.3821 4055.3784 5.47 × 10 13 5.42 × 10 13
4-4 4055.3762 4055.3735 5.27 × 10 13 5.23 × 10 13
3-2 4055.3852 4055.3828 4.17 × 10 13 4.12 × 10 13
3-3 4055.3807 4055.3769 0.36 × 10 13 0.33 × 10 13
3-4 4055.3747 4055.3712 0.01 × 10 13 0.01 × 10 13
Table 7
Hyperfine transition (5f — 4d) energies and transition rates in
pionic N (this work)
Transition F-F’ Trans. E (eV) Trans. rate (s -1 )
5f — 4d 4-3 4057.6821 4.52 × 10 13
3-2 4057.6914 3.11 × 10 13
3-3 4057.6793 2.93 × 10 13
2-1 4057.6954 2.09 × 10 13
2-2 4057.6892 2.21 × 10 13
2-3 4057.6768 0.01 × 10 13
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UDÑ 539.192
T. A. Florko, O. Yu. Khetselius, Yu. V. Dubrovskaya, D. E. Sukharev
tum Electrodyna-mics,10

INTRODUCTION
The short circuit current density J SC and open
circuit voltage U OC of photo-voltaic converters (PVC)
are increased with intensity growth of light flux penetrating
into their semiconductor base. It causes the
expediency of concentrated solar radiation (CSR)
used for increasing of such devices efficiency η , since
η∼ JSCUOCand UOC ∼ ln( JSC/ J0)
, where J 0 — diode
saturation current density [1-4].
One of the most favorable types of multi-junction
Si-PVC, specially created for the use in CSR conditions
[3,4] under the name of “photo-volt” represents
a monolithic design — the set (more than 10 devices)
silicon flatly-parallel diode cells with p–n junctions
on single crystal oriented perpendicularly to receiving
surface and connected in-series by means of metal layers
between adjacent cells.
The essential advantages of considered PVC type at
CSR conditions in comparison with single-junction Si-
PVC of planar design p–n junction which is oriented
parallel to receiving surface, are: i) potential capability
to much more effective conversion of CSR into electric
energy and ii) generation of 10–30 times greater output
voltage. The last circumstance simplifies the problem
of high-voltage photoelectric systems development and
provides reduction of electrical energy losses in solar
batteries interconnections as well as in the efficacy of
electrical energy transmission from solar batteries to
the consumer. The manufacturing of “photo-volt” type
PVC causes the necessity of the sufficiently expensive
photolithography process use, what disappears due to
the form of the receiving surface (in difference from
planar design PVC [2]) made as crested or grid currentcollecting
electrode with narrow and thin (~10 μm) elements
divided by the gaps less than 1 mm. However,
it is necessary to take into account that the significant
part of CSR is taken by the PVC receiving surface under
the angle α> 0 to the normal [5]. Therefore, J SC , U OC
and transfer efficacy should depend upon α , as far as
the irradiance E of PVC receiving surface changes with
α according to the law 0 cos E E = α, where ation of such type PVC with increased efficacy for the
use at CSR conditions.
On the other hand, the optical location systems
the Si-PVC of “photo-volt” type could be the serious
alternative to the well-known semiconductor radiation
sensors requiring the external source of electrical
energy. Thus, in this case, the angular dependence of
J SC and U OC should be more tangible as possible.
In the present work, the influence of single crystal
Si-PVC “photo-volt” design features on J SC and U OC
dependence upon α was investigated in connection
with the practical importance of two above mentioned
problems. While concerning both problems simultaneously,
the greatest interest is caused by the UOC ( α )
dependence due to the simplicity of this parameter
measurement.
EXPERIMENTAL DETAILES
The serial “photo-volt” type Si-PVC with the area
of receiving surface about 2 cm
E0= E at
α= 0 [6]. The problem of the angular dependence of
multi-junction Si-PVC output parameters’ minimization
is one of the urgent problems with regard to cre-
2 manufactured on the
basis of p-type conductivity single crystal silicon wafer
with resistivity about 10 Ohm∙cm were investigated.
Schematic image of the samples is presented on Fig.1.
Fig. 1. Principal scheme of “photovolt” type multijunction
Si-PVC cross–section: 1 — metal layer of thickness t ≈ 10 μm;
m
2 — layer of n + -type conductivity silicon; 3 — layer of ð-type
conductivity silicon; 4 — layer of p + -type conductivity silicon;
5 — metal electrode.
20
UDC 539.2:648.75
M. V. KIRICHENKO, V. R. KOPACH, R. V. ZAITSEV, S. A. BONDARENKO
National Technical University “Kharkiv Polytechnical Institute”,
21, Frunze Str., 61002, Kharkiv, Ukraine
e-mail:kirichenko_mv@mail.ru
SENSITIVITY OF SILICON PHOTO-VOLTAIC CONVERTERS
TO THE LIGHT INCIDENCE ANGLE
The results of output parameters dependences researches for multijunction silicon photovoltaic
converters (PVC) upon solar radiation incidence angle on their receiving surface are presented. It has
been shown that for improving of PVC efficiency is necessary to achieve the increased values of minority
charge carriers lifetime in their base crystals as well as the optical reflection coefficient for metal/Si
boundaries (interfaces) inside multijunction PVC, while for using multijunction PVC in the optical
location systems the forced reduction of these values is reasonable.
© M. V. Kirichenko, V. R. Kopach, R. V. Zaitsev, S. A. Bondarenko, 2009

Devices had overall dimensions 33 × 6 × 1 mm
and consisted of 35 elementary diode cells by thickness
150 μm each with n + -p-p + -structure which were
connected in-series through the metal inter-layers
with thickness about 10 μm.
The determination of J SC and U OC values for investigated
Si-PVC was carried out by measurement
and following analytical processing of loading illuminated
current versus voltage characteristics LI CVC.
The measurement of LI CVC was carried out similarly
to [7] under the Si-PVC receiving surface irradiation
power of 5712 W/m2 , what corresponds to the degree
of AM0 irradiation concentration equal to 4.2.
For the light incidence angle α change detection,
the investigated Si-PVC was fixed on angle measuring
device, which allows the angle α variation in the range
from 0° up to 90° with the accuracy of 0.01°. Measurements
of LI CVC were carried out at the following values
of α : from 0° up to 20° with a step 2°; from 20° up
to 40° with a step 4°; from 40° up to 60° with a step 5°.
Also, the LI CVC were measured precisely at angles
70°, 80°, 85o and 90°. Temperature of samples at LI
CVC measurements was at the level of 25 °Ñ with the
help of the thermostate. The analytical processing of
LI CVC data was realized similarly to [8].
RESULTS AND DISCUSSION
The normalized angular dependences of open cir-
norm
cuit voltage UOC ( α ) (curve 1) and short circuit cur-
norm
rent J SC ( α ) (curve 2), calculated according to the
experimental values of the corresponding magnitudes
norm J ( )
in the following way: ( ) SC α
J SC α =
,
J SC ( α= 0)
norm U ( )
( ) OC α
UOC
α =
, are presented on the
UOC
( α= 0)
Figure 2. Earlier [9] it was shown that in the range of
α values from 40o up to the Brewster angle ϕ B (74.5o
norm
for silicon) trend of UOC ( α ) dependence is well de-
ln ⎡f ( R,
α) cos α⎤
norm
scribed by the ratio UOC
( α) ≈ 1+
⎣ ⎦
,
2.3(
ξ2 −ξ1)
where 0 ≤ f( R,
α) ≤ 1 is a correcting function, taking
into account the real values of reflection coefficient
from the metal/Si boundaries into “photovolt” type
Si-PVC. In expanded form this ratio is presented in
[9], where ξ 1 < ξ 2 are absolute values of indexes in
degrees of short circuit current and diode saturation
current densities, accordingly. As a result of analysis
norm
of such UOC ( α ) dependence it has been established
that, varying parameters R and Δξ = ξ2 - ξ 1 it is possible
to purposefully effect on its character. So, for
example, it is necessary to maximally increase param-
norm
eters R and Δξ for minimization of UOC ( α ) angular
dependence with the purpose of “photovolt” type Si-
PVC efficiency rising.
Earlier, it was shown [9] that in the range of α values
from 40o up to the Brewster angle B ϕ (74.5o for
norm
silicon), the trend of UOC ( α ) dependence is well de-
ln ⎡f ( R,
α) cos α⎤
norm
scribed by the ratio UOC
( α) ≈ 1+
⎣ ⎦
,
2.3(
ξ2 −ξ1)
where 0 ≤ f( R,
α) ≤ 1 is a correction function taking
into account the real values of reflection coefficient
from the metal/Si boundaries into “photo-volt” type
Si-PVC.
Figure 2. Normalized values of open circuit voltage (1) and
short circuit current density (2) versus light incidence angle on Si-
PVC of “photovolt” type receiving surface.
In expanded form this ratio is presented in [9],
where 1 ξ < ξ 2 are absolute values of short circuit current
and diode saturation current densities, respec-
norm
tively. As a result of analysis of UOC ( α ) dependence,
it has been established that, varying parameters R
and Δξ = ξ2 - ξ 1 , it is possible to effect on its character
purposefully. For example, it is necessary to increase
parameters R and Δξ maximally, for the minimization
norm
of UOC ( α ) angular dependence with the purpose of
“photo-volt” type Si-PVC efficiency rise.
norm
Fig. 3. Theoretical U OC values versus α and Δξ for considered
Si-PVC of “photo-volt” type at the light reflection coefficient
values on metal/silicon boundaries: 1 – R = 1; 2 – R = 0.6;
3 — R = 0.2.
It is suggested to use the “photo-volt” type Si-
PVC as sensor in the optical location systems. Obviously,
for the successful solution of such a problem,
the device, used in the given volume, must provide the
ease of the output signal registration and, also, to have
the expressed, desirably linear dependence of the registered
parameter on the α angle.
As follows from mentioned above, the characteristic
detail of “photo-volt” type Si-PVC is the higher
photo-voltage that provides simple and reliable registration
of the parameter. At the same time, as it is
evident from Fig.2, the concerned “photo-volt” type
21

UOC α dependence
on the light incidence angles on their receiving surface
from 0 up to 74o . However, the results of work [9], allow
to suppose that varying parameters R and Δξ will
norm
provide the strikingly expressed character of UOC ( α)
dependence.
Therefore, we carried out the numerical simula-
ln ⎡f ( R,
α) cos α⎤
norm
tion of UOC
( α) ≈ 1+
⎣ ⎦
dependence
2.3Δξ
at 40î ≤ α ≤ 70î for different values of R and Δξ .
Results of the simulation are presented on Fig.3, as a
norm
family of UOC ( αΔξ , ) surfaces for different values of
the parameter R . From Fig.3 it follows evidently that
varying of parameter R practically does not result in
norm
∂UOC the varying ( α)
norm
being speed of U
∂α OC change
norm
on α , but provides the change of U OC absolute value,
causing this magnitude increase with R growing.
At the same time, as it is evident from Fig. 3, the
norm
∂UOC influence on the ( α)
renders Δξ parameter,
∂α
being the difference of J SC and J 0 orders of values.
Really, from named Fig.3, it is seen that by realization
of situation, characteristic for concerned “photo-volt”
type Si-PVC, when Δξ ≈ 7− 8,
the value
norm
∂UOC ( α) → 0 as well as on the Fig. 2 at α< 74°.
∂α
However, at decrease of difference between J SC and
J 0 , that corresponds to Δξ decrease, dependence of
norm
UOC ( α ) suffers substantial changes and at Δξ = 1− 2
obtains practically linear character in the concerned
range of α angles with sufficiently large value
norm
∂UOC ( α)
∂α ≈ -(7.3- 14.6)∙10-3 rel.un./deg.
Thus, the obtained results argue that in the case
of the “photo-volt” type Si-PVC use as sensors in the
optical location systems, the U OC sensitivity of such
sensors to the light incidence angle on their receiving
surface increase with decrease of the difference between
J SC and J 0 , characterized by parameter Δξ .
Value of the registered parameter U OC increases with
the growth of reflection coefficient from metal/Si
boundaries in “photo-volt” type Si-PVC. At the same
time, it is necessary to take into account the technological
difficulties of R → 1 achievement in the conditions
of the Si-PVC production, and, also, that, as it is
norm
seen from Fig. 3, the value of U OC is less only by 5%
at R = 0.6 than at R = 1.
Therefore, for the use of “photo-volt” type Si-
PVC as the sensor in the optical location systems,
the optimum is achieved at the next combination of
norm
parameters influencing the UOC ( α ) dependence:
Δξ = 1− 2 and R = 0.6 .
At the same time, the achievement of such reflection
coefficient from the metal/Si boundaries into
“photo-volt” type Si-PVC offers no complications at
the real conditions of Si-PVC production.
It is well known [1], that the values of J SC and 0 J
PVC as sensors, it is possible to achieve by a purposeful
decrease of τ np , values in base crystals bulk. Since
−1
τ np , Nr , where N r is bulk concentration of recombination
centers, then, with above mentioned purpose,
the base crystals for such sensors in the process
of appropriate devices manufacturing can be subject
to thermal, mechanical or other types of processing
directed to create in their bulk amount of recombination
centers as greater as possible. It will result in substantial
decrease of τnp , value. A similar effect could
be achieved as well by the use of heavily doped silicon
single crystal for manufacturing of concerned sensors.
Such type of silicon, produced for electronic industry,
has small τ np , values due to high doping level.
CONCLUSION
The results of experimental and theoretical research
of silicon photo-converters’ sensitivity to the
light incidence angle allow to make the following conclusion:
1. The character of UOC ( α ) dependence for multijunction
“photo-volt” type Si-PVC considerably
depends on the minority charge carriers lifetime τ np ,
value in the PVC base crystal, while reflection coefficient
R on metal/Si boundaries of PVC effects the absolute
value of U OC . It has been shown that purposeful
decrease of τ np , value and increase of R value will allow
to create the PVC with practically linear and easily
registered UOC ( α ) dependence.
2. The obtained character of UOC ( α ) dependence
will allow to use the multijunction “photo-volt” type
Si-PVC as sensors in the optical location systems.
References
1. Blakers A.W., Smeltik J., Proceedings of the 2
, and consequently Δξ , substantially depend from minority
charge carriers lifetime τ np , in PVC base crystals.
Therefore the required value of Δξ at using such
nd World Conference
and Exhibition on Photovoltaic Solar Energy Conversion;
July 6–10, 1998, Vienna, Austria, p. 2193.
2. Verlinden P.J. High–efficiency concentrator silicon solar cells,
p. 436–455. In: “Practical Handbook of Photovoltaics: Fundamentals
and Applications”, edited by T. Markvart and L.
Castaner; Elsevier Science Ltd., Kidlington, Oxford, 2003.
3. Sater B.L., Sater N.D. High voltage silicon VMJ solar cells for
up to 1000 suns intensities // Proceedings of the 29th IEEE
Photovoltaic Specialists Conference, May 20 — May 24,
2002. — New Orleans , USA, 2002. — P. 1019–1022.
4. Guk E.G., Shuman V.B., Shwartz M.Z. Proceedings of the
14th European Photovoltaic Solar Energy Conference, June
30 — July 4, 1997, Barcelona, Spain, P. 154.
5. Àíäðååâ Â.Ì., Ãðèëèõåñ Â.À., Ðóìÿíöåâ Â.Ä. Ôîòîýëåêòðè-
÷åñêîå ïðåîáðàçîâàíèå êîíöåíòðèðîâàííîãî ñîëíå÷íîãî
èçëó÷åíèÿ. — Ëåíèíãðàä: Íàóêà, 1999. — 310 ñ.
6. Ëàíäñáåðã Ã.Ñ. Îïòèêà. — Ìîñêâà: Íàóêà, 1996. — 928 ñ.
7. Keogh W., Cuevas A. Simple flashlamp I–V testing of solar
cells // Proceedings of the 26th IEEE Photovoltaic Specialists
Conference, Anaheim, CA, September 30 — October 3. —
1997. — P. 199–202.
8. Kerschaver E., Einhaus R., Szlufcik J., Nijs J.,Mertens R.
Simple and fast extraction technique for the parameters in
the double exponential model for I–V characteristic of solar
cells // Proceedings of the 14th European Photovoltaic Solar
Energy Conference, June 30 — July 4, 1997. — Barcelona,
Spain, 1997. — P. 2438–2441.
9. Kopach V.R., Kirichenko M.V., Shramko S.V. et al. New approach
to the efficiency increase problem for multijunction
silicon photovoltaic converters with vertical diode cells //
Functional Materials. — 2008. — Vol. — No. 2. — P. 253-
258.
norm
Si-PVC has weakly expressed ( )
22

UDC 539.2:648.75.
M. V. Kirichenko, V. R. Kopach, R. V. Zaitsev, S. A. Bondarenko
SENSITIVITY OF SILICON PHOTO-VOLTAIC CONVERTERS TO THE LIGHT INCIDENCE ANGLE
Àbstract
The results of output parameters dependences researches for multijunction silicon photovoltaic converters (PVC) upon solar radiation
incidence angle on their receiving surface are presented. It has been shown that for improving of PVC efficiency is necessary
to achieve the increased values of minority charge carriers lifetime in their base crystals as well as the optical reflection coefficient for
metal/Si boundaries (interfaces) inside multijunction PVC, while for using multijunction PVC in the optical location systems the forced
reduction of these values is reasonable.
Key words: sensitivity, photovoltaic converters, receiving surface.
ÓÄÊ 539.2:648.75
Ì. Â. Êèðè÷åíêî, Â. Ð. Êîïà÷, Ð. Â. Çàéöåâ, Ñ. À. Áîíäàðåíêî
×ÓÂÑÒÂÈÒÅËÜÍÎÑÒÜ ÊÐÅÌÍÈÅÂÛÕ ÔÎÒÎÝËÅÊÒÐÈ×ÅÑÊÈÕ ÏÐÅÎÁÐÀÇÎÂÀÒÅËÅÉ Ê ÓÃËÓ ÏÀÄÅÍÈß
ÑÂÅÒÀ ÍÀ ÈÕ ÏÐÈÅÌÍÓÞ ÏÎÂÅÐÕÍÎÑÒÜ
Ðåçþìå
Ïðèâåäåíû ðåçóëüòàòû èññëåäîâàíèé çàâèñèìîñòåé âûõîäíûõ ïàðàìåòðîâ ìíîãîïåðåõîäíûõ êðåìíèåâûõ ôîòîýëåêòðè-
÷åñêèõ ïðåîáðàçîâàòåëåé (ÔÝÏ) îò óãëà ïàäåíèÿ ñîëíå÷íîãî èçëó÷åíèÿ íà èõ ïðèåìíóþ ïîâåðõíîñòü. Ïîêàçàíî, ÷òî äëÿ óâåëè÷åíèÿ
ÊÏÄ ÔÝÏ íåîáõîäèìî îáåñïå÷èòü ïîâûøåíèå çíà÷åíèé âåëè÷èí âðåìåíè æèçíè íåîñíîâíûõ íîñèòåëåé çàðÿäà â
áàçîâûõ êðèñòàëëàõ è êîýôôèöèåíòà îïòè÷åñêîãî îòðàæåíèÿ îò ãðàíèö ìåòàëë/Si âíóòðè ìíîãîïåðåõîäíûõ ÔÝÏ, â òî âðåìÿ
êàê ïðè èñïîëüçîâàíèè ìíîãîïåðåõîäíûõ ÔÝÏ â ñèñòåìàõ îïòè÷åñêîé ëîêàöèè öåëåñîîáðàçíûì ÿâëÿåòñÿ ïðèíóäèòåëüíîå
ñíèæåíèå ýòèõ âåëè÷èí.
Êëþ÷åâûå ñëîâà: ôîòîýëåêòðè÷åñêèå ïðåîáðàçîâàòåëè, ÷óâñòèòåëüíîñòü, ïðè¸ìíàÿ ïîâåðõíîñòü.
ÓÄÊ 539.2:648.75
Ì. Â. ʳð³÷åíêî, Â. Ð. Êîïà÷, Ð. Â. Çàéöåâ, Ñ. Î. Áîíäàðåíêî
×ÓÒËȲÑÒÜ ÊÐÅÌͲªÂÈÕ ÔÎÒÎÅËÅÊÒÐÈ×ÍÈÕ ÏÅÐÅÒÂÎÐÞÂÀײ ÄÎ ÊÓÒÀ ÏÀIJÍÍß Ñ²ÒËÀ ÍÀ ¯Õ
ÏÐÈÉÌÀËÜÍÓ ÏÎÂÅÐÕÍÞ
Ðåçþìå
Íàâåäåíî ðåçóëüòàòè äîñë³äæåíü çàëåæíîñòåé âèõ³äíèõ ïàðàìåòð³â áàãàòîïåðåõ³äíèõ êðåìí³ºâèõ ôîòîåëåêòðè÷íèõ
ïåðåòâîðþâà÷³â (ÔÅÏ) â³ä êóòà ïàä³ííÿ ñîíÿ÷íîãî âèïðîì³íþâàííÿ íà ¿õ ïðèéìàëüíó ïîâåðõíþ. Ïîêàçàíî, ùî äëÿ çá³ëüøåííÿ
ÊÊÄ ÔÅÏ íåîáõ³äíî çàáåçïå÷èòè ï³äâèùåí³ çíà÷åííÿ ÷àñó æèòòÿ íåîñíîâíèõ íîñ³¿â çàðÿäó â áàçîâèõ êðèñòàëàõ òà
êîåô³ö³ºíòà îïòè÷íîãî â³äáèòòÿ â³ä ãðàíèöü ìåòàë/Si âñåðåäèí³ áàãàòîïåðåõ³äíèõ ÔÅÏ, ó òîé ÷àñ, ÿê ïðè âèêîðèñòàíí³ áàãàòîïåðåõ³äíèõ
ÔÅÏ ó ñèñòåìàõ îïòè÷íî¿ ëîêàö³¿ âèçíà÷åííÿ íàïðÿìó ðîçïîâñþäæåííÿ âèïðîì³íþâàííÿ äîö³ëüíèì º ïðèìóñîâå
çíèæåííÿ öèõ âåëè÷èí.
Êëþ÷îâ³ ñëîâà: ôîòîåëåêòðè÷í³ ïåðåòâîðþâà÷³, ïðèéìàëüíà ïîâåðõíÿ, ÷óòëèâ³ñòü.
23

24
UDC 535.5
L. S. MAXIMENKO 1 , I. E. MATYASH 1 , S. P. RUDENKO 1 , B. K. SERDEGA 1 ,
V. S. GRINEVICH 2 , V. A. SMYNTYNA 2 , L. N. FILEVSKAYA 2
1 Lashkarev Institute of Physics of Semiconductors, National Academy of Sciences of Ukraine,Kiev-28, Prospect Nauki,45
2 Odessa I.I. Mechnikov National University, Odessa, Ukraine, Odessa, 65082, Dvoryanskaya str.2 grinevich@onu.edu.ua
SPECTROSCOPY OF POLARISED AND MODULATED LIGHT
FOR NANOSIZED TINDIOXIDE FILMS INVESTIGATION
The peculiarities of Surface Plasmons Resonance (SPR) in nanosized tin dioxide films, deposited
on a prism of total interior reflection, were experimentally investigated using methods of the polarized
and modulated radiation of light (PM). It was found that the layers, obtained by special technology
using polymer materials as structuring additives are the combination of polycrystalline nanosized
grains with air pores. This result has confirmed the supposition about the considerable porosity of the
obtained layers. The obtained results confirm the considerable (PM) method’s sensitivity for the aims
of material’s optical parameters detecting.
INTRODUCTION
In the modern gas analyses there is a natural transition
to the thin films’ adsorptive sensitive elements
with a perfectly developed physical surface based on
oxide nanodimensional materials. One of such a material
is tin dioxide which has perfect sensitivity to
a composition of a environmental atmosphere and
chemical resistivity to a poisoning media. Transparent
Tin dioxide films with nano sized grains may be
applied as optical detectors of environmental compositions.
It has become possible due to the noticed
optical property of such films to answer the presence
of different chemical compounds in the environment
(both gaseous and liquid).
The later circumstance defined the urgency of the
detailed researches of such films’ optical properties.
Among possible diagnostic methods the surface
plasmons resonance phenomenon (SPR) is a unique
one because it is a basis of the most sensitive methods
applied for the registration of media dielectric
functions changes. The application of polarized and
modulated light for detecting of SPR in oxide materials
with nano grains is becoming proved and effective.
The peculiarities of the SPR in the nanosized Tin
dioxide films deposited on the surface of total internal
reflection prism were investigated using the technique
of modulation of polarized light radiation (PM). The
research supposed the presence of electrons’ plasma in
the obtained layers, which is indirectly confirmed by a
property of a considerable electrons’ degeneration in
the films.
TECHNOLOGY OF SAMPLES
PREPARATION AND THE INVESTIGATIONS
TECHNIQUE
Transparent nanodimensional Tin dioxide films,
obtained using polymer materials as structuring additives
and Tin containing precursor of SnO 2 were used as
samples. The samples’ preparation methods described
in [1] had several stages: preparation of tin containing
organic filler, preparation of the polymer material so-
lution, and introduction of tin containing compound
into it. The resultant gel was deposited on a glass substrate
and annealed in a muffle furnace. Temperature
(500 0 C) and the annealing time (2 hours) were chosen
as necessary parameters for both polymer and tin dioxide
precursor decomposition. Thin tin dioxide layers
with well developed nanostructure and considerable
porosity were formed after the complete removal of decay
products by means of annealing both of polymer
and tin dioxide containing precursor and also after the
complete oxidation of the films up to tin dioxide.
The nanostructure of the films was determined at
the AFM [2] investigations and the typical surface of
such films (AFM image) is shown on Fig. 1.
Fig. 1. The films investigated typical surface AFM image.
In the presented work the films were obtained from
solutions having 0,03% of PVA as a structural additive
and 1% of Tin containing SnO 2 precursor.
The total internal reflection on the border film-external
environment was used as a detecting phenomenon.
The theoretical evidence and the experimental
© L. S. Maximenko, I. E. Matyash, S. P. Rudenko, B. K. Serdega, V. S. Grinevich, V. A. Smyntyna, L. N. Filevskaya, 2009

technique of the total internal reflection measurement
are described in details in [3].
Fig. 2. The experimental equipment optical scheme for angles
characteristics of a polarization difference measurements
using modulation of polarization: LGN- Helium-Neon
Laser, PEM-photo elastic modulator of polarization, FP- the
phase plate, p,s linear polarizations, azimuths of them are parallel
and perpendicular to the plane of incidence, G-Glann s
prism, FD-photo detector, ôcr the total internal reflection critical
angle, N0, N1,N2- refraction indices of glass, films, air correspondingly.
The general optical scheme of the experimental
equipment for measuring of both total internal reflection
characteristics and polarization parameters difference
is given at Fig.2. Hellium-Neon laser, LGN-113
with the fixed wave lengths 0,63 mkm and 1,15 mkm
is used as a source of linearly polarized radiation, together
with monochromator MDR-4 with a halogen
lamp KGM-150 at the input and the polarizer on the
out let. A modulator of polarization –REM was used
as a dynamic phase plate functioning in two regimes.
In the both cases, by rotating the modulator round the
optical axe of the measuring device, it’s position was
chosen so, that the out let polarized radiation azimuth
was parallel and perpendicular in turn to the plane of
accident (p and s polarization, correspondingly ).
After the interaction with the half cylinder and the
surface of resonance sensitive Tin dioxide film, the radiation
was directed to photo detector, FD (Silicium
or Germanium photodiode) which after absorption of
radiation generates a signal comprising an alternative
component. It is proportional to the reflection indices
difference of p and s polarization of the detected
radiation.
Thus, the equipment with the modulation of polarized
light permits to obtain not only the angle dependant
reflection indices R and R correspondingly,
s p
but also their difference, ΔR. ΔR factor is not a result
of mathematical act, but is the physical value independently
and directly measured.
The investigated films were deposited on glass
substrates which permited to supplement the glass segment
to a half cylinder, using the contact of a substrate
with a segment by immersion liquid (glycerin).
THE MEASUREMENTS RESULTS AND
THEIR DISCUSSION
All the three characteristics (R s , R p and ΔR) for
one of the samples are given at Fig.3 in relative, but
comparable units. Wave length of the scanning radiation,
λ =630 nm.
ΔR, R , R , arb.un. ���. ���. ��. ��.
S P
5,0
4,5
4,0
3,5
3,0
2,5
2,0
1,5
1,0
0,5
0,0
-0,5
30 40 50 60 70
����, ����, ���. ���.
Angle, grad
ΔR
R S
R P
Fig. 3. Experimental dependencies for reflection indices Rs
and Rp and their difference ΔR of the investigated samples.
�R, ΔR, abs.un. ���. ��.
0,00
-0,01
-0,02
-0,03
-0,04
-0,05
400 500 600 700 800 900 1000
����� �����, ��
�, nm
experimental
�����������
theoretical ������
Fig. 4. The polarization difference vs wave length at a fixed
angle, which is more than critical.
The most interesting is the angles’ range where
their values are more than critical ones where an inequality
of R and R testifies about the broken total
s p
internal reflection, which is possible when an absorption
has place in the sample. As soon as, the difference
between R and R is registered on the background of
s p
considerable signals, then the big error is inevitable.
This not favourable situation may be eliminated in a
case when a polarization difference, which is measured
relatively zero, may be amplified and, hence, fixed
for sure. Thus, the polarization difference, ΔR=R - s
R certainly demonstrates the break of total internal
p
reflection which change its sign at an angle equal to
the critical one. It was a definite interest to retrace the
differential difference dependence vs wave length at a
fixed incidence angle which is more than critical. The
experimental results at the incidence angle of 460 are
shown at Fig.4 by the continues line in comparison
with the theoretically calculated ones on the basis of
Frehnels equations — by the broken line. The adjustment
parameters were refraction and absorption indices
for the Tin dioxide film.
As it is seen at Fig.4 the coincidence of experi-
25

mental and theoretical results is more than satisfactory
in the wave length range 500-1000 nm. It is appeared,
that n and k are linearly and uniquely dependent on the
wave length: n=1, 28+0,000005 * λ; k= 0,223-λ/4700,
λ in nm. Changes of n or k on more than 5 * 10 -3 gives
the mismatch of experimental and theoretical data.
Changes of k move a theoretical curve higher or
lower the experimental one, but variation of n changes
the theoretical curve’ slope.
The reflective index values obtained in our work
are in good agreement with other authors’ data [4]/
That is, the reflective index value obtained as a result
of our samples investigation is within the indices
values interval corresponding to indices of pure Tin
dioxide (n=1,56) and for air (n=1,003).The pores existence
was expected in the investigated layers which is
resulted from polymers application at the films’ production.
Pores within the said technology are formed
at polymer’s decay during the annealing procedure.
Thus, the above discussed results confirm the considerable
sensitiveness of the method for our material’s
optical parameters detecting.
26
CONCLUSION
The new technique for the Surface Plasmons
Resonans parameters measuring by means of modulation
of polarized light was applied to nanosized Tin
dioxide layers in order to obtain their optical indices.
UDC 535.5
The system’s — porous layer of SnO 2 reflection index
showed its satisfactory agreement with other authors’
data. The obtained reflection index values characterize
the object as a system of nanosize Tin dioxide with
air pores. This result confirms the supposition of such
pores presence in the films.
The polarized light modulation method has high
sensitivity for optical parameters detecting at Plasmons
Resonans in the investigated layers and, hence,
gives good perspectives in gaseous environment detecting.
Such a technique of PM in SPR of the layers
is, besides all, is a perfect confirmation of electrons’
plasma presence in them.
References
1. L.N. Filevskaya, V.A. Smyntyna, V.S. Grinevich. Morphology
of nanostructured SnO 2 films prepared with polymers
employment // Photoelectronics. Inter-universities scientific
articles, 2006, ¹ 15, p.p.11-13.
2. V.A. Smyntyna, L.N. Filevskaya, V.S. Grinevich, Morphology
and optical properties of SnO 2 nanofilms // Semiconductor
physics, quantum electronics & optoelectronics, Volume 11,
¹ 2, 2008, p.p.163-171.
3. Ë.È. Áåðåæèíñêèé, Ë.Ñ. Ìàêñèìåíêî, È.Å. Ìàòÿø,
Ñ.Ï. Ðóäåíêî, Á.Ê. Ñåðäåãà. Ïîëÿðèçàöèîííî-ìîäóëÿöèîííàÿ
ñïåêòðîñêîïèÿ ïîâåðõíîñòíîãî ïëàçìîííîãî
ðåçîíàíñà // Îïòèêà è ñïåêòðîñêîïèÿ. 2008. — Ò.105. —
¹2. — Ñ. 281-289.
4. M.Anastasescu, M.Gartner, S.Mihaiu, C.Anastasescu,
M.Purica, E.Manea, M.Zaharescu. Optical and structural
properties of SnO 2 — based sol-gel thin films // International
Semiconductor Conference, 2006, Volume 1, Issue, Sinaia,
Romania, 27-29 Sept. 2006, Page(s):163 — 166.
L. S. Maximenko, I. E. Matyash, S. P. Rudenko, B. K. Serdega, V. S. Grinevich, V. A. Smyntyna, L. N. Filevskaya
SPECTROSCOPY OF POLARISED AND MODULATED LIGHT FOR NANOSIZED TINDIOXIDE FILMS
INVESTIGATION
Abstract
The peculiarities of the Surface Plasmons Resonance (SPR) in nanosized tin dioxide films, deposited on the prism of total interior
reflection, were experimentally investigated using methods of the polarized and modulated radiation of light (PM). It was found that the
layers, obtained by special technology using polymer materials as structuring additives are the combination of polycrystalline nanosized
grains with air pores. This result has confirmed the supposition about the considerable porosity of the obtained layers. The obtained
results confirm the considerable PM method’s sensitivity for the aims of material’s optical parameters detecting.
Key words: polarizing modulation, thin film, tin dioxide.
ÓÄÊ 535.5
Ë. Ñ. Ìàêñèìåíêî, È. Å. Ìàòÿø, Ñ. Ï. Ðóäåíêî, Á. Ê. Ñåðäåãà, Â. Ñ. Ãðèíåâè÷, Â. À. Ñìûíòûíà, Ë. Í. Ôèëåâñêàÿ
ÏÎËßÐÈÇÀÖÈÎÍÍÎ-ÌÎÄÓËßÖÈÎÍÍÀß ÑÏÅÊÒÐÎÑÊÎÏÈß ÍÀÍÎÐÀÇÌÅÐÍÛÕ ÏËÅÍÎÊ ÄÂÓÎÊÈÑÈ
ÎËÎÂÀ
Ðåçþìå
Ýêñïåðèìåíòàëüíî ñ ïðèìåíåíèåì ìåòîäèêè, îñíîâàííîé íà ïîëÿðèçàöèîííîé ìîäóëÿöèè (ÏÌ) èçëó÷åíèÿ, èññëåäîâàíû
îñîáåííîñòè ïîâåðõíîñòíîãî ïëàçìîííîãî ðåçîíàíñà (ÏÏÐ) â íàíîðàçìåðíûõ ïëåíêàõ äèîêñèäà îëîâà, íàíåñåííûõ
íà ïîâåðõíîñòü ïðèçìû ïîëíîãî âíóòðåííåãî îòðàæåíèÿ. Èññëåäóåìûå ñëîè ÿâëÿþòñÿ ñî÷åòàíèåì ïîëèêðèñòàëëè÷åñêèõ
íàíîðàçìåðíûõ çåðåí ñ âîçäóøíûìè ïîðàìè, ÷òî ïîäòâåðäèëî ïåðâîíà÷àëüíîå ïðåäïîëîæåíèå î çíà÷èòåëüíîé ïîðèñòîñòè
ïîëó÷åííûõ ñ èñïîëüçîâàíèåì ïîëèìåðîâ ïëåíîê äâóîêèñè îëîâà. Ïîëó÷åííûå ðåçóëüòàòû ñâèäåòåëüñòâóþò î çíà÷èòåëüíîé
÷óâñòâèòåëüíîñòè ìåòîäà ÏÌ â îïðåäåëåíèè îïòè÷åñêèõ ïàðàìåòðîâ ìàòåðèàëà.
Êëþ÷åâûå ñëîâà: ïîëÿðèçàöèîííàÿ ìîäóëÿöèÿ, òîíêèå ïëåíêè, äâóîêèñü îëîâà.

ÓÄÊ 535.5
Ë. Ñ. Ìàêñèìåíêî, ². ª. Ìàòÿø, Ñ. Ï. Ðóäåíêî, Á. Ê. Ñåðäåãà, Â. Ñ. Ãð³íåâè÷, Â. À. Ñìèíòèíà, Ë. Ì. Ô³ëåâñüêà
ÏÎËßÐÈÇÀÖ²ÉÍÎ-ÌÎÄÓËßÖ²ÉÍÀ ÑÏÅÊÒÐÎÑÊÎÏ²ß ÍÀÍÎÐÎÇ̲ÐÍÈÕ Ï˲ÂÎÊ ÄÂÎÎÊÈÑÓ ÎËÎÂÀ
Ðåçþìå
Åêñïåðèìåíòàëüíî ³ç çàñòîñóâàííÿì ìåòîäèêè, çàñíîâàíî¿ íà ïîëÿðèçàö³éí³é ìîäóëÿö³¿ (ÏÌ) âèïðîì³íþâàííÿ, äîñë³äæåí³
îñîáëèâîñò³ ïîâåðõíåâîãî ïëàçìîííîãî ðåçîíàíñó (ÏÏÐ) ó íàíîðîçì³ðíèõ ïë³âêàõ ä³îêñèäó îëîâà, íàíåñåíèõ íà ïîâåðõíþ
ïðèçìè ïîâíîãî âíóòð³øíüîãî â³äáèòòÿ. Äîñë³äæóâàí³ øàðè º ñïîëó÷åííÿì ïîë³êðèñòàë³÷íèõ íàíîðîçì³ðíèõ çåðåí
ç ïîâ³òðÿíèìè ïîðàìè, ùî ï³äòâåðäèëî ïåðâ³ñíå ïðèïóùåííÿ ïðî çíà÷íó ïîðèñò³ñòü îòðèìàíèõ ç âèêîðèñòàííÿì ïîë³ìåð³â
ïë³âîê äâîîêèñó îëîâà. Îòðèìàí³ ðåçóëüòàòè ñâ³ä÷àòü ïðî çíà÷íó ÷óòëèâ³ñòü ìåòîäó ÏÌ ó âèçíà÷åíí³ îïòè÷íèõ ïàðàìåòð³â
ìàòåð³àëó.
Êëþ÷îâ³ ñëîâà: ïîëÿðèçàö³éíà ìîäóëÿö³ÿ, òîíê³ ïë³âêè, äâîîêèñ îëîâà.
27

28
UDC 621.315.592
O. O. PTASHCHENKO 1 , F. O. PTASHCHENKO 2 , O. V. YEMETS 1
1 I. I. Mechnikov National University of Odessa, Dvoryanska St., 2, Odessa, 65026, Ukraine
2 Odessa National Maritume Academy, Odessa, Didrikhsona St., 8, Odessa, 65029, Ukraine
EFFECT OF AMBIENT ATMOSPHERE ON THE SURFACE CURRENT
IN SILICON P-N JUNCTIONS
1. INTRODUCTION
Gas sensors on p-n junctions [1, 2] have some
advantages in comparison with these, based on oxide
polycrystalline films [3] and Shottky diodes [4]. P-n
junctions on wide-band semiconductors have high
potential barriers for current carriers, which results in
low background currents, high sensitivity and selectivity
to the gas components [5, 6].
The sensitivity of p-n sensors to donor gases as
ammonia is due to forming of a surface conducting
channel in the electric field induced by the ammonia
ions adsorbed on the surface of the natural oxide layer
[1, 2]. This mechanism is valid only for adsorbed molecules
which are ionized on the semiconductor surface.
And it causes the gas selectivity of these sensors.
The surface conducting channel is produced in these
sensors under condition
m
Ns > Ns
, (1)
m
where N s and Ns are the surface densities of adsorbed
molecules (ions) and surface electron states in
the semiconductor, respectively. This determines the
threshold gas concentration for these sensors.
Characteristics of p-n junctions in silicon as ammonia
sensors were studied in previous works [7, 8].
It was shown that ammonia sensitivity of these structures
is due to enhancing of the surface recombination,
caused by NH molecules adsorption. The
3
difference in the sensitivity mechanism can lead to
differences in selectivity and other characteristics of
sensors.
The purpose of this work is a comparative study of
the influence of ammonia, water and ethylene vapors
on stationary surface currents in silicon p-n junctions,
as well as on their kinetics.
2. EXPERIMENT
The influence of ammonia, water and ethylene vapors on I-V characteristics of forward and reverse
currents, as well as on the kinetics of the surface current in silicon p-n structures was studied.
All these vapors enhance both the forward and reverse currents. The gas sensitivity of p-n structures at
forward biases is due to enhanced surface recombination, while at reverse biases a surface conductive
channel shorts the p-n junction. The sensitivity to ammonia is much higher than to other vapors. It is
explained as a result of donor properties of NH 3 molecules. The response time of silicon p-n junctions
as gas sensors at room temperature is below 60 s.
I-V measurements were carried out on silicon pn
junctions with the structure described in previous
works [7, 8]. The effect of vapors over water solutions
of several NH 3 concentrations, over distilled water
and over liquid ethylene was studied on stationary I-V
characteristics, as well as on kinetics of surface current
in p-n junctions.
I-V characteristic of the forward current in a typical
p-n structure is presented as curve 1 in Fig. 1. Over
the current range between 10 nA and 1mA the I–V
curve can be described with the expression
IV ( ) = I0exp( qV/ nkT)
, (2)
where I is a constant; q is the electron charge; V de-
0
notes bias voltage; k is the Boltzmann constant; T is
temperature; n ≈ 1.1 is the ideality constant. Some deviation
from the value n=1 can be ascribed to recombination
on deep levels in p-n junction and (or) at the
surface [9]. Curves 2, 3, 4 in Fig. 1 were obtained in
air with vapors of water, ethylene, and ammonia, respectively.
The partial pressures of water, ethylene and
ammonia vapors were of 2000Pa, 5000Pa, and 50 Pa,
accordingly. A comparison between curves 1, 2, and
3 in Fig. 1 shows that the sensitivity of p-n structures
to ammonia vapors is the highest and to water — the
lowest.
10 -5
10 -6
10 -7
10 -8
I,A
2
0 0,1 0,2 0,3 0,4
V, Volts
Fig. 1. Forward branches of I-V characteristics of a p-n structure
in air (1) and in vapors of water (2), ethylene (3) and ammonia
(4).
© O. O. Ptashchenko, F. O. Ptashchenko, O. V. Yemets, 2009
3
4
1

Fig. 2 represents I–V characteristics of the reverse
current in a p-n junction. Curve 1 was measured in air,
and curves 2–4 were obtained in air with vapors of water,
ethylene, and ammonia, respectively. It is evident
from Fig. 2 that the studied vapors strongly enhance
the reverse current in silicon p-n structures.
10 -5
10 -6
10 -7
10 -8
I,A
4
0 1 2 3 4 5
V, Volts
Fig. 2. Reverse branches of I-V characteristics of a p-n structure
in air (1) and in vapors of water (2), ethylene (3) and ammonia
(4).
Curves 1, 2 and 3 in Fig. 3 depict I–V characteristics
of the additional current in a p-n structure, due
to adsorption of water, ethylene, and NH molecules,
3
accordingly. It is seen that, at a high enough reverse
voltage, the additional reverse currents are higher than
the corresponding forward currents.
2
0
-2
-4
-6
I, �A
1
1A
2
3
-8
-5 -4 -3 -2 -1 0
V, Volts
Fig. 3. I-V characteristics of the additional currents in a p-n
structure in vapors of water (1, 1A), ethylene (2) and ammonia (3).
Ordinates of curve 1A are multiplied by 10.
The (absolute, current-) sensitivity of a gas sensor
can be defined as
S =ΔI Δ P , (3)
I
3
2
1
where ΔI is the change in the current (at a fixed voltage),
which is due to a change ΔP in the corresponding
gas partial pressure [10]. And the relative sensitivity is
S =ΔI ( I Δ P)
, (4)
R
0
where I denotes the current in the pure air at the same
0
bias voltage.
The sensitivities of studied p-n junctions to water,
ethylene (C H OH) and ammonia vapors at a forward
2 5
bias voltage of 0.25 V and a reverse bias voltage of 3 V
are presented in Tab. 1.
Gas sensitivities of p-n structures
Table 1
H 2 O C 2 H 5 OH NH 3
S I (0.25 V), nA/kPa 6 11 11000
S I (–3 V), nA/kPa 70 800 20000
S R (0.25 V), 1/kPa 0.1 0.23 200
S R (-3 V), 1/kPa 3 50 900
It is seen in Tab. 1 that the studied p-n structures
can be used, practically, as ammonia selective sensors.
In an ammonia-free atmosphere these structures are
sensors of water and ethylene. The reverse bias is preferable
for the sensors.
Fig. 4 illustrates the kinetics of forward (a) and reverse
(b) currents in a p-n structure after let in- and
out of ammonia vapor with a partial pressure of 50 Pa.
Similar curves were measured for water- and ethylene
vapors. The response time t r for current rise was estimated
as the duration of the current increase to 90%
of its stationary value after letting in the corresponding
vapor into the container with the sample. And the decay
time t d was obtained in a similar way, for the current
decrease from the stationary value to 10% of it. These
procedures were carried out in regimes of forward and
reverse bias. The resulting response- and decay times
are presented in Tab. 2.
I, ��
0,70
0,68
0,66
0,64
0
I, �� ��
3,1
3,0
2,9
100 200 300
t, s
2,8
0 100 200 300
t, s
Fig. 4. Kinetics of forward (a) and reverse (b) currents
in a p-n structure after let in- and out of ammonia
vapor with a partial pressure of 50 Pa.
a
b
29

30
Rise- and decay times of p-n gas sensors
H 2 O C 2 H 5 OH NH 3
t r (0.25 V), s 30–35 10–16 25–40
t d (0.25 V), s 10–15 5–8 20–30
t r (-3 V), s 35–55 50–55 25–30
t d (-3 V), s 25–30 10–12 8–9
Table 2
The data in Tab. 2 show that the rise time of the
signal for all the studied vapors is longer than the decay
time in both regimes. And the response time of the
p-n structures as gas sensors does not exceed 55 s.
3. DISCUSSION
The mechanism of the ammonia sensitivity of the
forward current in silicon p-n structures was discussed
in previous works [7, 8]. Adsorbed and subsequently
ionized molecules of a donor gas form the electric
field which bends down c- and v- bands in the crystal
at the surface. Under a high enough gas partial pressure,
a surface channel with electron conductivity is
formed. This situation is realized in p-n structures on
wide-band semiconductors at low enough biases [1,
2, 5, 6]. With an increased bias voltage, electrons and
holes are injected into the channel, and a regime of
double injection is realized which results in a superlinear
rise of the current [6]. The double injection leads,
at high enough injection current, to destruction of the
channel.
In the case of silicon p-n junctions, the destruction
of the channel by injected charge currents occurs
at relatively low forward bias voltages of ~0.1V, and the
linear section of I–V curve practically is not realized
[6]. Our experiments confirm this conclusion. Curve
4 in Fig. 1 has a large section that corresponds to formula
(1) with ideality coefficient n=2.6. Such value
of n suggests that the excess current, due to ammonia
molecules adsorption, can be ascribed to the phononassisted
tunnel recombination at deep surface states
[9].
I–V characteristics 2 and 3 in Fig. 1, measured
in water- and ethylene vapors, respectively, have pronounced
linear sections in a semi-logarithmic plot,
with ideality coefficients of 1.13 and 2.1, which argues
that the increase of the forward current in these vapors
is due to enhanced surface recombination. Thus, the
mechanism of the sensitivity of silicon p-n junctions
to ammonia-, ethylene- and ammonia vapors is the
same.
I–V characteristics of the excess reverse current,
due to water- and ethylene molecules adsorption,
which are plotted as curves 1and 2 in Fig. 3, have large
linear sections. This means that the surface conductive
channel, formed as a result of water- and ethylene
molecules adsorption, is not destroyed at a reverse
bias. And this channel is responsible for gas sensitivity
of silicon p-n structures at reverse biases.
Curve 3 in Fig. 3, as I–V characteristic of the excess
reverse current in ammonia vapors, is superlinear.
This can be tentatively ascribed to injection processes
or (and) strong-field effects.
An interesting result of our study is that the sensitivity
of silicon p-n structures as gas sensors is higher
at reverse bias than at forward bias. Gas sensitivity of
the forward current was observed only at low bias voltages
V

studied vapors are of the same order of magnitude,
while the sensitivities differ by three orders. For the
electronic mechanism is also characteristic inequality
τ > τ , which was observed for all studied gases at for-
r d
ward and reverse biases, as seen in Tab. 3. Tentatively,
the response time of the studied p-n gas sensors is due
to the recharging of surface states, as a result of the adsorption
of molecules from the ambient atmosphere.
4. CONCLUSIONS
Forward and reverse currents in silicon p-n junctions
are sensitive to ammonia, ethylene and water vapors
in the ambient air. The sensitivity to NH 3 vapor
is by orders of magnitude higher than to other studied
vapors. Therefore silicon p-n junctions can be used
as selective ammonia vapor sensors. Selectivity of the
sensor is due to donor properties of NH 3 molecules.
The sensitivity of silicon p-n structures to the mentioned
vapors at forward biases is caused by enhancing
of surface recombination, as a result of band bending
in p-region, due to electric field of adsorbed ions.
The gas sensitivity of studied p-n structures at reverse
biases is due to forming of a surface conductive
channel which shorts the p-n junction.
The forward bias voltage of the sensor is limited by
exponential rise of bulk injection current and screening
of the electric field, induced by adsorbed ions, by
injected electrons and holes. Therefore the reverse
bias is preferable for the sensors and provides higher
gas sensitivity, than the forward bias.
The response time of silicon p-n sensors is below
UDC 621.315.592
O. O. Ptashchenko, F. O. Ptashchenko, O. V. Yemets
60 s at room temperature for all the studied vapors at
forward and reverse biases. This time can be ascribed
to recharging of slow surface centers.
References
1. Ïòàùåíêî Î. Î., Àðòåìåíêî Î. Ñ., Ïòàùåíêî Ô. Î.
Âïëèâ ãàçîâîãî ñåðåäîâèùà íà ïîâåðõíåâèé ñòðóì â pn
ãåòåðîñòðóêòóðàõ íà îñíîâ³ GaAs–AlGaAs // Ô³çèêà ³
õ³ì³ÿ òâåðäîãî ò³ëà . — 2001. — Ò. 2, ¹ 3. — Ñ. 481 — 485.
2. Ïòàùåíêî Î. Î., Àðòåìåíêî Î. Ñ., Ïòàùåíêî Ô. Î.
Âïëèâ ïàð³â àì³àêó íà ïîâåðõíåâèé ñòðóì â p-n ïåððåõîäàõ
íà îñíîâ³ íàï³âïðîâ³äíèê³â À3Â5 // Æóðíàë ô³çè÷íèõ
äîñë³äæåíü. — 2003. — Ò. 7, ¹4. — Ñ. 419 — 425.
3. Áóãàéîâà M. E., Koâaëü Â. M., Ëàçàðåíêî B. ². òà ³í. Ãàçîâ³
ñåíñîðè íà îñíîâ³ îêñèäó öèíêó (îãëÿä) // Ñåíñîðíà
åëåêòðîí³êà ³ ì³êðîñèñòåìí³ òåõíîëî㳿. — 2005. — ¹3. —
Ñ. 34 — 42.
4. Áàëþáà Â. È., Ãðèöûê Â. Þ., Äàâûäîâà Ò. À. è äð. Ñåíñîðû
àììèàêà íà îñíîâå äèîäîâ Pd-n-Si // Ôèçèêà è õèìèÿ
ïîëóïðîâîäíèêîâ. — 2005. — Ò. 39, ¹ 2. Ñ. 285 — 288.
5. Ptashchenko O. O., Artemenko O. S., Dmytruk M. L. et al.
Effect of ammonia vapors on the surface morphology and
surface current in p-n junctions on GaP // Photoelectronics.
— 2005. — No. 14. — P. 97 — 100.
6. Ptashchenko F. O. Effect of ammonia vapors on surface currents
in InGaN p-n junctions // Photoelectronics. — 2007. —
No. 17. — P. 113 — 116.
7. Ïòàùåíêî Ô. Î. Âïëèâ ïàð³â àì³àêó íà ïîâåðõõíåâèé
ñòðóì ó êðåìí³ºâèõ p-n ïåðåõîäàõ // ³ñíèê ÎÍÓ, ñåð.
Ô³çèêà. — 2006. — Ò. 11, ¹. 7. — Ñ. 116 — 119.
8. Ptashchenko O. O., Ptashchenko F. O., Yemets O. V. Effect
of ammonia vapors on the surface current in silicon p-n junctions
// Photoelectronics. — 2006. — No. 16. — P. 89 — 93.
9. Ðtashchenko A. A., Ptashchenko F. A. Tunnel surface recombination
in p-n junctions // Photoelectronics. — 2000. —
¹ 10. — P. 69 — 71.
10. Âàøïàíîâ Þ. À., Ñìûíòûíà Â. À. Àäñîðáöèîííàÿ ÷óâñòâèòåëüíîñòü
ïîëóïðîâîäíèêîâ. — Îäåññà: Àñòðîïðèíò,
2005. — 216 p.
EFFECT OF AMBIENT ATMOSPHERE ON THE SURFACE CURRENT IN SILICON P-N JUNCTIONS
Abstract
The influence of ammonia, water and ethylene vapors on I-V characteristics of forward and reverse currents, as well as on the kinetics
of the surface current in silicon p-n structures was studied. All these vapors enhance both the forward and reverse currents. The gas
sensitivity of p-n structures at forward biases is due to enhanced surface recombination, while at reverse biases a surface conductive channel
shorts the p-n junction. The sensitivity to ammonia is much higher than to other vapors. It is explained as a result of donor properties
of NH 3 molecules. The response time of silicon p-n junctions as gas sensors at room temperature is below 60s.
Key words: ambient atmosphere, surface current, silicon.
ÓÄÊ 621.315.592
À. À. Ïòàùåíêî, Ô. À. Ïòàùåíêî, Å. Â. Åìåö
ÂËÈßÍÈÅ ÎÊÐÓÆÀÞÙÅÉ ÀÒÌÎÑÔÅÐÛ ÍÀ ÏÎÂÅÐÕÍÎÑÒÍÛÉ ÒÎÊ Â ÊÐÅÌÍÈÅÂÛÕ P-N ÏÅÐÅÕÎÄÀÕ
Ðåçþìå
Èññëåäîâàíî âëèÿíèå ïàðîâ àììèàêà, âîäû è ýòèëåíà íà ÂÀÕ ïðÿìîãî è îáðàòíîãî òîêîâ, à òàêæå íà êèíåòèêó ïîâåðõíîñòíîãî
òîêà â êðåìíèåâûõ p-n ñòðóêòóðàõ. Âñå óêàçàííûå ïàðû ïîâûøàþò è ïðÿìîé, è îáðàòíûé òîêè. Ãàçîâàÿ ÷óâñòâèòåëüíîñòü
p-n ñòðóêòóð ïðè ïðÿìîì ñìåùåíèè îáóñëîâëåíà ðîñòîì èíòåíñèâíîñòè ïîâåðõíîñòíîé ðåêîìáèíàöèè, à ïðè
îáðàòíîì ñìåùåíèè ïðîâîäÿùèé êàíàë çàêîðà÷èâàåò p-n ïåðåõîä. ×óâñòâèòåëüíîñòü ê àììèàêó çíà÷èòåëüíî âûøå, ÷åì ê
äðóãèì ïàðàì. Ýòî îáúÿñíÿåòñÿ äîíîðíûìè ñâîéñòâàìè ìîëåêóë NH 3 . Âðåìÿ ñðàáàòûâàíèÿ êðåìíèåâûõ p-n ïåðåõîäîâ êàê
ãàçîâûõ ñåíñîðîâ ïðè êîìíàòíîé òåìïåðàòóðå íå ïðåâûøàåò 60 ñ.
Êëþ÷åâûå ñëîâà: ïîâåðõíîñòíûé òîê, îêðóæàþùàÿ àòìîñôåðà, êðåìíèé.
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32
ÓÄÊ 621.315.592
Î. Î. Ïòàùåíêî, Ô. Î. Ïòàùåíêî, Î. Â. ªìåöü
ÂÏËÈ ÍÀÂÊÎËÈØÍÜί ÀÒÌÎÑÔÅÐÈ ÍÀ ÏÎÂÅÐÕÍÅÂÈÉ ÑÒÐÓÌ Ó ÊÐÅÌͲªÂÈÕ P-N ÏÅÐÅÕÎÄÀÕ
Ðåçþìå
Äîñë³äæåíî âïëèâ ïàð³â àì³àêó, âîäè ³ åòèëåíó íà ÂÀÕ ïðÿìîãî ³ çâîðîòíîãî ñòðóì³â, à òàêîæ íà ê³íåòèêó ïîâåðõíåâîãî
ñòðóìó â êðåìí³ºâèõ p-n ñòðóêòóðàõ. Âñ³ óêàçàí³ ïàðè ï³äâèùóþòü ³ ïðÿìèé, ³ çâîðîòíèé ñòðóìè. Ãàçîâà ÷óòëèâ³ñòü p-n
ñòðóêòóð ïðè ïðÿìîìó çì³ùåíí³ îáóìîâëåíà çðîñòàííÿì ³íòåíñèâíîñò³ ïîâåðõíåâî¿ ðåêîìá³íàö³¿, à ïðè çâîðîòíîìó çì³ùåíí³
ïðîâ³äíèé êàíàë çàêîðî÷óº p-n ïåðåõ³ä. ×óòëèâ³ñòü äî àì³àêó çíà÷íî âèùà, í³æ äî ³íøèõ ïàð³â. Öå ïîÿñíþºòüñÿ äîíîðíèìè
âëàñòèâîñòÿìè ìîëåêóë NH 3 . ×àñ ñïðàöþâàííÿ êðåìí³ºâèõ p-n ïåðåõîä³â ÿê ãàçîâèõ ñåíñîð³â ïðè ê³ìíàòí³é òåìïåðàòóð³ íå
ïåðåâèùóº 60 ñ.
Êëþ÷îâ³ ñëîâà: ïîâåðõíåâèé ñòðóì, íàâêîëèøíÿ àòìîñôåðà, êðåìí³é.

UDC 621.315.592
V. A. BORSCHAK, M. I. KUTALOVA, N. P. ZATOVSKAYA, A. P. BALABAN, V. A. SMYNTYNA
Odessa I. I. Mechnikov National University, RL-3,
2, Dvorianskaya str., Odessa 65082, Ukraine. Tel. +38 048 — 7266356.
Fax +38 048 — 7266356, E-mail: wadz@mail.ru
DEPENDENCE OF SPACE-CHARGE REGION CONDUCTIVITY
OF NONIDEAL HETEROJUNCTION FROM PHOTOEXCITATION
CONDITIONS
It is shown that nonideal CdS-Cu 2 S heterojunction illumination results in essential space-charge
region width reduction and change of a potential barrier form. It is established that this change is the
most expressed near the heteroboundary and occurs even at very small intensity of stimulating light.
It is connected with the capture of nonequilibrium charge on local centers, presented in space-charge
region. Such change of the form of a potential barrier results in essential change of tunnel hopping
conductivity of a spatial charge nonideal heterojunction.
Investigation of the current transport mechanism
in heterojunction, used as optical and x-ray images
sensors inevitably takes in the account the light influence
on their tunnel-jumping conductivity. Impact of
light on nonideal heterojunction essentially influences
the parameters of its space charge region (SCR) [1],
and hence on tunnel-jumping conductivity of SCR,
and heterojunction as a whole. As the sensor generated
signal strongly depends on heterojunction conductivity,
the question about light influence on SCR and so
on conductivity is represented as rather significant.
Experimental investigations of light influence on
conductivity CdS-Cu 2 S heterojunction are described
in [2]. It is established, that with the increase of excitation
intensity with white or only short-wave (λ ≈
520nm) light heterojunction conductivity is essentially
increased both on direct and alternating current even
in a short-circuited condition, i.e. at constant barrier
height. At the same time, photocapacity growth is observed
even at light illumination essentially smaller than
the solar. Ratio Ñ ph /C d for some elements achieved 10
and more units that testifies the barrier width reduction.
Such phenomenon can result in essential growth
tunnel-jumping conductivity in SCR .
In [3] the current transport in heterojunction
without illumination was considered, but it was not
taken into account the SCR parameters change under
light influence. Therefore, the offered model cannot
be applied directly to the sensor work description. We
shall consider how it is possible quantitatively to take
into account the influence of light on jumping current
transport in nonideal heterojunction.
For definition SCR heterojunction conductivity it
is necessary to set the function Fermi E F (x) level position
in each point x [3]. Conductivity G σ (x) of SCR
part is calculated from 0 up to x as the solution of the
integral equation. However, the solution of this equation
is also determined by the form of a potential barrier
φ (x). For dark heterojunction φ (x) depends only
on submitted bias U and shows the known square-law
formula. At heterojunction illumination generated
in wide band CdS nonbasic carriers (holes) are captured
in SCR on the traps, presented there. We shall
assume, that holes are captured by the centers with a
© V. A. Borschak, M. I. Kutalova, N. P. Zatovskaya, A. P. Balaban, V. A. Smyntyna, 2009
single energy level, which concentration is equal N t .
Then, apparently from fig. 1, because of band bending
in SCR, the energy distance from level Fermi up
to a level of holes traps E Ft (determining their filling
degree) essentially depends on coordinate x. It results
in non-uniform filling, and concentration of the captured
charge (changeable along an x axis) will be determined
by expression:
⎡ϕ0⎛ω−x⎞⎤ px ( ) =Δp0exp⎢ ⎜ ⎟
kT ω
⎥
⎣ ⎝ ⎠⎦
(1)
here Δp — the concentration of photoexcited
0
holes in CdS quasineutral region. We shall note, that
in formula (1) capture holes centers concentration is
absent, because limits of considered here models the
capture centers number essentially exceed the number
of nonequilibrium holes, i.e. N > > p (x) or E > > kT.
t Ft
Thus, the dependence of a potential barrier φ (õ) can
be defined from Poisson equation:
2
d ϕ(
x) e
=− N 2
D + p x
dx εε0
[ ( )]
(2)
where N D — concentration of ionized sallow donors,
not compensated completely in CdS, determining
barrier width in darkness, when ð (õ) ≡ 0. Captured
charge dependence from coordinate õ results in a significant
deviation of a potential shape of a barrier φ (x)
from the square-law form, characteristic for constant
distribution of the charge creating a built-in field. The
potential barrier of illuminated heterojunction will be
described by expression:
ϕ − ⎡ ⎛ Δ ⎞
ϕ = + + − +
( x)
0 eU
1
Δp ⎢
α
1+ ( e −1−α) ⎢⎣ αN
D
2
x
2
ω
2 p
⎜
⎝αND x
2⎟
⎠ω
+
x
2Δp
⎛ −α
α ⎞⎤
ω ee 1 F
2 ⎜ − −α ⎟⎥+Δ
0
ND
(3)
α ⎝ ⎠⎦⎥
where α = (φ −ΕU)/kT. The parameter Δp, ,ncluded in
0
(3), can be determined knowing the character of distribution
of the captured nonequilibrium charge set by
the formula (3), and average value of a nonequilibrium
33

charge p` , captured on traps in SCR region, which can
t
be determined from photocapacity value (C ). Having
ph
measured heterojunction dark capacity and its photocapacity
at various stimulating light intensities under
the formula of the flat condenser
C=εε S/ω (4)
0
it is possible easily to determine appropriate to each
of these capacities barrier region width ω (Ñ , C ), so
d ph
also values N (C ) and p (C , C ). It is obvious, that
D T d d ph
the size of average captured in SCR nonequilibrium
charge is connected with ð (õ) by the ratio:
ω
1
p = p( x) dx
ω ∫ . (5)
34
t
0
Fig. 1. The zone diagram CdS-Cu S heterojunction with hole
2
traps in CdS
It is possible to determine the appropriate value of
parameter Δp, included in (3), for each value of stimulating
light intensity by means of calculating p (C , C )
t d ph
from (5) with the account (1) for each value of photocapacity
Ñ . ph
UDC 621.315.592
V. A. Borschak, M. I. Kutalova, N. P. Zatovskaya, A. P. Balaban, V. A. Smyntyna
From the equation (3) it is seen, that at absence
of photoexcitation of wide band material, i.e. at Δð =
0, the expression (3) transforms into the square-law
form. However, already at small values Δð there is an
essential deviation φ (õ) from a square-law dependence
especially near heterojunction where the captured
nonequilibrium charge is maximal and φ (õ) gets
the character close to exponential. At values Δð appropriate
to large capacities, change φ (õ) form also is
the most essential in frontier area where E F (x) has the
maximal value and which, hence, has minimal tunnel-jumping
conductivity. Thus, function φ (õ), and
also E F (x) essentially depend on intensity of illumination
and consequently from photocapacity which is
easily measured experimentally. As E F (x) determines
the values of parameters R’(E F ), N(E F ), W(E F ), which
determines tunnel-jumping conductivity mechanism
in SCR, the SCR conductivity G σ essentially depends
on a type of function φ (õ) and the stimulating light intensity.
It means, that illumination influences not only
barrier width reduction on current-transport, but also
the change of its form.
References
1. D.V.Vassilevski, V.A.Borschak, M.S.Vinogradov. “Influence
of tunnel effects on the kinetics of the photocapacitance in
nonideal heterojunctins” Solid-State Electronics, 1994,
Vol.37, No.9, p.1680-1682.
2. Smyntyna, V.A. Borschak, M.I. Kutalova, N.P. Zatovskaya,
A.P. Balaban. Investigation in temperature and frequency
dependences for conductivity in barrier region of nonideal
heterojunction. — Photoelectronics. — 2005. — ¹14. —
P. 5-7.
3. Smyntyna V. A., Borschak V. A., Kutalova M. I., Zatovskaya
N. P., Balaban A. P. External bias influence on the transmission
processes in nonideal heterojunction // Photoelectronics.
— 2008. — ¹17. — P. 23-26.
4. Â.À.Áîðùàê, Ä.Ë.Âàñèëåâñêèé Òîêîïåðåíîñ ïî ëîêàëèçîâàííûì
ñîñòîÿíèÿì â íåèäåàëüíûõ ãåòåðîñòðóêòóðàõ.
Çàâèñèìîñòü ïðîâîäèìîñòè îáëàñòè ïðîñòðàíñòâåííîãî
çàðÿäà íåèäåàëüíîãî ãåòåðîïåðåõîäà îò óñëîâèé ôîòîâîçáóæäåíèÿ.
Ïîëóïðîâîäíèêîâàÿ òåõíèêà. — 1999–
Âûï. 17. — ñ. 24-29.
DEPENDENCE OF SPACE-CHARGE REGION CONDUCTIVITY OF NONIDEAL HETEROJUNCTION FROM
PHOTOEXCITATION CONDITIONS
Abstract
It is shown that nonideal CdS-Cu 2 S heterojunction illumination results in essential space-charge region width reduction and
change of a potential barrier form. It is established that this change is the most expressed near the heteroboundary and occurs even at
very small intensity of stimulating light. It is connected with the capture of nonequilibrium charge on local centers, presented in spacecharge
region. Such change of the form of a potential barrier results in essential change of tunnel hopping conductivity of a spatial charge
nonideal heterojunction.
Key word: space — nonideal heterojunction, photoexcitation conditions.

ÓÄÊ 621.315.592
Â. À. Áîðùàê, Ì. È. Êóòàëîâà, Í. Ï. Çàòîâñêàÿ, À. Ï. Áàëàáàí, Â. À. Ñìûíòûíà
ÇÀÂÈÑÈÌÎÑÒÜ ÏÐÎÂÎÄÈÌÎÑÒÈ ÎÁËÀÑÒÈ ÏÐÎÑÒÐÀÍÑÒÂÅÍÍÎÃÎ ÇÀÐßÄÀ ÍÅÈÄÅÀËÜÍÎÃÎ
ÃÅÒÅÐÎÏÅÐÅÕÎÄÀ ÎÒ ÓÑËÎÂÈÉ ÔÎÒÎÂÎÇÁÓÆÄÅÍÈß
Ðåôåðàò
Ïîêàçàíî, ÷òî îñâåùåíèå íåèäåàëüíîãî ãåòåðîïåðåõîäà CdS-Cu 2 S ïðèâîäèò ê ñóùåñòâåííîìó ñîêðàùåíèþ øèðèíû
îáëàñòè ïðîñòðàíñòâåííîãî çàðÿäà è èçìåíåíèþ ôîðìû ïîòåíöèàëüíîãî áàðüåðà. Óñòàíîâëåíî, ÷òî âáëèçè ãåòåðîãðàíèöû
ýòî èçìåíåíèå ìàêñèìàëüíî âûðàæåíî è ïðîèñõîäèò äàæå ïðè î÷åíü íåáîëüøèõ èíòåíñèâíîñòÿõ âîçáóæäàþùåãî ñâåòà. Ýòî
ñâÿçàíî ñ çàõâàòîì íåðàâíîâåñíîãî çàðÿäà íà ïðèñóòñòâóþùèå â îáëàñòè ïðîñòðàíñòâåííîãî çàðÿäà ëîêàëüíûå öåíòðû. Òàêîå
èçìåíåíèå ôîðìû ïîòåíöèàëüíîãî áàðüåðà ïðèâîäèò ê ñóùåñòâåííîìó èçìåíåíèþ òóííåëüíî-ïðûæêîâîé ïðîâîäèìîñòè îáëàñòè
ïðîñòðàíñòâåííîãî çàðÿäà íåèäåàëüíîãî ãåòåðîïåðåõîäà.
Êëþ÷åâûå ñëîâà: ïðîñòðàíñòâåííûé çàðÿä, íåèäåàëüíûé ãåòåðîïåðåõîä, óñëîâèÿ ôîòîâîçáóæäåíèÿ.
ÓÄÊ 621.315.592
Â. À. Áîðùàê, Ì. ². Êóòàëîâà, Í. Ï. Çàòîâñüêà, À. Ï. Áàëàáàí, Â. À. Ñìèíòèíà
ÇÀËÅÆͲÑÒÜ ÏÐβÄÍÎÑÒ² ÎÁËÀÑÒ² ÏÐÎÑÒÎÐÎÂÎÃÎ ÇÀÐßÄÓ ÍŲÄÅÀËÜÍÎÃÎ ÃÅÒÅÐÎÏÅÐÅÕÎÄÓ
Â²Ä ÓÌΠÔÎÒÎÇÁÓÄÆÅÍÍß
Ðåçþìå
Äîâåäåíî, ùî çàñâ³òëåííÿ íå³äåàëüíîãî ãåòåðîïåðåõîäó CdS-Cu 2 S âèêëèêຠâàæëèâå ñêîðî÷åííÿ øèðèíè îáëàñò³ ïðîñòîðîâîãî
çàðÿäà òà çì³íè ôîðìè ïîòåíö³éíîãî áàð’ºðó.
Âñòàíîâëåíî, ùî ïîáëèçó ãåòåðîìåæ³ öÿ çì³íà — ìàêñèìàëüíà ³ â³äáóâàºòüñÿ ïðè äóæå íåâåëèêèõ ³íòåíñèâíîñòÿõ çáóäæóþ÷îãî
ñâ³òëà. Öå ïîâ’ÿçàíî ç çàõîïëåííÿì íåð³âíîâàæíîãî çàðÿäó íà ïðèñóòí³ ëîêàëüí³ öåíòðè. Òàê³ çì³íè ôîðìè ïîòåíö³éíîãî
áàð’ºðó âèêëèêàþòü ñóòòºâ³ çì³íè òóíåëüíî –ñòðèáêîâî¿ ïðîâ³äíîñò³ îáëàñò³ ïðîñòîðîâîãî çàðÿäó íå³äåàëüíîãî
ãåòåðîïåðåõîäó.
Êëþ÷îâ³ ñëîâà: ïðîñòîðîâèé çàðÿä, íå³äàëüíèé ãåòðîïåðåõ³ä, óìîâè ôîòîçáóäæåííÿ.
35

36
UDÑ 539.142, 539.184
V. KH. KORBAN, G. P. PREPELITSA, YU. BUNYAKOVA, L. DEGTYAREVA, A. KARPENKO,
S. SEREDENKO
Odessa National Polytechnical University, Odessa
Odessa State Environmental University, Odessa
PHOTOKINETICS OF THE IR LASER RADIATION EFFECT ON MIXTURE
OF THE CO 2 -N 2 -H 2 O GASES: ADVANCED ATMOSPHERIC MODEL
A kinetics of energy exchange in the mixture of the atmosphere CO 2 -N 2 -H 2 O gases under passing
the powerful CO 2 laser radiation pulses within the three-mode model of kinetical processes is studied.
More accurate data for the absorption coefficient are presented.
1. INTRODUCTION
At present time the environmental physics has
a great progress, provided by implementation of the
modern quantum electronics and laser physics methods
and technologies in order to study unusual features
of the “laser radiation- substance (gases, solids
etc.) interaction. A special interest attracts a problem
of interaction of the powerful laser radiation with an
aerosol ensemble and search of new non-linear optical
effects. The latter is directly related with problems of
modern aerosol laser physics (c.f.[1-13]). One could
remind that there is a redistribution of molecules on
the energy levels of internal degree of freedom in the
resonant absorption of IR laser radiation by the atmospheric
molecular gases. As a result of quite complicated
processes one could define an essential changing
of the gases absorption coefficient due to the saturation
of absorption [1].
One interesting effect else to be mentioned is an
effect of the kinetic cooling of environment (mixture
of gases), as it was at first predicted in ref. [2,5]. Usually
the effect of kinetical cooling (CO 2 ) in a process of
absorption of the laser pulse energy by molecular gas is
considered for the middle latitude atmosphere and for
special form of a laser pulse. Besides, the approximate
values for constants of collisional deactivation and
resonant transfer in reaction CO 2 -N 2 are usually used.
In series of papers (see, for example, [11-13], computational
modelling of the energy and heat exchange
kinetics in the mixture of the CO 2 -N 2 -H 2 0 atmospheric
gases interacting with IR laser radiation has been
carried out within the general three-mode kinetical
model. It is obvious that using more precise values for
all model constants and generally speaking the more
advanced atmospheric model parameters may lead to
quantitative changing in the temporary dependence of
the resonant absorption coefficient by CO 2 .
Let us remind that the creation and accumulation
of the excited molecules of nitrogen owing to the resonant
transfer of excitation from the molecules CO 2
results in the change of environment polarizability.
Perturbing the complex conductivity of environment,
all these effects are able to transform significantly the
impulse energetics of IR lasers in an atmosphere and
significantly change realization of different non-linear
laser-aerosol effects.
The aim of this paper is to present more accurate
data for kinetics of energy and heat exchange in the
mixture CO 2 -N 2 -H 2 0 gases in atmosphere under passing
the powerful CO 2 laser radiation pulses on the basis
of using the more advanced atmospheric model and
more precise values for all kinetical model constants.
2. ADVANCED THREE-MODE KINETICAL
MODEL FOR THE “LASER PULSE —
MEDIUM” INTERACTION
As usually, we start from the modified three-mode
model of kinetic processes (see, for example, [1,11-
13] in order to take into consideration the energy exchange
and relaxation processes in the ÑÎ 2 . — N 2 —
H 2 O mixture interacting with a laser radiation. As in
ref. [11-13] we consider a kinetics of three levels: 10°0,
00°1 (ÑÎ 2 ) and v = 1 (N 2 ). Availability of atmospheric
constituents O 2 and H 2 O is allowed for the definition
of the rate of vibrating-transitional relaxation of N 2 .
The system of balance equations for relative populations
is written in a standard form as follows:
dx1
0
=−βω+ ( 2 gP10 ) x1 +βω x2 + 2 β gP10 ) x1
,
dt
dx2
0
=ωx1−( ω+ Q+ P20) x2 + Qx3 + P20x2 , (1)
dt
dx 3
0
=δQx2 −( δ Q + P30) x3 + P30x3 .
dt
Here the following notations are used:
x = N / N 1 100 CO , 2
x = N / N 2 001 CO , (2)
2
x = N 3 N / N
2 CO2
δ ,
where N N are the level populations 10°0, 00°1
100, 001
(ÑÎ ); 2 2 N N is the level population v = 1 (N ); N 2 CO2
is the concentration of CO molecules; Δ is the ratio
2
of the common concentrations of ÑÎ and N in the
2 2
atmosphere (Δ = 3.85⋅10-4 0 0
); x 1 , x 2 and 0
x 3 are the
equilibrium relative values of populations under gas
temperature T:
© V. Kh. Korban, G. P. Prepelitsa, Yu. Bunyakova, L. Degtyareva, A. Karpenko, S. Seredenko, 2009

( )
x = exp − E T , (3)
0
1 1
( )
x = x = exp E T ;
0 0
2 3 2
The values E and E in (1) are the energies (K)
1 2
of levels 10°0, 00°1 (consider the energy of quantum
N equal to E ); P , P and P are the probabilities
2 2 10 20 30
(s-1 ) of the collisional deactivation of levels 10°0, 00°1
(ÑÎ ) and v = 1 (N ), Q is the probability (s 2 2 -1 ) of resonant
transfer in the reaction ÑÎ → N ,ω is the prob-
2 2
ability (s-1 ) of ÑÎ light excitation, g = 3 is the statisti-
2
cal weight of level 02°0, β = (1+g) -1 = 1/4.
As usually, the solution of the differential equations
system (1) allows defining a coefficient of absorption
of the radiation by the CO molecules according to the
2
formula:
α =σ( x − x ) N . (4)
CO2 1 2 CO2
The σ in (4) is dependent upon the thermodynamical
medium parameters as follows [2]:
1
2
P ⎛ T ⎞
σ=σ0 ⎜ ⎟
P0 T0
, (5)
⎝ ⎠
Here T and p are the air temperature and pressure,
σ is the cross-section of resonant absorption under
0
T = T , p = p .
0 0
One could remind that the absorption coefficient
for carbon dioxide and water vapour is dependent
upon the thermodynamical parameters of aerosol atmosphere.
In particular, for radiation of CO -laser the
2
coefficient of absorption by atmosphere defined as
α =α +α
g
CO2 H2O is equal in conditions, which are typical for summer
mid-latitudes, α g (H=0) = 2.4∙10 6 ñm -1 , from which
0.8∙10 6 ñm -1 accounts for CO 2 and the rest — for water
vapour (data are from ref. [2]) . On the large heights the
sharp decrease of air moisture occurs and absorption
coefficient is mainly defined by the carbon dioxide.
The changing population of the low level 10°0
(ÑÎ 2 ), population of the level 00°1, the vibratingtransitional
relaxation (VT-relaxation) and the inter
modal vibrating-vibrating relaxation (VV’-relaxation)
processes define the physics of resonant absorption
processes. Moreover, the above indicated processes
result in a redistribution of the energy between the
vibrating and transitional freedom of the molecules.
According to ref.[1], the threshold value, which corresponds
to the decrease of absorption coefficient in
two times, for the strength of saturation of absorption
in vibrating-rotary conversion give I sat = (2 ÷ 5) 10 5 W
cm -2 for atmospheric CO 2 . In this case the pulse duration
t i must satisfy the condition t R

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12. Turin A.V., Prepelitsa G.P., Kozlovskaya V.P., Kinetics of
energy and heat exchange in mixture CO 2 -N 2 -H 2 0 of atmospheric
gases interacting with IR laser radiation: Precise
3-mode kinetical model// Phys. Aerodisp. Syst. — 2003. —
N40. — P.123-128.
38
UDÑ 539.142, 539.184
V. Kh. Korban, G. P. Prepelitsa, Yu. Bunyakova, L. Degtyareva, A. Karpenko, S. Seredenko
13. Prepelitsa G.P., Shpinareva I.M., Bunyakova Yu.Ya., Photokinetics
of interaction and energy exchange for ir laser radiation
with mixture CO 2 -N 2 -H 2 0 of atmospheric gases//Photokinetics.
— 2006. — Vol.16. — P.139-141.
14. Wang, C, ENSO, climate variability, and the Walker and
Hadley circulations. The Hadley Circulation: Present, Past,
and Future (Eds H. F. Diaz and R. S. Bradley). Springer
(2004).
15. Boer G.J., Sargent N.E. Vertically integrated budgets of
mass and energy for the globe // J. Atmos. Sci. — 1995. —
Vol. 42. — P. 1592-1613.
16. Kistler R., Kalnay E., Collins W., Saha S., White G., Woollen
J., Chelliah M., Ebisuzaki W., Kanamitsu M., Kousky V.,
van den Dool H., Jenne R., Fiorino M. The NCEP-NCAR
50-year reanalysis: monthly means CD-ROM and documentation
// Bull. Amer. Meteor. Soc. — 2001. — Vol. 82. —
P. 247-267.
17. Fyfe J.C., Boer G.J., Flato G.M. Predictable winter climate
in the North Atlantic sector during the 1997–1999 ENSO
cycle // Geophysical Research Letters. — 1999. — Vol. 26. —
No. 21. — P. 1601-1604.
18. Plattner G-K., Joos F., Stocker T.F., Marchal O. Feedback
mechanisms and sensitivities of ocean carbon uptake under
global warming // Tellus. — 2001. — Vol. 53B. — No. 5. —
P. 564-592.
19. Jin X., Shi G. A simulation of CO 2 uptake in a three dimensional
ocean carbon cycle model // Acta Meteorologica Sinica.
— 2001. — Vol. 15. — No. 1. — P. 29-39.
20. Rivkin B.B., Legendre L. Biogenic carbon cycling in the
upper ocean: effect of microbial respiration // Science. —
2001. — Vol. 291. — P. 2398-2400.
PHOTOKINETICS OF THE IR LASER RADIATION EFFECT ON MIXTURE OF THE CO 2 -N 2 -H 2 O GASES: ADVANCED
ATMOSPHERIC MODEL
Abstract
A kinetics of energy exchange in the mixture of the atmosphere CO 2 -N 2 -H 2 O gases under passing the powerful CO 2 laser radiation
pulses within the three-mode model of kinetical processes is studied. More accurate data for the absorption coefficient are presented.
Key words: photokinetics, laser field, mixture of gases, atmospheric model.
ÓÄÊ 539.142, 539.184
Â. Õ. Êîðáàí, Ã. Ï.Ïðåïåëèöà, Þ. Áóíÿêîâà, Ë. Äåãòÿðåâà, À. Êàðïåíêî, Ñ. Ñåðåäåíêî
ÔÎÒÎÊÈÍÅÒÈÊÀ ÂÇÀÈÌÎÄÅÉÑÒÂÈß ÈÊ ËÀÇÅÐÍÎÃÎ ÈÇËÓ×ÅÍÈß ÑÎ ÑÌÅÑÜÞ CO 2 -N 2 -H 2 O ÃÀÇÎÂ:
ÓÒÎ×ÍÅÍÍÀß ÀÒÌÎÑÔÅÐÍÀß ÌÎÄÅËÜ
Ðåçþìå
Ðàññìîòðåíà ôîòîêèíåòèêà ýíåðãîîáìåíà â ñìåñè CO 2 -N 2 -H 2 0 àòìîñôåðíûõ ãàçîâ ïðè ïðîõîæäåíèè ÷åðåç àòìîñôåðó
ìîùíîãî èçëó÷åíèÿ CO 2 ëàçåðà â ðàìêàõ óòî÷íåííîé 3-ìîäîâîé ìîäåëè êèíåòè÷åñêèõ ïðîöåññîâ. Ïîëó÷åíû áîëåå òî÷íûå
çíà÷åíèÿ êîýôôèöèåíòà ïîãëîùåíèÿ.
Êëþ÷åâûå ñëîâà: ôîòîêèíåòèêà, ëàçåðíîå ïîëå, ñìåñü ãàçîâ, àòìîñôåðíàÿ ìîäåëü.
ÓÄÊ 539.142, 539.184
Â. Õ. Êîðáàí, Ã. Ï.Ïðåïåëèöà, Þ. Áóíÿêîâà Ë. Äåãòÿðåâà, À. Êàðïåíêî, Ñ. Ñåðåäåíêî
ÔÎÒÎʲÍÅÒÈÊÀ ÂÇÀªÌÎIJ¯ ²× ËÀÇÅÐÍÎÃÎ ÂÈÏÐÎ̲ÍÞÂÀÍÍß ²Ç ÑÓ̲ØÅÉ CO 2 -N 2 -H 2 O ÃÀDzÂ:
ÓÄÎÑÊÎÍÀËÅÍÀ ÀÒÌÎÑÔÅÐÍÀ ÌÎÄÅËÜ
Ðåçþìå
Ðîçãëÿíóòî ôîòîê³íåòèêó åíåðãîîáì³íó ó ñóì³øó CO 2 -N 2 -H 2 O àòìîñôåðíèõ ãàç³â ïðè ïðîõîäæåíí³ ñêð³çü àòìîñôåðó ì³öíîãî
âèïðîì³íþâàííÿ CO 2 ëàçåðà ó ìåæàõ óòî÷íåíî¿ 3-ìîäîâî¿ ìîäåë³ ê³íåòè÷íèõ ïðîöåñ³â. Îòðèìàí³ á³ëüø òî÷í³ îö³íêè äëÿ
êîåô³ö³ºíòà ïîãëèíàííÿ.
Êëþ÷îâ³ ñëîâà: ôîòîê³íåòèêà, ëàçåðíå ïîëå, ñóì³ø ãàç³â, àòìîñôåðíà ìîäåëü.

UDÑ 621.383:537.221
D. À. ÊUDIY, N. P. ÊLOCHKO, G. S. KHRYPUNOV, N. À. ÊÎVTUN, K. Y. ÊRIKUN,
Y. K. BELONOGOV 1
National technical university “Kharkiv polytechnic institute”,
Kharkiv, Frunze Street 21, 61002,
tel. (057) 731-56-91, kudiy@ukr.net, klochko_np@mail.ru, khrip@ukr.net, orcsin@gmail.com
1 Voronezh State technical university, Voronezh, Moscow Avenue 14.
belonogov@phys.vorstu.ru
ELABORATION OF CADMIUM SULPHIDE FILM LAYERS
FOR ECONOMICAL SOLAR CELLS
The structural and optical properties of CdS films received by the liquid-phase chemical deposition
method are investigated. The analysis of surface film was conducted by scanning electron microscopy
method. The structural parameters are determined by the X-Ray difractogram method while the
definition of dispersion coherent areas and microdeformations were defined by analytical processing
of X-Ray difractogram. The X-ray electron-probe microanalysis was fulfilled as well.
The mathematical processing of CdS layers transmittion
spectra was carried out. The structural and
optical properties of the investigated CdS films are
defined by the CdS layer thickness and its annealing
mode.
The film solar cells (SC) developed on the base of
heterojunction CdTe/CdS are the most perspective
for large-scale applications [1]. The cadmium telluride
base layers provide the maximal theoretical photovoltaic
conversion efficiency in ground conditions
for single-junction semiconductive SC — more than
29 % caused by optimal cadmium telluride band gap
(1,46 eV) [2]. Cadmium sulphide is the most suitable
hetero-partner for the formation of an effective separating
barrier to cadmium telluride according to the
theoretical diagram of the heterojunction p-CdTe/n-
CdS giving the height of a potential barrier equal to
1,02 eV [3]. The last fact allows to divide effectively the
non-equilibrium charge carriers concentration generated
under illumination and to increase the theoretical
open-circuit voltage limit up to 1V.
Moreover, the interface of CdTe and CdS have
the minimal lattice mismatching as compared to other
combinations of A II B VI semiconductors [4], what
causes the possibility to form high-quality separating
junction characterized by low density of saturation diode
current and by high shunt resistance.
The present-day effective thin film SC on the base
of CdS/CdTe have been developed by high-temperature
expensive vacuum manufacturing methods [5]
what limits the opportunities of the cost reduction of
such devices. At the same time, the application of thin
semiconductor film interfacing layers, deposited by
economical and high technology processes, allows the
creation of competitive film solar cells in comparison
with traditional electric power sources. It causes an
actuality of development of economical low-temperature
chemical technologies for the deposition of such
heterojunctions’components.
Traditionally, the film solar cells on the base of
CdS/CdTe are created on glass substrates covered by
sublayer of transparent conducting oxide, penetratable
to solar radiation absorbed in the cadmium tel-
© D. À. Êudiy, N. P. Êlochko, G. S. Khrypunov, N. À. Êîvtun, K. Y. Êrikun, Y. K. Belonogov, 2009
luride base layer. The typical design of CdS/CdTe film
SC is shown in Fig. 1.
Fig. 1. FTO/CdS/CdTe device structure scheme.
A maximal theoretical short current density of
CdTe solar cell equals to the 30.8 mÀ/cm2 if solar radiation
power is about 100 mW/cm2 [6].
However, approximately 7.1 mÀ/cm2 of this short
current density is an electricical part caused by generation
of non-equilibrium charge carriers as a result
of absorption of photons with energy exceeding the
CdS band gap.
Thus, the recombination of non-equilibrium
charge carriers in the CdS layer could influence negatively
on the CS photocurrent by means of essential
reduce of the contribution of the charge carriers generated
by photons in a spectral range from 350 up to
520 nm to the SC photovoltage. So, the short-wave
edge of the CdS/CdTe CS spectra is caused not only
by an absorption edge of transparent conducting electrode
prepared from FTO (fluoride doped tin oxide),
but also by absorption edge of the CdS.
The transparency of the cadmium sulphide layer
in a 520-850 nm range also influences significantly the
photocurrent, because it determines the flux density
of the photons arriving to the cadmium telluride layer
(note that the long wavelength edge of this spectral
range is caused by absorption edge of CdTe).
39

Thus, the decrease of cadmium sulphide layer
thickness in the case of equal other parameters, has
to enlarge the photocurrent. Therefore, traditionally
the only requirement to cadmium sulphide film used
in a solar cell design was the high transparency in the
visible range.
We consider, however, that the elaboration of cadmium
sulphide deposition technology must be fulfilled
by means of optimization of CdS layer when it becomes
a member of a multilayer composition of the SC device
structure. We have shown in [7], that the optimal thickness
of CdS films deposited by vacuum evaporation is
0.35 μm and the reduction of CdS thickness results in
shunting of the heterojunction as a sequence of direct
contact of the FTO frontal electrode with the CdTe
base layer through the cadmium sulphide pinholes.
So, the high transparency of cadmium sulphide
must go along with the formation of non-porous CdS
layer. As well as for the creation of sharp heterojunction
during high-temperature manufacture of the device
structure, it is important to minimize the diffusion interaction
between cadmium sulphide and cadmium telluride,
so traditionally before CdTe deposition, the CdS
layers were annealed at 400 î Ñ during 25 minutes in air.
Thus, it is necessary to provide the high transparency
and an absence of the pinholes not only in as-prepared
cadmium sulphide but in air-annealed one as well.
In this work, we investigate the structure and optical
properties of the cadmium sulphide films, prepared
by chemical bath deposition. Plates of borosilicate
glass Ê8, covered with FTO were used as substrates
for CdS films. Cadmium sulphide chemical bath deposition
was carried out in aqueous chloride solution,
consisted of cadmium chloride CdÑl 2 0,011M, thiourea
(NH 2 ) 2 CS 0,014M and ammonium hydroxide
NH 4 OH 3,0M at 75 î Ñ. The solution was magnetically
stirred in a vessel contained FTO covered glass substrate
for 10 minutes, and then the films were washed
out by distilled water and dried out on air.
The investigations of the films by scanning electron
microscopy method (SEM) on REM — 1M have
shown, that in the case of approximately 0.1 μm thick
as-deposited CdS films measured by profilometer Deflak,
the pinholes have not appeared as a result of air
annealing, but a compression of the film by means of
diminution f surface relief was observed (Fig. 2 a, b).
X-ray diffraction (XRD) patterns of the CdS/FTO
heterostructures, before and after air annealing, were
taken with a use of DRON — 4M diffractometer using
CuK α radiation and have testified only FTO reflections
for as-deposited films because of the amorphous
nature of CdS. However, the air-annealed compositions
glass/FTO/CdS demonstrated the appearance
of (100) reflection of cadmium sulphide of hexagonal
modification (Fig. 3 a, b).
The results of the X-ray electron-probe microanalysis
fulfilled by means of JSM-840 with the system
of the power dispersion analysis LINK-860 testify
the ratio of cadmium to sulfur atomic concentrations
in as-deposited CdS films equal to 1.1. The annealing
results in depletion of the volatile component sulfur,
and, as a sequence, this ratio grown up to 1.2.
The analysis of FTO/CdS transmission and reflection
spectra recorded by means of spectrophotometer
SF-46 (Fig. 4 a,b), has shown the direct allowed optical
40
transitions in cadmium sulphide films. Before the annealing
an optical band gap was 2.27 eV. The air-annealing
results in increase of the band gap up to 2.35 eV.
Fig. 2. SEM pattern of chemical bath deposited CdS film on
FTO/glass substrate as prepared (a) and after air annealing (b)
Fig. 3. XRD patterns of glass/FTO/CdS before (à) and after
air annealing (b)
In the wave lengths ranges 400-550 nm and 550-
850 nm, the increase of FTO/CdS transparency from
Ò 400-550 = 47,14 % up to Ò 400-550 = 50,57 % and from
Ò 550-850 = 75,29 % up to Ò 550-850 = 78,62 % were observed.

Fig. 4. The transmittance (a) and reflectance (b) of FTO/CdS
before (1) and after the procedure.
UDÑ 621.383:537.221
CONCLUSIONS
D. À. Êudiy, N. P. Êlochko, G. S. Khrypunov, N. À. Êîvtun, K. Y. Êrikun, Y. K. Belonogov
1. Thus, the cadmium sulphide films were deposited
by chemical bath deposition method. These
films are considered suitable for the use in the design
of highly effective solar cells on the base of cadmium
telluride, because after the air annealing of FTO/CdS
composition at 400 î Ñ for 25 minutes in accordance
with technology of the device heterostructure formation
this composition demonstrated a favourable combination
of optical and structural parameters.
2. After the air annealing the pinholes in cadmium
sulphide layers were absent, the CdS films were polycrystalline.
Owing to the air-annealing the transparency
of FTO/CdS layers in the range of wave lengths 400-
550 nm was Ò 400-550 = 50.57 %, and in a range of wave
lengths 550-850 nm it achieved Ò 550-850 . = 78, 62 %.
The work is supported by the grant of Russia ¹08-
08-99071-r_îfi
References
1. Goetzberger A., Luther J., Willere G. Solar cells: past, present,
future // Solar Energy Material & Solar Cells. — 2002. —
Vol. 74, ¹1-4. — P.1-11.
2. Hamakawa Y. Solar PV energy conversion and 21st century’s
civilization // Solar Energy Materials & Solar Cells.—
2002. — Vol. 74, ¹ 1- 4. — P. 13-23.
3. Andersson B.A. Materials Availability for large-scale thinfilm
photovoltaic // Progress of Photovoltaic: Research and
Applications. — 2000. — Vol. 8, ¹1. — P. 61-76.
4. Bube R. Properties of Semiconductors Materials. Photovoltaic
Materials. — USA: Imperial College Press, 2000. — vol.1,
¹6. — P. 69-72.
5. 16.5% — Efficiency CdS/CdTe polycrystalline thin-film solar
cells / Wu X., Keame J.C., Dhere R.G., De Hart C., Duda
A., Gessert T.A., Asher S., Levi D.H., Sheldon P. // Proceeding
17th European Photovoltaic Solar Energy Conference. —
Munich (Germany). — 2001. — P. 995- 999.
6. Device performance characterization and junction mechanisms
in CdS/CdTe solar cells / Oman D.M., Dugan K.M.,
Killian J.K., Cekala C.S., Ferikides C.S., Morel D.L. // Solar
Energy Materials Solar Cells. — 2000. — Vol. 58, ¹3. —
P. 361-373.
7. Õðèïóíîâ Ã.Ñ., Áîéêî Á.Ò., Êîïà÷ Ã.²., Ìåð³óö À.Â.,
Êóä³é Ä.À., Íîâèêîâ Â.Î. Îïòèì³çàö³ÿ ôîòîåëåêòðè÷íèõ
ïðîöåñ³â ó ïë³âêîâèõ ñîíÿ÷íèõ åëåìåíòàõ íà îñíîâ³
CdTe // Íàóêîâèé â³ñíèê ×åðí³âåöüêîãî óí³âåðñèòåòó. —
2005. — Â.237. — Ô³çèêà. Åëåêòðîí³êà. — Ñ.80-85.
ELABORATION OF CADMIUM SULPHIDE FILM LAYERS FOR ECONOMICAL SOLAR CELLS
Abstract
The structural and optical properties CdS films, which received by the liquid-phase chemical deposition method, are investigated.
The analysis of surface film has conducted by scanning electron microscopy method. The structural parameters are determined by the
X-Ray difractogram method, which the definition of dispersion cogerent areas and microdeformations were defined by analytical processing
X-Ray difractogram. The X-ray electron-probe microanalysis has fulfilled.
The mathematical processing of CdS layers transmittion specters are carried out. The structural and optical properties investigated
CdS films are defined by the thickness and annealing modes CdS layer.
Key words: liquid-phase chemical deposition method, X-Ray difractogram method, dispersion cogerent area, microdeformations,
scanning electron microscopy, X-ray electron-probe microanalysis.
41

42
ÓÄÊ 621.383:537.221
Ä. À. Êóäèé, Í. Ï. Êëî÷êî, Ã. Ñ. Õðèïóíîâ, Í. À. Êîâòóí, K. Þ. Êðèêóí, Å. K. Áåëîíîãîâ
ÐÀÇÐÀÁÎÒÊÀ ÏËÅÍÎ×ÍÛÕ ÑËÎÅ ÑÓËÜÔÈÄÀ ÊÀÄÌÈß ÄËß ÝÊÎÍÎÌÈ×ÍÛÕ ÑÎËÍÅ×ÍÛÕ ÝËÅÌÅÍÒÎÂ
Ðåçþìå
Èññëåäîâàíî ñòðóêòóðó è îïòè÷åñêèå ñâîéñòâà ïëåíîê ñóëüôèäà êàäìèÿ, ïîëó÷åííûõ ìåòîäîì æèäêîôàçíîãî õèìè-
÷åñêîãî îñàæäåíèÿ. Àíàëèç ïîâåðõíîñòè ïëåíêè ïðîâåäåí ñ ïîìîùüþ ðàñòðîâîé ýëåêòðîííîé ìèêðîñêîïèè. Ñòðóêòóðíûå
ïàðàìåòðû îïðåäåëåíû ðåíòãåí-äèôðàêòîìåòðè÷åñêèì ìåòîäîì, â êîòîðîì îáëàñòè êîãåðåíòíîãî ðàññåèâàíèÿ (î.ê.ð.) è
ìèêðîäåôîðìàöèè îïðåäåëÿëèñü ïóòåì àíàëèòè÷åñêîé îáðàáîòêè îòäåëüíûõ ðåíòãåíäèôðàêòîãðàìì. Âûïîëíåí ðåíòãåíîñïåêòðàëüíûé
ýëåêòðîííî-çîíäîâûé ìèêðîàíàëèç.
Ïðîâåäåíà ìàòåìàòè÷åñêàÿ îáðàáîòêà ñïåêòðîâ ïðîïóñêàíèÿ ñëîåâ ñóëüôèäà êàäìèÿ. Ñòðóêòóðíûå è îïòè÷åñêèå ñâîéñòâà
èññëåäîâàííûõ ïëåíîê CdS îïðåäåëÿþòñÿ òîëùèíîé è ðåæèìàìè îòæèãà ñëîåâ CdS.
Êëþ÷åâûå ñëîâà: Ìåòîä æèäêîôàçíîãî õèìè÷åñêîãî îñàæäåíèÿ, ðåíòãåíäèôðàêòîìåòðè÷åñêèé ìåòîä, îáëàñòü êîãåðåíòíîãî
ðàññåèâàíèÿ, ìèêðîäåôîðìàöèè, ðàñòðîâàÿ ýëåêòðîííàÿ ìèêðîñêîïèÿ, ðåíòãåíîñïåêòðàëüíûé ýëåêòðîííî-çîíäîâûé
ìèêðîàíàëèç.
ÓÄÊ 621.383:537.221
Ä. À. Êóä³é, Í. Ï. Êëî÷êî, Ã. Ñ. Õðèïóíîâ, Í. À. Êîâòóí, K. Þ. Êðèêóí, ª. K. Áºëîíîãîâ
ÐÎÇÐÎÁÊÀ Ï˲ÂÊÎÂÈÕ ØÀв ÑÓËÜÔ²ÄÓ ÊÀÄÌ²Þ ÄËß ÅÊÎÍÎ̲×ÍÈÕ ÑÎÍß×ÍÈÕ ÅËÅÌÅÍÒ²Â
Ðåçþìå
Äîñë³äæåíî ñòðóêòóðó ³ îïòè÷í³ âëàñòèâîñò³ ïë³âîê ñóëüô³äó êàäì³þ, îòðèìàíèõ ìåòîäîì ð³äèííîôàçîâîãî õ³ì³÷íîãî
îñàäæåííÿ. Àíàë³ç ïîâåðõí³ ïë³âêè ïðîâåäåíèé çà äîïîìîãîþ ðàñòðîâî¿ åëåêòðîííî¿ ì³êðîñêîﳿ. Ñòðóêòóðí³ ïàðàìåòðè âèçíà÷åí³
ðåíòãåí-äèôðàêòîìåòðè÷íèì ìåòîäîì, â ÿêîìó îáëàñò³ êîãåðåíòíîãî ðîçñ³ÿííÿ (î.ê.ð.) òà ì³êðîäåôîðìàö³¿ âèçíà÷àëèñü
øëÿõîì àíàë³òè÷íî¿ îáðîáêè îêðåìèõ ðåíòãåíäèôðàêòîãðàì. Âèêîíàíèé ðåíòãåíîñïåêòðàëüíèé åëåêòðîííî-çîíäîâèé
ì³êðîàíàë³ç.
Ïðîâåäåíà ìàòåìàòè÷íà îáðîáêà ñïåêòð³â ïðîïóñêàííÿ øàð³â ñóëüô³äó êàäì³þ. Ñòðóêòóðí³ òà îïòè÷í³ âëàñòèâîñò³ äîñë³äæåíèõ
ïë³âîê CdS âèçíà÷àþòüñÿ òîâùèíîþ òà ðåæèìàìè â³äïàëó øàð³â CdS.
Êëþ÷îâ³ ñëîâà: Ìåòîä ð³äèííîôàçíîãî õ³ì³÷íîãî îñàäæåííÿ, ðåíòãåí-äèôðàêòîìåòðè÷åñêèé ìåòîä, îáëàñòü êîãåðåíòíîãî
ðîçñ³ÿííÿ, ì³êðîäåôîðìàö³¿, ðàñòðîâà åëåêòðîííà ì³êðîñêîï³ÿ, ðåíòãåíîñïåêòðàëüíèé åëåêòðîííî-çîíäîâèé ì³êðîàíàë³ç.

UDC 621.315.592
I. K. DOYCHO 1 , S. A. GEVELYUK 1 , O. O. PTASHCHENKO 1 , E. RYSIAKIEWICZ-PASEK 2 , S. O. ZHUKOV 1
1 I. I. Mechnikov Odesa National University, Dvoryanska St., 2, Odesa, 65082, Ukraine
2 Institute of Physics, Wroc³aw University of Technology, W.Wyspianskiego 27, 50-370 Wroc³aw, Poland
POROUS GLASSES WITH CDS INCLUSIONS LUMINESCENCE KINETICS
PECULIARITIES
The kinetics of the luminescence of porous glasses with CdS inclusions was studied at liquid nitrogen
temperature. It is shown that the luminescence decay curves after excitation switch-off are different
for different types of glasses. For CdS in matrices with small enough pores, a short-time “flash”
of the luminescence was observed after the excitation turn-off. Additional doping of the samples with
Na 2 S enhanced the “flash”. The flash intensity and duration depended on the exciting photons energy.
The effect is explained by thermo-optical excitation of electrons.
1. INTRODUCTION
Nanocrystals of semiconductors and, in particular
III–V materials, in porous glass are prospective
for optical and electronic applications. The complexity
of porous glass morphology and a rich luminescent
spectrum of bulk CdS [1-4] allows to expect
the appearance of various point defects which could
be considered as shallow traps and, in other cases, are
the centers of luminescence. While studying the luminescence,
it is necessary to take into account both the
contribution of charge carrier recombination as well
as the changes in optical properties of the porous matrix
caused by the excitation. Some information about
the mechanism of the luminescence excitation, as well
as on the nature of radiative recombination, could be
obtained by an analysis of the luminescence rise and
decay curves [1, 5].
The present paper investigates photo-luminescence
stationary and transient characteristics of CdS
nano-formations in a porous glass matrix at the temperature
of 77 K. A tentative model is used in order to
explain some peculiarities of the luminescence decay
curves observed.
2. EXPERIMENTAL PROCEDURE
Porous silicate glasses obtained from the two-phase
sodium-boron-silica glasses by chemical etching of the
unstable sodium-borate phase in hydrochloric acid [6]
were used in our experiments as a model matrix medium
for forming the semiconductor nano-particles.
An initial two-phase glass was annealed at 760 K or
930 K for 100 and 150 hours, respectively, in order
to enhance the phase separation. After a subsequent
etching of the glass annealed at 760 K, we obtained
mesoporous glass with the mean pore radius about 15
nm (glass of À type). A similar treatment of the glass
annealed at 930 K gives the mean pore radius of 75 nm
(glass of C type).
The etching solution used for etching the sodiumborate
phase off, interacted also with the silicate skeleton,
which led to the formation of the secondary silica
gel inside the pores.
It is possible to remove the secondary silica gel
from pores almost completely by the subsequent treatment
in KOH solution. However, it leads to an excessive
etching of the pores. After such additional treatment
of A-glass we obtained a glass with gel-free pores
of 23 nm radius. It is referred in this paper as B-glass.
An additional KOH solution etching of C-glass
produced gel-free pores with the radius of 160 nm. It
is referred as D-glass.
CdS were impregnated into the glasses containing
silica gel (A) and also into B- and D-glasses which
were practically free of silica gel. CdS nanoclusters in
the porous matrices were obtained by chemical deposition
using the technique described in [3, 7].
For the increase of the of sulfur ions content (playing
the role of a luminescence activator), some of the
prepared samples were saturated with Na 2 S in water
solution [8].
Luminescence was excited by the monochromatized
light of a 1 kW Xenon lamp over the wavelength
range of 400-700 nm. The luminescence spectra, as
well as the excitation spectra, were measured in stationary
and transient regimes. Luminescence rise-
and decay curves were analyzed. All the measurements
were performed at the liquid nitrogen temperature (77
K) using a standard set-up.
Some of specimens were gamma-irradiated using
a Co 60 facility with the power of 9.8 rad/s. This power
was used to induce some modification of the material
recombination properties [9], called a small dose effect.
3. EXPERIMENTAL RESULTS
© I. K. Doycho, S. A. Gevelyuk, O. O. Ptashchenko, E. Rysiakiewicz-pasek, S. O. Zhukov, 2009
Curves 1 and 2 at Fig. 1 present the photoluminescence
spectra of CdS clusters in an A-matrix before
and after Na 2 S saturation, respectively. It is seen that
the main red luminescence band is strongly broadened.
The short-well shoulder shows that it is not
elementary one. Na 2 S saturation enhances the luminescence
intensity and shifts the spectrum to shorter
wavelengths.
Fig. 2 illustrates the luminescence spectrum evolution
after switch-off the excitation of A-sample with
Na 2 S excess. It is seen that the luminescence spectrum
changes in time. The phosphorescence band at 725
43

nm has much higher decay time than the short-wavelength
part of the spectrum. It suggests that the photon
generation of 725 nm band and the short-wavelength
radiative recombination are caused by the differently
located centers.
44
�, arb.un.
5
4
3
2
1
2
0
0.4 0.5 0.6 0.7 0.8
�, �m 0.9
Fig. 1. Photoluminescence spectra of CdS clus-ters in A-matrix:
1 — initial; 2 — after Na 2 S saturation
�, arb.un.
6
5 1
4
3
2
1
0
0.55 0.6 0.65 0.7 0.75
�, �m
Fig. 2. Phosphorescence spectra of A-sample with Na S ex- 2
cess at different times after switching off the excitation: 1 — 0.2 s;
2 — 0.8 s; 3 — 1.2 s; 4 — 2.0 s.
Curves 1, 2, and 3 at Fig. 3 show the luminescence
rise after switching on the excitation in A-, B-, and
D-samples. The rise curves for all of the glass types
practically coincide and are exponential:
Φ ( t) =Φ [1−exp( −t/ τ )] , (1)
0
where Φ 0 is a constant; τ r denotes the rise time. For all
the curves at Fig. 3 τ r =1.8 s.
2
3
4
1
r
�, arb.un.
1.0
0.8
0.6
0.4
0.2
0
3
1
2
0 3 6
Fig. 3. CdS nanoclusters photoluminescence rise curves for
different types of porous glass matrix after 500 nm excitation: 1 —
A; 2 — B; 3 — D.
Curve 1 at Fig. 4 represents the phosphorescence
decay for CdS in pores of B-glass (in pores with small
diameter). The curve has a shoulder at the beginning
of the decay. After γ-irradiation with a dose of 104 rad,
the shoulder disappears (low dose effect), what is illustrated
by curve 3, and the decay curve is practically
identical to curve 2 (for CdS in wide pores).
1.0
0.8
0.6
0.4
0.2
0
�, arb.un.
3
2
1
t, s
0 1 2 3 4
t, s
Fig. 4. CdS phosphorescence decay curves in B- (1 and 3) and
D-(2) matrices. 3 – after γ-irradiation with a dose of 10 4 rad.
The decay curve 2 at Fig. 4, measured on CdS in
D-matrix, is exponential:
Φ(t) = Φ exp(-t/τ ), (2)
o d
where τ is the decay time. For curve 2 τ =1.78 s. The
d d
rise- and decay times are very high:
τ , τ >> τ , (3)
r d n
where τ is the life time for electrons (τ ~1 ms). The
n n
strong inequality (3) suggests that CdS microcrystals
9

in pores have very high concentration of shallow traps,
which are in equilibrium with c-band.
Our measurements show that the phosphorescence
kinetics of CdS clusters in A-glass usually exhibits a
flash-up after the excitation turn-off, as demonstrated
at Fig 5. Curve 1, measured after excitation with photons
of λ = 550 nm (hν = 2.25 eV), has a pronounced
shoulder. Excitation at λ = 450 nm (hν = 2.76 eV)
leads to a flash, as illustrated with curve 2 at Fig. 5.
A treatment of the sample in Na 2 S enhances the flash,
as shown by curves 3, 4. A comparison of curves 3 and
4 at Fig. 5, obtained after excitation with photons of
hν = 2.25 eV and hν = 2.76 eV, correspondingly, demonstrates
that the flash becomes more detectable with
increasing photon energy.
�, arb.un.
1.2
1.0
0.8
0.6
0.4
0.2
0
0
2
1
3
4
1 2 3 4
t, s
Fig. 5. Decay kinetics of CdS nanoclusters phosphorescence
in A — matrices: 1, 2 – initial; 3, 4 – after Na 2 S-treatment.
Curves 1, 3 were measured after excitation with λ=550 nm; 2,
4 – after illumination with λ=450 nm.
The intensity of the flash is different for various
phosphorescence spectral bands. The most intensive
flash is observed in the band at 725 nm for CdS clusters
in A-matrix with the excess of Na 2 S after the 450
nm excitation. This band is dominant in the stationary
photoluminescence spectrum of these samples,
as shown by curve 2 at Fig. 1, and has a higher decay
time, as shown at Fig. 2.
4. MODEL AND DISCUSSION
The most interesting result of our experiment is
the effect of the mean pore size on the photoluminescence
and phosphorescence spectra and the kinetics.
We can analyze this effect by the use of a recombination
scheme represented at Fig. 6.
The electron-hole pair generation of intensity G
is provided by photons absorption. Additional generation
G t has photo-thermal nature. The observed very
long rise- and decay times suggest the presence of a
high concentration of shallow traps t, being in thermal
equilibrium with c-band. Radiative recombination
occurs at deep r-centers. Non-radiative recombination
takes place at deep s-centers (“fast recombination
centers”).The corresponding differential equations set
is as follows:
dn
= G+ Gt − Ctpn t + CtNctnt −Cspsn− Crprn ; (4)
dt
dpr
= Cnp ′ r r − Crpn r ; (5)
dt
dps
= Cnp ′ s s − Cspn s ; (6)
dt
dnt
= Cpn t t − CN t ct,
(7)
dt
where n, p are the free carriers concentrations; C , C , C t r s
denote the electron capture coefficients for t-, r- and
s- centers, respectively; C′ , C′ are the hole capture
r s
coefficients for r- and s- centers, correspondingly; n , t
n , n are the concentrations of electrons on t-, r- and
r s
s- centers, respectively; p , p , p are the concentrations
t r s
of empty t-, r- and s- centers, respectively;
N ≡ N exp( − E / kT)
, (8)
G
Gt
ct c ct
t
Fig. 6. Recombination scheme for photo-luminescence in
CdS clusters
N is the effective state density in c-band; E is the
c ct
depth of t-level; kT is the Boltzmann factor.
The neutrality equation can be written as
n+ nt 0
= pr − pr + ps,
(9)
0
where p r is determined by the concentration of electrons
on deep t traps. In (9) the strong inequality
d
n>>p
is taken into account as well.
(10)
For s-centers, as fast non-radiative recombination
centers in CdS, the inequalities
C>>C ; p p (13)
takes place.
td
s
c
r
v
45

The observed exponential rise- and decay curves,
depicted at Figs.3 and 4, suggest that differential equations
(4) — (7) for our case are linearized. It means
that in (12)
pr = const . (14)
And this could occur if we have in the equality (9)
0
pr ≅ pr >> n+ nτ, ps
. (15)
Moreover, it means that the concentration n of t
electrons, captured on shallow t-centers, is proportional
to free electrons concentration n. It could occur
in the case of
n gr /(1 − gr) G . (27)
Our measurements reveal the following conditions
for the flash-effect in CdS nanocrystals: a) the pores
in the matrix must be small enough. The effect occurs
only in A- and B-matrices; b) the flash is observed only
in 725 nm phosphorescence band; c) Na S treatment
2
enhances the effect; d) excitation with photons of hν =
2.75 eV gives more pronounced effect than of 2.25eV;
e) γ-irradiation suppresses the effect.
The first condition suggests that the flash-effect
is characteristic for small enough CdS nanocrystals.
This observation is in agreement with results [5] and
the fact that lowering the nanocrystals’ size makes
slower the CdS phosphorescence decay [3, 4, 7].
The influence of Na S treatment on the flash inten-
2
sity argues that point defects, containing sulfur atoms,
are responsible for this effect. Inhibition of the effect
by γ-radiation can be explained by destroying the lowsize
nanoclusters as a result of γ-quanta absorption [9].
The photoluminescence and phosphorescence of CdS
in D-glasses is less sensitive to radiation, which is in
accordance with previously reported results [9]. The
flash-effect disappeared after a long time storage (over
half a year; A-specimens were exposed to the air). It is
. also suppressed by low temperature annealing of the
As seen at Figs. 4 and 5, CdS clusters under certain samples in air. This phenomenon could be attributed
conditions exhibit a phosphorescence flash. The flash- to slow oxidation of excess sulfur during the storage in
effect could be explained by using the model presented the open air.
above. The role of photothermal electron generation
and presence of two kinds of recombination centers
are essential for this explanation. From equation (4),
in a stationary case, we obtain for the stationary elec-
5. CONCLUSIONS
tron concentration
1. The phosphorescence of CdS nanoclusters in
st 0 st
n = ( G+ Gt)/( Crpr + Csps )
and for the radiative recombination intensity
(20) porous glass exhibits a flash after excitation turn-off.
This effect occurs only in glass with sufficiently small
pores and can be ascribed to recombination in small
st
R
r
= gr( G+ Gt)
, (21)
enough CdS clusters. The flash is observed only in the
spectral band of hν = 1.71 eV which corresponds to
where
the recombination of free electrons at deep centers.
gr 0 0 st
≡ Crpr /( Crpr + Csps ) . (22)
2. The recombination model, that includes two
kinds of recombination centers and centers respon-
After turn off excitation G the intensity of the photothermal
excitation
Gt ≠ 0 , (23)
because the concentration of electrons on the corresponding
centers exceeds its equilibrium value. Moreover,
the fast recombination centers (s-centers) for a
short time are filled by electrons, so
sible for the photo-thermal electron generation, could
explain the flash-effect.
3. The introduction of the excess sulphur ions enhances
the effect. It suggests that the centers, responsible
for flash, contain sulphur atoms.
4. The flash-effect is suppressed by γ-irradiation
as well as by low-temperature annealing in air. This
instability could be ascribed to small CdS clusters destruction.
The γ-stability of CdS nanoclusters is en-
Ps → 0 , (24) hanced with the increase of their size.
and one could obtain for the electrons concentration References
n = G C p
(25)
1. Guyot-Sionnest P., Halas N.J., Mattoussi H., Wang Z.L.,
Woggon U. Quantum Confined Semiconductor Nanostruc-
46
0
t /( r r)

tures // MRS Symposium Proceedings. — 2004. — V. 789.
429 p.
2. Smyntyna V.A., Skobeeva V.M., Malushin N.V., Pomogailo
A.D. Influence of matrix on photoluminesence of CdS
nanocrystals // Photoelectronics. — 2006. — V. 15. P. 38-42.
3. Gevelyuk S.A., Doycho I.K., Mak V.T., Zhukov S.A. Photoluminescence
and structural properties of nano-size CdS inclusions
in porous glasses // Photoelectronics — 2007. — V. 16.
P. 75-79.
4. Rysiakiewicz-Pasek E., Polañska J., Gevelyuk S.A., Doycho
I.K., Mak V.T., Zhukov S.A. The photoluminescent
properties of CdS clusters of different size in porous glasses //
Optica Applicata. — 2008. — V. 38, ¹ 1. P. 93-100.
5. Gaponenko S.V. Optical Properties of Semiconductor Nanocrystals
// Cambridge University Press: 1998. — 300 p.
UDC 621.315.592
I. K. Doycho, S. A. Gevelyuk, O. O. Ptashchenko, E. Rysiakiewicz-Pasek, S. O. Zhukov
6. Rysiakiewicz-Pasek E., Gevelyuk S.A., Doycho I.K., VorobjovaV.A.
Application of Porous Glass in Ophtalmic Prosthetic
Repair // Journal of Porous Materials. — 2004. — V. 11, ¹ 1.
P. 21-29.
7. Rysiakiewicz-Pasek E., Zalewska M., Polañska J. Optical
Properties of CdS-doped Porous Glasses // Optical Materials.
— 2008. — V. 30, ¹ 5. P. 777-779.
8. Fu Z., Zhou S., Shi J., Zhang S. Effects of Precursors on
the Crystal Structure and Photoluminescence of CdS Nanocrystalline//
Material Research Bulletin. — 2005. — V. 40. P.
1591-1598.
9. Doycho I.K., Gevelyuk S.A., Kovalenko M.P., Prokopovich
L.P., Rysiakiewicz-Pasek E. Small doses γ-irradiation effect
on the photoluminescence properties of porous glasses //
Optica Applicata. — 2003. — V. 33, ¹ 1. P. 55-60.
POROUS GLASSES WITH CDS INCLUSIONS LUMINESCENCE KINETICS PECULIARITIES
Abstract
The kinetics of the luminescence of porous glass with CdS inclusions was studied at liquid nitrogen temperature. It is shown that
the luminescence decay curves after excitation switching-off are different for different types of glasses. For CdS in matrices with small
enough pores, a short-time “flash” of the luminescence was observed after the excitation turn off. Additional doping of the samples
with Na 2 S enhanced the “flash”. The flash intensity and duration depended on the exciting photons energy. The effect is interpreted by
thermo-optical excitation of electrons.
Key words: doped porous glasses, cadmium sulphide, luminescence kinetics.
ÓÄÊ 621.315.592
È. Ê. Äîé÷î, Ñ. À. Ãåâåëþê, À. À. Ïòàùåíêî, Å. Ðûñàêåâè÷-Ïàñåê, Ñ. À. Æóêîâ
ÎÑÎÁÅÍÍÎÑÒÈ ÊÈÍÅÒÈÊÈ ËÞÌÈÍÅÑÖÅÍÖÈÈ ÏÎÐÈÑÒÎÃÎ ÑÒÅÊËÀ Ñ ÂÊËÞ×ÅÍÈßÌÈ CDS
Ðåçþìå
Èññëåäîâàíà êèíåòèêà ôîòîëþìèíåñöåíöèè ïîðèñòîãî ñòåêëà ñ âêëþ÷åíèÿìè CdS ïðè òåìïåðàòóðå æèäêîãî àçîòà. Ïîêàçàíî,
÷òî êðèâûå ñïàäà ôîòîëþìèíåñöåíöèè ïîñëå âûêëþ÷åíèÿ âîçáóæäåíèÿ ðàçëè÷íû äëÿ ðàçëè÷íûõ òèïîâ ñò¸êîë. Äëÿ
CdS â ìàòðèöàõ ñ äîñòàòî÷íî ìàëûìè ïîðàìè íàáëþäàëàñü êðàòêîâðåìåííàÿ âñïûøêà ëþìèíåñöåíöèè ïîñëå âûêëþ÷åíèÿ
âîçáóæäåíèÿ. Äîïîëíèòåëüíîå íàñûùåíèå îáðàçöîâ Na 2 S óñèëèâàëî óêàçàííóþ âñïûøêó. Èíòåíñèâíîñòü è äëèòåëüíîñòü
âñïûøêè çàâèñåëà îò ýíåðãèè âîçáóæäàþùèõ ôîòîíîâ. Ýôôåêò îáúÿñí¸í òåðìîîïòè÷åñêèì âîçáóæäåíèåì ýëåêòðîíîâ.
Êëþ÷åâûå ñëîâà: êèíåòèêà ëþìèíåñöåíöèè, ïîðèñòîå ñòåêëî, ñóëüôèä êàäìèÿ.
ÓÄÊ 621.315.592
². Ê. Äîé÷î, Ñ. À. Ãåâåëþê, Î. Î. Ïòàùåíêî, Å. Ðèøÿêåâè÷-Ïàñåê, Ñ. Î. Æóêîâ
ÎÑÎÁËÈÂÎÑÒ² ʲÍÅÒÈÊÈ ËÞ̲ÍÅÑÖÅÍÖ²¯ ØÏÀÐÈÑÒÎÃÎ ÑÊËÀ Ç ÂÊÐÀÏËÅÍÍßÌÈ CDS
Ðåçþìå
Äîñë³äæåíî ê³íåòèêó ëþì³íåñöåíö³¿ øïàðèñòîãî ñêëà ³ç âêðàïëåííÿìè CdS ïðè òåìïåðàòóð³ ð³äêîãî àçîòó. Ïðîäåìîíñòðîâàíî,
ùî êðèâ³ ñïàäó ëþì³íåñöåíö³¿ ï³ñëÿ âèìêíåííÿ çáóäæåííÿ íåîäíàêîâ³ äëÿ ð³çíèõ òèï³â ñêëà. Äëÿ CdS â ìàòðèöÿõ
ç äîñòàòíüî ìàëèìè ïîðàìè ñïîñòåð³ãàâñÿ êîðîòêî÷àñíèé ñïàëàõ ëþì³íåñöåíö³¿ ï³ñëÿ âèìêíåííÿ çáóäæåííÿ. Äîäàòêîâå íàñè÷åííÿ
çðàçê³â Na 2 S ï³äñèëþâàëî çàçíà÷åíèé ñïàëàõ. ²íòåíñèâí³ñòü ³ òðèâàë³ñòü ñïàëàõó çàëåæàëà â³ä åíåð㳿 çáóäæóþ÷èõ
ôîòîí³â. Åôåêò ïîÿñíåíî òåðìîîïòè÷íèì çáóäæåííÿì åëåêòðîí³â.
Êëþ÷îâ³ ñëîâà: ê³íåòèêà ëþì³íåñöåö³¿, øïàðèñòå ñêëî, ñóëüô³ä êàäì³þ.
47

48
UDÑ 539.186
N.V. MUDRAYA
Odessa National Polytechnical University, Odessa
DENSITY FUNCTIONAL APPROACH TO ATOMIC AUTOIONIZATION
IN AN EXTERNAL ELECTRIC FIELD: NEW RELATIVISTIC SCHEME
Within the S-matrix Gell-Mann and Low formalism and the relativistic perturbation theory we
present a new relativistic density functional theory scheme to description of the atomic autoionization
in an external dc electric and laser field.
INTRODUCTION
The photo- and autoionization phenomena in
atomic and molecular systems, solids, semiconductors
etc attracts a great interest because of the very
perspective applications in the quantum electronics,
laser physics, technical physics and creation of the
new types of devices in the opto- and molecular electronics
[1-6]. In the last years extensive experimental
and theoretical studies of photo-, auto- and multiple
ionization in strong laser fields have revealed a number
of unexpected effects and features. Moreover,
some phenomena should can be described as multiphoton
ones and independent electron processes
(see e.g. [1]). This was concluded on the basis of a
detailed analysis of experimental data together with
precise calculations of single photo-ionization rates
[2, 3]. Several experiments (see e.g.[4]) then revealed
a pronounced “knee” structure in the yield vs peak
laser intensity, typically plotted with logarithmic axis
because of the wide range of values covered. Further
ingenious experiments that resolved the joint momentum
distributions of the outgoing electrons then
showed that they often leave the atom with the same
moments. This has triggered a number of theoretical
studies of this process, including S-matrix calculations
for the full cross sections [3], and investigations
of simplified classical and quantum models. Among
the models are so-called aligned-electron models,
in which electrons move in a one-dimensional (1D)
regularized Coulomb potential, or quasi three-dimensional
(3D) ones with the centre of mass of the
electrons confined to move along the field polarization
axis. At the same time, an exact solution of the
time-dependent Schrödinger equation even for two
electrons in a laser field remains a formidable task.. It
is well known that the autoionization phenomena in
the heavy atomic systems should be considered exclusively
within the relativistic formalism. The suitable
basis is the time-dependent Dirac equation, which
is remained by the very complicated problem to be
solved. Surely, if one consider a dc electric field and
its effect on the autoionization process in the atomic
system, the standard atomic relativistic approaches
can be used as the zeroth approximation. Besides, one
must take into account a group of the known complicated
correlation effects. Here we mean, for example,
the relaxation processes due to Coulomb interaction
between moving away electron (electrons in a case of
the laser induces multiple ionization) and resulting in
the electron distribution in the vacancy field have no
time to be over prior to the transition. It is known that
a consistent theory of the atomic autoionization is to
take into account correctly a definite number of the
correlation (polarization, relaxation) effects, including
the energy dependence of the vacancy mass operator,
the continuum pressure, spreading of the initial
state over a set of configurations etc. [1-5]. It should
be reminded that hitherto these effects are not described
adequately in the modern theoretical scheme.
As example, let us remind such wide-spread methods
as the : Dirac-Fock, relativistic Hartree-Fock methods,
random phase approximation (RPA) and RPA
with exchange, different model and pseudo potential
schemes, density-functional formalism and its relativistic
generalization etc. (see e.g. [3-10]).
In this paper we present a new relativistic density
functional theory scheme to description of the atomic
autoionization in an external dc electric and laser field
within the S-matrix Gell-Mann and Low formalism
and the relativistic perturbation theory. New scheme
has to be applied to studying the autoionization phenomena
characteristics in the atomic and molecular
(obviously heavy) systems, and quasi-molecules and
solids. The novel elements consist in an implementation
of the relativistic Dirac-Kohn-Sham density
functional theoretical scheme to the S-matrix Gell-
Mann and Low formalism and using the optimized
electron wave functions basis’s of the relativistic perturbation
theory in order to describe the fundamental
atomic characteristic of autoionization in an external
field [3,10].
AN OPTIMIZED RELATIVISTIC DENSITY
FUNCTIONAL APPROACH TO AN ATOMIC
AUTOIONIZATION
As usually, we will describe the multielectron system
(atom, molecule etc.) by the Dirac relativistic
Hamiltonian (the atomic units are used) (see e.g.[3]):
∑ i ∑ ( i j)
(1)
H = h(r ) + V rr
i i> j
Here h(r) is one-particle Dirac Hamiltonian for
electron in a field of a nucleus (nuclei), V is potential
of the inter-electron interaction. In order to take into
account the retardion effect and magnetic interaction
© N.V. Mudraya, 2009

in the lowest order on parameter α 2 (the fine structure
constant) one could write :
( 1−αα
i j)
( i j) ( ij ij)
V r r = exp iω r ⋅ (2)
rij
where ω is the transition frequency; α ,α are the Di-
ij i j
rac matrices. The Dirac equation potential includes
the electric potential of a nucleus and exchange-correlation
potentials. The standard KS exchange potential
is as follows [7]:
V () r (1/ )[3 ()] r
KS
X
2 1/3
=− π πρ (3)
In the local density approximation the relativistic
potential is as follows [7-9]:
δEX[ ρ(
r)]
VX[ ρ ( r), r]
=
(4)
δρ()
r
where EX[ ρ ( r)]
is the exchange energy of the multielectron
system corresponding to the homogeneous
density ρ () r , which is obtained from a Hamiltonian
having a transverse vector potential describing the
photons. In this theory the exchange potential is [10]:
2 1/2
KS 3 [ β+ ( β + 1) ] 1
VX[ ρ ( r), r] = VX ( r)
⋅{ ln − } (5)
2 1/2
2 ββ ( + 1) 2
where
2 1/3
β= 3 πρ ( r)] / c.
The corresponding correlation functional is [3]:
1/3
VC[ ρ ( r), r] = −0.0333⋅b⋅ ln[1 + 18.3768 ⋅ρ ( r)
] , (6)
where b is the optimization parameter (look details in
ref. [3,11]). Earlier it has been shown [3,9,10] that an
adequate description of the atomic characteristics requires
using the optimized basis’s of wave functions.
Within the frame of QED PT approach [3] to the
atomic autoionization effect, the corresponding transition
probability is knowingly defined by the square
of an electron interaction matrix element having the
form (see details also in ref. [12]):
( )( )( )( )
ω
V1234 = ⎡⎣ j1j2j3j4⎡⎣ ×
μ ⎛ jj 1 3
× ∑ ( − 1) ⎜
λμ m −m λ ⎞
⎟×
ReQλ ( 1234)
;
μ
= + . (7)
⎝ 1 3 ⎠
Qλ Qul
Qλ Br
Qλ
Qul
Br
The terms Qλ and Qλ correspond to subdivision
of the potential into Coulomb part cos|ω|r /r 12 12
and Breat one, cos|ω|r α α /r . The real part of the
12 1 2 12
electron interaction matrix element is determined using
expansion in terms of Bessel functions:
12 1 2
∑() J 1 ( r< ) J 1 ( r> ) Pλ(
cosrr
1 2)
. (8)
λ+ −λ−
λ= 0
cos ω r12
π
= ×
r 2 rr
× λ ω ω
2 2
where J is the 1st order Bessel function, (λ)=2λ+1.
Qul
The Coulomb part Qλ is expressed in terms of radial
integrals R λ , angular coefficients S λ [3]:
1 2
ReQ
Qul
λ
{ Rl( ) Sλ( ) R ( %
λ
% ) S ( %
λ
% )
( 1243) ( 1243) ( 1243) ( 1243 )} .
1
= Re
Z
1243 1243 + 1243 1243
+ R %% S %% + R %%%% S %%%% (9)
λ λ λ λ
As a result, the Auger decay probability is expressed
in terms of ReQ (1243) matrix elements:
λ
Re R 1243 =
∫∫
=
λ ( )
() () () ()
() 1 () 1
( ) ( )
= drr r f r f r f r f r ×
2 2
11 2 1 1 3 1 2 2 4 2
× Zλ r< Zλ r
. (10)
>
where f is the large component of radial part of single
electron state Dirac function and function Z is defined
as follows [3]:
λ+ 1
2
1 ( 13 )
() ⎡ 2 ⎤ J αω r
λ+
1 2
Zλ
= ⎢ ⎥
.
13 Z λ
⎢⎣ ω α ⎥⎦ r Γ( λ+ 3
2)
The angular coefficient is defined by standard way
[7]. The other items in (9) include small components
of the Dirac functions; the sign “∼” means that in (9)
the large radial component f is to be changed by the
i
small g one and the moment l is to be changed by
i i
l% i = li
−1for
Dirac number æ > 0 and l +1 for æ

50
2
∑ ( ) ( )
()( )
∑∑ Qλ αkγβ Qλ βγkα , (14)
λ λ j βγ≤ f k> f
α
The formula (14) defines the total autoionization
level width. The partial items of the ∑∑ sum an-
βγ k
swer to contributions of α-1→(βγ) -1K channels resulting
in formation of two new vacancies βγ and one free
electron k: ω =ω +ω –ω . The final expression for
k α β α
the width in the representation of jj-coupling scheme
of single-electron moments has the form:
o o
1 1
o o
2 2 ∑
jl k k
o o
1 1
o o
2 2 o
2
(15)
Γ (2 jl,2 jl; J) = 2 | Γ(2
jl,2 jl;1 l, kjl)|
Here the summation is made over all possible
decay channels. The formulas for the autoionization
probability include the radial integrals R α (αkγβ),
where one of the functions describes electron in the
continuum state. When calculating this integral, the
correct normalization of the function Ψ k is a problem.
Naturally, the correctly normalized function should
have the following asymptotic at r→0
1
⎧ −2
−
2
⎡ ( Z) ⎤
f ⎫
sin(
kr ) ,
− 1 ⎪ ω+ α +δ
2 ⎣ ⎦
⎬→( πω)
⎨
(16)
1
g
−2
−
⎭ ⎪⎡ 2
ω−( α Z) ⎤ cos(
kr +δ)
.
⎩⎣
⎦
When integrating the master system, the function
is calculated simultaneously:
()
N r
{ ( ) ( ) } 1 −
2 −2 2 2
2
⎡
k f ⎡
k k Z ⎤ −
g ⎡ k k Z ⎤ ⎤
⎣ ⎦ ⎣ ⎦
= πω ω + α + ω + α
⎣ ⎦ .
It can be shown (see [3] that at r → ∞, N(r)→N , k
where N is the normalization of functions f , g of
k k k
continuous spectrum satisfying the condition (17). In
this relation, the procedure is equivalent to the same
procedure in a case of the Auger decay probability determination
[12].
UDÑ 539.186
N. V. Mudraya
=
CONCLUSION
Therefore, we describe a new relativistic density
functional theory scheme to description of the atomic
autoionization in an external dc electric and laser
field, starting from the S-matrix Gell-Mann and Low
formalism and the relativistic perturbation theory. The
important new element is in the using the generalized
Dirac-Kohn-Sham procedure for generation of the
wave functions basis’s, which is based on the condition
that the calibration-non-invariant contribution of the
second order polarization diagrams to the imaginary
part of the multi-electron system energy is minimized
already at the first non-disappearing approximation
of the relativistic perturbation theory [11]. Besides,
we use the correct relativistic exchange-correlation
functionals that hitherto has not done in any paper.
Application of the new scheme to studying the autoionization
phenomena in the heavy atomic systems is
now in progress.
References
1. Aglitsky E.V., Ñàôðîíîâà Ó.è. Ñïåêòðîñêîïèÿ àòîìíûõ
ñèñòåì. Ýíåðãîàòîèçäàò.: Ìîñêâà, 1999.
2. Êàëåêøîâ Â.ô., Êóõàðåíêî Þ. A., Ôðàéäðàéõîâ Ñ.À.
Ñïåêòðîñêîïèÿ è ýëåêòðîííàÿ äèôðàêöèÿ ïîâåðõíîñòåé.
Íàóêà: Ìîñêâà, 1999.
3. Ãëóøêîâ À.â., Ðåëÿòèâèñòñêàÿ êâàíòîâàÿ òåîðèÿ. Êâàíòîâàÿ
ìåõàíèêà àòîìíîé ñèñòåìû.Îäåññà: Àñòðîïðèíò.
2008. — Ñ 900.
4. Amusia M.Ya. Atomic photoeffect. Acad.Press: N. — Y.,
1998.
5. Ëåòîõîâ V. Íåëèíåéíûå ôîòîïðîöåññû â àòîìàõ è ìîëåêóëàõ.
Íàóêà: Ìîñêâà, 1999.
6. Ivanova E.P., Ivanov L.N., Aglitsky E.V., Modern Trends
in Spectroscopy of Multicharged Ions// Physics Rep. —
1991. — Vol.166,N6. — P.315-390.
7. Kohn W., Sham L.J. Quantum density oscillations in an
inhomogeneous electron gas//Phys. Rev. A. — 1995. —
Vol.137,N6. — P.1697–1706.
8. Hohenberg P., Kohn W., Inhomogeneous electron gas //Phys.
Rev.B. — 1999. — Vol.136,N2. — P.864-875.
9. Gross E.G., Kohn W. Exchange-correlation functionals in
density functional theory. — N-Y: Plenum, 2005. — 380P.
10. Wilson S., The Fundamentals of Electron Density, Density
Matrix and Density Functional Theory in Atoms, Molecules
and the Solid State, Series: Progress in Theoretical Chemistry
and Physics, Eds. Gidopoulos N.I. and Wilson S. — Amsterdam:
Springer, 2004. — Vol.14. — 244P.
11. Glushkov A.V., Ivanov L.N. Radiation Decay of Atomic
States: atomic residue and gauge non-invariant contributions
// Phys. Lett.A. — 1997. — Vol.170,N1. — P.33-37
12. Ambrosov S.V., Glushkov A.V., Nikola L.V., Sensing the
Auger spectra for solids: New quantum approach// Sensor
Electr. and Microsyst. Techn. — 2006. — N3. — P.46-50.
DENSITY FUNCTIONAL APPROACH TO ATOMIC AUTOIONIZATION IN AN EXTERNAL ELECTRIC FIELD: NEW
RELATIVISTIC SCHEME
Abstract
Within the S-matrix Gell-Mann and Low formalism and the relativistic perturbation theory we present a new relativistic density
functional theory scheme to description of the atomic autoionization in an external dc electric and laser field.
Key words: autoionization, density functional theory, electric field.

ÓÄÊ 539.186
Í. Â. Ìóäðàÿ
ÌÅÒÎÄ ÔÓÍÊÖÈÎÍÀËÀ ÏËÎÒÍÎÑÒÈ Â ÎÏÈÑÀÍÈÈ ÀÒÎÌÍÎÉ ÀÂÒÎÈÎÍÈÇÀÖÈÈ ÂÎ ÂÍÅØÍÅÌ
ÝËÅÊÒÐÈ×ÅÑÊÐÎÌ ÏÎËÅ: ÍÎÂÀß ÐÅËßÒÈÂÈÑÒÑÊÀß ÑÕÅÌÀ
Ðåçþìå
 ðàìêàõ S-ìàòðè÷íîãî ôîðìàëèçìà Ãåëë-Ìàíà è Ëîó è ðåëÿòèâèñòñêîé òåîðèè âîçìóùåíèé èçëîæåíà íîâàÿ ðåëÿòèâèñòñêàÿ
ñõåìà ìåòîäà ôóíêöèîíàëà ïëîòíîñòè äëÿ îïèñàíèÿ õàðàêòåðèñòèê àòîìíîé àâòîèîíèçàöèè âî âíåøíåì ýëåêòðè-
÷åñêîì è ëàçåðíîì ïîëå.
Êëþ÷åâûå ñëîâà: àâòîèîíèçàöèÿ, òåîðèÿ ôóíêöèîíàëà ïëîòíîñòè, ýëåêòðè÷åñêîå ïîëå.
ÓÄÊ 539.186
Í. Â. Ìóäðà
ÌÅÒÎÄ ÔÓÍÊÖ²ÎÍÀËÓ ÃÓÑÒÈÍÈ Â ÎÏÈÑÀÍͲ ÀÒÎÌÍί ÀÂÒβÎͲÇÀÖ²¯ Ó ÇÎÂͲØÍÜÎÌÓ
ÅËÅÊÒÐÈ×ÍÎÌÓ ÏÎ˲: ÍÎÂÀ ÐÅËßÒȲÑÒÑÜÊÀ ÑÕÅÌÀ
Ðåçþìå
 ìåæàõ S- ìàòðè÷íîãî ôîðìàë³çìó Ãåëë-Ìàíà òà Ëîó ³ ðåëÿòèâ³ñòñüêî¿ òåî𳿠çáóðåíü âèêëàäåíà íîâà ðåëÿòèâ³ñòñüêà
ñõåìà ìåòîäà ôóíêö³îíàëó ãóñòèíè äëÿ îïèñó õàðàêòåðèñòèê àòîìíî¿ àâòî³îí³çàö³¿ ó çîâí³øíüîìó åëåêòðè÷íîìó òà ëàçåðíîìó
ïîë³.
Êëþ÷îâ³ ñëîâà: àâòî³îí³çàö³ÿ, òåîð³ÿ ôóíêö³îíàëó ãóñòèíè, åëåêòðè÷íå ïîëå.
51

52
UDC 537.311.33:622.382.33
V. A. SMYNTYNA, O. V. SVIRIDOVA
I. I. Mechnikov National University of Odessa, Dvoryanskaya Str., 2, Odessa, 65026, Ukraine, e-mail: sviridova_olya@mail.ru
INFLUENCE OF IMPURITIES AND DISLOCATIONS ON THE VALUE
OF THRESHOLD STRESSES AND PLASTIC DEFORMATIONS IN SILICON
The dependence of a plastic flow stress and deformation values on the presence of clear and
precipitated by impurity initial structural defects in epitaxial p — silicon without foreign impurity and
in epitaxial p — silicon with oxygen impurity is investigated. It is established, that, boron doping of
silicon is the reason of threshold stress reduction in comparison with threshold stress for clear from
defects silicon and leads to reduction of its hardness. Presence of oxygen atoms, precipitating dislocations
in plates, stimulates the increase of threshold stress.
1. INTRODUCTION
Structural and impurity defects, their distribution
in initial semiconductor plates at technological processing,
can make decisive influence on the process of
new defects’ generation that influences on degradation
properties and on percentage yield of devices. In
spite of the fact that it has been studied many years,
the problem of defects in silicon remains actual till
now. First of all, it is connected with the increase of
electronic microcircuits integration, and with transition
from micro technologies to nano technologies.
Many works are devoted to studying recombination
active defects arising in the course of silicon crystals
cultivation [1]; defects in silicon nanowires [2]; problems
of iron gettering in silicon by means of oxygen
precipitates [3, 4]; optical attenuation on silicon divacancies
[5]; controllable cultivation of dislocations
[6]; redistributions of dislocations in silicon [7] and
other defect properties.
It is informed [8] that silicon crystals, containing
appreciable quantity of oxygen atoms, are the best basis
for integrated microcircuits creation, than clearer
crystals. Despite of considerable amount of works on
this problem [9, 10], a number of questions connected
with impurity influence on the stress of the beginning
of a plastic flow remain unsolved.
The purpose of given work is the establishment of
laws of stresses and relative deformations changes under
the influence of structural and impurity variations
of silicon plates.
2. OBJECTS AND METHODS OF RESEARCH
We studied epitaxial boron-doped silicon plates of
grade BDS 10 (111) with the diameter of 60 mm and
thickness of 405 microns.
Following methods and equipment were used for
studying defects on a silicon surface:
– a method of selective chemical etching by Sirtle
[11];
– scanning electronic microscopy of a surface
(SEMS), by means of scanning electronic microscope-analyzer
“Cam Scan” — 4D with a system of
the energetic dispersive analyzer “Link — 860” (with
the usage of “Zaf” program, mass sensitivity of the de-
vice is 0,01 %, beam diameter ranges from 5∙10 -9 to
1∙10 -6 ) [12];
– optical methods of researches with the usage of
metallographic microscope “ÌÌÐ — 2Д;
– Ozhe electronic spectroscopy (OES), by means
of spectrometer LAS-3000, manufactured by “Riber”
(with spatial resolution of 3 microns and energetic
permission of analyzer of 0,3 %).
Selective chemical etching was applied to samples
before studying of their defects with the usage of metallographic
microscope “ÌÌÐ — 2Д and of electronic
microscope “Cam Scan”. For etching of plates with
(111) -oriented surface plane Sirtle etchant was used.
Its chemical compound is as following: 50 g of CrO 3
+100 ml of H 2 O + 100 ml of HF (46 %). Etching time
was from 2 till 15 minutes, etching speed was about
2 — 3 microns/minute. Preliminary processing of
plates in Caro and hydrogen-ammonia compositions
[13] was made before selective etching. It allowed us to
raise revealing properties of selective etchant. The revealed
defects looked like dislocational etching poles,
lines of dislocations or dislocational grids.
3. RESEARCH AND CALCULATION
PECULIARITIES
It is established, that deformations of a rigid body
arise under the influence of mechanical stresses. Stress
τ dependence on deformation ε is presented on the
graph of (fig. 1) [14].
Crystal deformation occurs not only under the influence
of external mechanical stresses. Crystal doping,
presence of uncontrollable oxygen, carbon, hydrogen
impurities and impurities of other elements in
the course of cultivation always leads to the change of
lattice constant, and, hence, to existence of areas with
changed mechanical potential [15]. Elastic stresses in
silicon lattice, caused by implantation of atoms of another
size, are described by Poisson formula [11]:
1+υ
τ=ω⋅2μ⋅ ⋅C
, (1)
1−υ
with ω — Vegard constant;
υ= - S / S — Poisson constant (tab. 1); (2)
12 11
© V. A. Smyntyna, O. V. Sviridova, 2009

μ= 1/ S44
— shear modulus (tab. 1); (3)
С — impurity concentration;
S — elastic compliance coefficient [14].
mn
Fig. 1. Typical dependence of τ= f () ε for covalent crystals:
τ UFL , τ LFL , ε UFL , ε LFL — shear stresses τ and the deformations
е , corresponding upper fluidity limit (UFL) and lower
fluidity limit (LFL).
In the given work the area of plastic flows (from
( τUFL , ε UFL ) to ( τLFL, ε LFL ) ) on the curve of fig. 1 was
investigated. Namely, we studied the value of residual
stresses and deformations, arising in a crystal after
cancellation of deformation and formation of structural
defects. We were not interested in mechanical
deformation of a crystal (stretching, compression,
blow, bend, cave-in and other), but in initial (internal)
deformation which possesses the crystal before exposure
to external deformation. This initial deformation
of a crystal is formed in the course of growth and subsequent
doping. Stresses and deformations brought
into a crystal by defects, formed in the course of its
growth, were investigated in this work. Useful (doping)
impurity as, for example, boron in p-silicon and
phosphorus in n-silicon, as well as any other impurity,
refers to the category of point defects.
Table 1
Results of required calculations of critical stresses and
deformations, and also intermediate values for clear silicon.
Lattice constant 0 , A a & [18] 5,431
Vegard constant for boron ω boron [17]
3
2,8 10 −
⋅
Vegard constant for oxygen ω oxygen [17]
4
110 −
⋅
Elastic compliance
2
m
coefficient,
N [14]
S11
12
2,14 10 −
⋅
S11
12
7,68 10 −
S44
⋅
12
12,6 10 −
⋅
Shear modulus м, 2
N
m (3)
Poisson constant х (2)
13
7,94⋅10 0,28
Atom concentration С, -3
cm [18]
22
510 ⋅
N
Critical stress value τ UFL , [14] 2
m
8
10
Critical deformation value ε UFL (8)
3
1, 3 10 −
⋅
For silicon plates, containing dislocations with
residual stresses around dislocation cores, the top of
fluidity limit achievement comes at smaller stresses,
than for crystals without dislocations. Studying a defect
picture on a surface of silicon plates, it is possible
to define value of these residual stresses and deformations,
and, also, concentration of point defects.
After selective chemical etching, two types of
defect distribution picture in boron-doped epitaxial
silicon plates were found out by means of SEMS.
Thereupon the investigated plates were divided into 2
groups. By methods of x-ray and OES analyses it was
established, that plates of the second group contain
oxygen impurity, and plates of the first group do not
contain oxygen atoms. A typical representative of the
first group of plates is the plate ¹ 1 (fig. 2) with big
period of dislocational grid, consisting of 60 0 dislocations.
A typical representative of the second group of
plates is the plate ¹ 2 (fig. 3) with small period of dislocational
grid, highly precipitated by oxygen atoms.
SEMS analysis with a system of the energetic dispersive
analyzer “Link — 860” showed that oxygen atoms
are placed not only lengthways of dislocational grid,
but also in its lattice sites (spheres on fig. 3).
Dislocational grids considered to be repeating
linear defects, density of which is expressed through
a number of dislocational lines, crossing a surface of
unit area, perpendicular to dislocational lines [16].
After definition of dislocations’ amount n from
the pictures of plates’ surface (tab. 2), we calculated
surface density of dislocations, using formula
N
surf .
n ⋅image
increase
= . (4)
image square
Fig. 2. Image of boron precipitated dislocational grid in psilicon,
received after selective chemical etching by Sirtle (depth
of analysis x = 5 mkm, image increase is 2300 times, (111) — orientated
surface plane).
Value of surface density of dislocations is represented
in table 2.
53

The surface density of dislocations is connected
with value of relative deformation е (tab. 2) and with
silicon lattice constant a by a well-known ratio
0
[11]:
2
ε= a0 ⋅ Nsurf
. . (5)
Relative deformation, described by Vegard law,
arises at the process of impurity diffusion [17]:
ε=ω⋅ С , (6)
with ω — Vegard constant, С — impurity concentration
in relative dimensionless units (tab. 2).
In the case of several kinds of impurity resultant
relative deformation is defined as the sum of contributions:
ε= ∑ εi
. (7)
i
Shear stress τ UFL and deformation еUFL in the isotropic
structure are connected by ratio [14]
with μ – shear modulus (tab. 1).
54
τ
UFL
ε UFL = , (8)
μ
Fig. 3. Image of oxygen precipitated dislocational grid in psilicon,
received after selective chemical etching by Sirtle (depth
of analysis x = 5 mkm, image increase is 2300 times, (111) — orientated
surface plane).
In the process of dislocation multiplication internal
stresses become comparable with external and the
real stresses effecting dislocation, will differ from the
external. It is considered [14], that the real stresses effecting
dislocation are equal to
τ=τ eff . +τ inn.
, (9)
with τ eff . — external stresses, effecting a crystal,
τ inn.
— internal stresses.
Long-range (internal) mechanical stress of uniformly
distributed dislocations can be calculated, con-
sidering additive character of internal stresses of each
dislocation, according to expression
1/2
τ inn. =α⋅ b ⋅μ⋅Nsurf.
, (10)
Here
α= 1 −υ/(2 π ) , (11)
with х — Poisson constant (2), N surf . — dislocation
density, b — Burgers’ vector magnitude.
Table 2
Results of stresses and relative deformations calculations, and also
intermediate values for the investigated silicon plates
Plates
¹ 1
Plates
¹ 2
Surface orientation plane (111) (111)
Amount n of dislocations on figure,
averaged for all plates of one type
17 260
Value of relative deformations in the
area of dislocational grids е (5)
6
110 −
⋅
6
210 −
⋅
Surface density of dislocations
-2
. , Nsurf cm (4)
Stress value in the area of dislocational
357 1320
grids , 2
N
τ
m
(13)
6
9,3 ⋅10
7
1, 8 ⋅10
Concentration of boron impurity
С boron ,% (6)
0,04 0,04
Concentration of boron impurity
-3
Сboron, cm [18]
19
210 ⋅
19
210 ⋅
Concentration of oxygen impurity
С oxygen ,% (6)
0,01
Concentration of oxygen impurity,
-3
Сoxygen , cm [18]
18
510 ⋅
As it is seen from fig. 2 and fig. 3, observable dislocational
grids consist of 600 dislocations. The Burgers’
vector magnitude of 600 dislocations equals to the lattice
constant 0 a = b . Introducing the expressions of
е and б , given by Eqs. (5) and (11) in Eq. (10) one
gets:
1−υ
τ inn.
= ⋅ε⋅μ . (12)
2π
As the surface picture was taken without any external
stresses, for τ eff . one gives: τ eff . = 0 . Real stresses,
effecting dislocation are equal to internal stress (tab.
2) of uniformly distributed dislocations:
τ=τ inn.
(13)
On the other hand, apparently from Eq. (10), the
stress, effecting dislocation for lack of external stresses,
applied to a crystal, is in direct ratio to a square
root from dislocation density.
4. RESULTS AND DISCUSSION
Data, used in presented work and received from
the analysis of pictures of a surface and as a result of
calculations, averaged for each type of plates, are given
in tables 1 and 2. Steams of stress values, received as a
result of calculations, and deformations are tabulated
for the analysis in table 3.

Table 3
Values of residual stresses and deformations for plates ¹1 and
plates ¹ 2, and also threshold values of stresses and deformations
for clear from defects silicon.
Plates ¹ 1
Plates ¹ 2
Threshold values for clear
from defects silicon
ε , 2
N
τ
m
6
9,3 ⋅10
7
1, 8 ⋅10
6
110 −
⋅
6
210 −
⋅
3
1, 3 10 −
⋅
8
10
As it follows from table 3, residual stresses and deformations
for a case of boron-doped silicon (plates
¹ 1) on the curve of fig. 1 are placed more to the left
of threshold stresses and deformations for clear from
defects silicon that is they correspond to areas of elastic
stresses and deformations. It means that in a result
of boron precipitation of dislocations the new phase of
Si-B was formed. Its threshold of plasticity is more to
the left of a threshold of plasticity of clear silicon and,
taking into account the formation of dislocations,
more to the left of residual stresses and deformations
for a plate ¹ 1. Thus, the received values of residual
stresses and deformations for a plate ¹ 1 correspond
not to silicon, but to Si-B. As the threshold of a plastic
flow for this phase is less, than for silicon it is possible
to draw a conclusion that in a result of boron doping
hardness of silicon plates reduces.
In a case of oxygen presence in boron-doped silicon
plates, (plates ¹ 2) residual stresses and deformations
are more to the left of threshold stresses and
deformations for clear from defects silicon, but more
to the right of residual stresses and deformations for a
case of plates ¹ 1.
It is experimentally proved, that value of ф UFL and,
hence, of е UFL for germanium monotonously increases
with the increase of oxygen concentration [14]. It
is informed; that similar results were found out for
silicon, only the mechanism of strengthening of these
crystals in the presence of oxygen is not investigated
up to the end [9].
5. CONCLUSION
The accessory of residual stresses and deformations’
values of plates ¹ 1 to areas of elastic stresses
and deformations for clear from defects silicon is
caused by the fact, that boron atoms have smaller covalent
radius (0,08 nanometers) [19] in comparison
with covalent radius of silicon atoms (0,1175 nanometers)
[19]. As a result the period of silicon crystal lattice
increases when boron is placed in lattice sites. It is
connected with the fact, that placing of boron atoms
in silicon crystal lattice sites leads to lattice compression
in the doped area, and, hence, to corresponding
stretching of silicon crystal lattice [20]. As a result mechanical
stresses leading to existence of stretching area
appear in silicon crystal [21]. Therefore at the application
of mechanical stresses, smaller, than threshold
stresses for clear from defects silicon, the plastic flow
is observed in plates ¹ 1. As residual stresses and deformations
for plates ¹ 1 are less than threshold values
for clear from defects silicon, it is obvious (fig. 1),
that threshold values of stresses and deformations for
p — silicon are placed in the area, more to the left of
residual stresses and deformations.
In the case of oxygen atoms in lattice sites of silicon
crystal, because of larger covalent radius of oxygen
atoms in comparison with covalent radius of silicon
atoms, compression areas (caused by lattice stretching
in the field of oxygen atom placement [22]) will be
formed in silicon crystal. Interstitials (both boron and
oxygen) in silicon crystal lattice form areas of compression
[22]. Strength reduction of plates ¹ 1 justifies
to primary placement of boron in silicon lattice
sites. Position of residual stresses and deformations for
plates ¹ 2 to the right of residual stresses and deformations
for plates ¹ 1 (increase of deformation value)
is caused by oxygen presence in plates ¹ 2. Concentration
of oxygen atoms equal to 0,01 % in plates ¹
2, is enough for compensation of hardness reduction
effect, called by boron presence in the plates [23]. The
presented results justify that controllable introduction
of oxygen impurity can be used for increase of mechanical
hardness of silicon crystals.
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55

ãèðóþùåé ïðèìåñè ïî ïëàñòèíå ìîíîêðèñòàëëè÷åñêîãî
êðåìíèÿ // Ñåíñîð, 21 (3), ñòð. 19 — 23 (2006).
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Ìèð, Ì. (1974). 464 ñ.
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18. Ï. È. Áàðàíñêèé, Â. Ï. Êëî÷êîâ, Ì. Â. Ïîòûêåâè÷, Ïîëóïðîâîäíèêîâàÿ
ýëåêòðîíèêà. Ñïðàâî÷íèê. Íàóêîâà
äóìêà, Êèåâ. (1995). 704 ñ.
19. Â. È. Ïëåáàíîâè÷, À. È. Áåëîóñ, À. Ð. ×åëÿäèíñêèé, Â. Á. Îäæàåâ,
Ñîçäàíèå áåçäèñëîêàöèîííûõ èîííî-ëåãèðîâàííûõ
ñëîåâ êðåìíèÿ // ÔÒÒ 50 (8), ñòð. 1378 — 1382 (2008).
20. È. Í. Ñìèðíîâ, Èçìåíåíèÿ ïåðèîäà êðèñòàëëè÷åñêîé ðå-
56
UDC 537.311.33:622.382.33
V. A. Smyntyna, O. V. Sviridova
øåòêè êðåìíèÿ, âûçûâàåìûå äèôôóçèåé áîðà, ìûøüÿêà
è ñóðüìû // Äîêëàäû Àêàäåìèè íàóê ÑÑÑÐ. Òåõíè÷åñêàÿ
ôèçèêà 221 (2), ñòð. 332 — 334 (1975).
21. È. Í. Ñìèðíîâ, È. È. Ïåòðîâ, Ò. Ô. Ãîðÿ÷åâà, Èññëåäîâàíèå
äèôôóçèè áîðà â êðåìíèé ðåíòãåíîâñêèìè äèôðàêöèîííûìè
ìåòîäàìè // Ýëåêòðîííàÿ òåõíèêà. Ñåðèÿ 2
(Ïîëóïðîâîäíèêîâûå ïðèáîðû) 97 (5), ñòð. 11 — 18
(1995).
22. È. Í. Ñìèðíîâ, Äåôîðìàöèÿ êðèñòàëëè÷åñêîé ðåøåòêè
êðåìíèÿ, âûçûâàåìàÿ áîìáàðäèðîâêîé èîíàìè áîðà è
êèñëîðîäà // Äîêëàäû Àêàäåìèè íàóê ÑÑÑÐ. Ôèçè÷åñêàÿ
õèìèÿ 225 (3), ñòð. 621 — 623 (1995).
23. Î. Â. Ñâ³ð³äîâà, Çì³öíþþ÷èé âïëèâ äîì³øêè êèñíþ íà
êðèñòàëè êðåìí³þ // ÅÂÐÈÊÀ — 2008, Â22 (2008).
INFLUENCE OF IMPURITIES AND DISLOCATIONS ON THE VALUE OF THRESHOLD STRESSES AND PLASTIC
DEFORMATIONS IN SILICON
Abstract
The dependence of a plastic flow stress and deformation values on the presence of clear and precipitated by impurity initial structural
defects in epitaxial p — silicon without foreign impurity and in epitaxial p — silicon with oxygen impurity is investigated. It is
established, that, boron doping of silicon is the reason of threshold stress reduction in comparison with threshold stress for clear from
defects silicon and leads to reduction of its hardness. Presence of oxygen, precipitating dislocations in plates, stimulates the increase of
threshold stress.
Key words: dislocations, threshold stresses, plastic deformations.
ÓÄÊ 537.311.33:622.382.33
Â. À. Ñìûíòûíà, Î. Â. Ñâèðèäîâà
ÂËÈßÍÈÅ ÏÐÈÌÅÑÅÉ È ÄÈÑËÎÊÀÖÈÉ ÍÀ ÂÅËÈ×ÈÍÓ ÏÎÐÎÃÎÂÛÕ ÍÀÏÐßÆÅÍÈÉ È ÏËÀÑÒÈ×ÅÑÊÈÕ
ÄÅÔÎÐÌÀÖÈÉ Â ÊÐÅÌÍÈÈ
Ðåçþìå
Èññëåäîâàíà çàâèñèìîñòü âåëè÷èíû íàïðÿæåíèé è äåôîðìàöèé íà÷àëà ïëàñòè÷åñêîãî òå÷åíèÿ îò ïðèñóòñòâèÿ ÷èñòûõ
è ïðåöèïèòèðîâàííûõ ïðèìåñÿìè èñõîäíûõ ñòðóêòóðíûõ äåôåêòîâ â ýïèòàêñèàëüíîì p- êðåìíèè áåç ñòîðîííèõ ïðèìåñåé
è â ýïèòàêñèàëüíîì p- êðåìíèè ñ ïðèìåñüþ êèñëîðîäà. Óñòàíîâëåíî, ÷òî, ëåãèðîâàíèå êðåìíèÿ áîðîì ÿâëÿåòñÿ ïðè÷èíîé
óìåíüøåíèÿ ïîðîãîâûõ íàïðÿæåíèé ïî ñðàâíåíèþ ñ ïîðîãîâûìè íàïðÿæåíèÿìè äëÿ ÷èñòîãî îò äåôåêòîâ êðåìíèÿ è ïðèâîäèò
ê óìåíüøåíèþ åãî ïðî÷íîñòè. Ïðèñóòñòâèå â ïëàñòèíàõ êèñëîðîäà, ïðåöèïèòèðóþùåãî äèñëîêàöèè, ñòèìóëèðóåò âîçðàñòàíèå
ïîðîãîâûõ íàïðÿæåíèé.
Êëþ÷åâûå ñëîâà: äèñëîêàöèè, ïîðîãîâîå íàïðÿæåíèå, ïëàñòè÷åñêèå äåôîðìàöèè.
ÓÄÊ 537.311.33:622.382.33
Â. À. Ñìèíòèíà, Î. Â. Ñâ³ð³äîâà
ÂÏËÈ ÄÎ̲ØÎÊ ² ÄÈÑËÎÊÀÖ²É ÍÀ ÂÅËÈ×ÈÍÓ ÏÎÐÎÃÎÂί ÍÀÏÐÓÃÈ ² ÏËÀÑÒ×Íί ÄÅÔÎÐÌÀÖ²¯
 ÊÐÅÌͲ¯
Ðåçþìå
Äîñë³äæåíî çàëåæí³ñòü âåëè÷èíè íàïðóãè ³ äåôîðìàö³¿ ïî÷àòêó ïëàñòè÷íî¿ òå÷³¿ â³ä íàÿâíîñò³ ÷èñòèõ ³ ïðåöèï³òîâàíèõ
äîì³øêàìè ïî÷àòêîâèõ ñòðóêòóðíèõ äåôåêò³â â åï³òàêñ³àëüíîìó p- êðåìí³¿ áåç ñòîðîíí³õ äîì³øîê ³ â åï³òàêñ³àëüíîìó
p- êðåìí³¿ ç äîì³øêîþ êèñíþ. Âñòàíîâëåíî, ùî, ëåãóâàííÿ êðåìí³þ áîðîì º ïðè÷èíîþ çìåíøåííÿ ïîðîãîâî¿ íàïðóãè â
ïîð³âíÿíí³ ³ç ïîðîãîâîþ íàïðóãîþ äëÿ ÷èñòîãî â³ä äîì³øîê êðåìí³þ ³ ïðèçâîäèòü äî çíèæåííÿ éîãî ì³öíîñò³. Ïðèñóòí³ñòü â
ïëàñòèíàõ êèñíþ, ïðåöèï³òóþ÷îãî äèñëîêàö³¿, ñòèìóëþº çðîñòàííÿ ïîðîãîâî¿ íàïðóãè.
Êëþ÷îâ³ ñëîâà: äèñëîêàö³¿, ïîðîãîâà íàïðóãà, ïëàñòè÷í³ äåôîðìàö³¿.

UDÑ 530.145; 539.1;539.18
O. YU. KHETSELIUS
I. I. Mechnikov Odessa National University
ADVANCED MULTICONFIGURATION MODEL OF DECAY
OF THE MULTIPOLE GIANT RESONANCES IN THE NUCLEI
1. INTRODUCTION
As it is well known, the multipole giant resonances
are the highly excited states of nuclei, which are interpretive
as the collective coherent vibrations with a
participance of large number of nucleons [1-8]. Experimentally,
the multipole giant resonances are manifested
as the wide maximums in the dependence of
cross-section of the nuclear reactions on the incident
particle energy r in the spectrum of incident particles.
A classification of the multipole giant resonances as
the states of collective type is usually fulfilled on the
quantum numbers of vibration excitations: entire angle
momentum (J) and parity π (J π ). The multipole
giant resonances are observed in the spectra of majority
of nuclei and situated ,as a rule, in the continuous
spectrum of excitations in a nucleus (with width of order
of several MeV). Two main theoretical approaches
to a description of the multipole giant resonances are
usually used [1-5]. In the phenomenological theories
it is supposed that the strong collectivization of states
allows to apply the hydrodynamic models to the description
of vibrations of the nuclear form and volume.
The microscopic theory is in fact based on the shell
model of a nucleus. It is well known different versions
of the quasiparticle-phonon model of a nucleus, designed
for describing littlie-quasiparticle components
of the wave functions for low, intermediate and high
excitation energies (see [2,3,6]). In the simple interpretation
an excitation of the multipole giant resonances
is the result of transition of the nucleons from
one closed shell to another one, i.e. the multipole giant
resonances is the result of the coherent summation
of many particle-hole (p-h) transitions with the necessary
corresponding momentum and parity.
As a rule, the multipole giant resonances are situated
under the excitation energies, which exceed the
thresholds of emission of the particles from a nucleus.
Studying the multipole giant resonances decay channels
allows to reveal the mechanisms of its forming, connection
with other excitations etc. The interaction of a
nucleus with external field with forming the multipole
giant resonances occurs during several stages. There is
a production of the p-h excitation which is corresponding
to the 1p-1h states over the Fermi surface (the first
stage). Then the excited pair interacts with nuclear
nucleons with the creating another 1p-1h excited state
or two p-h pairs ( 2p-2h state; second stage). Then the
© O. Yu. Khetselius, 2009
It is presented an advanced generalized multiconfiguration approach to describe a decay of highexcited
states (the multipole giant resonances), which is based on the mutual using the shell models
(with extended basis) and microscopic model of pre-equilibrium decay with statistical account for
complex configurations 2p2h, 3p3h etc. The new model is applied to an analysis of the reaction (μ - n)
on the nucleus 40 Ca.
3p-3h and more complicated states are created till the
statistical equilibrium takes a place. The full width of
the multipole giant resonances is provided by the direct
decay to continuum (Γ ↑ ) and decay of the 1p-1h
configurations on more complicated multi-particle
(Γ ↓ ) ones. The mixing with complex configurations
leads to the loss of the coherence and creating states
of the compound nucleus. It’s known that an account
of complex configurations has significant meaning for
adequate explanation of the widths, structure and decay
properties of the multipole giant resonances (see
[2-5]). Here we present generalized multiconfiguration
model to describe a decay of high-excited states, which
is based on the mutual using the shell models (with
limited basis) and microscopic Zhivopistsev-Slivnov
model [5] of the pre-equilibrium decay with statistical
account for complex 2p2h, 3p3h configurations etc.
The model is applied to analysis of reaction (μ - n) on
the nucleus 40 Ca. The comparison with experimental
and other theoretical data is presented.
2. GENERALIZED MULTICONFIGURATION
MODEL OF THE MULTIPOLE GIANT
RESONANCES DECAY
The multipole giant resonances are treated on
the basis of the multiparticle shell model. Process of
creation of the collective state (of the multipole giant
resonance) and an emission process of nucleons are
described by the diagram in fig.1.
Here V is effective Hamiltonian of interaction,
μ
resulted in capture of muon by nucleus with transformation
of proton to neutron and emission by antineutrino.
Isobaric analogs of isospin and spin-isospin
resonances of finite nucleus are excited. The diagrams
n
for photonuclear reactions look to be analogous; Γ 22
%
is the full vertex part (full amplitude of interaction,
which transfers the interacting p-h pair to the finite
n
npnh state. The full vertex Γ Γ 22
% is defined by the
system of equations within quantum Green function
modified approach [3,5].
All possible configurations are divided on two
groups: i). group of complicated configurations “n ”, 1
which must be considered within shell model with
account for residual interaction; ii). statistical group
“n ” of complex configurations with large state den-
2
sity p(n,E)>> and strong overlapping the states
57

G n >>D n-1 >D n (D n is an averaged distance between
states with 2n exciton; G n is an averaged width). Matrix
elements of bond are small and characterized
by a little dispersion. To take into account a
collectivity of separated complex configurations for
input state a diagonalization of residual interaction on
the increased basis (ph,ph+phonon, ph+2 phonon) is
used. All complex configurations are considered within
the pre-equilibrium decay model by Feschbach-
Zhivopistsev et al [5] with additional account of “n 1 ”
group configurations. The input wave functions of the
multipole giant resonances for nuclei with closed or
almost closed shells are found from diagonalization of
residual interaction on the effective 1p1h basis [9-15].
58
μ
V
~
ν
n
p
ϕ
~
Γ
22n
Fig. 1. Diagram of process for production of the collective
state (multipole giant resonances) and emission of nucleons (or
more complex particles).
Statistical multistep negative muon capture
through scalar intermediate states of compound nucleus
is important. Intensities of nucleon spectra can
be written by standard way [1,2]. In particular, an intensity
of nucleonic spectra is defined as follows:
dI
( Eμ, l, εf, Jπ
) =
dε
f
↑
(, , ) n 1 ↓
Γn l εf Jπ ⎡ − Γk( J π)
⎤
= ⋅⎢ ⎥⋅Λμ(
Eμ, Jπ)
n= 1, Γn( Jπ) ⎢⎣ k = 1 Γk( Jπ)
⎥⎦
Δ n=
1
where
∑ ∏ (1)
•
•
•
•
Γ (, l ε , Jπ ) = 2 π⋅ρ( , ε ) ρ ( , ,
↓
2
Γk( Jπ ) = 2 π⋅
k+
1
( b)
>ρ ( Nk+ 1,
Jπ , Eμ)
Eμ =ε f + UB + BN
Here l is the orbital moment of the emission nucleon,
ε is its energy; B is the bond energy of nucleon
f N
in the compound nucleus; Λμ( Eμ, Jπ
) is probability of
μ-capture with excitation of the state φ (E , Jπ) with
in μ
energy E , spin J and parity π. In oppositeness to stan-
μ
dard theories [2,5], we take into account an interference
between contributions of separated “dangerous”
configurations. From the other side, above indicated
features of the statistical group of configurations arte
not fulfilled for the “dangerous” configurations. However,
the value n ( 1)
n
↓
Γ for some dangerous configura-
2
tion is weakly dependent upon the energy. Indeed,
configuration n 1 is the superposition of the large number
of configurations, i.e. [2]:
2
| < n1 | In1, n+
1 | n+
1 > |
↓
Γ n ( n1
) = ∑
2 2
n+ 1 ( Eμ − En+
1) +Γn+
1/4
Generally, the expressions for the n-step contribution
to the emission spectrum are modified as follows:
dI Γ (, l ε, Jπ) Γ ( Jπ)
E l ε Jπ
= ⋅ +
dε Γ ( Jπ) Γ ( Jπ)
( μ , , f , ) (
↑
n2 n−1, n2
f n2n−1 ∑
{ n1 }
↑
n1 l
n1 f
J
J
↓
n−1, n J
1
n−1J n−
2
∏
k = 1
↓
k
k
J
J
+
Γ (, ε
Γ (
, π) Γ
⋅
π) Γ
( π) ⎡
⋅ ⎢
( π) ⎢⎣ Γ (
Γ (
π)
⎤
⎥×
π)
⎥⎦
×Λ% ( E , Jπ)
where
∑
μ μ
Γ = Γ +Γ
↓ ↓ ↓
n−1 { n1
}
n−1, n1 n−1, n2
| | Γ
Γ =
↓
Nn−1 Nn−1, Nn ( n1
)
Nn 2
n1
n−1, n1
2 2
( Eμ− En
) +Γ /4
1 n1
(2)
Supposing the input state is isolated, in formalism
of the input ph-states one could write as follows:
Γ1( Jπ) Λμ( ϕin ( E , ))
i i Jπ
Λ %
μ =
2 2
( Eμ− Ei)
+Γn
/4
1
where
∑
Γ ( ϕ ) =Γ +Γ + Γ
↑ ↓ ↓
1 in 1 1, n2 { n1
}
1, n1
The other technical details of the presented approach
can be found in refs. [2,4,5, 15,16,18].
3. RESULTS AND CONCLUSION
The wave functions of the input state {φ in } in the
reaction 40 Ca (μ - n) are calculated within the shell
model [12,15,18]. As one could wait for that a col-
lectivity of initial input state leads to significant de-
↓ creasing Γ . The separation into groups n1 and n is
i
2
naturally accounted for the 2p2h configuration space
[2,18] and the contribution of configurations “ph +
phonon” and weakly correlated 2p2h states is revealed
[4,5,16]. A probability of transition to the “dangerous”
configurations 2p2h is defined by the value of
matrix element:
2
| |
and additionally by density ρ(2p2h,Jπ,E) for statistical
group n . The contribution of weakly correlated 2p2h
2
configurations is defined by the following expression:
↓
2
Γ 2p2h= 2 π⋅ | >ρ 2p2h The residual interaction has been chosen in the
form of Soper forces (see [5]):
V=g (1-α+α⋅σ σ )⋅Δ(r -r ),
0 1 2 1 2
3 where g /(4πr )=-3 MeV, α=0,135.The phonons have
0 o
been considered in the collective model and calculation
parameters in the collective model and generalized

andom phase approximation are chosen according to
ref.[4,5]. The phonons contribution is distributed as
follows: 2 + (E=3,9 MeV; β=0,075)~ 42%, 3 - (E=3,736
MeV; β=0,345)~8%, 5 - (E=4,491 MeV; β=0,216)~3%
etc. with growth of the phonon moment.
Our theoretical results are compared with experimental
data and other calculation results [2] in fig.2,3.
In the range of 5-13MeV the experiment gives the intensity
~10% from the equilibrium one. As it has been
shown earlier (c.f.[4,5], the 1 - , 2 - states do not give the
significant contribution. However, these states exhaust
~80% of the intensity of the μ - -capture. This fact is
completely corresponding to results [16] and independently
to the data from ref. [5] and ref. [19].
The analysis shows also that only an accurate mu-
tual account for 0 ± ,1 +
, 2+ ,3 + and more high multipoles
(plus more less correct microscopic calculation of
↓
Γin ( Jπ , E)
, the input and 2p2h states, separation of
the 2p2h space n configurations n and n etc.) allows
1 2
to fill the range of high and middle part of the spectrum.
Preliminary estimates show that an agreement
between theoretical and experimental data is more
improved in this case, especially, in the high energy
part of the spectrum.
1,0
0,1
0,0
0 3 6 9 12, MeV
Fig. 2. The comparison of the calculated spectra (curve 1)
with experimental data (curve 3) [20] and theoretical data from
the Zhivopistsev-Slivnov model (curve 2) [5].
0,1
0,0
0 3 6 9 12, MeV
± ±
Fig. 3. The mutual account of the 0 ± , 1 + , 2 + , 3 ± , 4 - , 5 - — multipoles:
the curve 1 — the present paper; the curve 1 is corresponding
to the pre-equilibrium and direct part of the spectrum and the
curve 3 is corresponding to the equilibrium part (see text).
References
1. Bohr O., Mottelsson B., Structure of atomic nucleus. — N-Y.:
Plenum, 1995. — 450P.
2. Ñîëîâü¸â Â.Ã. Òåîðèÿ àòîìíîãî ÿäðà. Êâàçè÷àñòèöû è
ôîíîíû. — Ìîñêâà:, Ýíåðãîèçäàò 1999. — 300P.
3. Izenberg I., Grainer B., Models of nuclei. Collective and onebody
phenomena. — N-Y. :Plenum Press, 2005. — 360P.
4. Paar N., Vretenar D., Ring P., Neutrino-nuclei reactions with
relativistic quasiparticle RPA// J. Phys. G. Nucl. and Particle
Phys. — 2008. — Vol.35. — P.014058.
5. Zhivopistsev F.A., Slivnov A.M., multiconfiguration model
of decay of the multipole giant resonances // Izv.AN Ser.
Phys. — 1994. — Vol.48. — P.821-825.
6. Serot B.D., Walecka J.D., Advances in Nuclear Physics: The
Relativistic Nuclear Many Body Problem. — N. — Y.: Plenum
Press, 1999. — Vol.16.
7. Tsoneva N., Lenske H., Low energy dipole excitations in
nuclei at the N=50,82 and Z=50 shell closures as signatures
for a neutron skin// J. Phys. G. Nucl. and Particle Phys. —
2008. — Vol.35. — P.014047.
8. Glushkov A.V., Malinovskaya S.V., Cooperative laser-nuclear
processes: border lines effects// In: New projects and
new lines of research in nuclear physics. Eds. G.Fazio and
F.Hanappe, Singapore : World Scientific. — 2003. — P.241-
250.
9. Nagasawa T., Haga A., Nakano M., Hyperfine splitting of
hydrogenlike atoms based on relativistic mean field theory//
Phys.Rev.C. — 2004. — Vol.69. — P.034322.
10. Benczer-Koller N., The role of magnetic moments in the determination
of nuclear wave functions of short-lived excited
states// J.Phys.CS. — 2005. — Vol.20. — P.51-58.
11. Tomaselli M., Schneider S.M., Kankeleit E., Kuhl T., Ground
state magnetization of 209 Bi in a dynamic-correlation model//
Phys.Rev.C. — 1999. — Vol.51, N6. — P.2989-2997.
12. Dikmen E., Novoselsky A., Vallieres M., Shell model calculation
of low-lying states of 110 Sb// J.Phys.G.: Nucl.Part.
Phys. — 2007. — Vol.34. — P.529-535.
13. Stoitsov M., Cescato M.L., Ring P., Sharma M.M., Nuclear
breathing mode in the relativistic mean-field theory//J. Phys.
G: Nucl. Part. Phys. — 1994. — Vol.20. — P.L149-L156.
14. Khetselius O.Yu., Hyperfine structure of atomic spectra. —
Odessa: Astroprint, 2008. — 210P.
15. Khetselius O.Yu., Relativistic Calculating the Hyperfine
Structure Parameters for Heavy-Elements and Laser Detecting
the Isotopes and Nuclear Reaction Products//Physica
Scripta. — 2009. — Vol.62. — P.71-76.
16. Khetselius O.Yu. et al, Generalized multiconfiguration model
of decay of the multipole giant resonances applied to analysis
of reaction (μ - n) on the nucleus 40 Ca//Trans. of SLAC
(MENU, Stanford). — 2008. — Vol.1. — P.186-192.
17. Khetselius O.Yu., Relativistic Calculating the Spectral Lines
Hyperfine Structure Parameters for Heavy Ions // Spectral
Line Shapes (AIP). — 2008. — Vol. 15. — P.363-365.
18. Khetselius O.Yu., Turin A.V., Sukharev D.E., Florko T.A.,
Estimating of X-ray spectra for kaonic atoms as tool for sensing
the nuclear structure// Sensor Electr. and Microsyst.
Techn. — 2009. — N1. — P.P.11-16.
19. Glushkov A.V., Malinovskaya S.V., Quantum theory of the
cooperative muon-nuclear processes: Discharge of metastable
nuclei during negative muon capture// Recent Advances
in Theory of Phys. and Chem. Systems (Springer). — 2006. —
Vol.15. — P.301-328.
20. Waitkovskaya I. et al, Analysis of reaction (μ - n) on the nucleus
40 Ca//Nucl.Phys. — 1999. — Vol.15. — P.2154-2158.
59

60
UDÑ 530.145; 539.1;539.18
O. Yu. Khetselius
ADVANCED MULTICONFIGURATION MODEL OF DECAY OF THE MULTIPOLE GIANT RESONANCES IN THE
NUCLEI
Abstract
It is presented an advanced generalized multiconfiguration approach to describe a decay of high-excited states (the multipole giant
resonances), which is based on the mutual using the shell models (with extended basis) and microscopic model of pre-equilibrium decay
with statistical account for complex configurations 2p2h, 3p3h etc. The new model is applied to an analysis of the reaction (μ - n) on the
nucleus 40 Ca.
Key words: multipole giant resonances, generalized multiconfiguration model, reaction (μ - n) on the nucleus 40 Ca.
ÓÄÊ 530.145; 539.1;539.18
O. Þ. Õåöåëèóñ
ÓÑÎÂÅÐØÅÍÑÒÂÎÂÀÍÍÀß ÌÍÎÃÎÊÎÍÔÈÃÓÐÀÖÈÎÍÍÀß ÌÎÄÅËÜ ÐÀÑÏÀÄÀ ÌÓËÜÒÈÏÎËÜÍÛÕ
ÃÈÃÀÍÒÑÊÈÕ ÐÅÇÎÍÀÍÑΠ ßÄÐÀÕ
Ðåçþìå
Ðàçðàáîòàí óñîâåðøåíñòâîâàííûé îáîáùåííûé ìíîãîêîíôèãóðàöèîííûé ïîäõîä äëÿ îïèñàíèÿ ðàñïàäà âûñîêî âîçáóæäåííûõ
ñîñòîÿíèé (ìóëüòèïîëüíûå ãèãàíòñêèå ðåçîíàíñû) ÿäåð, êîòîðûé áàçèðóåòñÿ íà îäíîâðåìåííîì èñïîëüçîâàíèè
îáîëî÷å÷íîé ìîäåëè (ñ ðàñøèðåííûì áàçèñîì) è ìèêðîñêîïè÷åñêîé ìîäåëè ïðåäðàâíîâåñíîãî ðàñïàäà ñî ñòàòèñòè÷åñêèì
ó÷åòîì ñëîæíûõ êîíôèãóðàöèé òèïà 2p2h, 3p3h è äðóãèõ. Íîâûé ïîäõîä èñïîëüçîâàí äëÿ àíàëèçà ðåàêöèè (μ - n) íà ÿäðå
40 Ca.
Êëþ÷åâûå ñëîâà: ìóëüòèïîëüíûå ãèãàíòñêèå ðåçîíàíñû, îáîáùåííàÿ ìíîãî-êîíôèãóðàöèîííàÿ ìîäåëü, ðåàêöèÿ (μ - n)
íà ÿäðå 40 Ca.
ÓÄÊ 530.145; 539.1;539.18
O. Þ. Õåöåë³óñ
ÓÄÎÑÊÎÍÀËÅÍÀ ÁÀÃÀÒÎÊÎÍÔ²ÃÓÐÀÖ²ÉÍÀ ÌÎÄÅËÜ ÐÎÇÏÀÄÓ ÌÓËÜÒÈÏÎËÜÍÈÕ Ã²ÃÀÍÒÑÜÊÈÕ
ÐÅÇÎÍÀÍѲ  ßÄÐÀÕ
Ðåçþìå
Ðîçâèíóòî óäîñêîíàëåíèé óçàãàëüíåíèé áàãàòî êîíô³ãóðàö³éíèé ï³äõ³ä äëÿ îïèñó ðîçïàäó âèñîêî çáóäæåíèõ ñòàí³â
(ìóëüòèïîëüí³ ã³ãàíòñüê³ ðåçîíàíñè) ÿäåð, ÿêà áàçóºòüñÿ íà îäíî÷àñíîìó âèêîðèñòàíí³ îáîëîíêîâî¿ ìîäåë³ (ç ðîçøèðåíèì
áàçèñîì) òà ì³êðîñêîï³÷íî¿ ìîäåë³ ïðåäðàâíîâ³ñíîãî ðîçïàäó ³ç ñòàòèñòè÷íèì óðàõóâàííÿì ñêëàäíèõ êîíô³ãóðàö³é òèïó 2p2h,
3p3h òà ³íøèõ. Íîâèé ï³äõ³ä âèêîðèñòàíî äëÿ àíàë³çó ðåàêö³¿ (μ - n) íà ÿäð³ 40 Ca.
Êëþ÷îâ³ ñëîâà: ìóëüòèïîëüí³ ã³ãàíòñüê³ ðåçîíàíñè, óçàãàëüíåíà áàãàòîêîíô³ãóðàö³éíà ìîäåëü, ðåàêö³ÿ (μ - n) íà ÿäð³ 40 Ca.

UDÑ 621.315.592
YU. F. VAKSMAN 1 , YU. A. NITSUK 1 , V. V. YATSUN 1 , YU. N. PURTOV 1 , A. S. NASIBOV 2 , P. V. SHAPKIN 2
1 I. I. Mechnikov National University, 65026 Odessa, Ukraine
2 P. N. Lebedev Physical Institute, Russian Academy of Sciences,
117924 Moscow, Russia
OPTICAL PROPERTIES OF ZnSe:Mn CRYSTALS
ZnSe single crystals with diffusion doping of Mn have been investigated. Absorption, luminescence
and photoconductivity of ZnSe:Mn crystals have been studied and analyzed in the visible region
of the spectrum. Concentration of Mn impurity was estimated from absorption edge. The electron
transition scheme in ZnSe:Mn was proposed.
1. INTRODUCTION
Semiconductor compounds A 2 B 6 with dopants
of transition metals are described by internal transitions
in 3d states — absorption and luminescence.
Investigation of internal transitions luminescence on
these states and luminescent centers formed by Mn
is interesting because ZnS:Mn and ZnSå:Mn crystals
are rather good phosphors [1]. In this work, diffusion
doping of ZnSe single crystals with Mn is described.
The optical absorption, luminescence and photoconductivity
of ZnSe:Mn crystals have been investigated
and analyzed in the visible range of the spectrum.
Concentration of Mn impurity was estimated from
absorption edge shift.
The purpose of this study is to develop the procedure
of diffusion Mn doping of the ZnSe crystals,
to identify the optical absorption, luminescence and
photoconductivity spectra of obtained samples.
2. EXPERIMENTAL
The samples for study were prepared via diffusion
Mn doping of pure ZnSe single crystals. Undoped
crystals were obtained by the method of free growth on
a single-crystal ZnSe substrate with the growth plane
(111) or (100). This method was described in detail,
and the main characteristics of the ZnSe crystals were
obtained in [2, 3]. The selection of temperature profiles
and design of the growth chamber excluded the
possibility of a contact between the crystal and chamber
walls. The dislocation density in the crystals obtained
was no higher than 10 4 cm –2 .
Initially, the crystal doping was provided by impurity
diffusion towards crystal bulk from evaporated
surface layer of metallic Mn in He+Ar atmosphere.
Then, the crystals have been annealed at 1173-1223Ê.
Diffusion process time was 5 hours. However, this
method didn’t form crystals with high concentration
of Mn, thus Mn atoms diffused into the crystal bulk
resulted from high diffusion coefficient of Mn. As result,
ZnSe:Mn crystals with low Mn concentration
(10 16 cm -3 ) were obtained.
The method described in [4,5] was used for highly
doped ZnSe:Mn crystals obtaining. Metal powderlike
Mn was used as the source of impurity. To prevent
crystal etching, Mn powder was mixed with ZnSe
© Yu. F. Vaksman, Yu. A. Nitsuk, V. V. Yatsun, Yu. N. Purtov, A. S. Nasibov, P. V. Shapkin, 2009
powder in 1:1 ratio. Diffusion process was performed
in He+Ar atmosphere in the temperature range from
1173 to 1223 K. The diffusion process was 5h long.
The spectra of optical density were measured using
an MDR-6 monochromator with diffraction grating
1200 grooves/mm in the visible region. The light
intensity was registered by photomultiplier FEU-100.
The optical density spectra were measured at 77 and
293 K.
Photoluminescence spectra were measured by
ISP-51 quartz prism spectrograph. Photoluminescence
excitation was provided by super luminescent
diode EDEV-3LA1 Edison Opto Corporation with
λ max =400 nm.
Indium contacts were deposited on the surface
of crystals for photoconductivity measurements. The
contacts were formed by firing in vacuum at 600 K.
Monochromator MUM-2 was used for photoconductivity
spectra measurements. Halogen lamp was used
for excitation of the spectra.
3. OPTICAL ABSORPTION OF ZnSe:Mn IN
THE VISIBLE REGION SPECTRUM
The optical density (D * ) spectra of ZnSe:Mn crystals,
obtained at different annealing temperatures,
are presented in fig.1. The spectra of undoped ZnSe
crystals characterized by absorption edge at 2.82 eV
(fig 1, curve 1) at Ò =77K. The second linear area was
located at 2.76 eV, associated with an unresilient exciton-exciton
interaction [3]. No features was observed
at the energies lower than 2.6 eV.
Mn doping led to absorption edge shift (fig.1,
curves 2-4). The shift value increased with annealing
temperature raise. The change of the band gap (meV)
as the function of impurity concentration was discussed
in [3]:
13 13
5 ⎛3⎞ eN
Δ Eg
= −210 ⋅ ⎜ ⎟
⎝π⎠ 4πε0εs
, (1)
where å-electron charge, N-impurity concentration
(cm -3 ), ε s =8.66 — ZnSe dielectric constant. As result,
Mn-dopant concentrations have been calculated. The
obtained values are presented in Table. Maximum of
Mn concentration was observed (6∙10 19 cm -3 ) for the
samples annealed at 1223Ê.
61

(D * ) 2
300
250
200
150
100
50
0
62
2.65 2.7 2.75 2.8 2.85 2.9
3
2
1
E, eV
Fig. 1. The optical-density spectra of ZnSe (1) and ZnSe:Mn
(2,3) crystals doped with Mn at temperatures of (2) 1173 and (3)
1223K. T =77 K.
m
In the visible region ZnSe:Mn optical-density
spectra have several absorption lines, which intensity
increases with Mn concentration enhance (fig.2).
Three absorption lines at 2.31, 2.47 and 2.67 eV can
be separated
Table
The change of the band gap (meV) in the ZnSe:Mn crystals
Crystal type 77 Ê 300 Ê ΔÅ g , meV N, cm -3
ZnSe, undoped 2.82 2.68 --- ---
ZnSe:Mn,
doped at 1173K
2.78 2.64 40 2∙1018 ZnSe:Mn,
doped at 1223K
2.69 2.55 130 6∙1019 Absorption measurements at 77-300Ê showed that
lines at 2.31, and 2.47 eV didn’t change their positions
with temperature raise. Line at 2.67 eV at 300 K is located
at the conductivity band because the band gap of
ZnSe:Mn is 2.55-2.64 eV at this temperature. The one
can suppose that intracenter transitions are the origins
of those lines. According to [6], absorption line at 2.31
eV is due to transition from the ground state 6 À 1 (G) to
excited state 4 Ò 1 (G) of Mn 2+ ion. The line at 2.47 eV
is due to 6 À 1 (G)→ 4 T 2 (G) transitions and the line at
2.67 eV is due to 6 À 1 (G)→ 4 Å 1 (G) intracenter transitions.
3. ZnSe:Mn PHOTOLUMINESCENCE
SPECTRA
Photoluminescence measurements have been performed
at 77-600 K. At 77K ZnSe:Mn crystals spectra
had two narrow lines at 2.12 and 2.31 eV. The intensity
of the lines increased with Mn concentration increase
(fig.3, curves 1,2). Lines positions didn’t change with
the temperature increase that evidences about intracenter
nature of this lines.
D *
3.3
3.2
3.1
3
2.9
2.8
2.7
2.6
2.5
3
2
1
2.4
1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7
E, eV
Fig. 2. The optical-density spectra of ZnSe (1) and ZnSe:Mn
(2,3) crystals in the visible region of the spectrum at 77 K. Curve
2 corresponds to the sample annealed at 1173 K and curve 3 corresponds
to annealing at 1223 K.
I, arb. un.
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1.8 1.9 2 2.1 2.2 2.3 2.4
3
2
1
E, eV
Fig. 3. The photoluminescence spectra of ZnSe:Mn crystals at
77(1,2) and 400 K (3). Curve 1 corresponds to the sample annealed
at 1173 K and curves 2,3 correspond to annealing at 1223 K.
The temperature dependence of the luminescence
at 300-600 K showed that line at 2.31 eV disappeared

at 400 K (fig.3, curve 3) and line at 2.12 eV disappeared
at 600 K. Luminescence lines half-width increases
with the temperature increase:
⎛2kT ⎞
E1/2 = E0⎜
⎟ , (2)
⎝ hΩ
⎠
The equation (2) is obtained from the model of
configuration coordinates, where Å is the lines half-
0
width at 0 K.
1/2
4. ZnSe:Mn PHOTOCONDUCTIVITY
SPECTRA
It is established, that ZnSe:Mn crystals had photosensitivity.
ZnSe:Mn crystals photoconductivity spectra
at different temperatures are shown in fig.4. The
one can see, one line is observed at 2.78 eV under 77 K
(fig.4). This line present in spectra of undoped ZnSe
crystals and could be associated with intraband transitions.
Low-energy photoconductivity part increases
with the temperature increase (fig4, curves 2-4).
Ip.c., arb. un.
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
4
0
1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8
3
2 1
�, eV
Fig. 4. The photoconductivity spectra of ZnSe:Mn crystals at
77(1), 293 (2), 323 (3) and 403Ê (4).
The permanent lines at 2.31 and 2.47 eV appeared
in spectra at temperatures over 293 K. These lines positions
are identical to absorption lines. The intensity
of photoconductivity lines was changed with the temperature.
At room temperatures high energy lines were
dominated whereas at 403 K 2.31 eV lines intensity
becomes maximal.
Electron transitions scheme of ZnSe:Mn based on
optical properties investigations, is shown in fig.5.
As it is mentioned above, absorption lines at 2.31,
2.47 and 2.67 eV are the result of transitions from the
ground state 6À (G) to Mn excited states (fig.5, transi-
1
tions 1-3). According to [1], the ground state of Mn
ion is located 0.1 eV higher than valence band.
Photoluminescence lines at 2.12 and 2.31 eV
are resulted by transitions from excited states to the
ground state of Mn ion (fig.5, transitions 4,5).
Presented scheme allows to explain photoconductivity,
which is due two stage process. First, optical
transitions 2 and 3 take place and then thermal electron
transition to conductance band starts (transitions
6 and 7). The absence of low energy photoconductivity
up to 300 K, can be explained by the impossibility
of thermal transitions of electrons from 4 E 1 (G) to conductance
band. It is worth to say that similar results
have been obtained by us before for ZnSe:Cr [8].
Eg
Mn 2+
6
1
7
2
3
4 5
6 �1(G)
Fig. 5. The electron transition scheme in ZnSe:Mn crystals.
5. CONCLUSIONS
Ec
EV
The studies carried out allow us to conclude the
following.
1. A procedure of diffusion Mn doping of the ZnSe
crystals has been developed. Maximal Mn concentration,
estimated from the absorption edge, was 6∙1019 cm-3 .
2. The nature of ZnSe:Mn crystals absorption
lines in the visible region of the spectrum have been
identified.
3. The identity of absorption, photoluminescence
and photoconductivity lines in ZnSe:Mn was
shown.
4. The electron transition scheme in the ZnSe:Mn
crystals was proposed.
References
1. Àãåêÿí Â.Ô. Âíóòðèöåíòðîâûå ïåðåõîäû èîíîâ ãðóïïû
æåëåçà â ïîëóïðîâîäíèêîâûõ ìàòðèöàõ òèïà À 2 Â 6 //
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Vapour growth and doping of ZnSe single crystals // J.Cryst.
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3. Âàêñìàí Þ.Ô., Íèöóê Þ.À., Ïóðòîâ Þ.Í., Øàïêèí
Ï.Â. Ñîáñòâåííûå è ïðèìåñíûå äåôåêòû â ìîíîêðèñòàëëàõ
ZnSe:In, ïîëó÷åííûõ ìåòîäîì ñâîáîäíîãî ðîñòà
// ÔÒÏ. — 2001. — Ò.35, ¹8. — ñ. 920-926.
4. Âàêñìàí Þ.Ô., Ïàâëîâ Â.Â., Íèöóê Þ.À., Ïóðòîâ Þ.Í.,
Íàñèáîâ À.Ñ. Øàïêèí Ï.Â. Îïòè÷åñêîå ïîãëîùåíèå è
äèôôóçèÿ õðîìà â ìîíîêðèñòàëëàõ ZnSe // ÔÒÏ. —
2005. — Ò. 39, ¹4. — Ñ. 401-404.
5. Âàêñìàí Þ.Ô., Ïàâëîâ Â.Â., Íèöóê Þ.À., Ïóðòîâ Þ.Í.,
Íàñèáîâ À.Ñ., Øàïêèí Ï.Â. Ïîëó÷åíèå è îïòè÷åñêèå
ñâîéñòâà ìîíîêðèñòàëëîâ ZnSe, ëåãèðîâàííûõ êîáàëüòîì
//ÔÒÏ. — 2006. — Ò.40, ¹.7. — Ñ. 815-818.
6. Õìåëåíêî Î.Â., Îìåëü÷åíêî Ñ.À Âëèÿíèå ïëàñòè÷åñêîé
63

64
äåôîðìàöèè íà çàðÿäîâîå ñîñòîÿíèå èîíîâ Mn 2+ â êðèñòàëëàõ
ZnSe // Âåñòíèê Äíåïðîïåòðîâñêîãî óíèâåðñèòåòà.
— 2008. — ¹15.
7. Áóëàíûé Ì.Ô., Êîâàëåíêî À.Â., Ïîëåæàåâ Á.À. Ýëåêòðîëþìèíåñöåíòíûå
èñòî÷íèêè ñâåòà íà îñíîâå ìîíîêðèñòàëëîâ
ZnSe:Mn ñ îïòèìàëüíûìè ÿðêîñòíûìè
UDÑ 621.315.592
Yu. F. Vaksman, Yu. A. Nitsuk, V. V. Yatsun, Yu. N. Purtov, A. S. Nasibov, P. V. Shapkin
OPTICAL PROPERTIES OF ZnSe:Mn CRYSTALS
õàðàêòåðèñòèêàìè // ÆÒÔ. — 2003. — Ò.73, ¹.2. —
Ñ. 133-135.
8. Âàêñìàí Þ.Ô., Ïàâëîâ Â.Â., Íèöóê Þ.À., Ïóðòîâ Þ.Í.
Îïòè÷åñêèå ñâîéñòâà êðèñòàëëîâ ZnSe, ëåãèðîâàííûõ
ïåðåõîäíûìè ýëåìåíòàìè // ³ñíèê Îäåñüêîãî íàö. óíòó.
— 2006. — Ò.11, âèï. 7. — Ô³çèêà. — Ñ. 47-53.
Abstract
ZnSe single crystals with diffusion doping of Mn have been investigated. Absorption, luminescence and photoconductivity of ZnSe:
Mn crystals have been studied and analyzed in the visible region of the spectrum. Concentration of Mn impurity was estimated from
absorption edge. The electron transition scheme in ZnSe:Mn was proposed.
Key words: diffusion doping, optical-density, photoluminescence, photoconductivity, intracenter transition.
ÓÄÊ 621.315.592
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ÎÏÒÈ×ÅÑÊÈÅ ÑÂÎÉÑÒÂÀ ÊÐÈÑÒÀËËΠZnSe:Mn
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ÎÏÒÈ×Ͳ ÂËÀÑÒÈÂÎÑÒ² ÊÐÈÑÒÀ˲ ZnSe:Mn
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UDÑ 539.19+539.182
A. V. GLUSHKOV
Odessa State University, Odessa
QUASIPARTICLE ENERGY FUNCTIONAL FOR FINITE TEMPERATURES
AND EFFECTIVE BOSE-CONDENSATE DYNAMICS: THEORY AND SOME
ILLUSTRATIONS
INTRODUCTION
At present time a density functional theory became
by a powerful tool in studying the electron structure of
different materials, including atomic and molecular
systems, solids, semiconductors etc. [1-16]. A construction
of the correct energy functionals of a density
for multi-body systems represents very actual and
important problem of the modern theory of semiconductors
and solids, thermodynamics, statistical physics
(including a theory of non-equilibrium thermodynamical
processes), quantum mechanics and others.
In last time a development of formalism of the energy
density functional has been considered in many
papers (see [1–7]). Its application is indeed based on
the two known theorems by Hohenbreg-Kohn (τ = 0,
where τ is a temperature) and Mermin (τ ≠ 0) [1,2].
According to these theorems, an energy and thermodynamical
potential of the multi-body system are
universal density functionals. Though these theorems
predict an existence of such a density functional, however
its practical realization is connected with a number
of the significant difficulties (see [1-3,8-17]). The
problem is complicated under consideration of the
non-stationary tasks (the known theorem by Runge-
Gross about 1-1 mapping between time-dependent
densities and the external potentials [2]).
Let us remind some important results of the density
functional theory. It should be mentioned a constructive
approach to delivering optimal representations
for an exact density functional [1,2,8-16], which has
been used for generalization of the Hohenberg-Kohn
theorem in order to get an effective density functional
for large molecules. As alternative version one could
consider a quasiparticle density functional formalism
by Beznosjuk-Kryachko (see [1-3,8]). The latter develops
a quasiparticle conception of Kohn-Sham and
the Levi-Valone method [2,3]. In fact it has been done
an attempt practically to realize an idea of the Hohenberg-Kohn
theorem. More advanced analogous approach
with account of the multi-particle correlations
is developed in ref. [8,17,18]. It has been shown a fundamental
feature of the Weizsacker universal density
functional, which describes an energy of the effective
condensate of interacting bosons. In ref. [14] (see also
[8,19-21]) it has been firstly developed a QED theory
© A. V. Glushkov, 2009
It is considered a theory of the quasiparticle energy functional under non-zeroth temperatures τ
and some its applications. A thermodynamical potential for multielectron system in external stationary
field for given τ is defined by dynamics of effective Bose-condensate in atoms of the physical space
of electrons. Structure of this space is defined by the cell system of surfaces of zeroth flux for entropy
pulse under availability of the zeroth current of the Bose-condensate density.
of a density functional formalism and constructed an
optimized one-quasiparticle representation in a theory
of multi-electron systems. The lowest order multibody
effects, in particular, the gauge dependent radiative
contribution for the certain class of the photon
propagators calibration are treated in QED formulation
and new density functional integral-differential
equations are derived. The minimal value of the gauge
dependent radiative contribution is considered to be
the typical representative of the multi-electron correlation
effects, whose minimization is a reasonable
criteria in the searching for the optimal QED perturbation
theory one-electron basis.
New several schemes for application of the density
functional theory are based on using so called hybrid
functionals [9-13,15], which improve the description
of the optical absorption spectra and related properties
for solids, semiconductors etc. However, the principal
problems are remained. For example, one could
remind the limitations stemming from (semi) local
density approximation (LDA) functionals [2,15] (
A thermochemistry: up to 1 eV error; The structural
properties: 23% error; The elastic constants: 10% error;
great problems for the strongly correlated systems
(transition metal oxides); The Van der Waals bonding
missing; Band gap problem; Problem of description of
the electronic excitations, etc). There is a little more
situation in the Perdew-Burke-Ernzenhof (PBE0) and
Heyd-Scuseria- Ernzerhof (HSE0) hybrid schemes.
In particular, in the last scheme the lattice constants
and bulk modules are clearly improved for insulators
and semiconductors in comparison with the LDA and
even PBE0 schemes. The band gaps are excellent for
wide range of semiconductors, except for very large
gap systems. The transition metals are problematic,
at least in terms of the bulk modules. At last, the atomization
energies are not improved compared to the
PBE scheme. Sufficiently full review of the modern
state of art for the density functional theories and their
applications in theory of semiconductors is presented
in the recent report [15] (see also [9-13]).
Further, it is natural to note that a density functional
theory for the zeroth temperatures τ = 0 is developed
in a majority of the papers. At the same time,
similar theories for τ ≠ 0 have a whole number of the
significant problems [1-4]. It is self-understood that
65

their applications are not widely known. In ref. [8] it is
considered a theory of the quasiparticle energy functional
under non-zeroth temperatures τ and shown
that a thermodynamical potential for multielectron
system in external stationary field for given τ is defined
by dynamics of effective Bose-condensate in atoms of
the physical space of electrons. Below we will consider
an advanced version of this theory and give some its
illustrations regarding the molecular structure mapping,
a theory of semiconductors in a laser field etc.
66
2. A QUASIPARTICLE DENSITY
FUNCTIONAL THEORY
A formalism of the energy density functional theory
for non-zeroth temperatures, developed below (see
also [8]), is based on the two fundamental results [1].
In a large canonical ensemble under given temperature
a density distribution ï( r ) directly defines a value
of V( r ) — μ (here μ is a chemical potential). For given
V( r ) and μ it is existed a functional of ï( r ):
r r r 3 r
Ω V −μ ⎡⎣n′ () r ⎤⎦
= ∫(
V() r −μ ) n′ () r d r+ F( n′ () r ) , (1)
which reaches an absolute minimum, when a density
ï′( r ) is a regular density ï( r ) ~ V( r ). A value
of Ω is in minimum equal to a thermodynamical
V-μ
potential; F is an universal density functional, which
represents an internal energy of a system and is dependent
upon τ. A distribution ï( r ) is searched as a
solution of the fundamental equation (naturally under
corresponding boundary conditions) of the following
type:
N r
δF⎡ ⎣n () r ⎤
⎦ r
V N r + () r =μ.
(2)
δn
() r
An universal functional of the electrons (fermions)
is described for a given temperature τ as follows [8]:
r ⎛ 1 ⎞
FF⎡⎣n′ () r ⎤⎦ = Spρ ′ ⎜T + U − ln ρ ′ ⎟=
⎝ β ⎠
r r r
= U ⎡⎣n′ () r ⎤⎦+Δ S⎡⎣n′ () r ⎤⎦+ G⎡⎣n′ () r ⎤⎦,
r r r
G⎡⎣n′ () r ⎤⎦ = T ⎡⎣n′ () r ⎤⎦+τS⎡⎣n′ () r ⎤⎦,
(3)
where β = (k τ) B -1 , ρ′ is a large canonical operator of
a matrice of density; G is a free Helmholtz energy of
the non-interacting electrons, S is an entropy, ΔS is
an effective energy of correlation; TU , are the operators
of the kinetical energy and energy of the Coulomb
interaction:
2 N e 1
U = ∑ r r ,
2 i, j= 1(
ri − rj)
N
N — represented density nF() r is created by a set of
N N N N
the fermionic wave functions { nF ←Ψ F }; F0F n ⎡ ⎤ Ψ ⎣ ⎦
realizes a minimal mathematical expectation of inter-
N
nal energy of the electrons for the fixed density nF() r .
Let us turn attention on the following important circumstance:
ρ′ in the equation (3) is an operator of a
density of the interacting particles system and it does
not reduced to anti-symmetrized multiplying the den-
sity matrices. That’s why an entropy in (3) differs from
an ideal gas entropy. There is an effective energy of
correlation ΔS besides the Coulomb energy U in the
cited formulae.
Generalizing above noted results, we define the
universal energy density functionals of the effective interacting
and non-interacting bosons, every of which
has a mass and a charge of electrons (in the second
case only a mass) [4]:
N N N N
F ⎡ b ⎣n ⎤ b ⎦ = G⎡ ⎣n ⎤ b ⎦+ U ⎡
⎣n ⎤ b ⎦+ΔS⎡ ⎣n ⎤ b ⎦ , (4)
N N
F ⎡ b0⎣n ⎤ b ⎦ = G⎡ ⎣n ⎤ b ⎦ , (5)
Here N — represented density of bosons N
n b is cre-
N N
ated by a set of N — boson wave functions b b n Ψ → ;
N N
b 0 b n ⎡ ⎤ Ψ ⎣ ⎦ and N N
b 0’
b n ⎡ ⎤ Ψ ⎣ ⎦ are the wave functions of the
interacting and non-interacting bosons correspondingly,
which realize a minimal mathematical expectation
of the internal energy of bosons for the fixed density
N
n b ( r ). The conditions of the N — representation
for a matrice of density of the first order for fermions
and bosons are reduced to the expansion conditions
as follows:
Φ 1 r 2
F ()
N r ηα Ψα r ηα
1
nF() r = N∑
,0≤
≤ , (6)
β( εα−μ) β( εα−μ) α 1+ e 1+
e N
b 1 r 2
b ()
N r ηα Ψα r ηα
nb() r = N∑
,0≤ ≤1,
(7)
βε ( α−μ) βε ( α−μ)
α 1+ e 1+
e
Naturally, a set of the fermionic densities
is contained in a set of the bosonic densities
N r N r
{ nF () r } ⊂{
nb () r } in the ideal gas approximation.
Further a class of the N — represented fermionic
densities for system of N — electrons is considered.
A thermodynamical potential can be written as follows:
NF N N r N r
Ω ( ) = G ⎡ b n ⎤ i + V( ⎡n ⎤ i , r iV ) ni () r dω
−μ ⎣ ⎦ ∫ ⎣ ⎦
. (8)
ω
A potential of the external effective field of the
interacting bosons system is defined by the following
auxiliary universal density functionals:
N r r N r
V( ⎡
⎣n ⎤
⎦, r) = V() r −μ+ VH( ⎡
⎣n ⎤
⎦,
r)
, (9)
∫
ω
r r
( , ) ()
N N N N
V ⎡ H ⎣n ⎤
⎦ r n r dω= H ⎡ b ⎣n ⎤
⎦+ H ⎡ bF ⎣n ⎤
⎦,
(10)
N N N
H ⎡ b ⎣n ⎤
⎦ = F ⎡ b ⎣n ⎤
⎦−G ⎡ b ⎣n ⎤
⎦ ,
N N N
H ⎡ bF ⎣n ⎤
⎦ = F ⎡ F ⎣n ⎤
⎦−F ⎡ b ⎣n ⎤
⎦ ,
N
where H ⎡ b ⎣n ⎤
⎦ is an energy of correlation of the N
N
interacting bosons, H ⎡ bF ⎣n ⎤
⎦ is a correction to an energy
of correlation of the bosons, accounting for the
Pauli principle.
The wave function of the inhomogeneous Bosecondensate
is as follows:
N
N r r i D N r
( ⎡n ⎤; r, , r ) exp S ( ⎡n ⎤,
r)
Ψ bђ0H⎣ ⎦i1 K N =
⎧
⎨∑ ⎩ i=
1 h
b ⎣ ⎦
⎫
⎬.
⎭
Here:

N r
D N r ih ⎛n () r ⎞ i
Sbђ( ⎡
⎣n ⎤
⎦, ir)
= S⎜
⎟
2 ⎜ N ⎟
⎝ ⎠
is a generalized action function, which is proportional
to the specific entropy of “i” boson, where it is right
the following definition S(n) = -lnn.
Starting from D
S bђ , it is easy to define a functional
of a pulse of the entropy for “i“ boson as follows:
r N r r D N r
PEђ( ⎣
⎡n ⎦
⎤, ri i ) = Im { ∇rSb
( ⎡
⎣n ⎤
⎦,
r)
} ,
which is directly connected with the Heisenberg principle
of indefiniteness.
A mathematical expectation of operator of the ki-
N N
netical energy on the wave functions b 0’
n ⎡ ⎤ Ψ ⎣ ⎦ is defined
as follows:
r r r
T n = P n r n r mdω
=
( ) ()
M
N 2 N N
⎡ b ⎣
⎤
⎦ ∑∫ ⎡ E ⎣
⎤
⎦,
/2 j
j=
1
r r r
= h m ∇ n r n r dω
M
2
N N
∑∫ ( /8 ) ⎡
⎣ () ⎤
⎦
/ ()
j=
1
r j
N
( ⎡
⎣
⎤
⎦ ) () ∑ { rђ b(
⎡
⎣
⎤
⎦j
) }
r
i=
1
(11)
when the following condition r of the zeroth flux for a
N r
pulse of the entropy PE( ⎡
⎣n ⎤
⎦r)
:
r N r r r
P ( ⎡ E ⎣n ⎤
⎦r)
⋅ lЈ() r = 0, j = 1, K , M . (12)
j
r∈Ј
j
is fulfilled Mon
the boundaries {£} of M atoms (the relationship
∑ ω j =ω is fulfilled for volumes ω ).A math-
j
ematical expectation j= 1 of the Bose-condensate density
current is as follows:
N N N D N
j n , r = n r Re ∇ S n , r = 0
r r r r
.
The conditions (12), i.e. the conditions of the zeroth
flux for a pulse of entropy of distribution for the
Bose-condensate density define in fact the surfaces,
the cell system of which defines an atomic structure
of the physical space of electrons under availability of
zeroth current of a density. Taking into account of the
equations (2), (8)–(12) it is clear that the electrons
system states in an external scalar field V( r ) fro given
temperature τ are defined by the iterative solution of
the following system of the differential equations for
each r ∈ ω [4]: j
r 2
2 2 N r
h r N r h ⎡∇r r n () r ⎤
∇ r
n () r + ⎢ N r ⎥ −
4m 8m⎢⎣
n () r ⎥⎦
N
δS⎡ ⎣n ⎤
⎦ r
−τ + V() r = μ,
N r
%
(13)
δn
() r
N r
δV ( ⎡ H n ⎤,
r)
N N
V% r r r ⎣ ⎦ r
() r = V() r + VH( ⎡
⎣n ⎤
⎦, r) +
n N r () r , (14)
δn
() r
r N r r
∇r r n () r ⋅ l r
J 0
j r∈J = . (15)
j
Here the functional Ò [n b N ] is the well known Weizsacker
correction [1] that is a fundamental part of the
universal density functional for particles of quantum
statistics. The obtained system of the functional
equations (13)–(15) is transferred to the analogous
Beznosjuk system under τ → 0. Further if the multibody
correlations corrections (an effect of energy
dependence of the interparticle interaction, the continuum
pressure etc.) are taken into account in an energy
of interaction between particles, then the system
(13)–(15) coincides with the corresponding equations
system from ref. [8].
Thus, from all consideration it is followed that a
thermodynamical potential for multielectron system
in an external local scalar stationary field V( r r ) for a
given temperature τ is defined by a dynamics of the effective
N-particle Bose-condensate in semi-spaces —
atoms of the physical space of the electrons system.
An atomic structure of the physical space of electrons
is defined by the cell system of surfaces of zeroth flux
for entropy pulse (condition (12)) under availability
of the zeroth current of the Bose-condensate density.
Probably, the same results can be received within the
Lagrange density functional theory [17,18], which is
based on the Green’s functions method. In fact speech
is about using equations for the Matzubarian Green’s
functions.
3. SOME ILLUSTRATIONS OF THEORY AND
CONCLUSION
It is obvious that there is a whole set of the different
applications of the developed formalism. As
an obvious perspective application of the presented
theory else it should be mentioned a quantum geometry
and hadrodynamics [21-23]. As a natural application
of the theory one could indicate a description
of the Bader lodges [3,24,25]. Really, the conditions
(15) are equivalent to the Bader conditions for topological
breaking of the physical space of electrons on
atoms. So, all structural constructions, developed in
this theory, are true in the presented density functional
formalism under non-zeroth temperature.
Such constructions can be manifested in an excitation
dynamics of the semiconductors by a short
(femto-second diapason) laser pulse within the description
by non-equilibrium Green’s function too
[26,27]. It is interesting to note that all theoretical results
(fundamental final formula) of the Bonits method
are reproduced in two new approaches: i). the Ullrich-Erhard-Gross
version of the density functional
approach to multi-electron systems in a laser field [28]
and ii).S-matrix Gell-Mann and Low QED approach
to atomic systems in a laser field, developed in refs.
[29-31]. However the authors of the last cited papers
did not carry out the calculation for semiconductors
in a laser filed.
The next illustration of the theory application
may be as follows. The well known phenomenon of
the Benar’s cells convection in a thermodynamics (a
property of structurization by a net of the hexahedrons
for the non-perturbed atmosphere in a position of the
blocking high pressure crest) can be in the known essence
indicated into correspondence to above mentioned
topological breaking of the physical space of
electrons on atoms [32-37]. The region of a crest is
covered by a grid of the hexahedrons as some fractal of
the density tightening for a barical surface to minimal
one when decreasing of the air density in the clouds
region is treated as the tightening hedrons of a fractal
due to the movement to equilibrium on density. On
67

the mathematical language an operation of covering
the Benar convection region by a net of the hexahedrons
is fulfilled by a conform transformation of the
indicated region on series of multi-angles by means of
the Christoffel-Schwarz integral [32].
The above cited topological breaking the physical
space of electrons on atoms can be taken into accordance
recently discovered [38] (see also [39]) phenomenon
of the cells structurization in the hypothetical
π-electron nano-organic superconducting analog
system , which imitates the “human brain” on the
basis of the computer simulation with using effective
polarization interaction potentials in the π-electron
system of organic supermolecules.
At present time a great attention is turned to a development
of the advanced methods of the numerical
statistical Monte-Carlo modeling for many-body systems
[40] (see also [41]). The known success is reached
in the Monte-Carlo modeling the Bose-systems, where
a great number of the useful results is received. At the
same time, this approach for the Fermi-systems deals
with the well known problems (excluding the electron
gas). This circumstance is connected with the fact that
the trial function must be anty-symmetrized one and
a calculation of the determinants in the trial function
is very slow and complicated procedure. Using the
above constructed boson density functional for multielectron
systems allows in principle to overcome this
problem in the significant manner. Naturally, here it
is required a correct definition of the correction Í in bF
equation (10), which takes into account a difference
between the Bose and Fermi-systems.
Acknowledgement. Author would like to thank
Prof. W. Kohn, L.Sham, E. Gross, I. Kaplan, C. Roothaan,
Yu.Lozovik , A.Theophilou, S. Wilson, for useful
discussions. Besides, author would like to thank
Prof. M.Bonits for providing results of the Green’s
functions method calculation for a laser field excitation
dynamics of a semiconductor.
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35. Ðóçîâ Â.ä., Ãëóøêîâ À.â., Âàñ÷åíêî Â.í., Àñòðîôèçè÷åñêàÿ
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UDÑ 539.19+539.182
A. V. Glushkov
model of Earth global climate// Bound Vol. of Observatorie
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amines. Laser and neutron capture effects// Theory and Applications
of Computational Chemistry 2009. — Vol.1102. —
P.131-150.
QUASIPARTICLE ENERGY FUNCTIONAL FOR FINITE TEMPERATURES AND EFFECTIVE BOSE-CONDENSATE
DYNAMICS: THEORY AND SOME ILLUSTRATIONS
Abstract
It is considered a theory of the quasiparticle energy functional under non-zeroth temperatures τ and some its applications. A thermodynamical
potential for multielectron system in external stationary field for given τ is defined by dynamics of effective Bose-condensate
in atoms of physical space of electrons. Structure of this space is defined by the cell system of surfaces of zeroth flux for entropy pulse
under availability of the zeroth current of the bose-condensate density.
Key words: density functional, effective Bose-condensate, atoms of physical space of electrons.
ÓÄÊ 539.19+539.182
À. Â. Ãëóøêîâ
ÊÂÀÇÈ×ÀÑÒÈ×ÍÛÉ ÝÍÅÐÃÅÒÈ×ÅÑÊÈÉ ÔÓÍÊÖÈÎÍÀË ÏÐÈ ÊÎÍÅ×ÍÛÕ ÒÅÌÏÅÐÀÒÓÐÀÕ È ÄÈÍÀÌÈÊÀ
ÝÔÔÅÊÒÈÂÍÎÃÎ ÁÎÇÅ-ÊÎÍÄÅÍÑÀÒÀ: ÒÅÎÐÈß È ÍÅÊÎÒÎÐÛÅ ÈËËÞÑÒÐÀÖÈÈ
Ðåçþìå
Ðàññìîòðåíû òåîðèÿ êâàçè÷àñòè÷íîãî ýíåðãåòè÷åñêîãî ôóíêöèîíàëà ïðè íåíóëåâîé òåìïåðàòóðå τ è å¸ íåêîòîðûå
èëëþñòðàöèè. Òåðìîäèíàìè÷åñêèé ïîòåíöèàë ìíîãî-ýëåêòðîííîé ñèñòåìû âî âíåøíåì ñòàöèîíàðíîì ïîëå äëÿ äàííîé τ
îïðåäåëÿåòñÿ äèíàìèêîé ýôôåêòèâíîãî ìíîãî÷àñòè÷íîãî áîçå-êîíäåíñàòà â àòîìàõ ôèçè÷åñêîãî ïðîñòðàíñòâà ýëåêòðîíîâ.
Ñòðóêòóðà èñêîìîãî ïðîñòðàíñòâà îïðåäåëÿåòñÿ ÿ÷åèñòîé ñèñòåìîé ïîâåðõíîñòåé íóëåâîãî ïîòîêà èìïóëüñà ýíòðîïèè ïðè
íàëè÷èè íóëåâîãî òîêà ïëîòíîñòè áîçå-êîíäåíñàòà.
Êëþ÷åâûå ñëîâà: ôóíêöèîíàë ïëîòíîñòè, ýôôåêòèâíûé áîçå-êîíäåíñàò, àòîìû ôèçè÷åñêîãî ïðîñòðàíñòâà ýëåêòðîíîâ.
ÓÄÊ 539.19+539.182
Î. Â. Ãëóøêîâ
ÊÂÀDz×ÀÑÒÈÍÊÎÂÈÉ ÅÍÅÐÃÅÒÈ×ÍÈÉ ÔÓÍÊÖ²ÎÍÀË ÏÐÈ ÑʲÍ×ÅÍÈÕ ÒÅÌÏÅÐÀÒÓÐÀÕ ² ÄÈÍÀ̲ÊÀ
ÅÔÅÊÒÈÂÍÎÃÎ ÁÎÇÅ-ÊÎÍÄÅÍÑÀÒÓ: ÒÅÎÐ²ß ² ÄÅßʲ ²ËÞÑÒÐÀÖ²¯
Ðåçþìå
Ðîçãëÿíóòî òåîð³þ êâàç³-÷àñòèíêîâîãî åíåðãåòè÷íîãî ôóíêö³îíàëó ïðè íåíóëüîâ³é òåìïåðàòóð³ τ òà äåÿê³ ³¿ ³ëþñòðàö³¿.
Òåðìîäèíàì³÷íèé ïîòåíö³àë áàãàòîåëåêòðîííî¿ ñèñòåìè ó çîâí³øíüîìó ñòàö³îíàðíîìó ïîë³ äëÿ äàíî¿ τ âèçíà÷àºòüñÿ
äèíàì³êîþ åôåêòèâíîãî áàãàòî÷àñòèíêîâîãî áîçå-êîíäåíñàòó â àòîìàõ ô³çè÷íîãî ïðîñòîðó åëåêòðîí³â. Ñòðóêòóðà òàêîãî
ïðîñòîðó âèçíà÷àºòüñÿ êîì³ðêîâîþ ñèñòåìîþ ïîâåðõîíü íóëüîâîãî ïîòîêó ³ìïóëüñó åíòðîﳿ ïðè íàÿâíîñò³ íóëüîâîãî òîêó
ãóñòèíè áîçå-êîíäåíñàòó.
Êëþ÷îâ³ ñëîâà: ôóíêö³îíàë ãóñòèíè, åôåêòèâíèé áîçå-êîíäåíñàò, àòîìè ô³çè÷íîãî ïðîñòîðó åëåêòðîí³â.
69

70
UDC 74.78.
R. M. BALABAY, P. V. MERZLIKIN
Krivoi Rog State Pedagogical University, Department of Physics, Krivoi Rog, Ukraine,
phone:(0564)715721, e-mail: oks_pol@cabletv.dp.ua.
ELECTRONIC STRUCTURE OF HETEROGENEOUS COMPOSITE: ORGANIC
MOLECULE ON SILICON THIN FILM SURFACE
Atomic composites such as molecule on silicon film substrate are interesting for molecular electronics
and other applications. Therefore, the better understanding of mechanisms of interactions
inside such systems is important. The space distribution of the valence electron density was calculated
using Car-Parrinello molecular dynamic and ab initio norm-conserving pseudopotential. CH 4 N 2 O
and CONH 5 molecules on silicon thin film (100) surface were examined.
INTRODUCTION
Nanoscience performs fundamental investigations
of properties of nanomaterials and phenomena
which appear in nanomaterials. Within the list of nanoobjects,
the objects with lowered dimensionality are
stood out. They are: quasi-2D electron gas (quantum
wells), quasi-1D electron gas (quantum wires) and
quasi-0D electron gas (quantum dots) [1]. Quantum
wires are not observed spontaneously in nature and
must be produced in a laboratory. Quantum wires
could be created with the use of the semiconductor
heterostructures [2] or through other way (for example
with use of heterogeneous composition: organic molecule
on silicon film surface).
Atomic composites such as molecule on silicon
film substrate are of great interest for a wide range
of technological applications. For the latter, organic
molecules are used to modify the electronic properties
of metal and semiconductor surfaces.
During the last few years there has been noticed
the growth of interest from molecular electronics side
stimulated largely by the experimental realization of
molecular wires and systems where a single organic
molecule or a few molecules carry an electric current
between a pair of metal contacts [3, 4]. In some cases,
such systems exhibit switching behavior and/or negative
differential resistance [5, 6] phenomena that may
be exploited in future molecular electronic devices.
Hybride molecular/semiconductor nano-electronic
devices are another intriguing possibility and fundamental
research that may ultimately lead to their creation
is also being pursued at the present time [7, 8,
9, 10].
SCOPE OF THE WORK
The task of our research is the exploration of the
possibility of forming of quantum wires in heterogeneous
composites: organic molecule on silicon film
and the topology of 1D electron gas channel created.
The better understanding of mechanisms of interactions
inside such systems is important for practical applications.
One of the fundamental problems of semiconductor
nanotechnology is the electron distribution
and the electron move type in complicated geometry
structures. It is very difficult to realize the experimental
solution of this problem. Therefore, the ab initio
calculation methods which not require experimental
data are applicable the best.
One of such methods is the electron density functional
theory. The central place in this theory is occupied
by self-consistent charge density which completely
determines the system’s ground state. Besides
presenting the information about the total energy,
forces and stresses, the charge density is interesting itself
and could often provide the illuminating insights
which help to understand the physical properties of
the solid. It opens a “window” for viewing the chemical
bonds, it allows one to judge the nature of interatomic
forces as well as to find the plausible interstitial
positions. Therefore, the numerical ab initio calculation
is required for detection particulars of forming
of quantum wires in heterogeneous composition: organic
molecule on silicon film. For this purpose, the
Car-Parrinello molecular dynamic [11] and ab initio
norm-conserving pseudopotential [12] realized within
special software [13] were used.
METHOD OF CALCULATION
The Car-Parrinello method (CP method) is based
on density-functional theory (DFT) and the Born-
Oppenheimer (OB) adiabatic approximation. For
conventional DFT electronic structure calculations,
the Kohn-Sham (KS) equations are solved self-consistently.
In the BO approximation, wave function
are r considered
r r as the functions of ionic positions
{}:{ Rl ψi(
r; Rl)}
, but in the CP method, the { i ( ) } r
ψ
are treated as classical dynamical variables independent
on { Rl} r
. They are postulated to evolve by Newton’s
equations of motion so that “dynamical simulated
annealing” could be performed to search a global
minimum of the electronic configuration.
The Lagrangian in the CP method is introduced as
r r
r 2 r 1
r
2
L{ ψψ , &, R, R&, } =μ∑∫ψ & i( r) dr + ∑MlR&
l −
i 2 l
r
, (1)
r * r r
E[{ ψ ( r)},{ R}] + ε ψ ( r) ψ ( r) dr−δ
∑∑ ∫
( )
l l ij i j ij
i j
© R. M. Balabay, P. V. Merzlikin, 2009

where { ψ i}
are the single-electron orbitals, and the
electronic density pr ( )
r is assumed to be given by
r
pr ( ) =
r 2
ψ ( r)
. (2)
∑
i
The first term of Eq. (1) is a fictitious classical mechanical
kinetic energy of { ψ i}
. The second term is
an ionic kinetic energy, and E is the total energy (the
sum of the electronic energy and the ion-ion Coulomb
interaction energy). Lagrangian multipliers ε ij are introduced
to satisfy the orthonormality constraints on
{ ψ i}
. The details of the electronic energy are described
in a lot of literature in the field.
From Eq. (2), equations of motion for i ψ and l Rr
are derived as
r δE
r
μψ i( r) = − ( )
* r + ∑ε
ijψj r (3)
δψi
( r ) j
r
MR&& l l =−∇lE
(4)
If an electronic structure reaches the state where
no force acts on ψ i , that is, the left-hand side of Eq.
(3) is equal to zero and this equation is identical to
the KS equation and ψ i becomes the eigenstate of
the KS equation. To attain this, the kinetic energy of
{ ψ i}
is gradually reduced until { ψ i}
are frozen. This
procedure is called “dynamical simulated annealing.”
If one also relaxes the ions with Eq. (4), the minimization
with respect to electronic and ionic configurations
could be executed simultaneously.
It is also possible to evolve { R i}
and { ψ i}
without
reducing the kinetic energy. If { ψ i}
are kept close
to eigenstates during the time evolution, ionic trajectories
generated by Eq. (4) are physically meaningful.
When the CP method is applied to study the
dynamical evolution of a system consisting of ions
and electrons, it is called the “ab initio molecular dynamics.”
THE CALCULATION RESULTS AND
DISCUSSION
Worked calculations allow to obtain the information
on the details of electronic construction of some
organic molecules (Fig.1 — Fig.2) and on the charges’
redistribution in heterogeneous system: adsorbed organic
molecule on silicon thin film (100) surface with
4 Å thickness (Fig.3 — Fig.4).
The density space partial distributions of valence
electrons (taking into account only valence electrons)
is determined by the theory of pseudopotential and
by the fact that only the valence electrons undergo
catastrophic changes under interactions for different
iso-values, allow to determine the levels of hierarchy
of connection between atoms in molecule CH 4 N 2 O
(Fig.1), CONH 5 (Fig.2).
As seen from Fig. 1 flat CH 4 N 2 O molecule has
three weakly connected parts: CO, NH 2 , NH2, which
contain most of electronic density of molecule. An
absence of distinctly expressed spherical contour in
distribution points leads to the absence of ionic and
the presence of covalence polar (strong) and van der
Waal’s (weak) types of the bounds.
i
Fig. 1. Density space partial distributions of valence electrons
in CH4N2O molecule for iso-values: (a) 0.8-0.9 from maximal
value, (b) 0.7-0.8 from maximal value, (c) 0.6-0.7 from maximal
value, (d) 0.5-0.6 from maximal value, (e) cross section in molecule
plane.
71

Fig. 2. Density space partial distributions of valence electrons in CONH 5 molecule for iso-values: (a) 0.9-1.0 from maximal value
(b) 0.8-0.9 from maximal value, (c) 0.7-0.8 from maximal value, (d) 0.6-0.7 from maximal value, (e) 0.5-0.6 from maximal value, (f)
0.4-0.5 from maximal value, (g) 0.3-0.4 from maximal value(look-out over the two inversely situated molecules in primitive cell), (h)
cross section of molecule in vicinity of O atom.
A review of the density partial distributions of
valence electrons in CONH 5 molecule for different
iso-values allows to divide the two fragments in the
molecule: ÑH 3 and NOH 2 . A part of electronic density
inside these fragments is more than one in area
between them what could be seen in cross section of
molecule in the vicinity of O atom (Fig. 2(h)).
For creation of the heterogeneous composite, the
molecules are situated on distance of 1 Å from the film
surface and 10.86 Å from each other. The film thickness
is 4 Å. On both surfaces of film, the two molecules
are situated with inversion symmetry in respect
to atomic system’s center of symmetry (Fig. 3(a)).
The calculation algorithm means the use of periodic
space lattice with atomic basis (it reflects the features
of the investigating system) which certainly ought to
have the inverse symmetry. The atomic basis of the
primitive cubic unit cell of the superlattice which rep-
72
resents thin silicon film with two (100) surfaces with
CH 4 N 2 O or CONH 5 molecule on each side of film
and consisted of 48 atoms (32 of them are Si atoms
and 16 atoms of two molecules). In such a way, there is
the space-periodic system of molecules on silicon film
surface. Maps of density of valence electrons, shown
on Fig.3-4, demonstrate the interaction between electrons
of thin silicon film and the molecules considered
above. The analysis of these distributions allows to
segregate the two types of electronic system realignment:
one concerned with reaction of molecules with
surface and other concerned with molecules’ influence
of the formation of the new quantum objects in
silicon film: i.e. the electronic wires. More distinct
space realignment of electrons with quantum wires
(with thickness about 1 Å) formation is observed under
flat molecule CH 4 N 2 O more clear than under the
non- flat CONH 5 .

Fig. 3. Density space partial distributions of valence electrons in heterogeneous composition: two inversely situated symmetric molecules
CH 4 N 2 O on (100) silicon surface for iso-values: (a) 0.9-1.0 from maximal value, (b) (110) cross section of primitive cell.
Fig. 4. Density space partial distributions of valence electrons in heterogeneous composition: two inversely situated symmetric
molecules CONH 5 on (100) silicon surface for iso-values: (a) 0.8-0.9 from maximal value, (b) 0.7-0.8 from maximal value, (c) 0.6-0.7
from maximal value, (d) 0.5-0.6 from maximal value, (e) 0.4-0.5 from maximal value, (f) 0.3-0.4 from maximal value, (g) (110) cross
section of primitive cell.
73

74
CONCLUSIONS
1. The analysis of valence electrons’ density allows
to affirm the creation of space-periodic arrays of
quantum wires in silicon film obtained by periodic deposition
flat organic molecules onto film surface, for
instance the CH N O molecule.
4 2
2. Precise deposition of the flat molecules onto
the surface is quite realistic considering the modern
technologies and these composites will play the role
of the gate under which the conductive 1D dimension
channel is formed.
3. The atomic heterogeneous composite could be
used to develop the next generation of computing devices
with switching mechanisms of signal amplification.
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äåðæàâíîãî óí³âåðñèòåòó. — Ëóãàíñüê. — 1998. —
ñ.124-128.
ELECTRONIC STRUCTURE OF HETEROGENEOUS COMPOSITE: ORGANIC MOLECULE ON SILICON THIN FILM
SURFACE
Abstract
Atomic composites such as molecule on silicon film substrate are interesting for molecular electronics and other applications.
Therefore the better understanding of mechanisms of interactions inside such systems is important. Space distribution of the valence
electron density was calculated using Car-Parrinello molecular dynamic and ab initio norm-conserving pseudopotential. CH 4 N 2 O and
CONH 5 molecules on silicon thin film (100) surface were examined.
Key words: heterogeneous composite, electronic structure, film surface.
ÓÄÊ 74.78 73.21
Ð. Ì. Áàëàáàé, Ï. Â. Ìåðçëèêèí
ÝËÅÊÒÐÎÍÍÀß ÑÒÐÓÊÒÓÐÀ ÃÅÒÅÐÎÃÅÍÍÎÉ ÊÎÌÏÎÇÈÖÈÈ: ÎÐÃÀÍÈ×ÅÑÊÈÅ ÌÎËÅÊÓËÛ ÍÀ
ÏÎÂÅÐÕÍÎÑÒÈ ÒÎÍÊÎÉ ÏËÅÍÊÈ ÊÐÅÌÍÈß
Ðåçþìå
Èçó÷àåòñÿ âîçìîæíîñòü ôîðìèðîâàíèÿ êâàíòîâûõ íèòåé â ãåòåðîãåííîé êîìïîçèöèè: îðãàíè÷åñêèå ìîëåêóëû íà ïîâåðõíîñòè
òîíêîé ïëåíêè êðåìíèÿ.
Èíôîðìàöèþ î ôèçè÷åñêèõ ñâîéñòâàõ òàêèõ ñèñòåì ìîæíî èçâëå÷ü èç ðàñïðåäåëåíèÿ ýëåêòðîííîé ïëîòíîñòè. Äëÿ ðàñ-
÷åòà òàêîãî ðàñïðåäåëåíèÿ èñïîëüçîâàëàñü êâàíòîâî-ìåõàíè÷åñêàÿ ìîëåêóëÿðíàÿ äèíàìèêà Êàð-Ïàðèíåëëî (Car-Parrinello).
Ðàñ÷åò ïðîâîäèëñÿ äëÿ ìîëåêóë CH 4 N 2 O è CONH 5 íà ïîâåðõíîñòè Si(100).
Àíàëèç ðàñïðåäåëåíèé ýëåêòðîííîé ïëîòíîñòè ïîçâîëÿåò ãîâîðèòü î ïîëó÷åíèè ïðîñòðàíñòâåííî ïåðèîäè÷åñêèõ ìàññèâîâ
êâàíòîâûõ íèòåé â êðåìíèåâîé ïëåíêå ïðè ïåðèîäè÷åñêîì íàíåñåíèè íà ïîâåðõíîñòü ïëåíêè ïëîñêèõ îðãàíè÷åñêèõ
ìîëåêóë, íàïðèìåð CH 4 N 2 O.
Êëþ÷åâûå ñëîâà: ãåòåðîãåííàÿ êîìïîçèöèèÿ, îðãàíè÷åñêèå ìîëåêóëû ïîâåðõíîñòü ïëåíêè.

ÓÄÊ 74.78 73.21
Ð. Ì. Áàëàáàé, Ï. Â. Ìåðçëèê³í
ÅËÅÊÒÐÎÍÍÀ ÑÒÐÓÊÒÓÐÀ ÃÅÒÅÐÎÃÅÍÍί ÊÎÌÏÎÇÈÖ²¯: ÎÐÃÀͲ×Ͳ ÌÎËÅÊÓËÈ ÍÀ ÏÎÂÅÐÕͲ ÒÎÍÊί
Ï˲ÂÊÈ ÊÐÅÌͲÞ
Ðåçþìå
Âèâ÷àºòüñÿ ìîæëèâ³ñòü ôîðìóâàííÿ êâàíòîâèõ äðîò³â â ãåòåðîãåíí³é êîìïîçèö³¿: îðãàí³÷í³ ìîëåêóëè íà ïîâåðõí³ òîíêî¿
ïë³âêè êðåìí³þ.
²íôîðìàö³þ ïðî ô³çè÷í³ âëàñòèâîñò³ òàêèõ ñèñòåì ìîæíà îòðèìàòè ç ðîçïîä³ëó åëåêòðîííî¿ ãóñòèíè. Äëÿ ðîçðàõóíêó
òàêîãî ðîçïîä³ëó âèêîðèñòîâóâàëàñü êâàíòîâî-ìåõàí³÷íà ìîëåêóëÿðíà äèíàì³êà Êàð-Ïàð³íåëëî (Car-Parrinello). Ðîçðàõóíîê
ïðîâîäèâñÿ äëÿ ìîëåêóë CH 4 N 2 O òà CONH 5 íà ïîâåðõí³ Si(100).
Àíàë³ç ðîçïîä³ë³â åëåêòðîííî¿ ãóñòèíè äîçâîëÿº ãîâîðèòè ïðî îòðèìàííÿ ïðîñòîðîâî ïåð³îäè÷íèõ ìàñèâ³â êâàíòîâèõ íèòîê
â êðåìí³ºâ³é ïë³âö³ ïðè ïåð³îäè÷íîìó íàíåñåíí³ íà ïîâåðõíþ ïë³âêè ïëîñêèõ îðãàí³÷íèõ ìîëåêóë, íàïðèêëàä CH 4 N 2 O.
Êëþ÷îâ³ ñëîâà: ãåòåðîãåííà êîìïîçèö³ÿ, îðãàí³÷í³ ìîëåêóëè, ïîâåðõíÿ ïë³âêè.
75

Many physical and radiotechnical systems —
multielement semiconductors and gas lasers, different
radiotechnical devices, etc can be considered
in the first approximation as set of autogenerators,
coupled by different way (c.f.[1,2]). Scheme of two
autogenerators (semiconductor quantum generators
(1), coupled by means optical waveguide (2), is
presented been in figure 1. An important feature of
these systems is connected with possibility of realizing
so called synchronic (sinphase) regimes of auto
oscillations, when relative phases of oscillations of
different elements are fixed. Another important feature
is realizing the stochastic regime of oscillations
and chaos elements. In refs.[1-4] it has been numerically
studied a regular and chaotic dynamics of
the system of the Van-der-Poll autogenerators with
account of finiteness of the signals propagation time
between them and also with special kind of interoscillators
interaction forces. Chaos theory establishes
that apparently complex irregular behaviour
could be the outcome of a simple deterministic system
with a few dominant nonlinear interdependent
variables.
Fig. 1. The grid of autogenerators (semiconductor quantum
generators (SQG), coupled by means of the general resonator:
1 — SQG, 2 — resonator (dielectric plate)
The past decade has witnessed a large number of
studies employing the ideas gained from the science of
chaos to characterize, model, and predict the dynamics
of various geophysical phenomena (c.f.[1-20]).
The outcomes of such studies are very encouraging, as
they not only revealed that the dynamics of the apparently
irregular phenomena could be understood from
a chaotic deterministic point of view but also reported
76
UDÑ 539.124 : 541.47
A. A. SVINARENKO, A. V. LOBODA, N. G. SERBOV
Odessa State Environmental University
MODELING AND DIAGNOSTICS OF INTERACTION OF THE NON-
LINEAR VIBRATIONAL SYSTEMS ON THE BASIS OF TEMPORAL SERIES
(APPLICATION TO SEMICONDUCTOR QUANTUM GENERATORS)
It is studied an employing a variety of techniques for characterizing the dynamics of the coupled
semiconductor quantum generators and identifying the presence of chaotic dynamics in this time (frequency)
series. The statistical techniques used are the autocorrelation function and the Fourier power
spectrum, whereas the mutual information approach, correlation integral analysis, false nearest neighbour
algorithm, Lyapunov exponents analysis, and surrogate data method are used for comprehensive
characterization.
very good predictions using such an approach for different
systems.
The present study attempts to employ a variety
of techniques for characterizing the dynamics of the
coupled semiconductor quantum generators (autogenerators)
More specifically, we attempt to identify the
possible presence of chaotic dynamics in this time (frequency)
series. The techniques employed range from
standard statistical techniques that can provide general
indications regarding the dynamics of the phenomenon
to specific ones that can provide comprehensive characterization
of the dynamics. The statistical techniques
used (c.f.[17-20]) are the autocorrelation function and
the Fourier power spectrum, whereas the mutual information
approach, the correlation integral analysis, the
false nearest neighbour algorithm, the Lyapunov exponents
analysis, and the surrogate data method are employed
for comprehensive characterization.
2. INVESTIGATION OF CHAOS IN THE
VIBRATION DYNAMICS
In ref.[2-4,19] it has been studied a regular and
chaotic dynamics of the system of the Van-der-Poll
autogenerators with account of finiteness of the signals
propagation time between them and also with special
kind of inter-oscillators interaction forces. The cases
of little and large non-linearity in the system were
considered. Phase diagram for system of two coupled
autogenerators, interacting with retardion, has been
obtained and the regions, where single-frequency sinphase
oscillation regime (1), multi-frequency sinphase
one (2), chaotic one (3) are realized, were found.. In
general the same situation takes a place in a case of the
grid of autogenerators (semiconductor quantum generators,
coupled by means of the general resonator. In
ref. [3,4,19] we have carried out an analysis of oscillations
in system (Fig.2) for a grid of the coupled (N>2)
semiconductor quantum generators (autogenerators).
This case is more complicated in comparison with a
case of the system of two coupled autogenerators.
Figure 1 shows the vibration dynamics time series
for a grid of autogenerators for the time interval
t=nτ (τ=25[2π/w 0 ]). As it can be seen in Fig. 1, the
© A. A. Svinarenko, A. V. Loboda, N. G. Serbov, 2009

systems exhibits significant variations without any apparent
cyclicity. It is clear that a visual inspection of
the (irregular) amplitude level series does not provide
any clues regarding its dynamical behaviour, whether
chaotic or stochastic. To detect some regularity (or irregularity)
in the time series, the Fourier power spectrum
is often analyzed.
For a purely random process, the power spectrum
oscillates randomly about a constant value, indicating
that no frequency explains any more of the variance of
the sequence than any other frequency. For a periodic
or quasi-periodic sequence, only peaks at certain frequencies
exist; measurement noise adds a continuous
floor to the spectrum. Chaotic signals may also have
sharp spectral lines but even in the absence of noise
there will be continuous part (broadband) of the spectrum.
The broad power spectrum falling as a power of
frequency is a first indication of chaotic behaviour,
though it alone does not characterize chaos [5,15,18].
From this point of view, the corresponding series analyzed
in this study is presumably chaotic [8] However,
more well-defined conclusion on the dynamics of the
time series can be made after the data will be treated
by methods of chaos theory.
Let us consider scalar measurements s(n) = s(t 0 +
nΔt) = s(n), where t 0 is the start time, Δt is the time
step, and is n the number of the measurements. In a
general case, s(n) is any time series, particularly the
amplitude level.
3
2
1
0
-1
-2
-3
62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100 102 104
Fig. 2. The vibration dynamics time series for a grid of autogenerators
Since processes resulting in the chaotic behaviour
are fundamentally multivariate, it is necessary to reconstruct
phase space using as well as possible information
contained in the s(n). Such a reconstruction
results in a certain set of d-dimensional vectors y(n)
replacing the scalar measurements. Packard et al. [7]
introduced the method of using time-delay coordinates
to reconstruct the phase space of an observed dynamical
system. The main idea is that the direct use of
the lagged variables s(n + τ), where τ is some integer to
be determined, results in a coordinate system in which
the structure of orbits in phase space can be captured.
Then using a collection of time lags to create a vector
in d dimensions,
y(n) = [s(n), s(n + τ), s(n + 2τ), …,
s(n + (d−1)τ)], (1)
the required coordinates are provided. In a nonlinear
system, the s(n + jτ) are some unknown nonlinear
combination of the actual physical variables that comprise
the source of the measurements. The dimension
d is also called the embedding dimension, d E . The example
of the Lorenz attractor given by Abarbanel et
al. [5,6] is a good choice to illustrate the efficiency of
the method.
3.1. CHOOSING TIME LAG
The statement of Mañé [13] and Takens [12] that
any time lag will be acceptable is not terribly useful for
extracting physics from data. If τ is chosen too small,
then the coordinates s(n + jτ) and s(n + (j + 1)τ) are
so close to each other in numerical value that they
cannot be distinguished from each other. Similarly, if τ
is too large, then s(n + jτ) and s(n + (j + 1)τ) are completely
independent of each other in a statistical sense.
Also, if τ is too small or too large, then the correlation
dimension of attractor can be under- or overestimated
respectively [8,18]. It is therefore necessary to choose
some intermediate (and more appropriate) position
between above cases.
First approach is to compute the linear autocorrelation
function
N 1
∑[(
sm+δ) −s][( sm) −s]
N m=
1
CL
( δ ) =
, (2)
N 1
2
∑[(
sm) − s]
N m=
1
N 1
where s = ∑ s( m)
, and to look for that time lag
N m=
1
where C (Δ) first passes through zero (see [18]). This
L
gives a good hint of choice for τ at that s(n + jτ) and
s(n + (j + 1)τ) are linearly independent. However, a
linear independence of two variables does not mean
that these variables are nonlinearly independent since
a nonlinear relationship can differs from linear one.
It is therefore preferably to utilize approach with a
nonlinear concept of independence, e.g. the average
mutual information.
Briefly, the concept of mutual information can
be described as follows. Let there are two systems, A
and B, with measurements a and b . The amount one
i k
learns in bits about a measurement of a from a mea-
i
surement of b is given by the arguments of informa-
k
tion theory [9] as
⎛ PAB ( ai, b ) ⎞ k
IAB ( ai, bk)
= log2⎜
⎟,
(3)
⎝PA( ai) PB( bk)
⎠
where the probability of observing a out of the set of
all A is P (a ), and the probability of finding b in a
A i
measurement B is P (b ), and the joint probability of
B i
the measurement of a and b is P (a , b ). The mutual
AB i k
information I of two measurements a and b is sym-
i k
metric and non-negative, and equals to zero if only
the systems are independent. The average mutual information
between any value a from system A and b i k
from B is the average over all possible measurements
of I (a , b ),
AB i k
I () τ =∑ P ( a , b ) I ( a , b ) . (4)
AB AB i k AB i k
ai, bk
To place this definition to a context of observations
from a certain physical system, let us think of the
77

sets of measurements s(n) as the A and of the measurements
a time lag τ later, s(n + τ), as B set. The average
mutual information between observations at n and
n + τ is then
78
I () τ =∑ P ( a , b ) I ( a , b ) . (5)
AB AB i k AB i k
ai, bk
Now we have to decide what property of I(τ) we
should select, in order to establish which among the
various values of τ we should use in making the data
vectors y(n). In ref. [11] it has been suggested, as a prescription,
that it is necessary to choose that τ where
the first minimum of I(τ) occurs. Figure 3a presents
the variations of the autocorrelation coefficient for the
amplitude level.
Fig. 3 (a) Autocorrelation function and (b) average mutual
information
As it can be seen, the autocorrelation function exhibits
some kind of exponential decay up to a lag time
of about 100 time units (sec). Such an exponential
decay can be an indication of the presence of chaotic
dynamics in the process of the level variations. On the
other hand, the autocorrelation coefficient failed to
achieve zero, i.e. the autocorrelation function analysis
not provides us with any value of τ. Such an analysis
can be certainly extended to values exceeding 1000,
but it is known [15] that an attractor cannot be ad-
equately reconstructed for very large values of τ. Figure
3b shows the variation of the mutual information
function against the lag time. The mutual information
function exhibits an initial rapid decay (up to a lag
time of about 10) followed more slow decrease before
attaining near-saturation at the first minimum. Thus,
we can use in following investigations the value of τ
equals to 40 that is obtained by using the average mutual
information analysis.
Let us also note that the autocorrelation function
and average mutual information ca be to some extent
considered as analogues of the linear redundancy and
general redundancy, respectively, which was applied
in the test for nonlinearity. If a time series under consideration
have an n-dimensional Gaussian distribution,
these statistics are theoretically equivalent as it is
shown by Paluš (see [15]). The general redundancies
detect all dependences in the time series, while the linear
redundancies are sensitive only to linear structures.
Although we do not perform the test for nonlinearity
of Paluš in full, the simple comparison of the curves
in Figs. 3a and 3b shows that most of features observed
in the autocorrelation function values are missing in
the average mutual information. In other words, the
nature of curves in Figs. 3a and 3b is substantially
different. From this fact, a possible nonlinear nature
of process resulting in the vibrations amplitude level
variations can be concluded.
3.2. CHOOSING EMBEDDING DIMENSION
The goal of the embedding dimension determination
is to reconstruct a Euclidean space R d large
enough so that the set of points d A can be unfolded
without ambiguity. In accordance with the embedding
theorem, the embedding dimension, d E , must
be greater, or at least equal, than a dimension of attractor,
d A , i.e. d E > d A . In other words, we can choose
a fortiori large dimension d E , e.g. 10 or 15, since the
previous analysis provides us prospects that the dynamics
of our system is probably chaotic. However,
two problems arise with working in dimensions larger
than really required by the data and time-delay embedding
[5,6,18] . First, many of computations for
extracting interesting properties from the data require
searches and other operations in R d whose computational
cost rises exponentially with d. Second, but
more significant from the physical point of view, in
the presence of noise or other high dimensional contamination
of the observations, the extra dimensions
are not populated by dynamics, already captured by
a smaller dimension, but entirely by the contaminating
signal. In too large an embedding space one is
unnecessarily spending time working around aspects
of a bad representation of the observations which are
solely filled with noise. It is therefore necessary to determine
the dimension d A .
There are several standard approaches to reconstruct
the attractor dimension (see, e.g., [5,6,15]), but
let us consider in this study two methods only. The correlation
integral analysis is one of the widely used techniques
to investigate the signatures of chaos in a time
series. The analysis uses the correlation integral, C(r),
to distinguish between chaotic and stochastic systems.

To compute the correlation integral, the algorithm of
Grassberger and Procaccia [10] is the most commonly
used approach. According to this algorithm, the correlation
integral is computed as
2
Cr () = lim H( r−||
i − j || )
N →∞ Nn ( −1) ∑ y y , (6)
i, j
(1 ≤< i j≤N) where H is the Heaviside step function with H(u) = 1
for u > 0 and H(u) = 0 for u ≤ 0, r is the radius of
sphere centered on y or y , and N is the number of data
i j
measurements. If the time series is characterized by an
attractor, then the correlation integral C(r) is related to
the radius r given by
log Cr ( )
d = lim , (7)
r→0
log r
N→∞
where d is correlation exponent that can be determined
as the slop of line in the coordinates log C(r)
versus log r by a least-squares fit of a straight line over
a certain range of r, called the scaling region. If the
correlation exponent attains saturation with an increase
in the embedding dimension, then the system is
generally considered to exhibit chaotic dynamics. The
saturation value of the correlation exponent is defined
as the correlation dimension (d ) of the attractor. The
2
nearest integer above the saturation value provides the
minimum or optimum embedding dimension for reconstructing
the phase-space or the number of variables
necessary to model the dynamics of the system.
On the other hand, if the correlation exponent increases
without bound with increase in the embedding
dimension, the system under investigation is generally
considered stochastic. In this study, the correlation
functions and the exponents was computed for the
hourly amplitude level. Figure 4 shows the correlation
dimension results, i.e. the relationship between
the correlation exponent and embedding dimension
values.
Fig. 4. Relationship between correlation exponent and embedding
dimension for vibrations amplitude level data for original
time series (line 1), mean values of surrogate data sets (line 2),
and one surrogate realization (line 3). Error bars indicate minimal
values of correlation exponent among all realizations of surrogate
data.
As it can be seen, the correlation exponent value
increases with embedding dimension up to a certain
value, and then saturates beyond that value.
The saturation of the correlation exponent beyond a
certain embedding dimension is an indication of the
existence of deterministic dynamics. The saturation
value of the correlation exponent, i.e. correlation dimension
of attractor, for the amplitude level series
is about 3.5 and occurs at the embedding dimension
value of 6. The low, non-integer correlation dimension
value indicates the existence of low-dimensional
chaos in the vibrations dynamics of the autogenerators.
.
The nearest integer above the correlation dimension
value can be considered equal to the minimum
dimension of the phase-space essential to embed the
attractor. The value of the embedding dimension at
which the saturation of the correlation dimension occurs
is considered to provide the upper bound on the
dimension of the phase-space sufficient to describe the
motion of the attractor. Furthermore, the dimension
of the embedding phase-space is equal to the number
of variables present in the evolution of the system dynamics.
Therefore, the results from the present study
indicate that to model the dynamics of process resulting
in the amplitude level variations the minimum
number of variables essential is equal to 4 and the
number of variables sufficient is equal to 6. Therefore,
the amplitude level attractor should be embedded at
least in a four-dimensional phase-space. The results
indicate also that the upper bound on the dimension
of the phase-space sufficient to describe the motion of
the attractor, and hence the number of variables sufficient
to model the dynamics of process resulting in
the level variations is equal to 6.
There are certain important limitations in the use
of the correlation integral analysis in the search for
chaos. For instance, the selection of inappropriate
values for the parameters involved in the method may
result in an underestimation (or overestimation) of the
attractor dimension [8]. Consequently, finite and low
correlation dimensions could be observed even for a
stochastic process [18]. To verify the results obtained
by the correlation integral analysis, we use surrogate
data method.
The method of surrogate data [16] is an approach
that makes use of the substitute data generated in accordance
to the probabilistic structure underlying
the original data. This means that the surrogate data
possess some of the properties, such as the mean,
the standard deviation, the cumulative distribution
function, the power spectrum, etc., but are otherwise
postulated as random, generated according to a specific
null hypothesis. Here, the null hypothesis consists
of a candidate linear process, and the goal is to
reject the hypothesis that the original data have come
from a linear stochastic process. One reasonable statistics
suggested by Theiler et al. [16] is obtained as
follows.
Let Q orig denote the statistic computed for the original
time series and Q si for the ith surrogate series generated
under the null hypothesis. Let μ s and σ s denote,
respectively, the mean and standard deviation of the
distribution of Q s . Then the measure of significance S
is given by
79

| Qorig
−μs
|
S =
. (8)
σs
An S value of ∼2 cannot be considered very significant,
whereas an S value of ∼10 is highly significant
[16]. The details on the null hypothesis and surrogate
data generation are described in ref. [18].
To detect nonlinearity in the amplitude level data,
the one hundred realizations of surrogate data sets were
generated according to a null hypothesis in accordance
to the probabilistic structure underlying the original
data. The correlation integrals and the correlation exponents,
for embedding dimension values from 1 to 20,
were computed for each of the surrogate data sets using
the Grassberger-Procaccia algorithm as explained earlier.
Figure 4 shows the relationship between the correlation
exponent values and the embedding dimension
values for the original data set and mean values of the
surrogate data sets as well as for one surrogate realization.
It is interesting to note that the similar picture
takes a place in the principally other geophysical system
[17], that confirms the fundamental idea about genesis
of the fractal dimensions and chaotic features in physically
different systems. One can be stressed, however
the similar features are manifested in such complicated
system as “cosmic plasma — galactic-origin rays — turbulent
pulsation in planetary atmosphere system” [20].
As it can be seen from Fig. 4, a significant difference
in the estimates of the correlation exponents, between
the original and surrogate data sets, is observed. In the
case of the original data, a saturation of the correlation
exponent is observed after a certain embedding
dimension value (i.e., 6), whereas the correlation exponents
computed for the surrogate data sets continue
increasing with the increasing embedding dimension.
The significance values (S) of the correlation exponent
are computed for each embedding dimension and are
shown in Fig. 5. The significance values lie mostly in
the range between 10 and 50. The high significance
values of the statistic indicate that the null hypothesis
(the data arise from a linear stochastic process) can be
rejected and hence the original data might have come
from a nonlinear process.
Fig. 5. Relationship between significance values of correlation
dimension and embedding dimension
80
Let us consider another method for determining
d that comes from asking the basic question addressed
E
in the embedding theorem: when has one eliminated
false crossing of the orbit with itself which arose by
virtue of having projected the attractor into a too low
dimensional space? In other words, when points in
dimension d are neighbours of one other? By examining
this question in dimension one, then dimension
two, etc. until there are no incorrect or false neighbours
remaining, one should be able to establish, from
geometrical consideration alone, a value for the necessary
embedding dimension. Such an approach was
described by Kennel et al. [6]. In dimension d each
vector
y(k) = [s(k), s(k + τ), s(k + 2τ), …,
s(k + (d−1)τ)] (9)
has a nearest neighbour yNN (k) with nearness in the
sense of some distance function. The Euclidean distance
in dimension d between y(k) and yNN (k) we call
R (k): d
2 NN 2 NN
2
Rd( k) = [ sk ( ) − s ( k)] + [ sk ( +τ) − s ( k+τ
)] +
(10)
NN
2
... + [ sk ( +τ( d−1)) − s ( k+τ( d−1))]
.
R (k) is presumably small when one has a lot a
d
data, and for a dataset with N measurements, this distance
is of order 1/N1/d . In dimension d + 1 this nearest-neighbour
distance is changed due to the (d + 1)st
coordinates s(k + dτ) and sNN (k + dτ) to
2 2 NN
2
Rd+ 1 ( k) = Rd( k) + [ s( k+ dτ) − s ( k+ dτ
)] . (11)
We can define some threshold size R to decide
T
when neighbours are false. Then if
NN
| sk ( + dτ) − s ( k+ dτ
)|
> RT
, (12)
R ( k)
d
the nearest neighbours at time point k are declared
false. Kennel et al.[6] showed that for values in the
range 10 ≤ R T ≤ 50 the number of false neighbours
identified by this criterion is constant. In practice,
the percentage of false nearest neighbours is determined
for each dimension d. A value at which the
percentage is almost equal to zero can be considered
as the embedding dimension. Figure 6 displays the
percentage of false nearest neighbours that was determined
for the amplitude level series, for phase-spaces
reconstructed with embedding dimensions from 1 to
20. As it can be seen, the percentage of false neighbours
drops to almost zero at 4 or 5. This indicates
that a four or five-dimensional phase-space is necessary
to represent the dynamics (or unfold the attractor)
of the amplitude level series. From the other
hand, the mean percentage of false nearest neighbours
computed for the surrogate data sets decreases
steadily but at 20 is about 35%. Such a result seems
to be in close agreement with that was obtained from
the correlation integral analysis, providing further
support to the observation made earlier regarding the
presence of low-dimensional chaotic dynamics in
the amplitude level variations.

Fig. 6. Embedding dimension estimation using false nearest
neighbour method for amplitude level data for original time series
(line 1), mean values of surrogate data sets (line 2), and one surrogate
realization (line 3). Error bars indicate minimal percentage of
false nearest neighbour among all realizations of surrogate data
3.3. LYAPUNOV EXPONENTS
Lyapunov exponents are the dynamical invariants
of the nonlinear system. They are very useful when
physics of process is considered. Using the spectrum
of Lyapunov exponents, the average predictability of
nonlinear system can be estimated. In a general case,
the orbits of chaotic attractors are unpredictable, but
there is the limited predictability of chaotic physical
system, which is defined by the global and local
Lyapunov exponents. A concept of Lyapunov exponents
existed long before the establishment of chaos
theory, and was developed to characterize the stability
of absolute value of the eigenvalues of the linearized
dynamics averaged over the attractor. A negative
exponent indicates a local average rate of contraction
while a positive value indicates a local average rate of
expansion. In the chaos theory, the spectrum of Lyapunov
exponents is considered a measure of the effect
of perturbing the initial conditions of a dynamical
system. Note that both positive and negative Lyapunov
exponents can coexist in a dissipative system, which is
then chaotic.
Since the Lyapunov exponents are defined as asymptotic
average rates, they are independent of the
initial conditions, and therefore they do comprise an
invariant measure of attractor. In fact, if one manages
to derive the whole spectrum of Lyapunov exponents,
other invariants of the system, i.e. Kolmogorov entropy
and attractor’s dimension can be found. The
Kolmogorov entropy, K, measures the average rate at
which information about the state is lost with time.
An estimate of this measure is the sum of the positive
Lyapunov exponents. The inverse of the Kolmogorov
entropy is equal to the average predictability. The estimate
of the dimension of the attractor is provided by
the Kaplan and Yorke conjecture (see [15,18]):
j
∑ λα
α= 1
dL= j+
| λ
,
|
(13)
j
j+
1
j+ 1
where j is such that ∑ λ α > 0 and ∑ λ α < 0 , and the
α= 1
α= 1
Lyapunov exponents λ are taken in descending order.
α
There are several approaches to computing the Lyapunov
exponents (see, e.g., [5,6]); in this paper, we use
one [18] which computes the whole spectrum and is
based on the Jacobin matrix of the system function
[14]. To calculate the spectrum of Lyapunov exponents
from the amplitude level data, we use the time
delay τ = 40 and embed the data in the four-dimensional
space. Such a choice of the input parameters is
the result of the previous calculations. Table 2 summarizes
the results of the Lyapunov exponent analysis.
For the time series under consideration, there exist two
positive exponents (indicating expansion along two
directions) and two negative ones (indicating contraction
along remaining directions). The Kaplan-Yorke
dimension is equal to 3.33; this value is very close to
the correlation dimension which was defined by the
Grassberger-Procaccia algorithm. The estimations
of the Kolmogorov entropy and average predictability
can show a limit, up to which the amplitude level
data can be on average predicted. Surely, the important
moment is a check of the statistical significance
of results.
Table 2
Results of Lyapunov exponents analysis for amplitude level: λ 1 −λ 4
are the Lyapunov exponents in descending order, d L is the Kaplan-
Yorke attractor dimension, K is the Kolmogorov entropy, and P is
the average predictability
λ 1 λ 2 λ 3 λ 4 d L K P
0.0082 0.0017 −0.0047 −0.0167 3.33 0.0094 124.3
It is worth to remind that results of state-space
reconstruction are highly sensitive to the length of
data set (i.e. it must be sufficiently large) as well as to
the time lag and embedding dimension determined.
Indeed, there are limitations on the applicability of
chaos theory for observed (finite) time series arising
from the basic assumptions that the time series must
be infinite. A finite and small data set may probably
results in an underestimation of the actual dimension
of the process. Nevertheless, we check the robustness
of our results with respect to the size of time series by
dividing the data in 2 sets of 4500 points and in 4 sets
of 2250 points and using the methods described above
for these subsets. The main assumption is that the results
obtained for the subsets are close to the results
obtained for the whole time series. We received the dimensions
determined for various time lags. It has been
found the value τ = 40, which is the time lag provided
by the mutual information approach, and the correlation
dimension is 3.33 due to the saturation at the embedding
dimension 6 (see Fig. 4). Thus, the statistical
convergence tests, described here, together with surrogate
data approach that, was above applied, provide
the satisfactory significance of our data regarding the
state-space reconstruction.
81

82
4. CONCLUSIONS AND DISCUSSION
This paper investigated the existence of chaotic
behaviour in the non-linear vibrational systems on the
basis of temporal series, in particular, for a grid of the
semiconductor autogenerators. The mutual information
approach, the correlation integral analysis, the
false nearest neighbour algorithm, the Lyapunov exponent’s
analysis, and the surrogate data method were
used in the analysis. The mutual information approach
provided a time lag which is needed to reconstruct
phase space. Such an approach allowed concluding
the possible nonlinear nature of process resulting in
the amplitude level variations. The correlation dimension
method provided a low fractal-dimensional
attractor thus suggesting a possibility of the existence
of chaotic behaviour. The method of surrogate data,
for detecting nonlinearity, provided significant differences
in the correlation exponents between the original
data series and the surrogate data sets. This finding
indicates that the null hypothesis (linear stochastic
process) can be rejected. The main conclusion is that
the system exhibits a nonlinear behaviour and possibly
low-dimensional chaos. Thus, a short-term prediction
based on nonlinear dynamics is possible. The Lyapunov
exponents analysis supported this conclusion. It
can be noted that the nonleading exponents are notoriously
difficult to estimate from time series data.
Moreover, the interpretation of inverse Lyapunov exponents
as predictability times can results in ambiguous
conclusions.
Though a large number of studies employed the
ideas gained from the science of chaos, there have also
been widespread criticisms on the application of chaos
theory. The fact that observational time series are almost
always finite and are inherently contaminated by
noise, such as errors arising from measurements, necessitate
addressing the above issues in the application
of chaos theory. The basis for the criticisms of studies
investigating and reporting existence of chaos in the
amplitude variations is our strong belief that they are
influenced by a large number of variables and, therefore,
are stochastic. On the other hand, the outcomes
of the present study provide support to the claims that
the (seemingly) highly irregular processes could be the
result of simple deterministic systems with a few degrees
of freedom. Therefore, the hypothesis of chaos
in is reasonable and can provide an alternative approach
for characterizing and modelling the dynamics
of processes resulting in the vibrations processes in
the complicated system. The future investigations can
be realized and include , for example, the nonlinear
prediction method or artificial neural network approach.
In any case the presented analysis has a great
importance for correct treating dynamics of different
semiconductors and quantum electronics devices,
nanoelectronics and corresponding nano-devices, including
the molecular electronics.
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UDÑ 539.124 : 541.47
A. A. Svinarenko, A. V. Loboda, N. G. Serbov
MODELING AND DIAGNOSTICS OF INTERACTION OF THE NON-LINEAR VIBRATIONAL SYSTEMS ON THE BASIS
OF TEMPORAL SERIES (APPLICATION TO SEMICONDUCTOR QUANTUM GENERATORS)
Abstract
It is studied an employing a variety of techniques for characterizing the dynamics of the coupled semiconductor quantum generators
and identifying the presence of chaotic dynamics in this time (frequency) series. The statistical techniques used are the autocorrelation
function and the Fourier power spectrum, whereas the mutual information approach, correlation integral analysis, false nearest
neighbour algorithm, Lyapunov exponents analysis, and surrogate data method are used for comprehensive characterization.
Key words: non-linear vibrational systems, quantum generators, statistical techniques.
ÓÄÊ 539.124 : 541.47
À. À. Ñâèíàðåíêî, À. Â. Ëîáîäà, Í. Ã. Ñåðáîâ
ÌÎÄÅËÈÐÎÂÀÍÈÅ È ÄÈÀÃÍÎÑÒÈÊÀ ÂÇÀÈÌÎÄÅÉÑÒÂÈÉ Ó ÍÅËÈÍÅÉÍÛÕ ÊÎËÅÁÀÒÅËÜÍÛÕ ÑÈÑÒÅÌÀÕ
ÍÀ ÎÑÍÎÂÅ ÀÍÀËÈÇÀ ÂÐÅÌÅÍÍÛÕ ÐßÄΠ(ÏÐÈÌÅÍÅÍÈÅ Ê ÏÎËÓÏÐÎÂÎÄÍÈÊÎÂÛÌ ÊÂÀÍÒÎÂÛÌ
ÃÅÍÅÐÀÒÎÐÀÌ)
Ðåçþìå
Íîâûå ñòàòèñòè÷åñêèå ìåòîäèêè èñïîëüçîâàíû äëÿ èçó÷åíèÿ äèíàìèêè ïîëóïðîâîäíèêîâûõ êâàíòîâûõ ãåíåðàòîðîâ è
èäåíòèôèêàöèè õàîñà â ñîîòâåòñòâóþùèõ âðåìåííûõ ðÿäàõ. Äëÿ âûÿâëåíèÿ õàðàêòåðíûõ îñîáåííîñòåé äèíàìèêè ñèñòåì
ïðèìåíåíû ìåòîä àâòîêîððåëÿöèîííûõ ôóíêöèé, Ôóðüå — ñïåêòðû, ìåòîäèêà âçàèìíîé èíôîðìàöèè, ìåòîä êîððåëÿöèîííûõ
èíòåãðàëîâ, àëãîðèòì “ëîæíûõ áëèæàéøèõ ñîñåäåé”, àíàëèç íà îñíîâå ýêñïîíåíò Ëÿïóíîâà, ìåòîä ñóððîãàòíûõ äàííûõ.
Êëþ÷åâûå ñëîâà: íåëèíåéíûå êîëåáàòåëüíûå ñèñòåìû, êâàíòîâûå ãåíåðàòîðû, ñòàòèñòè÷åñêèå ìåòîäû àíàëèçà.
ÓÄÊ 539.124 : 541.47
À. À. Ñâèíàðåíêî, À. Â. Ëîáîäà, Ì. Ã. Ñåðáîâ
ÌÎÄÅËÞÂÀÍÍß ÒÀ IJÀÃÍÎÑÒÈÊÀ ÂÇÀªÌÎÄ²É Ó ÍÅ˲ͲÉÍÈÕ ÊÎËÈÂÀËÜÍÈÕ ÑÈÑÒÅÌÀÕ ÍÀ ÎÑÍβ
ÀÍÀ˲ÇÓ ×ÀÑÎÂÈÕ ÐßIJ (ÇÀÑÒÎÑÓÂÀÍÍß ÄÎ ÍÀϲÂÏÐβÄÍÈÊÎÂÈÕ ÊÂÀÍÒÎÂÈÕ ÃÅÍÅÐÀÒÎв )
Ðåçþìå
Çàñòîñîâàí³ íîâ³ ñòàòèñòè÷í³ ìåòîäèêè äëÿ ç’ÿñóâàííÿ äèíàì³êè íàï³âïðîâ³äíèêîâèõ êâàíòîâèõ ãåíåðàòîð³â òà ³äåíòèô³êàö³¿
õàîñó ó ÷àñîâèõ ðÿäàõ. Äëÿ âèÿâëåííÿ õàðàêòåðíèõ îñîáëèâîñòåé ñèñòåìè âèêîðèñòàí³ ìåòîä àâòîêîðåëÿö³éíèõ ôóíêö³é,
Ôóð’º — ñïåêòðîñêîï³ÿ, ìåòîäèêà âçàºìíî¿ ³íôîðìàö³¿, ìåòîä êîðåëÿö³éíèõ ³íòåãðàë³â, àëãîðèòì “õèáíèõ íàéáëèæ÷èõ
ñóñ³ä³â”, àíàë³ç íà ï³äñòàâ³ åêñïîíåíò Ëÿïóíîâà, ìåòîä ñóðîãàòíèõ äàíèõ.
Êëþ÷îâ³ ñëîâà: íåë³í³éí³ êîëèâàëüí³ ñèñòåìè, êâàíòîâ³ ãåíåðàòîðè, ñòàòèñòè÷í³ ìåòîäè àíàë³çó.
83

Semiconductor crystals of cadmium sulphide with shifted to excited R’ one [2]. And the occupation of
S- and R-centers were applied in the studies. When these levels with holes is determined by the corre-
samples treated by visible light and intensive IR-illusponding maxima. For the same reason the first maximination,
their relaxation characteristics, lux-current mum (shortwave one) is more sensible to changes in
dependencies, photocurrent spectral distribution and each light intensities.
curve for quenching coefficient distribution corresponded
to Bube-Rose model [1,2]. The dependence
The lower intensity of quenching light at Lв = const ,
the lower Q becomes. And at lower intensities of in-
of quenching value on wavelength had two maxima trinsic excitation this dependence shows evidently. At
within the range 1000-1400 μm, that certified the the same time the value of quenching coefficient in-
presence of R-centers excited states [2].
We investigated the change in quenching value uncreases
with decrease of L в excitation at unchanging
intensity of quenching light. The increase was higher if
der various intensities of applied light fluxes. All the
measurements were carried out under the stationary
conditions. The relaxation maintained in each point
the applied intensities L were insignificant.
g
Experimental particularities of Q (L , L ) men-
g B
tioned above confirm the validity of formula (1) in our
(up to 20 minutes) to avoid the processes described in case. There are some limits imposed during its deriva-
[3, 4].
tion, and one was the following: all the holes knocked
For Q(L L ) there is only one expression in lit-
g B
erature [5] that requires to measure the variables such
out of R — R’ levels by light remain in valence band
and decrease capturing to S — centers. But this sup-
as free carriers and complicated considerably the calposition is not valid. Cross-section of holes capture by
culations, made them low exact and practically unac- S- and R — centers are equal. The hole being newly
ceptable.
photoexcited locates dimensionally near R’ — cen-
We used the dependence of IR-quenching value ter and most probably will be captured by it [7]. The
on intensities of applied light flows, being given earlier similar, probably multiple, oscillations does not show
in [6]:
on registered external parameters and lead to useless
⎡⎛ τp ⎞ L ′ ′ gαβ τp
⎤
Q = 1− + ⋅100
0
⎢⎜ ⎟ ⎥ 0
⎢⎣⎝ τnв⎠ nL
αβτ ⎥⎦
(1)
absorption of IR-light photons. Obviously this process
can mask the dependence on intensity of IR-light.
As critical levels of illumination both by exciting
and quenching light we will observe such light fluxes
where Q - IR-quenching coefficient; τn, τ p — lifetimes
for nonequilibrium electrons and holes; L в ,
L — the value for incident quanta of exiting and
g
quenching light; α , α ′ — the part of photons absorbed
by our sample; β , β ′ — quantum yields under exciting
and quenching light treatment.
Expression (1) shows the dependence of optical
quenching value on intensities of exciting L в and
quenching L light. It should be noted that the men-
g
tioned ratio is valid for low intensities of quenching
light and high levels of photoexcitation, when the
changes in recombination centers occupation can not
be taken into consideration.
The studies showed that under various intensity
combinations the shortwave maximum occurred lower
than long-wave one. This is explained by thermal
supply of captured carriers. At the expense of photon
absorption, the part of holes from the basic R-level
when in spectral allocation of quenching coefficient
not only the mentioned numerical changes is seen at
spectral distribution of quenching coefficient, but the
qualitative changes become.
As it was noted previously, with increase of intrinsic
excitation intensity and decrease of IR-light flux
the value of quenching decreases in accordance to formula
(1). The conditions, when shortwave maximum
disappeared completely in curve of spectral distribution
Q (λ) but long-wave maximum still presented,
were created (Fig. 1a). Formula (1) can not be applied
for such a case because tolerance limits made at its
derivation were broken.
The processes took place in the case could be explained
as follows. The lower the value L the lower
g
the number of holes is knocked out of R-centers by
IR-photons. Respectively, the lower number of holes
enters the centers of quick recombination and the
84
UDC 621.315.592
YE. V. BRYTAVSKYI, YU. N. KARAKIS, M. I. KUTALOVA, G. G. CHEMERESYUK
Odesa I. I. Mechnikov National University, E-mail: wadz@mail.ru, t 8048-7266356
EFFECTS CONNECTED WITH INTERACTION OF CHARGE CARRIERS
AND R-CENTERS BASIC AND EXITED STATES
The critical modes of illumination for samples with sensitization centers by exciting and quenching
light were investigated. And the conditions when the spectral distribution of infrared quenching
coefficient changed qualitatively have been founded. Disappearance of quenching shortwave maximum
within the range of 1000 μm connected with photoexcitation of holes from R-centers under the
high intrinsic conductivity. The anomalous shape of quenching curve without long-wave maximum in
the range of 1400 μm was obtained. The observed dependence is explained by the decrease of quantum
yield for infrared illumination.
© Ye. V. Brytavskyi, Yu. N. Karakis, M. I. Kutalova, G. G. Chemeresyuk, 2009

losses of main carriers (electrons) become lower. The
value of coefficient Q estimates (through current)
namely this relative decrease. The higher the intensity
of intrinsic light and, respectively, the initial concentration
of free electrons, the quickly their decrease by
recombination becomes negligibly small. In the first
place, the shortwave maximum Q (λ) disappears from
the curve, because it is connected with holes release
from basic state of R-centers, and charge concentration
there is lower at the expense of thermal pumping
to R’- states [2].
Q ,% (�)
20 20
10 10
20
10
800 1200
λ , ��,
1600
Q ,% (�)
��, λ,
��
800 1200 1600
Figure 1. Qualitative changes in quenching. (à) — L â ” L g ;
L g → 0; (á) — L â ↑, L g
At maximum flux of IR-light and maximum level
of intrinsic excitation we observed the disappearance
of long-wave maximum for photocurrent quenching
(1300-1400 μm), whereas shortwave maximum Q (λ)
within the range 950-1000 μm still remained (Figure
1b). This phenomenon was not described in literature
previously.
The maximum levels of exposure were determined
by the possibilities of experimental equipment. Within
the maximum of sample photosensitivity (520-530
μm) the intensity of monochromatic light provided
the illumination of order 5-6 lx.
In infrared part of spectrum we ran into the obstacle
of equal raise in illumination within spectral regions
of both maxima. The known procedures to control
light flux by the width of monochromator output
slit or by application of neutral light filter gave nonproportional
values, because these regions were located
far from each other (up to 400 μm). And we took
up the procedure to vary the tube filament at rather
narrow output slit of monochromator.
The assumptions of this procedure consist in the
following: with increase of filament according to Wein
law the spectrum of source emittance shifts slightly
to shortwave part. As the result, illumination in near
shortwave part of IR-spectrum increases somewhat
quickly, than in long-wave part. In this case the greater
influence gives the mechanisms to form Q (λ) maxima.
Shortwave maximum of quenching always locates
lower than long-wave one because of redistribution in
captured holes concentration and it should disappear
first at non-optimized ratio for exposure intensities.
The anomalous shape of Q (λ) curve (Fig. 1b) is
explained as follows. In accordance with formula (1),
the value of coefficient Q does not depend on intensity
L g itself but on product βL g ‘ which includes the value
of quantum yield. The authors [8] noted, that at some
ratios of light flux intensities the value of quantum
yield can quickly decrease for infrared illumination in
the samples with R-centers. The magnitudes of order
β’= 0,026÷0,072 [7] were registered experimentally.
At such low values namely the decrease of β’ can be
decisive factor even under the considerably high magnitudes
in numerator (1).
The mechanism to explain the shape of Figure 1b
dependence is suggested as follows. Under illumination
by light with wavelength corresponded to activation
energy of R’-centers (Figure 2), the number of
free sites there increases. And decrease of thermally
excited holes from R-level must raise. In its turn this
leads to increase of free sites on these levels. As the
result, the recurrent captures of holes to R’-centers
increase, and quantum yield for IR-illumination becomes
lower.
f
e +
e –
I
S
Figure. 2 Diagram for transitions of electrons and holes under
considerable intensity of exciting light and infrared illumination.
We note that the described effect can be achieved
for each specified temperature only within very narrow
range of existing R-center concentration and applied
intensities of intrinsic light and infrared illumination.
The studies are carried out under the condition when
only the intensity of intrinsic light changes in relation
to the other three registered parameters. If the intrinsic
excitation is considerably high, there is the great
number of free holes in V-band. The additional charge
knocked out from R-centers by IR-illumination does
not significantly change their concentration, and in
the end, the current flow. Besides, R-centers become
strongly occupied by holes (probably, even p r ≈ N r ;
p r′ ≈ N r′ [1]). Respectively small changes caused by
II
kT
R
Ec
Ev
R�
h�
85

IR-photons are unable to influence the existed ratio
of charge concentration on these centres. And the free
places created there will be occupied immediately by
holes from valence band.
If intensity of intrinsic light is sufficiently high,
concentration of localized vacancies will be low too.
In this case, there are a lot of sites on R-centres not
occupied by holes before IR-light switched on. And
IR-excitation can not change their number and the
balance of capture — emptying processes considerably.
The studies carried out correspond to the movement
along AB line of sketch figure 3.
Area 1 in Figure 3 shows the intensities when
the standard Rose mechanism is carried out [1]. The
families of Q (λ) curves were measured under such
conditions and formula (1) was obtained for such
light fluxes. During its derivation the authors made
simplifications required the conditions L g ↑ > L â ↑
[6], when collection of quanta of intrinsic and infrared
light is incident on the sample, and the value of
quenching light L g is higher. And formula (1) can not
be applied in area 2 in Figure 3 because of the abovementioned
cause.
�
86
Lg
2
1
Figure 3. The shape of possible relationships between the intensities
of exciting and quenching light: 1 — the area for photocurrent
IR-quenching effect; 2 — the area for intensities without
quenching; 3 — the area with anomalous quenching effect.
The quenching effect can not carry out because of
the following three reasons:
I. Firstly, under low intrinsic excitation (L → â
0) the number of free nonequilibrium carrier pairs is
found smaller than the value, that can provide their
recombination only through S-centres (see Fig. 2);
3
�
�
L�
II. Secondly, insignificant activation of holes from
R-centres (L →0) L concealed almost completely
â g
by dissipation processes, captures to traps etc. These
traps do not practically reach S-centres;
III. Small numbers of additional holes that however
reach fast-recombination centres lead to small
decrease of main carriers — electrons and practically
do not influence on photocurrent change.
Let’s make the observation when the area 3 of Figure
3 can be reached along the line CB. This means
that the level of intrinsic excitation is registered at the
highest position and infrared flux increases gradually.
At low L magnitudes the quenching does not occur
g
because of the third reason for area 2. At middle Lg magnitudes the quenching can be observed but it is
insignificant. This corresponds to range condition of
area 1 in Figure 3, showed by curve in Figure 1a. For
the higher intensities the mechanism of anomalous
quenching described above becomes valid.
At that time the quenching maxima of Q (λ) dependence
conduct differently. Shortwave maximum
within the range 1000 μm can increase slightly at the
expense of complete emptying in basic state of R-centers.
Long-wave maximum (area of 1400 μm) can not
appear even under these conditions because of the
small magnitudes for quantum yield. The holes photoexcited
from R’-states remain in R-centers areas at
the expense of repeated captures and do not contribute
to recombination on S-centers.
References:
1. À.Ðîóç Îñíîâû òåîðèè ôîòîïðîâîäèìîñòè Ìîñêâà,
Ìèð,1998-Ñ.192
2. Ð.Áüþá Ôîòîïðîâîäèìîñòü òâ¸ðäûõ òåë, Ìîñêâà, 2002ã.,Ñ
558.
3. ÊàðàêèñÞ.Í., Êóòàëîâà Ì.È.,Çàòîâñêàÿ Í.Ï. Îñîáåííîñòè
ðåëàêñàöèè ôîòîòîêà â êðèñòàëëàõ ñóëüôèäà êàäìèÿ
Ïåðâàÿ Óêðàèíñêàÿ êîíôåðåíöèÿ ïî ôèçèêå ïîëóïðîâîäíèêîâ,
Îäåññà,Òåçèñû äîêëàäîâ, Ò 2, 2002ã.,
4. Karakis Yu.N., Borschak V.F., Zotov V.V., Kutalova M.I. Relaxation
characteristics of cadmium sulphide crystals with IRquenching.
— Photoelectronics, vol. 11, 2002. — P. 51-55.
5. Ñåðäþê Â.Â., ×åìåðåñþê Ã.Ã., Òåðåê Ì. Ôîòîýëåêòðè÷åñêèå
ïðîöåññû â ïîëóïðîâîäíèêàõ , Êèåâ ,1992 — Ñ151.
6. Novikova M.A., Karakis Yu.N., Kutalova M.I. Particularities
of current transfer in crystals with two types of recombination
centres. — Photoelectronics, vol. 14, 2005. — P. 58-61.
7. Dragoev A.A., Karakis Yu.N., Kutalova M.I. Peculiarities in
photoexcitation of carriers from deep traps. — Photoelectronics,
vol. 15, 2006. — P. 54-56.
8. Dragoev A.A., Zatovskaya N.P., Karakis Yu.N., Kutalova
M. I. Sensors of infrared illumination controlled by electric
field. — 2nd International Scientific and Technical Conference
Sensor Elec –tronics and Microsystems Technology,
Book of abstracts , P. 115.

UDC 621.315.592
Ye. V. Brytavskyi, Yu. N. Karakis, M. I. Kutalova, G. G. Chemeresyuk
EFFECTS CONNECTED WITH INTERACTION OF CHARGE CARRIERS AND R-CENTERS BASIC AND EXITED
STATES
Abstract
The critical modes of illumination for samples with sensitization centers by exciting and quenching light were investigated. And the
conditions when the spectral distribution of infrared quenching coefficient changed qualitatively have been founded. Disappearance of
quenching shortwave maximum within the range of 1000 μm connected with photoexcitation of holes from R-centers under the high
intrinsic conductivity. The anomalous shape of quenching curve without long-wave maximum in the range of 1400 μm was obtained. The
observed dependence is explained by the decrease of quantum yield for infrared illumination.
Key words: quantum yield, spectral distribution, infrared illumination.
ÓÄÊ 621.315.592
Å. Â. Áðèòàâñêèé, Þ. Í. Êàðàêèñ, Ì. È. Êóòàëîâà, Ã. Ã. ×åìåðåñþê
ÝÔÔÅÊÒÛ, ÑÂßÇÀÍÍÛÅ ÑÎ ÂÇÀÈÌÎÄÅÉÑÒÂÈÅÌ ÍÎÑÈÒÅËÅÉ ÇÀÐßÄÀ Ñ ÎÑÍÎÂÍÛÌ
È ÂÎÇÁÓÆĨÍÍÛÌ ÑÎÑÒÎßÍÈÅÌ R-ÖÅÍÒÐÎÂ
Ðåçþìå
Èññëåäîâàíû êðèòè÷åñêèå ðåæèìû îñâåùåíèÿ âîçáóæäàþùèì è ãàñÿùèì ñâåòîì îáðàçöîâ ñ öåíòðàìè î÷óâñòâëåíèÿ.
Îðåäåëåíû óñëîâèÿ, ïðè êîòîðûõ ñïåêòðàëüíîå ðàñïðåäåëåíèå êîýôôèöèåíòà èíôðàêðàñíîãî ãàøåíèÿ ïðåòåðïåâàåò êà÷åñòâåííûå
èçìåíåíèÿ. Èñ÷åçíîâåíèå êîðîòêîâîëíîâîãî ìàêñèìóìà ãàøåíèÿ â îáëàñòè 1000íì ñâÿçàíî ñ ôîòîâîçáóæäåíèåì
äûðîê ñ R — öåíòðîâ â óñëîâèÿõ áîëüøîé ñîáñòâåííîé ïðîâîäèìîñòè. Îïðåäåë¸í àíîìàëüíûé âèä êðèâîé ãàøåíèÿ áåç äëèííîâîëíîâîãî
ìàêñèìóìà â îáëàñòè 1400íì. Íàáëþäàåìàÿ çàâèñèìîñòü îáúÿñíÿåòñÿ óìåíüøåíèåì êâàíòîâîãî âûõîäà äëÿ èíôðàêðàñíîãî
èçëó÷åíèÿ.
Êëþ÷åâûå ñëîâà: íîñèòåëè çàðÿäà, èíôðàêðàñíîe èçëó÷åíèå, êâàíòîâûé âûõîä.
ÓÄÊ 621.315. 592
Å. Â. Áðèòàâñüêèé, Þ. Í. Êàðàê³ñ, Ì. ². Êóòàëîâà, Ã. Ã. ×åìåðåñþê
ÅÔÅÊÒÈ, ÏΠ, ßÇÀͲ Dz ÂÇÀªÌÎIJªÞ ÍÎѲ¯Â ÇÀÐßÄÓ Ç ÎÑÍÎÂÍÈÌ ² ÇÁÓÄÆÅÍÈÌ ÑÒÀÍÎÌ R-ÖÅÍÒвÂ.
Ðåçþìå
Äîñë³äæåí³ êðèòè÷í³ óìîâè çàñâ³òëåííÿ çáóäæóþ÷èì ³ ãàñíó÷èì ñâ³òëîì çðàçê³â ç öåíòðàìè ÷óòëèâîñò³. Çíàéäåí³ óìîâè,
ïðè ÿêèõ ñïåêòðàëüíèé ðîçïîä³ë êîåô³ö³åíòà ³íôðà÷åðâîíîãî ãàñ³ííÿ â³ä÷óâຠÿê³ñí³ çì³íè. Çíèêíåííÿ êîðîòêîõâèëüîâîãî
ìàêñèìóìà ãàñ³ííÿ â îáëàñò³ 1000íì ïîâ , ÿçàíî ç ôîòîçáóäæåííÿì ä³ðîê ç R — öåíòð³â çà óìîâ á³ëüøî¿ âëàñíî¿ ïðîâ³äíîñò³.
Ðîçðàõîâàíî àíîìàëüíèé âèãëÿä êðèâî¿ ãàñ³ííÿ áåç äîâãîõâèëüîâîãî ìàêñèìóìà â îáëàñò³ 1400íì. Ñïîñòåð³ãàºìà çàëåæí³ñòü
ïîÿñíþºòüñÿ çìåíüøåííÿì êâàíòîâîãî âèõîäó äëÿ ³íôðà÷åðâîíîãî âèïðîì³íþâàííÿ.
Êëþ÷îâ³ ñëîâà: íîñ³¿ çàðÿäó, ³íôðà÷åðâîíå âèïðîì³íþâàííÿ, êâàíòîâèé âèõ³ä.
87

88
UDÑ 539.184
I. N. SERGA
Odessa National Polytechnical University, Odessa
ELECTRON INTERNAL CONVERSION IN THE 125,127 Ba ISOTOPES
The work is devoted to a theoretical studying of the electron internal conversion phenomenon in
the 125,127 Ba nuclides. The relativistic Dirac-Fock (DF) method (modified Dirac code) is used in order
to estimate the electron conversion coefficients in the 125,127 Ba nuclides.
INTRODUCTION
Hitherto a problem of the internal conversion
studying attracts a great interest, which is provided
by significant difficulties in theoretical and experimental
definition of the corresponding electron internal
conversion coefficients despite on the known
progress in development of the experimental methodologies
and technique [1-20]. From physical; point
of view, an internal conversion is a radioactive decay
process where an excited nucleus interacts with an
electron in one of the lower atomic orbitals, causing
the electron to be emitted from the atom. Thus, in an
internal conversion process, a high-energy electron is
emitted from the radioactive atom, but without beta
decay taking place. Decay spectroscopy using on-line
mass separators [2] has the advantage of allowing the
study of level properties in the low energy region, including
band head information, since gamma transitions
between low-spin states can be measured more
intensively under lower background conditions than
can those with in-beam spectroscopy measurements.
Below we consider spectra of the barium isotopes and
turn attention on definition of the corresponding internal
conversion electron coefficients. The neutronde@cient
nuclides of 125,127 Ba have been studied by
means of in-beam spectroscopy, and the level structures
for high-spin states were interpreted within the
framework of the IBFM model [2]. Decay studies of
these nuclides have rarely been reported. Therefore,
the last 1996, 1999 evaluations were mainly based
on in-beam studies. The E1 transitions between parity
doublets are characterized by a two to four orders
of magnitude enhancement compared to those of
more normal cases. The 127–130 Ba isotopes were studied
by in-beam conversion electron measurements
by Cottle-Glasmacher-Johnson-Kemper (1993) and
Cottle-Glasmacher-Kemper (1992) ( see full review
in ref. [2]) to investigate for parity doublets, and no
evidence of them was observed [13-16]. These studies,
however, focused only on the conversion electron
measurements; the transition probabilities were
not measured. It is necessary to measure not only the
conversion electrons, but also the half-lives of the excited
states in order to explain this feature. The aim
of this investigation is to study theoretically the level
properties of 125,127 Ba in the low energy region, focusing
on consideration of the E1 transitions, and their
electron conversion characteristics using the relativistic
DF method (modified Dirac code) (see refs. [5-
7]). Below we present the key details of this approach
and then consider the low energy levels spectrum and
internal conversion schemes in nuclides of 125,127 Ba.
2. THE RELATIVISTIC DIRAC-FOCK
METHOD
Standard approach to calculating the electron
conversion characteristics is based on the usual nonrelativistic
Hartree-Fock (HF) or Hartree-Fock-Slater
(HFS) approach with account of the finite nuclear
size [17]. More comprehensive calculation must be
based on the relativistic approaches, in particular, the
well known DF method (see e.g. [5-7]). Though these
methods are the most wide-spread calculation methods,
but, as a rule, the corresponding orbital basis’s are
not optimized. It often lead to the quite large errors
in calculating the fundamental atomic characteristics.
Besides, some problems are connected with correct
definition of the nuclear size effects, QED corrections
etc. In ref. [17] calculation was based on relativistic
HFS wave functions with the coefficient C = 1 for the
exchange term and on the assumption that the potential
is the same for all electrons, including the emitted
one. Experimental binding energies were used. Finite
nuclear size is taken into account, but the penetration
terms are not tabulated. In our work we use ab initio
relativistic DF (modified Dirac code) approach [5-7]
to calculating wave functions basis’s and electron conversion
coefficients for Ba isotopes with account of the
nuclear effects.
To define a nuclear potential it is usually used the
Fermi model for a charge distribution ρ () r :
с( r) = с0 /{1 + exp[( r− c) / a)]}
(1)
where the parameter a=0.523 fm, the parameter ñ is
chosen by such a way that it is true the following condition
for average-squared radius:
1/2 =(0.836⋅A1/3 +0.5700)fm.
Further let us present the formulas for the finite
size nuclear potential and its derivatives on the nuclear
radius. If the point-like nucleus has the central potential
W( R), then a transition to the finite size nuclear
potential is realized by exchanging W(r) by the potential
[8]:
r
2 2
( ) = () ∫ ρ ( ) + ∫ ()( ρ ) . (2)
W r R W r dr r r R dr r W r r R
0
∞
r
© I. N. Serga, 2009

We assume it as some zeroth approximation. The
nuclear potential for spherically symmetric density
ρ rR is:
( )
nucl ( ) (
r
∞
' '2 ' ' ' '
( 1 ) ( ) ( )
∫ ∫ (3)
V r R =− r drr ρ r R + drrρr R
0
It is defined by the following system of differential
equations [7]:
r
'
nucl
2 ' '2 ' 2
0
2
( , ) = ( 1 ) ρ( , ) ≡(
1 ) ( , )
V r R r ∫ drr r R r y r R (4)
0
( ) = ρ ( )
y' r, R r r, R
с '( r) = ( с / a)exp[( r− c) / a]{1+ exp[( r− c) / a)]}
with corresponding boundary conditions. The master
system of equations includes the equations for density
distribution function too. The normalisation of electron
radial functions f and g provides the behaviour of these
i i
functions for large values of radial valuable as follows:
g (r)→r i -1 [(E+1)/E] 1/2 sin(pr +Δ ), (5)
i
f (r)→r i -1 (i/|i|) [(E-1)/E] 1/2 cos (pr+Δ ). i
The DF equations for N-electron system are written
and contain the potential: V(r)=V(r|nlj)+V +V(r|R),
ex
which includes the nuclear, electric and mean-filed potentials.
The general analysis shows that the DF method
allow getting the results, which are more precise in
comparison with analogous HF or HFS data. From the
other side, it is well known in the modern atomic physics
that above cited mean-filed methods are needed to
be improved by means using obligatorily optimization
of the relativistic orbital basis’s (see details in ref. [7]).
3. LOW ENERGY LEVEL SPECTRUM AND
INTERNAL CONVERSION IN 125,127 BA
NUCLIDES
In ref. [2] the half-lives and electron conversion
coefficients were measured for the first time through
the decays of 125,127 La, by means of a delayed coincidence
technique and a cooled Si (Li) detector, respectively.
In this work the radioactivities of 125,127 La were
produced with the heavy-ion-induced fusion evaporation
reactions of nat Mo( 32 S, pxn) with a 160-MeV 32 S
beam (~50 pnA) from a tandem accelerator (MP20)
of JAERI [2]. Internal conversion electrons were measured
with a cooled Si (Li) detector (500mm 2 x 3 mm;
2.5-keV full width at half maximum at 976-keV electrons
of 207 Bi). Simultaneously, gamma rays were measured
with a 20% HPGe detector with 180° geometry
in order to obtain the peak intensity ratios between the
electrons and g rays. Some conversion coefficients of
transitions below 100 keV were determined by means
of x-gamma or γ-γ coincidence measurements with
the LEPS and the Ge detector with 180° geometry.
In addition, gamma-ray intensity measurements were
performed with the HPGe detector and the LEPS with
source-todetector distances of 10 and 5 cm, respectively.
The full energy peak efficiencies for the detectors
were determined using standard sources of 56 Co,
133 Ba, 152 Eu, and 241 Am. Further, the half-life of 127m Ba
r
2
was deduced to be 1.93(7) s from the decay curves of
the 24.0-, 56.3-, and 80.2-keV gamma rays by spectrum
multiscaling measurements with an A=127 beam
[2], which mainly consisted of the metallic state of
barium. The contribution of 127 La decay to the 56.3keV
gamma ray was corrected using the other gammaray
intensities of 127 La. It should be also noted that the
relative intensities of the three gamma-rays associated
with the decay of 127m Ba were obtained on experiment
[2] much more precisely than were those of Liang et
al. It is important to note that above 100 keV, the a K s
were determined in experiment [2] by taking the peak
intensity ratios of the electrons to the simultaneously
measured gamma rays. These values were normalized
by using the pure E2 (2 + →0 + ) 230-keV transition in
124 Ba. The experimental values and the assigned multipolarities
are shown in Fig. 1 and are also listed in.
Table 1,2 together with our theoretical data and calculation
values by Rossel et al. [17, 18]. In 125 Ba nuclide
the a K values of the 43.7- and 67.2-keV transitions
were deduced from the x-gamma coincidence method
with the 281.9- and 521.6-keV g rays, respectively. In
this method, the coincidence events with β + -particles
were also taken into account to distinguish the K x rays
from the originating EC decay and the internal conversion
process. Assuming the multipolarity of the
56.3-keV transition to M1 or E2, the a T value of the
25.1-keV transition was deduced to be 6.9–20.2. The
calculated value by Rossel et al. [17] supports that the
25.1-keV transition is M1. Similarly, the a T value of the
24.0-keV transition was deduced to be (0.6–1.6)⋅10 3
from the gamma-ray relative intensity. It is interesting
to compare here our theoretical estimates and data
by by Rossel et al [17], which are 1.1⋅10 3 and 8.5⋅10 4
for M2 and E3, respectively, the 24.0-keV transition
can be considered mainly an M2 transition. The other
a K values of the 79.4-, 114.3-, 128.7-, 134.3-, 220.4-,
243.0-, 253.3-,269.6-, 285.6-, and 318.7-keV γ transitions
associated with the decay of 127 La are deduced
from the electron internal conversion measurements.
E i t l K i ffi i t f t iti i 125 B (
Fig. 1. Experimental K conversion coefficients of transitions
in 125 Ba (a) and 127 Ba (b).
89

Table 1
The theoretical and experimental internal conversion coefficients
of transitions in 125 Ba.
E γ
(keV)
43.7
98.7
134.0
168.5
193.5
216.3
237.3
281.9
90
Assign.
Multip.
M1/E2
M1/E2
M1/E2
M1/E2
M1/E2
M1/E2
E2
E2
Exp.
[2]
8.9(5)
1.0(4)
0.36(14)
0.21(8)
0.12(4)
0.13(4)
0.056(17)
0.046(14)
Theory
[17]
E2
7.71
1.28
0.486
0.236
0.149
0.104
0.0770
0.0446
Theory
[17]
M1
9.37
0.895
0.378
0.200
0.137
0.101
0.0791
0.0510
Our
Theory
E2
7.5039
1.1183
0.4951
0.2396
0.1504
0.1307
0.0782
0.0459
Our
Theory
M1
9.0562
0.9340
0.3824
0.2113
0.1480
0.1298
0.0801
0.0522
The analysis of theoretical data shows that at first
as DF theory as HFS [17] theory provide in principle
physically reasonable description of the electron internal
conversion phenomenon and its characteristics.
It is obvious that using DF approach gives more high
accuracy for majority of transitions. At the same time
more accurate account for the correlation, QED, nuclear
effects is needed to get more comprehensive description
of the phenomenon. One of the obvious ways
to reach it is in using more sophisticated theoretical
schemes, in particular, optimized QED perturbation
theory with the optimized DF zeroth approximation
(see e.g. [5,7]).
Table 2
The theoretical and experimental internal conversion coefficients
of transitions in 127Ba E γ
(keV)
25.1
56.3
79.4
114.3
128.7
220.4
243.0
253.3
269.6
285.6
318.7
Assign.
Multip.
M1
M1/E2
M1/E2
M1/E2
M1/E2
M1/E2
M1/E2
M1/E2
E2
M1/E2
E2
Experiment
[2]
6.9–20.2
5.0(4)
2.0(1)
1.0(5)
1.2(5)
0.097(30)
0.078(25)
0.087(30)
0.062(28)
0.047(15)
0.035(10)
Theory
[17]
E2
537
5.50
1.26
0.803
0.553
0.0975
0.0713
0.0625
0.0513
0.0428
0.0305
Theory
[17]
M1
8.46
4.53
0.666
0.591
0.423
0.0963
0.0742
0.0665
0.0564
0.0484
0.0364
Our
Theory
E2
108
5.7220
1.5812
0.9320
0.7791
0.0988
0.0746
0.0693
0.0568
0.0447
0.0323
Our
Theory
M1
7.0421
4.7010
1.0292
0.7062
0.6851
0.0973
0.0771
0.0735
0.0621
0.0502
0.0388
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I.N. Serga
ELECTRON INTERNAL CONVERSION IN THE 125,127 BA ISOTOPES
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Radiation and Isotopes. — 2000. — Vol.52, N3. — P.557-
567.
10. Nica N., Hardy J.C., Iacob V.E., Rockwell W.E., Trzhaskovskaya
M.B., Internal conversion coefficients for rheavy elements,
Phys. Rev. C-2007. — Vol.75. — P.024308.
11. Raman, S., Nestor Jr., C.W., Ichihara, A. and Trzhaskovskaya,
M.B., How good are the internal conversion coefficients
now// Phys. Rev. — 2002. — Vol.C66. — P.044312.
12. Band I.M., Trzhaskovskaya M.B., Nestor Jr., C.W., Tikkanen
P.O. and Raman S., Dirac-Fock internal conversion
coefficients// Atomic Data and Nucl Dat Tables. — 2002. —
Vol.81. — P.1-334.
13. Kibedi T., Burrows T., Trzhaskovskaya M.B., Davidson P.,
Nestor C., Evaluation of theore-tical conversion coefficients
using BrIcc // Nucl. Instr. and Meth. — 2008. — Vol.A589. —
P.202-229
14. Hofmann, C.R., Soff, G., Total and differential conversion
coefficients for the internal pair creation in extended nuclei//
Atomic Data and Nucl Dat Tables. — 1996. — Vol.63. —
P.189-273.
15. Coursol N., Gorozhankin V. M. , Yakushev E. A. , Briançon C.
and Vylov V., Analysis of internal conversion coefficients//Applied
Rad. and Isotopes. — 2000. — Vol.52,N3. — P.557-567.
16. Safronova U.I., Mancini R., Atomic data for dielectronic satellite
lines and dielectronic recombination into Ne 5+ // Atomic
Data and Nucl. Data Tabl. — 2009. — Vol.95. — P.54-95.
17. Rossel F., Fries H.M., Alder K., Pauli H.C., Internal conversion
coefficients for all atomic shells //Atomic Data Nucl.
Tables. — 1998. — Vol.21. — P.91-289.
18. Firestone R.B., Shirley V.S., Table of Isotopes, 8th ed. —
N.-Y.: Wiley, 2006.
Abstract
The work is devoted to a theoretical studying of the electron internal conversion phenomenon in the 125,127 Ba nuclides. The relativistic
Dirac-Fock (modified Dirac code) method is used in order to estimate the electron conversion coefficients in the 125,127 Ba nuclides.
Key words: electron internal conversion, relativistic theory, barium isotopes.

ÓÄÊ 539.184
È. Í. Ñåðãà
ÂÍÓÒÐÅÍÍßß ÊÎÍÂÅÐÑÈß ÝËÅÊÒÐÎÍÎÂ Â ÈÇÎÒÎÏÀÕ 125,127 BA
Ðåçþìå
Ðàáîòà ïîñâÿùåíà òåîðåòè÷åñêîìó èçó÷åíèþ ýôôåêòà âíóòðåííåé êîíâåðñèè ýëåêòðîíîâ â èçîòîïàõ 125,127 Ba. Íà îñíîâå
îïòèìèçèðîâàííîãî ðåëÿòèâèñòñêîãî ìåòîäà Äèðàêà-Ôîêà (Dirac êîä) âûïîëíåíà îöåíêà êîýôôèöèåíòîâ âíóòðåííåé êîíâåðñèè
ýëåêòðîíîâ â íóêëèäàõ 125,127 Ba.
Êëþ÷åâûå ñëîâà: âíóòðåííÿÿ êîíâåðñèÿ ýëåêòðîíîâ, ðåëÿòèâèñòñêàÿ òåîðèÿ, èçîòîïû áàðèÿ.
ÓÄÊ 539.184
². Ì. Ѻðãà
ÂÍÓÒвØÍß ÊÎÍÂÅÐÑ²ß ÅËÅÊÒÐÎͲ  ²ÇÎÒÎÏÀÕ 125,127 BA
Ðåçþìå
Ðîáîòà ïðèñâÿ÷åíà òåîðåòè÷íîìó âèâ÷åííþ åôåêòó âíóòð³øíüî¿ êîíâåðñ³¿ åëåêòðîí³â â ³çîòîïàõ 125,127 Ba. Íà îñíîâ³ îïòèì³çîâàíîãî
ðåëÿòèâ³ñòñüêîãî ìåòîäó ijðàêà-Ôîêà (Dirac êîä) âèêîíàíà îö³íêà êîåô³ö³ºíò³â âíóòð³øíüî¿ êîíâåðñ³¿ åëåêòðîí³â
ó íóêë³äàõ 125,127 Ba.
Êëþ÷îâ³ ñëîâà: âíóòð³øíÿ êîíâåðñ³ÿ åëåêòðîí³â, ðåëÿòèâ³ñòñüêà òåîð³ÿ, ³çîòîïè áàð³ÿ.
91

Previously, the influence of hydrogen peroxide
concentration, dissolved in water solutions upon intensity
of a luminescence of aluminium metal-oxide
films, dipped in these solutions, has been investigated
[1]. Because of the fact that aluminum oxide films are
structures with high catalytic activity surface, it is possible
the using these films as environment composition
sensors.
In [2] the presence of a series of thermostimulated
luminescence (TSL) maxima, thermostimulated exoelectronic
emission (TSEE) is shown and also the occurrence
of potential difference between electrodes of
Al-Al 2 O 3 -SnO 2 structure was observed for aluminum
oxide films, which adsorbed only water or water vapours
[3]. It indicates the sensitivity of investigated
structures to a level of humidity, and, obviously, is
caused by surface metal oxide states. In this connection,
it was interesting to continue studying of influence
of chemical processing upon aluminum oxide
films on intensity of an arising luminescence in water
solutions of various compounds. With this purpose it
is important to study TSL spectra. Besides, it was of
interest also to find out the influence of other substances,
dissolved in water solutions, on intensity of
aluminum oxide films luminescence dipped into these
solutions.
In this work, aluminum oxide films, formed on
aluminum foil of the technical cleanliness by an electrochemical
method in a water solution of sorrel acids
[3] were investigated. TSL curves have been measured
on the experimental setup, consisting of the lightproof
box, IR-absorbing filter, photoelectronic multiplier,
low current measuring device, copper-constantan
thermocouple and recorder. Heating speed was maintained
constant and was 0,3 Ê/sec.
It is known [2], that in the temperature interval
from room up to 600 K some maxima are observed
in TSL spectra of aluminum oxide films. They correspond
to various forms adsorbate and adsorbent binding.
We have established, that as result of processing
aluminum oxide in water solutions of some inorganic
compounds, additional ÒSL bands appear and peaks,
which existed earlier, quench. Chemical processing
was carried out by boiling in Na 2 SO 4 , NaCl, NaI 0,1
N water solutions.
In fig. 1 ÒSL curves of Al 2 O 3 films are presented
in the temperature interval from 450 up to 630 K,
processed in: 1 — water, 2 — NaCl, 3 — Na 2 SO 4 ,
4 — NaI. Only the centers, responsible for TSL in this
temperature interval, are not deactivated by sodium
92
UDC 535.37
L. N. VILINSKAYA, G. M. BURLAK
The Odessa State Academy of Building and Architecture
4, Didrichson str., Odessa, 65082 Ukraine, ph. 8 (048) 7-206-743
SENSORS ON THE BASIS OF ALUMINIUM METAL-OXIDE FILMS
Aluminum oxide films sensitivity to water solutions of inorganic compounds, the ammonia dissolved
in water and in a gas atmosphere, and also to water vapours is established. The possibility of
sensors’ fabrication on base of metal oxide films is shown.
ions which were contained in all compounds we used.
From fig. 1 it is seen, that the maximum at 560 K is
observed in all samples. Therefore, obviously, is connected
with dissociative water adsorption which also
was available in all cases.
B, rel.un.
10
8
6
4
2
0
460 480 500 520 540 560 580 600 620 640
T, K
Fig. 1. TSL curves of Al 2 O 3 films processed in: 1 — water,
2 — NaCl, 3 — Na 2 SO 4 , 4 — NaI
The observed catalytic activity increase develops
in the fact that after processing in sodium chloride
the effective lightsum storage of the sample takes not
hours but minutes. It can be explained by the fact that
chlorine ions in a small amount increase catalytic
activity of aluminum oxide surface. Chlorine forms
strong bonds with valence and coordinated unsaturated
aluminum atoms. While samples are in the air
the dissociative adsorption of water and its vapour appears
with creation of charged dopant OH - complexes
which carry out a role of adsorptive nature traps. This
process occurs quickly enough. As the energy distance
between the levels created by hydroxyl and chlorine
ions on a surface is very small (approximately 0,06 eV)
[3], a part of carriers transfers to chlorine levels even
at room temperatures and then are thermally released
to the conduction band. As to others used anions, they
do not change surface catalytic activity. Therefore,
enough quantity charged hydroxyl groups has no time
to be created.
The influence of ammonia concentration dissolved
in water solutions (in particular, sea water) on
the intensity of aluminum oxide films luminescence,
dipped in these solutions has been studied. The luminescence
intensity was weak. Thus, the alternating
1
2
3
4
© L. N. Vilinskaya, G. M. Burlak, 2009

voltage of about 1,3 V was applied providing electrolyte
ions to the semiconductor surface but insufficient
for electroluminescence excitation. Preliminary,
the intensity aluminum oxide films luminescence in
NaCl 3 % solution has been determined. After that,
concentration of ammonia in this electrolyte was created.
Luminescence intensity changes were measured.
The addition of the few doses of ammonia increased
aluminum oxide films emission intensity (Fig.2). The
sensors sensitivity depends on technology metal oxide
films preparation and temperature. The sensors were
investigated in a temperature interval 278-354 K.
The threshold of detecting is maximal in temperature
interval 288-302 K. These results allow us to create
sensors for ammonia concentration measurements
in water solutions, operating at temperature range of
278-353 K.
B, rel.un.
10
8
6
4
2
0
10 -9
10 -7
N, mol/l
Fig. 2. Dependence aluminum metal-oxide films luminescence
intensity on concentration of ammonia dissolved in water
UDC 535.37
L. N. Vilinskaya, G. M. Burlak
SENSORS ON THE BASIS OF ALUMINIUM METAL-OXIDE FILMS
10 -5
10 -3
The influence water vapour and ammonia concentration
in a gas atmosphere on value EMF generated
by structures Al-Al O -SnO was studied. Such struc-
2 3 2
tures were also created by electrochemical oxidizing of
aluminum foil in sorrel acid water solution with next
deposition of SnO layer on aluminum oxide film by
2
SnCl pyrolysis method. It is established, that the ap-
4
pearance of EMF occurs in following way. Because
porosity of SnO layers, a penetration of adsorbed
2
molecules of water or ammonia from a gas atmosphere
into micro pores of oxide film is possible. The aluminum
oxide surface is catalytically active and consequently
adsorbed molecules dissociation takes place.
Dissociation products (positive and negative charged
ions and electrons) get space separation along the film
thickness because of the difference in their diffusion
coefficients. The space separation continues until an
internal electric field will arise and balance the diffusion
flow of dissociation products. As a result, potential
difference between aluminum and SnO electrode
2
arises. The value of this potential difference depends
on ammonia concentration in a gas atmosphere. Detection
threshold of these sensors is 0,1 g/m3 .
It can be concluded, that aluminum oxide films
are able to be used as sensors for ammonia detection in
a gas atmosphere, in water and some inorganic compound
solutions.
References
1. Áóðëàê Ã.Ì., Âèëèíñêàÿ Ë.Í. Âëèÿíèå ïåðåêèñè âîäîðîäà
íà èíòåíñèâíîñòü ëþìèíåñöåíöèè ïîëóïðîâîäíèêîâûõ
ïëåíîê. //Ñåíñîðíàÿ ýëåêòðîíèêà è ìèêðîñèñòåìíûå
òåõíîëîãèè.. ¹4. 2008. Ñ.53-55.
2. Ìèõî Â.Â., Ðîáóë Þ.Â., Òèìîôååâà Å.Þ., Áàëàáàí
À.Ï.//Ôîòîýëåêòðîíèêà. — 2000. — Âûï.9. — Ñ.35-37.
3. Ìèõî Â.Â., Ñåìåíþê Ë.Í. Ãåíåðàöiÿ ÝÐÑ ó ïëiâêàõ
îêñèäó àëþìiíiþ //ÓÔÆ. 1995. — Ò.40. — ¹11-12. —
Ñ.1209-1211.
Abstract
Aluminum oxide films sensitivity to water vapors, to water solutions of inorganic compounds, the ammonia dissolved in water and
a gas atmosphere is established. The possibility of sensors fabrication on a basis of metal oxide films is shown.
Key words: sensors, sensitivity, aluminum oxide.
ÓÄÊ 535.37
Ë. Í. Âèëèíñêàÿ, Ã. Ì. Áóðëàê
ÑÅÍÑÎÐÛ ÍÀ ÎÑÍÎÂÅ ÏËÅÍÎÊ ÎÊÑÈÄÀ ÀËÞÌÈÍÈß
Ðåçþìå
Óñòàíîâëåíà ÷óâñòâèòåëüíîñòü îêñèäíûõ ïëåíîê àëþìèíèÿ ê âîäíûì ðàñòâîðàì íåîðãàíè÷åñêèõ ñîåäèíåíèé, àììèàêà,
ðàñòâîðåííîãî â âîäå è â ãàçîâîé àòìîñôåðå, à òàêæå ê ïàðàì âîäû. Ïîêàçàíà âîçìîæíîñòü ñîçäàíèÿ ñåíñîðîâ íà îñíîâå
îêñèäíûõ ïëåíîê.
Êëþ÷åâûå ñëîâà: ÷óâñòâèòåëüíîñòü, ñåíñîðû, îêñèä àëþìèíèÿ.
93

94
ÓÄÊ 535.37
Ë. Í. ³ë³íñüêà, Ã. Ì. Áóðëàê
ÑÅÍÑÎÐÈ ÍÀ ÎÑÍβ Ï˲ÂÎÊ ÎÊÑÈÄÓ ÀËÞ̲ͲÞ
Ðåçþìå
Âñòàíîâëåíî ÷óòëèâ³ñòü îêñèäíèõ ïë³âîê àëþì³í³þ äî âîäÿíèõ ðîç÷èí³â íåîðãàí³÷íèõ ñïîëóê, àì³àêó, ðîç÷èíåíîãî ó âîä³
òà ó ãàçîâ³é àòìîñôåð³, à òàêîæ äî âîäÿíî¿ ïàðè. Ïîêàçàíî ìîæëèâ³ñòü ñòâîðåííÿ ñåíñîð³â íà îñíîâ³ îêñèäíèõ ïë³âîê.
Êëþ÷îâ³ ñëîâà: ÷óòëèâ³ñòü, ñåíñîðè, îêñèäí³ ïë³âêè àëþì³í³þ.

UDC 621.315.592
O. O. PTASHCHENKO 1 , F. O. PTASHCHENKO 2 , V. V. SHUGAROVA 1
1 I. I. Mechnikov National University of Odessa, Dvoryanska St., 2, Odessa, 65026, Ukraine
2 Odessa National Maritime Academy, Odessa, Didrikhsona St., 8, Odessa, 65029, Ukraine
TUNNEL SURFACE CURRENT IN GaAs–AlGaAs P-N JUNCTIONS, DUE
TO AMMONIA MOLECULES ADSORPTION
1. INTRODUCTION
P-n junctions as gas-sensitive devices [1, 2] have
some advantages in comparison with structures, based
on oxide polycrystalline films [3, 4] and Shottky diodes
[5, 6]. P-n junctions have high potential barriers
for current carriers, which results in low background
currents. Sensors on p-n junctions [1, 2] have crystal
structure, high sensitivity at room temperature
In previous papers the gas sensitivity of p-n structures
on GaAs and GaAs–AlGaAs [1, 2], GaP [7],
InGaN [8], and Si [9, 10] was investigated. . It was
shown that the gas sensitivity of all these p-n junctions
is due to forming of a surface conducting channel in
the electric field induced by the ammonia ions adsorbed
on the surface of the natural oxide layer. The
gas-sensitivity of the forward current in p-n junctions
is limited by strong rise of the injection current with
the bias voltage. The voltage-limit for the reverse current
is substantially higher. Therefore, under some
conditions, the gas-sensitivity of the reverse current
can be higher than the forward one.
The aim of this work is a study of the influence
of ammonia vapors on the forward and reverse currents
in a GaAs–AlGaAs p-n heterostructure with a
degenerated p + -GaAs layer. It is shown that, at high
enough concentration of ammonia in the ambient
atmosphere, a surface conducting channel with degenerated
electrons is formed and tunnel forward and
reverse currents are observed.
2. EXPERIMENT
The influence of ammonia vapors on I-V characteristics of forward and reverse currents and kinetics
of surface currents in GaAs-AlGaAs p-n junctions with degenerated p + region was studied. It
is shown that ammonia molecules adsorption, under sufficiently high NH 3 partial pressure, forms in
p-AlGaAs a surface conducting channel with degenerated electrons. P-n junctions with degenerated
p + region have higher gas sensitivity at reverse bias than at forward bias. This effect is explained by
tunnel injection of electrons into the conducting channel from the degenerated p + region at a reverse
bias. The rise time of the surface current in an ammonia vapor atmosphere of ~20s is due to filling up
deep electron traps.
The measurements were carried out on p+-
GaAs(Zn) — p-Ga 0.45 Al 0.55 (Ge) — p-Ga 0.65 Al 0.35 (Ge) —
n- Ga 0.45 Al 0.55 (Ge) structures with a degenerated p +
layer.
I-V characteristics of the forward and reverse currents
were measured in air with various concentrations
of ammonia vapors. The current kinetics at the change
of the ambient atmosphere was observed.
Fig.1 represents I–V characteristics of the forward
current in a p-n structure in air (1) and in air with am-
© O. O. Ptashchenko, F. O. Ptashchenko, V. V. Shugarova, 2009
monia vapors of various partial pressures. The forward
current increases with enhanced NH 3 concentration.
At an ammonia pressure P>1000Pa a pronounced
peak in the I-V curve is observed witch can be ascribed
to electron tunneling between the c–band in the surface
conducting channel and the v– band in the degenerated
p + region. It means also that electrons in the
channel are degenerated.
10 -6
10 -7
10 -8
I, A
0
5
6
4
3
0.5 1.0
V, Volts
1.5
Fig. 1. I–V characteristics of the forward current in a p-n
structure in air (1) and in ammonia vapors of a pressure: 2 — 50 Pà;
3 — 100 Pà; 4 — 200 Pà; 5 — 1000 Pà; 6 — 4000 Pà
Curves 1– 4 in Fig. 2 delineate the I–V curves of
he forward and reverse currents in a p–n junction,
placed in air with various ammonia partial pressures. It
is seen that the reverse current is greater than forward
one at the same ammonia pressure. It is characteristic
for tunnel currents in tunnel- and inverted diodes.
2
1
95

96
3. DISCUSSION
Curves 1 and 2 in Fig. 2 were obtained at ammonia
pressures of 20 Pa and 100 Pa, respectively. As seen
from the I–V curves sections, corresponding to V>0,
the tunnel forward current under these pressures is
small. And the reverse currents are remarkably higher
than forward ones. It is characteristic of inverted diodes
and argues that tunneling of electrons at reverse
biases occurs from the degenerated p + region.
I, μA
0.8
0.4
0
-0.4
1
2
3
-0.8
-6 -4 -2 0
V, Volts
2
4
Fig. 2. I–V characteristics of a p-n structure in ammonia
vapors of a pressure: 1 — 20 Pà; 2 — 100 Pà; 3 — 1000 Pà; 4 —
4000 Pà
Fig. 3 shows a simplified band diagram of the p-n
junction with degenerated p + region. The Fermi level
F is located in the v-band in p + 0
0 0,2 0,4 0,6
Vr, Volts
region. The occupied
states area is dashed. However the Fermi level lies by
ΔE below c-band in n-region. In our case n-region
Fig. 4. Low-bias sections of I–V characteristics of the reverse
current in a p-n structure in ammonia vapors of a pressure: 1 —
20 Pà; 2 — 50 Pà; 3 — 100 Pà; 4 — 4000 Pà
corresponds to the conducting surface channel. De- The dependence of the cutoff voltage on the ampending
on the ammonia partial pressure, ΔE change monia partial pressure P is shown in Fig. 5. This depen-
can be estimated from the expression
dence is logarithmic, however, the proportionality coef-
ns = Nc exp( −Δ E/ kT)
, (1)
ficient is nkT p / q with n =1.4 — 1.5 instead kT / q .
p
The discrepancy between the model prediction
where n is the electrons concentration in the channel
s
at the surface; N is the effective density of states in c-
c
band; k is the Boltzmann constant; T is temperature.
It is evident from Fig. 3, that the strong rise of the current
with reverse bias voltage V must begin at
r
Vr= V0 = Δ E/ q,
(2)
where q is the electron charge. Therefore the cutoff reverse
bias voltage V must logarithmic depend on the
0
electrons concentration in the conducting channel,
formed by the electric field of ammonia ions:
and the experimental data can be ascribed to a variety
of factors. The most important of them are: a) dependence
of the effective channel width on the surface
electrons concentration n ; b) non-linearity of the de-
s
pendence n (P), caused by deep traps in the channel.
s
A strong influence of trapping processes on the
surface current in studied p-n structures is evident
from a comparison between the rise- and decay curves
of the surface current after let in- and off ammonia
vapor in the container with the p-n structure.
Fig. 6 illustrates the kinetic of the surface current
in a p-n structure after let in and removal of ammo-
V0 = kT / qln( Nc / ns)
. (3)
Fig. 4 represents low-bias sections of I–V characnia
vapor from the container with the sample. The rise
curve is exponential, i. e.
teristics of the reverse current in a p-n structure, situated
in ammonia vapors of various partial pressures.
The cutoff voltage was estimated as the intersection of
linearly extrapolated I-V curve with the abscise.
It ( ) = Ist[1 −exp( −t/ τ r )] , (4)
where I is the stationary value of I; the rise time τ =19.5 s.
st r
The decay curve is not exponential, with the 90% decay
F
�E
Fig. 3. Band diagram of an inverted diode at thermal equilibrium
I, nA
20
15
10
5
1
2
3
4
C
V

time τ 90 =4s. This time is comparable with the time of
changing the atmosphere in the container. Therefore the
true value of the surface current decay time τ d

98
surface current in p-n junctions on GaP // Photoelectronics.
— 2005. — No. 14. — P. 97 — 100.
8. Ptashchenko F. O. Effect of ammonia vapors on surface currents
in InGaN p-n junctions // Photoelectronics. — 2007. —
No. 17. — P. 113 — 116.
9. Ïòàùåíêî Ô. Î. Âïëèâ ïàð³â àì³àêó íà ïîâåðõõíåâèé
ñòðóì ó êðåìí³ºâèõ p-n ïåðåõîäàõ // ³ñíèê ÎÍÓ, ñåð.
Ô³çèêà. — 2006. — Ò. 11, ¹. 7. — Ñ. 116 — 119.
UDC 621.315.592
O. O. Ptashchenko, F. O. Ptashchenko, V. V. Shugarova
10. Ptashchenko O. O., Ptashchenko F. O., Yemets O. V. Effect
of ammonia vapors on the surface current in silicon p-n
junctions // Photoelectronics. — 2006. — No. 16. — P. 89 —
93.
11. Ptashchenko O. O., Ptashchenko F. O., Masleyeva N. V. et
al. Effect of sulfur atoms on the surface current in GaAs p-n
junctions // Photoelectronics. — 2007. — No. 17. — P. 36 —
39.
TUNNEL SURFACE CURRENT IN GaAs–AlGaAs P-N JUNCTIONS, DUE TO AMMONIA MOLECULES ADSORPTION
Abstract
The influence of ammonia vapors on I-V characteristics of forward and reverse currents and kinetics of surface currents in GaAs-
AlGaAs p-n junctions with degenerated p + region was studied. It is shown that ammonia molecules adsorption, under sufficiently high
NH 3 partial pressure, forms in p-AlGaAs a surface conducting channel with degenerated electrons. P-n junctions with degenerated p +
region have higher gas sensitivity at reverse bias than at forward bias. This effect is explained by tunnel injection of electrons into the conducting
channel from the degenerated p + region at a reverse bias. The rise time of the surface current in an ammonia vapor atmosphere
of ~20 s is due to filling up deep electron traps.
Key words: tunnel surfeace current, adsorbption, junctions.
ÓÄÊ 621.315.592
À. À. Ïòàùåíêî, Ô. À. Ïòàùåíêî, Â. Â. Øóãàðîâà
ÒÓÍÍÅËÜÍÛÉ ÏÎÂÅÐÕÍÎÑÒÍÛÉ ÒÎÊ Â P-N ÏÅÐÅÕÎÄÀÕ ÍÀ ÎÑÍÎÂÅ GaAs–AlGaAs, ÎÁÓÑËÎÂËÅÍÍÛÉ
ÀÄÑÎÐÁÖÈÅÉ ÌÎËÅÊÓË ÀÌÌÈÀÊÀ
Ðåçþìå
Èññëåäîâàíî âëèÿíèå ïàðîâ àììèàêà íà ÂÀÕ ïðÿìîãî è îáðàòíîãî òîêîâ è íà êèíåòèêó ïîâåðõíîñòíûõ òîêîâ â p-n
ïåðåõîäàõ íà îñíîâå GaAs-AlGaAs ñ âûðîæäåííîé p + îáëàñòüþ. Ïîêàçàíî, ÷òî àäñîðáöèÿ ìîëåêóë àììèàêà ïðè äîñòàòî÷íî
âûñîêîì ïàðöèàëüíîì äàâëåíèè NH 3 ñîçäàåò â p-AlGaAs ïîâåðõíîñòíûé ïðîâîäÿùèé êàíàë ñ âûðîæäåííûìè ýëåêòðîíàìè.
P-n ïåðåõîäû ñ âûðîæäåííîé p + îáëàñòüþ èìåþò áîëåå âûñîêóþ ãàçîâóþ ÷óâñòâèòåëüíîñòü ïðè îáðàòíîì ñìåùåíèè, ÷åì
ïðè ïðÿìîì ñìåùåíèè. Ýòîò ýôôåêò îáúÿñíÿåòñÿ òóííåëüíîé èíæåêöèåé ýëåêòðîíîâ â ïðîâîäÿùèé êàíàë èç âûðîæäåííîé
p + îáëàñòè ïðè îáðàòíîì ñìåùåíèè. Âðåìÿ íàðàñòàíèÿ ïîâåðõíîñòíîãî òîêà ~20 ñ â ïàðàõ àììèàêà ñâÿçàíî ñ çàïîëíåíèåì
ãëóáîêèõ ýëåêòðîííûõ ëîâóøåê.
Êëþ÷åâûå ñëîâà: òóííåëüíûé ïîâåðõíîñòíûé òîê, àäñîðáöèÿ, ïåðåõîä.
ÓÄÊ 621.315.592
Î. Î. Ïòàùåíêî, Ô. Î. Ïòàùåíêî, Â. Â. Øóãàðîâà
ÒÓÍÅËÜÍÈÉ ÏÎÂÅÐÕÍÅÂÈÉ ÑÒÐÓÌ Â P-N ÏÅÐÅÕÎÄÀÕ ÍÀ ÎÑÍβ GaAs–AlGaAs, ÎÁÓÌÎÂËÅÍÈÉ
ÀÄÑÎÐÁÖ²ªÞ ÌÎËÅÊÓË À̲ÀÊÓ
Ðåçþìå
Äîñë³äæåíî âïëèâ ïàð³â àì³àêó íà ÂÀÕ ïðÿìîãî ³ çâîðîòíîãî ñòðóì³â òà íà ê³íåòèêó ïîâåðõíåâèõ ñòðóì³â ó p-n ïåðåõîäàõ
íà îñíîâ³ GaAs-AlGaAs ç âèðîäæåíîþ p + îáëàñòþ. Ïîêàçàíî, ùî àäñîðáö³ÿ ìîëåêóë àì³àêó ïðè äîñòàòíüî âèñîêîìó ïàðö³àëüíîìó
òèñêó NH 3 ñòâîðþº â p-AlGaAs ïîâåðõíåâèé ïðîâ³äíèé êàíàë ç âèðîäæåíèìè åëåêòðîíàìè. P-n ïåðåõîäè ç âèðîäæåíîþ
p + îáëàñòþ ìàþòü âèùó ãàçîâó ÷óòëèâ³ñòü ïðè çâîðîòíîìó çì³ùåíí³, í³æ ïðè ïðÿìîìó çì³ùåíí³. Öåé åôåêò ïîÿñíþºòüñÿ
òóíåëüíîþ ³íæåêö³ºþ åëåêòðîí³â â ïðîâ³äíèé êàíàë ³ç âèðîäæåíî¿ p + îáëàñò³ ïðè çâîðîòíîìó çì³ùåíí³. ×àñ íàðîñòàííÿ ïîâåðõíåâîãî
ñòðóìó ~20 ñ â ïàðàõ àì³àêó ïîâ’ÿçàíèé ³ç çàïîâíåííÿì ãëèáîêèõ åëåêòðîííèõ ïàñòîê.
Êëþ÷îâ³ ñëîâà: òóíåëüíèé ïîâåðõíåâèé ñòðóì, àäñîðáö³ÿ, ïåðåõ³ä.

UDC 544.187.2; 621.315.59
SH. D. KURMASHEV, T. M. BUGAEVA, T. I. LAVRENOVA, N. N. SADOVA
Odessa I.I.Mechnicov National University
Odessa, 65026, Ukraine, e-mail: kurm@mail.css.od.ua. Tel. (0482) — 746-66-58.
INFLUENCE OF THE GLASS PHASE STRUCTURE ON THE RESISTANCE
OF THE LAYERS IN SYSTEM “GLASS-RuO 2 ”
Influence of quantitative and qualitive (phase and granule-metric) composition of initial components
on the electro physical properties of thick films on the base of the systems “glass — clusters
RuO 2 , Bi 2 Ru 2 O 7 ” was investigated. At the fixed values of functional material content m f (RuO 2 ) and
glass phase m g , the increase of mass of crystalline phase m cr leads to decrease of conductivity, therefore
to the increase of resistance of resistive layer.
1. INTRODUCTION
Development of submicron and nanotechnology
in electronics involves not only active elements (lasers,
photodetectors and etc) but also those elements,
which are recognized as passive. They also include the
resistors of the integrated circuits. As it is generally
known, the resistance compositions on the basis of
dioxide of ruthenium (RuO 2 ) have good electro physical
properties [1]. Thick-film structures on the basis
of the systems “glass-RuO 2 , Bi 2 Ru 2 O 7 ” used as the
conductive resistive elements of the hybrid integrated
circuits, are little affected by high temperatures, as dioxide
of ruthenium does not dissolve in a glass matrix.
It allows to increase annealing temperature of resistance
pastes up to 1000 î Ñ. But the problems, related
to structural-phases transitions resulted from external
factors, which influence electro physical properties
of thick films on the base of RuO 2, Bi 2 Ru 2 O 7 , are still
unsolved. There is no one statifactory model of conductivity
mechanisms in the separate components
of ceramic layers and also information about contribution
of micro- and nano-geometry defects to the
conductivity mechanisms of thick resistance films.
Composition materials belong to multi phase heterosystems,
which include components with different
physical and chemical properties.
The study of properties of initial components,
organic and inorganic compositions, conductive and
dielectric phases, morphology and particle size distribution
become the primary goals in production of
thick-film elements.
In the present work , the influence of quantitative
and qualitive composition (phase and granule-metric)
of initial components on the electro physical parameters
of thick films on the base of the systems “glass —
clusters RuO 2 , Bi 2 Ru 2 O 7 ” was investigated.
2. EXPERIMENTAL
The main components of the composition systems
of thick film elements are:
– small-dispersion powders of functional material
(metals, oxides of metals), which provide formation of
conducting paths;
© Sh. D. Kurmashev, T. M. Bugaeva, T. I. Lavrenova, N. N. Sadova, 2009
– special glass frit carrying out the role of permanent
binder.
Functional materials (conducting phase) are
brought into paste as ultrafine particles with the maximal
size lower than 5 μm. The glasses are used as permanent
binder. On one side, the glass frit provides the
adherence of metal-enamel elements. On the other
side it creates “hard framework”, fixing position of
conducting particles inside the structure.
The shape and dispersion of particles of conducting
phase (RuO 2 ) strongly depends on the ruthenium
dioxide powder fabrication method. Usually, it is obtained
by hydrochloric ruthenium decomposition. At
a temperature a 300-400 î Ñ ruthenium dioxide forms
as ultrafine spherical particles. The optimal size of
annealed particles is (0,05 ÷ 0,1) μm. Maximal size
of the ruthenium dioxide particles shouldn’t exceed
(0,2 ÷ 0,3) parts of thickness of annealing layer. Character
of conductivity of resistive layers concerns by
potential barrier height of dielectric layer between
conducting particles. If the dielectric layer between
conducting particles is less than 100 Å, the tunnel
current is the basic mechanism of conductivity. If the
layer is more than 100 Å, tunnel effect is improbable
and charge carriers with energy higher than the height
of barrier can go over it. Thermal emission becomes
the basic mechanism of conductivity.
The influence of permanent binder (glasses of different
types) seems to be not so strong in chemical
interaction with a conducting phase, but it increases
through moistening and dissolution of its particles.
Moistening of functional material by glass and chemical
activity of glass have more important meaning. If
glass forms a thick continuous layer round every conductive
particle, the contact between particles is violated.
Consequently, it is needed, that glass moistened
particles not fully, but rather enough, that particles
were fixed in a matrix.
Electro physical properties of capacitance-resistance
elements largely depend on ratio of conductor
phase and permanent binder concentrations. Dependence
of electro physical properties of composition
structures on the basis of “glass-RuO 2 ” from ratio of
conducting phase RuÎ 2 and glass concentrations, sizes
of particles of glass and temperature of annealing
was investigated. The films were made from powders
of lead-boron-silicate glass of marked ¹ 279, 2005
99

(PbÎ, S³Î 2 , B 2 O 3 , Al 2 O 3 ) with the fixed sizes of particles
(0.5; 1; 3 and 5 μm) and functional material RuÎ 2
with the sizes of particles (0.05 ÷ 0.1) μm.
The system of analysis of images “QUANTIM-
ET — 720” and raster electronic microscope were used
for researches. Investigations of glasses phase composition
were carried by x-ray technique on DRON-2
with silicon grating monochromator (voltage 16 kV,
intensity of current 2 mA).
Dependence of resistance of the resistors from
concentration ratio of conductor phase and glass at
the fixed temperature of annealing (870 î Ñ) has been
obtained (fig. 1).
Fig. 1. Dependence of surface resistivity of thick layers from
concentration ratio of conductor phase and glass. Size of glass particles,
μm: 1 — 0.5; 2 — 1; 3 — 3; 4 — 5
The samples with low content of ruthenium dioxide
had the most influence from glass-frit particle size
on resistance of resistors. Resistance of films increased
with the enhance of glass portion. The highest rate of
resistance raise took place for glass-frit with the particles
size of 0,5 μm. With increase of RuO 2 concentration,
the resistance approaches to the saturated value
and does not depend on the glass-frit particles size.
Dependence of resistance from the particle sizes
for high resistivity films is affected by coalescence
of the particles and the influence of the components
dispersion on the geometrical sizes of. With glass particles
size decreasing, the current chainlets length
increases and their cross section area decreases. It is
observed mixed type of conductivity in the systems
“RuÎ 2 — glass”. The charge transport processes take
place in the conducting phase and glass-frit. In layers
with high resistivity, the main contribution in conductivity
is performed by glass-frit. Therefore, the state of
this phase acts important role in the process of charge
transport.
If the influence of high-quality composition of
conducting (functional) material is usually investigated
in details, usually, the glass is considered an
amorphous homogeneous environment. However, in
the process of investigations it is set, that glasses can
be crystallized as result of heat treatment. The x-ray
radiation can stimulate crystallization [2]. In addition,
100
particles of functional material can become the nucleation
centers of crystallization of glass matrix. The
presence of the crystallites in a matrix can cause local
changes of glass melt point and coating of functional
material particles by glass at heat treatment of film. It
leads to change of the parameters of the formed layer.
The phase composition of glasses has been determined
by XRD method. At first, the initial content of
the particles has been investigated. It was found XRD
peak at θ=15,50 (d = 3,35 Å) on the XRD diagram of
glasses ¹2005 in the initial state. The XRD diagram
of glass ¹279 did not have any peaks, related to crystalline
phase.
For determination of influence of heat treatment
on the phase state of glass, it was performed the annealing
procedure at 8700Ñ during 10 minutes. At the
same time, the samples were separated on two groups
to take in account influence of x-ray radiation. The
first group was annealed with subsequent XRD analysis.
The second one was processed by the consequence
XRD-annealing-XRD.
After annealing, XRD peak at θ=15,50 of ¹2005
samples (first group) increased in comparison to the initial
state. Weak peaks appeared at θ=12,10 (d = 4,27 о
А )
and θ=29,50° (d = 1,82 о
А ) in XRD curve of the second
group after x-ray irradiation and annealing, that
testifies to the increase of concentration of crystalline
phase. Identification of the observed peaks within
card index of ASTM showed that the peaks belonged
to α-SiO (quartz) modification. Comparison of the
2
XRD diagrams of glasses ¹2005 before and after heat
treatment showed that X-ray reflections from crystalline
phase increased as a result of increase of volume of
crystalline phase in these glasses after heat treatment.
Glasses ¹279 of first and second groups remained
amorphous.
The obtained results allowed to make some conclusions
about the influence of heat treatment on
phase composition of glasses:
– glass ¹279 had strong amorphous structure,
the crystalline phase nucleation disappeared by time
and never appear after the heat treatment;
– glass ¹2005 already contained the crystalline
phase in the initial state, the volume of crystalline
phase increased with time in all stages of heat treatment.
Thus, it is found that heat treatment caused formation
of new phases, and also rebuilding of energetic
zones of the system. As the crystalline phase found
in glass α-SiO had the temperature of melting over
2
15000Ñ, and coalescence of resistance layers took
place usually at 870 0Ñ. The crystalline phase of glass
didn’t melt and there were local structural deviations
in the volume of matrix, that influenced the formation
of conducting chainlets. In addition, the random
breaks of conducting chainlets made disorder of structure
of chainlets of conductivity in the volume of the
film. It is set that presence of crystalline phase α-SiO2 in glass increases resistance of the sample (∼ 10%).
Properties of glass phase play an important role in
conductivity of films. In fiq.2, the dependence of surface
resistivity of thick films from the percent concentration
of crystalline phase m in glass-frit is presented.
cr
It is seen that with the increase of m the resistance of
cr,
films increased.

Fig. 2. Dependence of surface resistivity of films from percent
concentration of crystalline phase m cr in glass-frit. Table of
contents of glass-frit in the system “glass — clusters RuO 2 ” m g , %:
1 — 40; 2 — 50; 3 — 60
3. DISCUSSION
Electrical properties of the films on the base of the
systems “glass — clusters RuO 2 , Bi 2 Ru 2 O 7 ” are defined
by the mechanisms of conductivity, which strongly depend
on physical properties of initial components and
microstructure of layers. The structure of films depends
on the technological factors of their fabrication
and properties of initial components. Phase composition
of glass-frit is also an important factor.
In [2] it was obtained mixed character of conductivity
as combination of processes which flow in conducting
phase and glass-phase. The conducting phase
had metallic conductivity. Charge transport through
the thin layers of glass-phase, surrounding the conducting
phase, takes place by means of tunneling effect
in a low energetic zone, which appears after doping of
glass with ions, diffunding from the conducting phase.
Through research of resistance layers on basis RuO 2 ,
it was determined traces of presence of cristobalite in
the layers– one of crystalline modifications SiO 2 , which
decreased conductivity of resistors. According to that, it
is interesting to develop a model which explains influencing
of crystalline phase α-SiO 2 in amorphous glass
matrix on conductivity of thick resistance films, based
on the system “glass — clusters RuO 2 ”.
A thick-film element can be presented as aggregate
of conducting chainlets from one electrode to other,
which consist of conducting particles of functional
material. Conducting ³-chain appears with probability
p ³ , which includes probability of that all elements of
chainlet are conductors (p 1 ) and probability of continuity
of chainlet in a glass matrix from one electrode to
other (p 2 ). It means that p ³ = p 1 ⋅ p 2 . In this model probability
p 1 of conductivities of all elements of chainlet is
proportional to mass part of functional material m f in
bulk of dry powder in paste m p : p 1 = k 1 ∙m f / m p . Here k 1
is coefficient of proportion. Probability of formation
of continuous chainlet from one electrode to other is
proportional to mass of functional material m f and inversely
proportional to mass of glass-frit m g : p 2 = k 2 ∙
m f /m g . Here, k 2 is coefficient of proportion. Mass of
powder m p = m f + m g .
In the case of presence of crystalline phase in
glass it is necessary to take into account another factor.
The presence of crystalline phase SiO in fusible
2
glass is equivalently adding unfire-polished particles
in the glass, beacause temperature of melting of any
of modifications SiO is considerably higher than the
2
temperature of sintering of layer. Under sintering, the
local regions of the “not-melts” are formed in the glass,
which prevent the process of forming of structure in the
limited areas. The “not-melts” restrict the distribution
of liquid glass and formation of homogeneous sintered
structure. The particles of functional material in these
regions do not form good contacts because of lack of
pressing forces which arise up at sintering of glass. Thus,
the non sintered and non conductive contacts appear,
what is equal to the breaks of leading chainlets.
For calculation of possibility of formation of nonconducting
contacts, it is necessary to put p (the prob-
3
ability of that all contacts are conducting between the
elements of chainlet) in equation for p , that is equal
³
to p = p ⋅ p p . With the increase of mass of crystalline
³ 1 2 3
phase m in glass-frit and functional material powder
cr
mass m , the probability p is decreased: p = 1–k ∙m /m .
p 3 3 3 cr p
Here k is coefficient of proportion. From the resulted
3
equations for p , p and p , it is not difficult to get p .
1 2 3 ³
As a thick-film resistor in this case is presented
as system which consists of aggregate of conducting
N
chainlets, its conductivity equals σ= ∑ σipi
, where
i=
1
σ is conductivity of i –th chainlet, N is the amount
i
of chainlets.
If all chainlets are formed in identical terms, it is
possible to assume that p =p. Then
³
2
N mf(
m 3 ) N
f + mg −k
mcr
∑ i 1 2 2 ∑ i .
σ= p σ = k k
σ
i= 1 mm g p
i=
1
It is obviously seen from this expression, that increase
of maintenance of crystalline constituent m in cr
a glass phase m results to increase of resistance of thick
g
film, what was confirmed experimentally (fig.2).
CONCLUSIONS
Most influence of sizes of particles of glass-frit on
resistance of resistors at the fixed temperature of annealing
takes place for samples with low content of
ruthenium dioxide. Resistance of layers increases with
the increase of content of glass.
At the fixed values of functional material content
m (RuO ) and glass phase m , the increase of mass of
f 2 g
crystalline phase m leads to decrease of conductiv-
cr
ity, therefore to the increase of resistance of resistive
layer.
References
1. Ïàíîâ Ë. È. Îïûò ñîâåðøåíñòâîâàíèÿ òîëñòîïëåíî÷íîé
òåõíîëîãèè / Ë. È. Ïàíîâ, Ð. Ã. Ñèäîðåö // Òåõíîëîãèÿ è
êîíñòðóèðîâàíèå â ýëåêòðîííîé àïïàðàòóðå. — 2002. —
¹1. — Ñ. 43-46.
2. Êóðìàøåâ Ø. Ä. Âëèÿíèå êðèñòàëëè÷åñêîé ôàçû SiO 2
íà ýëåêòðîôèçè÷åñêèå êîìïîíåíòû êîìïîçèöèîííûõ
ñòðóêòóð íà áàçå ñòåêëî-Bi 2 Ru 2 O 7 / Ø. Ä. Êóðìàøåâ,
Ò. È. Ëàâðåíîâà, Ò. Í. Áóãàåâà // Òåçèñû äîêë. XXII
íàó÷í. êîíô. ñòðàí ÑÍà “Äèñïåðñíûå ñèñòåìû”. —
Îäåññà, 2006. — Ñ. 215.
101

102
UDC 544.187.2; 621.315.59
Sh. D. Kurmashev, T. M. Bugaeva, T. I. Lavrenova, N. N. Sadova
INFLUENCE OF THE GLASS PHASE STRUCTURE ON THE RESISTANCE OF THE LAYERS IN SYSTEM
“GLASS-RuO 2 ”
Influence of quantitative and qualitive (phase and granule-metric) composition of initial components on the electro physical properties
of thick films on the base of the systems “glass — clusters RuO 2 , Bi 2 Ru 2 O 7 ” was investigated. At the fixed values of functional
material content m f (RuO 2 ) and glass phase m g , the increase of mass of crystalline phase m cr leads to decrease of conductivity, therefore to
the increase of resistance of resistive layer.
Key words: sructure, phase, resistance, layer.
ÓÄÊ 544.187.2; 621.315.59
ÂËÈßÍÈÅ ÑÒÐÓÊÒÓÐÛ ÑÒÅÊËßÍÍÎÉ ÔÀÇÛ ÍÀ ÑÎÏÐÎÒÈÂËÅÍÈÅ ÐÅÇÈÑÒÈÂÍÛÕ ÏËÅÍÎÊ Â ÑÈÑÒÅÌÅ
“ÑÒÅÊËÎ-RuO 2 ”
Ø. Ä. Êóðìàøåâ, Ò. Í. Áóãàåâà, Ò. È. Ëàâðåíîâà, Í. Í. Ñàäîâà
Èññëåäîâàíî âëèÿíèå êîëè÷åñòâåííîãî è êà÷åñòâåííîãî (ôàçîâûé è ãðàíóëîìåòðè÷åñêèé) ñîñòàâà èñõîäíûõ êîìïîíåíòîâ
íà ýëåêòðîôèçè÷åñêèå ïàðàìåòðû òîëñòûõ ïëåíîê íà áàçå ñèñòåì “ñòåêëî — êëàñòåðû RuO 2 , Bi 2 Ru 2 O 7 ”. Ïðè çàäàííûõ
âåëè÷èíàõ ñîäåðæàíèÿ ôóíêöèîíàëüíîãî ìàòåðèàëà (RuO 2 ) è ñòåêëÿííîé ôàçû óâåëè÷åíèå ìàññû êðèñòàëëè÷åñêîé ôàçû
ïðèâîäèò ê óâåëè÷åíèþ ñîïðîòèâëåíèÿ ðåçèñòèâíîé ïëåíêè.
Êëþ÷åâûå ñëîâà: ñòðóêòóðà, ôàçà, ñîïðîòèâëåíèå, ïë¸íêà.
ÓÄÊ 544..187.2; 621.315.59
ÂÏËÈ ÑÒÐÓÊÒÓÐÈ ÑÊËßÍί ÔÀÇÈ ÍÀ ÎϲРÐÅÇÈÑÒÈÂÍÈÕ Ï˲ÂÎÊ Â ÑÈÑÒÅ̲ “ÑÊËÎ-RuO 2 ”
Ø. Ä. Êóðìàøåâ, Ò. Í. Áóãàåâà, Ò. È. Ëàâðåíîâà, Í. Í. Ñàäîâà
Äîñë³äæåíî âïëèâ ê³ëüê³ñíîãî òà ÿê³ñíîãî (ôàçîâèé ³ ãðàíóëîìåòðè÷íèé) ñêëàäó âèõ³äíèõ êîìïîíåíò³â íà åëåêòðîô³çè÷í³
ïàðàìåòðè òîâñòèõ ïë³âîê íà áàç³ ñèñòåì “ñêëî — êëàñòåðè RuO 2 , Bi 2 Ru 2 O 7 ”. Ïðè çàäàíèõ âåëè÷èíàõ âì³ñòó ôóíêö³îíàëüíîãî
ìàòåð³àëó (RuO 2 ) ³ ñêëÿíî¿ ôàçè çá³ëüøåííÿ ìàñè êðèñòàë³÷íî¿ ôàçè ïðèçâîäèòü äî çìåíøåííÿ âåëè÷èíè ïðîâ³äíîñò³,
òîáòî äî çá³ëüøåííÿ îïîðó ðåçèñòèâíî¿ ïë³âêè.
Êëþ÷îâ³ ñëîâà: ñòðóêòóðà, ôàçà, îï³ð, ïë³âêà.

UDÑ 539.19+539.182
A. V. IGNATENKO, A. A. SVINARENKO, G. P. PREPELITSA, T. B. PERELYGINA, V. V. BUYADZHI
Odessa National Polytechnical University
OPTICAL BI-STABILITY EFFECT FOR MULTI-PHOTON ABSORPTION
IN ATOMIC ENSEMBLES IN A STRONG LASER FIELD
Within the density matrices formalism it is considered the multi-photon absorption in the atomic
ensemble of the two-level atoms, which interacts with resonant laser filed. The hysteresis dependence
of output amplitude on the input electromagnetic wave under 3-photon absorption (bi-stability effect)
is found in the caesium vapour (the pressure 0.1 Torr, particle density 3.5⋅10 15 cm -3 ).
INTRODUCTION
The interaction of atomic ensembles s with the
external alternating fields, in particular, laser fields,
has been the subject of intensive experimental and
theoretical investigation in the quantum optics and
electronics [1-15]. The appearance of the powerful
laser sources allowing to obtain the radiation field amplitude
of the order of atomic field in the wide range
of wavelengths results to systematic investigations of
the nonlinear interaction of radiation with atomic ensembles.
A whole number of interesting non-linear
optical phenomena may take a place, in particular,
multi=photon absorption and emission, multi-photon
excitation and ionization, at last different be-stability
and hysteresis phenomena. Another important topic
is a problem of governing and control of non-linear
processes in a stochastic, multi-mode laser field [4,5].
The principal aim of quantum coherent control is to
steer an atomic ensemble towards a desired final state
through interaction with light while simultaneously
inhibiting paths leading to undesirable outcomes. This
type of quantum interference is inherent in non-linear
multi-photon processes. Controlling mechanisms
have been proposed and demonstrated for atomic,
molecular and solid-state systems [1-3]. In ref. [12]
the effect of pulse-shaping on transient populations
of the excited Rb atoms ensembles is tested. At present
time, a progress is achieved in the description of
the processes of interaction atoms with the harmonic
emission field [1,2]. But in the realistic laser field the
according processes are in significant degree differ
from ones in the harmonic field. The latest theoretical
works claim a qualitative study of the phenomenon
though in some simple cases it is possible a quite acceptable
quantitative description [1-3,15].
Among existed approaches one could mention the
Green function method, the density-matrix formalism,
time-dependent density functional formalism,
direct numerical solution of the quantum-mechanical
equations, multi-body multi-photon approach, the
time-independent Floquet formalism, S-matrix Gell-
Mann and Low formalism etc. [1-13]. The effects of
the different laser line shape on the intensity and spectrum
of resonance fluorescence from a two-level atom
are studied in many papers (c.f. [1-5]). Nevertheless,
in a whole one can note that a problem of correct description
of the non-linear atomic dynamics in a sto-
© A. V. Ignatenko, A. A. Svinarenko, G. P. Prepelitsa, T. B. Perelygina, V. V. Buyadzhi, 2009
chastic, multi-mode laser field is quite far from the
final solution. It requires developing the advanced approaches
to description of multi-photon dynamics of
atomic ensembles in a strong laser field and adequate
treating different non-linear optical and photon-correlation
effects. In this paper within the density matrices
formalism it has been considered the multi-photon
absorption in the atomic ensemble of the two-level
atoms, which interacts with resonant laser filed. The
bi-stability effect for three-photon absorption in the
Cs vapors is found.
Figure 1. Calculated hysteresis dependence of the
output field upon the input electromagnetic wave amplitude
for the 3-photon absorption in the Cs vapor
2. OPTICAL BI-STABILITY EFFECT FOR
MULTI-PHOTON ABSORPTION
Below we consider the optical passing bi-stability
effect for multiphoton absorption in the atomic
ensemble and calculate the hysteresis dependence of
output amplitude on the input electromagnetic wave
under multi-photon absorption. We use the formalism
of the density matrices [3,4].
Let us suppose that the ensemble of N two-level
atoms interacts with a resonant laser radiation field.
The sum of frequencies of the external light fields is
ω+ω s =ω o (where ω o is the quantum transition frequency
in a two-level system). Besides, there are the
103

“exchange forces”, which may have the different nature.
In particular they are connected with exchange
through the radiation field, dipole-dipole electrostatic
interaction etc.
Let us suppose that an electromagnetic field (including
two waves) acts on the system:
104
− −
Er ( , t) = E( r, t) + E( r, t)
+ ê.ñ. =
j L j s j
− −
EсL exp( −ω i t+ ikLrj) + Eso( rj)exp( −ω i st)
+ c.
. (1)
Here ω+ω =ω -Δ, Δ is the detuning from the two-
s o
photon resonance, r is a radius-vector of the “j” atom.
j
The resulting field for frequency ω is defined likely (1)
s
as follows:
− −
Es ( rj, t) = Eso( rj)exp( −iω st)
+
) )
+ ∂ ∂
∑
2
(1/ c ) (1/ rij )
2
[[ Psi ( t') nij ] nij ] /
2
t .
ii ( ≠ j)
Here t’=t-r ij /c=t-τ ij , σ i are the Pauli matrices and
(2)
+
Psi () t =−rELσi−()exp( t −ω i t−ikLrj) - polarization, (3)
−1
r = h [( d
)
e ) d /( ω +ω ) + d ( d
)
e ) /( ω +ω ) ;
∑
α
bα L αa bα bα αa L bα s
The equations for atomic variables, which describe
the processes of the two-photon amplifying and
absorption, have a standard form [3-5]:
∂σ j+ / ∂t−i( ω 0 + i/ T2)
σ j+
=
+ +
=−(/ i h)
rEs ( rj,) t EL( rj,) t σj3,
o
∂σ j3 / ∂ t+ ( σ j3 − σ j3)
T1
=
+ +
= (2 i/ h)
xrE ( r , t) E ( r , t) σ −cc
. .]
s j L j j−
(4)
where σ j3 = σ jaa - σ jbb is a difference of populations in
the “j” atom. Then the full populations difference is
defined as follows:
∑
j
j3(), j3
()/ . (5)
D = σ t σ ≈ D t N
Transition to slowly changing density matrice:
ρ j− =σj−exp[ i( ω+ωs) t− ikLrj] (6)
allows to get the following system of equations for
density matrice:
∂ρ / ∂ t+ i( Δ − iT ) ρ =
= ( iD / h N) d E ( r ) + ( GD /2 N) C ρ ( t),
(7)
j+ −1
2 j+
* +
s j ∑
j
ij j+
∂D/ ∂ t+ ( D− D )/ T ) =
= ρ − −
0 1
* −
(2 iкс / h)
∑(
d Esо( rj)
j
+ . .)
∑∑
−G C [ ρ ( t) ρ ( t) +ρ ( t) ρ ( t)]
i j
ij i− i+ i+ j−
(8)
where G- is a constant of the “k”-photon decay of
atom and Ñ ij =sin k s r ij /( k s r ij ).
Let us introduce the notations for normalizing
amplitudes of the falling and passing fields:
y (4 TT / ) d E so
+
= h
x = (4 TT / h ) [ d ε + d E ], (9)
2 1/2 *
1 2 ,
2 1/2 * + * +
1 2
so so
+
( q) * +
∑ d Es ( rj) j
q( rj)
ε = Ψ
We use the eigen-functions Ψ(q) and eigen-values
of the q matrice of the inter-atomic interaction
Ñ ij . [4]. The system of the differential equations in fact
describes the bi-stable behavior of an ensemble of the
two-level atoms system under the multi-photon absorption
for different possible geometries of the radiated
medium (different Frenel numbers) [5].
3. THE MULTI-PHOTON ABSORPTION IN
THE CESIUM ENSEMBLE
Let us consider a process of the multi-photon absorption
for three-photon absorption in the Cs vapors
(the cesium ensemble). This process is characterized
by the bi-stability effect The corresponding Cs level
energies are presented in table 1 (from ref. [6]). In figure
1 we present the calculated hysteresis dependence
of output field upon the input electromagnetic wave
amplitude for the three-photon absorption in the Cs
vapor (this is corresponding to transition 6F-7D). The
following parameters have been used: particle concentration
n=3.5⋅1015 cm-3 , pressure 0,1 Torr, time
T =5⋅10 2 -10 s and time T =130ns (the time of spontane-
1
ous transition 6F-7D). Really, the time of realizing the
stationary regime is less than Ò . 1
Table 1
Energies of the cesium terms
Term of the ground
state
Cs (6s-2S ) 1/2
31435.5
Term of the excited
state
6p( 2P ) 1/2
6p( 2P ) 3/2
7d( 2D ) 5/2
6f( 2F ) 7/2
Energy of the level,
cm -1
11256
11813
26134
28120
It is obvious, a great interest attracts an experimental
study of the cited effect, that is a non-trivial
task because of the increased energetic of laser fields
and other factors. (Fig.1).
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P.71-74.
OPTICAL BI-STABILITY EFFECT FOR MULTI-PHOTON ABSORPTION IN ATOMIC ENSEMBLES IN A STRONG
LASER FIELD
Abstract
Within the density matrices formalism it is considered the multi-photon absorption in the atomic ensemble of the two-level atoms,
which interacts with resonant laser filed. The hysteresis dependence of output amplitude on the input electromagnetic wave under 3photon
absorption (bi-stability effect) is found in the caesium vapour (the pressure 0.1 Torr, particle density 3.5⋅10 15 cm -3 ).
Key words: atomic ensembles, laser field, multi-photon processes, bi-stability effect.
ÓÄÊ 539.19+539.182
À. Â. Èãíàòåíêî, À. À. Ñâèíàðåíêî, Ã. Ï. Ïðåïåëèöà, T. Á. Ïåðåëûãèíà, Â. Â. Áóÿäæè
ÝÔÔÅÊÒ ÎÏÒÈ×ÅÑÊÎÉ ÁÈ-ÑÒÀÁÈËÜÍÎÑÒÈ ÏÐÈ ÌÍÎÃÎÔÎÒÎÍÍÎÌ ÏÎÃËÎÙÅÍÈÈ ÄËß ÀÒÎÌÍÛÕ
ÀÍÑÀÌÁËÅÉ Â ÑÈËÜÍÎÌ ÏÎËÅ ËÀÇÅÐÍÎÃÎ ÈÇËÓ×ÅÍÈß
Ðåçþìå
 ðàìêàõ ôîðìàëèçìà ìàòðèö ïëîòíîñòè ðàññìîòðåíî ìíîãîôîòîííîå ïîãëîùåíèå â àòîìíûõ àíñàìáëÿõ äâóõóðîâíåâûõ
àòîìîâ, êîòîðûå âçàèìîäåéñòâóþò ñ ïîëåì ðåçîíàíñíîãî ëàçåðíîãî èçëó÷åíèÿ. Îïðåäåëåíà ãèñòåðåçèñíàÿ çàâèñèìîñòü
âûõîäíîãî ïîëÿ îò àìïëèòóäû ïàäàþùåé âîëíû ïðè òðåõôîòîííîì ïîãëîùåíèè (ýôôåêò áè-ñòàáèëüíîñòè) â ïàðàõ öåçèÿ
(ïëîòíîñòü ÷àñòèö 3,5⋅10 15 ñì -3 , äàâëåíèå 0.1 Toðð.).
Êëþ÷åâûå ñëîâà: àòîìíûå àíñàìáëè, ëàçåðíîå ïîëå, ìíîãîôîòîííûå ïðîöåññû, ýôôåêò áè-ñòàáèëüíîñòè.
ÓÄÊ 539.19+539.182
Ã. Â. ²ãíàòåíêî, À. À. Ñâèíàðåíêî, Ã. Ï. Ïðåïåëèöà, T. Á. Ïåðåëèã³íà, Â. Â. Áóÿäæ³
ÅÔÅÊÒ ÎÏÒÈ×Íί Á²-ÑÒÀÁ²ËÜÍÎÑÒ² ÏÐÈ ÁÀÃÀÒÎÔÎÒÎÍÍÎÌÓ ÏÎÃËÈÍÀÍͲ ÄËß ÀÒÎÌÍÈÕ
ÀÍÑÀÌÁË²Â Ó ÑÈËÜÍÎÌÓ ÏÎ˲ ËÀÇÅÐÍÎÃÎ ÂÈÏÐÎ̲ÍÞÂÀÍÍß
Ðåçþìå
 ìåæàõ ôîðìàë³çìó ìàòðèöü ãóñòèíè ðîçãëÿíóòî áàãàòîôîòîííå ïîãëèíàííÿ â àòîìíèõ àíñàìáëÿõ äâîð³âíåâèõ àòîì³â,
ùî âçàºìîä³þòü ç ïîëåì ðåçîíàíñíîãî ëàçåðíîãî âèïðîì³íþâàííÿ. Âèçíà÷åíà ã³ñòåðåçèñíà çàëåæí³ñòü âèõ³äíîãî ïîëÿ â³ä
àìïë³òóäè ïàäàþ÷î¿ õâèë³ ïðè òðüîõôîòîííîìó ïîãëèíàíí³ (åôåêò á³-ñòàá³ëüíîñò³) ó ïàðàõ öåç³ÿ (ãóñòèíà ÷àñòèíîê 3,5⋅10 15
ñì -3 , òèñê 0,1 Toðð.).
Êëþ÷îâ³ ñëîâà: àòîìí³ àíñàìáë³, ëàçåðíå ïîëå, áàãàòîôîòîíí³ ïðîöåñè, åôåêò á³-ñòàá³ëüíîñò³.
105

106
UDC 633.9
L. V. MYKHAYLOVSKA 1 , A. S. MYKHAYLOVSKA 2
1 I.I,Mechnikov Odesa National University, 65082, Odesa, Ukraine
2 Ruhr-Universität Bochum, 44780, Bochum, Germany
Å-mail: lidam@onu.edu.ua
INFLUENCE OF THE STEP IONIZATION PROCESSES ON THE
ELECTRONIC TEMPERATURE IN THIN GAS-DISCHARGE TUBES
Taking into account the processes of the direct and step ionization and on the basis of the closed
system of the balance equations we have performed theoretical analysis of electronic temperature dependence
on the external parameters such as the value of the discharge current, pressure of the working
gas and the diameter of the discharge capillary. The conditions were found which indicate the
decisive role of the step ionization in charged particles creation.
INTRODUCTION
The study of the low-temperature plasma of the
positive column in thin tubes is interesting not only
as of the active medium of the wave-guiding lasers
but also for the possible creation of the small-size energy
sources for the gas laser emitting devices of low
pressure. The out-come characteristics of the devices
which use the gaseous discharge depend on the inner
parameter of the positive column (PC) which is characteristic
for the discharge. A significant number of
theoretical and experimental papers [1-5] is devoted to
the studies of the inner parameters in the active media
of gaseous lasers. In these papers the main attention is
paid to the influence of the discharge current I r the ,
gas pressure p and the inner radius of the discharge
capillary R 0 on the longitudinal electric field strength
E z , the electronic concentration N e , as well as on the
electronic temperature T e [3-6] assuming their Maxwell-type
distribution over the velocity values. The inner
parameters of the discharge processes are defined
by the given external parameters.
The condition required for the stationary gaseous
discharge existence is the temporal stability of the
electronic concentration. The balance of the charged
particles in the plasma of low-pressure PC is formed
by ionization processes in the gaseous volume and the
following deficiency of the charged particles due to the
drift of electrons and ions towards the wall of the tube.
It should be noted that the probability of the charged
particles creation as well as the processes concerning
the decrease of the charged particles, depend on the
electronic temperature.
SCOPE OF THE WORK
In the present paper, basing on the closed system
of equations obtained in [7], for the evaluation
of the inner parameters of PC of the discharge tube,
the stable value of electronic temperature with the simultaneous
account of the direct and step ionization.
Usually, either the ionization of non-excited atoms
(direct ionization), or the ionization of the excited atoms
(step ionization) is taken into account [4, 6]. The
simultaneous account of the direct and step ionization
allows to evaluate and compare the input of these two
processes into atoms’ ionization. The analysis is conducted
with the use of two main approximations — the
diffuse regime of the discharge and the Maxwell distribution
of electrons over the velocity values.
Let us write down the simplified (interpolated)
equations for direct and step ionizations with the simultaneous
account of the balance between the number
of charged particles e N and metastable atoms m N
in the discharge controlled by the diffusion
ν 0iNe +ν miN e=ν adNe. (1)
( )
ν ⋅ N = ν +ν ⋅ N . (2)
0m e md mj m
Here
tion, mi
0i k0iN0 kmi Nm
ν = – the frequency of direct ioniza-
ν = — the frequency of step ionization
from the metastable level, ν ad — the frequency of the
diffuse departures of the electrons towards the tube
walls, ν 0m = k0mN0 — the frequency of the metastable
level’s excitation as a result of the atoms, being in the
basic state, coincidence with the free electrons, ν md —
the frequency of diffuse departure of metastable atoms
to the walls of the tube, ν mj = kmj Ne—
the frequency of
the metastable atoms extinguishing due to their coincidence
with free electrons, 0 , k i k mi — the constants
of the direct and step ionization velocity, correspondingly,
k0m and kmj = kmi + km0—
the constants of the
excitation and extinguishing velocities of the metastable
state by electron impact, correspondingly. The
main role in the process of states’ destruction is played
by the metatstable state ionization with the constant
k mi , as well as the transition of the excited atom to the
k .
ground state with the constant m0
MODEL AND DISCUSSION
It is known that the frequency of the diffuse departures
in the cylindrical PC is being expressed by
2
d D ν = Λ , where D — the corresponding diffusion
coefficient, 0 2.405 R Λ= — diffusion length,
R 0 — the discharge tube capillary radius. For the
charged particles, the ambipolar diffusion coefficient
is: Dad =μ i kTee , where μ i — the ions’ mobility. According
to [2], the ions’ mobility with the account of
© L. V. Mykhaylovska, A. S. Mykhaylovska, 2009

the resonant recharging, is proportional to the ion’s
velocity and inversely proportional to the gas pressure.
That’s why, the ambipolar diffusion coefficient is:
Dad = Da0⋅ TeT p,
ànd the corresponding frequency
equals to ( )( ) 2
ν ad = Da0 TeT p 2.405 R0
.
For metastable atoms, the diffusion coefficient
is proportional to the atoms’ velocity and inversely
proportional to the density of gas. Thus, one obtains
Dmd = Dm0⋅ T T p and then the corresponding of
diffusive departures is ( )( ) 2
ν md = Dm0 T T p 2.405 R0
. The values of the constants Da0, D m0
are defined by
the type of gas and the system of units chosen [7].
In the written above simplified balance equations
the particles’ space distribution over the area of
the capillary cross-section is not considered. It is assumed
that 0 , N Nmcorrespond to the values of the
particles’ concentration in the ground and metastable
states at the center of the tube and N e — the concentration
of the electrons at the center of the tube.
It should be noted that according to the Mendeleev-
Clapeiron law, the density of atoms N0 is mutually
connected with gas temperature through the relation
N0 = p kT = N00⋅ p T (ð –gas pressure in the discharge
tube, T — gas temperature, and the constant N 00 value
is determined by the system of units choice).
According to [2], while the energy spectrum of
electrons is of the Maxwellian type, the frequency of
the direct ionization of the atom from the ground state
and that for the atom transfer from the ground to the
excited one the following expression could be used:
v0i = veCi( eU0i + 2kTe) exp(
−eU0i kTe) ⋅ N0.
(3)
Here ve = 8kTe
π m — average thermal velocity
of the electron, C i – the constant characteristic for
the given process, U 0i — ionization potential for the
atom transfer to the excited state.
The frequency of the step ionization is determined
by Thomson formula and could be written as:
Cmi ⋅ve
ν mi = ×
kTe ⋅eU
mi
⎛ ⎞
∞
⎜ eU mi eU mi exp( −tdt
) ⎟
× ⎜exp( − ) − ⋅ Nm
kTe kT ∫ ⎟⋅
,
⎜ e eU t
mi ⎟
⎝ kTe
⎠
(4)
ãäå mi C — the constant for given process, earlier, for ad
U mi — the
excited atom ionization potential.
It is seen that one could get the following expressions
for the density of metastable atoms and electronic
density from the balance equations (1-2) as a
functions of electronic temperature, pressure and the
temperature of the working gas and of the radius of the
discharge tube:
( νad −ν0i) νmd
Ne( Te, p, T, R0)
= , (5a)
ν0mkmi −( νad −ν0i)
kmj
νad −ν0iν0mNe Nm( Te, p, T, R0)
= = . (5b)
kmi ν md + kmj Ne
It is seen, also, that for Nm ≥ 0 and Ne ≥ 0 only
if νad −ν0i≥ 0 and ν0mkmi −( νad −ν 0i) kmj
> 0 . From
these equations, with the use of the definitions made
D and N 0 , the following boundary value
could be proposed for the combination pR 0 :
2
Da0⋅Te ⋅T T ⎛ pR0 ⎞ Da0⋅Te ⋅T
T
< ⎜
00 ( 0 0 ) 2.405
⎟ ≤
. (6)
N ⋅ k N i + k mkmi kmj
⎝ ⎠
00 ⋅ k0i
The two boundary equations for the electronic
temperature follow the simplified balance equations
(1) and (2). So, when the excited atoms are absent in
the plasma of gaseous discharge, and only the non-excited
atoms are being ionized the Schottky condition
could be obtained from (1) or (5b) for the evaluation
of the electronic temperature:
ν ad ( Te) =ν 0i
( Te)
(7à)
what means the equality of the frequencies of the ionization
and of the diffuse departures of electrons to the
walls of the tube. Inserting the expressions for the frequencies
into this equality, one could obtain the following
equation for the T e under the given pressure
p and the gas temperature T in the tube of the radius
R 0
2
TeN00 ⎛ pR0⎞
1
=
k0i( Te) D
⎜
a0
2.405
⎟ . (7b)
⎝ ⎠ T T
During the increase of the electrons’ density caused
by the increase of the discharge current the number of
the metastable atoms increases as well and the mechanism
of the step ionization starts to act. In the limit of
Ne →∞ one could obtain from (5à) or (5b) the other
following equation for the evaluation of e T
kmj ( Te)
ν 0m( Te) = ⎡ ad( Te) 0i(
Te)
kmi ( T
⎣ν −ν ⎤⎦
, (8à)
e )
which is the analog of Schottky condition with the account
of the processes of creation and destruction of
the metastable atoms. Using the expressions for the
frequencies, we obtain the following equation for e T
Tk e mj( Te)
=
k0i( Te) kmj( Te) + k0m( Te) kmi( Te)
2
N00 ⎛ pR0⎞
1
=
D
⎜
a0
2.405
⎟
. (8b)
⎝ ⎠ T T
CALCULATION RESULTS
At Fig.1 are presented the solutions of the equations
(7b) (curves 1) and of the equation (8b) (curves
2), as well as the difference between these solutions
(curves 3) in dependence of the product pR 0 . It is seen
that the solutions of these equations behave almost
uniformly in the chosen range of pR 0 . The difference
between these solutions decreases with the increase of
pR 0 . The increase of the working gas temperature T
causes the somewhat increase of the corresponding
electronic temperature along with the non-significant
increase difference between solutions. The character
of the dependencies is not changing.
107

Te, eV
15
10
5
108
1
2
3
0
0 0.2 0.4 0.6 0.8 1 1.2
pRo, mmHg*cm
4
Te, eV
3
2
1
1 1.2 1.4 1.6 1.8
pRo, mmHg*cm
2
Fig.1. The dependencies of the equations (7) and (8) solutions
on the product pR 0 for two regions of pR0 changes. Curves
1 — solutions of equation (7), curves 2 – solutions of equation (8),
curves 3 – the difference of these solutions
In two limiting cases which correspond to Ne → 0
and Ne →∞, the equations (7) and (8) for the electronic
temperatures do not include the electronic concentration.
From other part, in general case, the electronic
density depends on the total discharge current, which
R0
could be written in the form Ir = 2πeμeEz∫
rNe() r dr ,
0
where e e( , ) pT
μ =μ - the electronic mobility, z E
- the longitudinal field strength, which stabilizes in
the discharge. In the PC of the discharge, the electronic
distribution over the section area is Besselian
Ne( r) = Ne0⋅ J0(2.405 r R0)
. Then, under the given
discharge current, it is possible to obtain the following
N
expression for e0
( , , , , )
1
2
3
Ir
2
⎛2.405 ⎞
πμ e eEz ⎝ R0
⎠
Ne0 Te p R0 T Ir
= ⎜ ⎟ . (9)
5
This value of electronic density should coincide
with the value obtained from the balance equations
(5à). That’s why it is necessary to solve the following
equation taking into account the both the direct and
step ionization
( 0 )
( )
2
νad −ν i νmd I ⎛ r 2.405 ⎞
= ⎜ ⎟
ν0mkmi − νad −ν0i kmj 5πeμeEz
⎝ R0
⎠
. (10)
The strength of the longitudinal electric field held
in the discharge Ez = Ez( Te, p, R0, T)
is determined by
the balance equation for the electronic energy with the
account of the elastic energy losses during the impact
energy exchanges between electrons and atoms of the
working gas as well as of the non-elastic losses on the
excitation and ionization of the atoms. Besides, the
energy balance in thin gas-discharge tubes includes
the energy transferred by the charged particles to the
tube walls [4]. In present paper the longitudinal field
strength Ez is calculated through the following equation
obtained in [7]:
∑
eE = mν
⋅( ν ⋅Δε +ν ⋅Δε + ν ⋅Δε ) . (11)
2 2
z m c g w w i i
i
Here ν m — the effective electron collision frequency,
ν c — elastic collisions frequency for electronneutral
atom pairs, which in general case depends
on the electronic temperature and atoms’ density,
Δε g = (2 mM) ⋅ (3kTe 2) — energy losses during elastic
collisions of electrons with neutral atoms, νw− electron collisions frequency with discharge tube walls
which equals to the frequency of electronic diffuse
departures to the walls ν w =ν ad , Δεw − energy losses
of the charged particles on the tube walls, ν i — frequency
of non-elastic collisions of the electrons with
atoms which excites or ionizes the atom, Δε i — electron
energy losses given to the excitation or ionization
of the atoms.
We would like to limit ourselves to the case of account
only the electron energy losses on the tube walls
when the power contains only the recombination
energy for positive ions and electrons eU and of ki-
i
netic energy they possessed before the recombination
Δε w = eU0i + Wkp + 2kTe,
where U 0i is the ionization
potential of the atom in the recombination state, 2kT e
and W kp -are the average kinetic energies of the electron
and ion during their approach the wall.
Taking into account the processes of direct and
step ionization, one could rewrite the last term in
brackets in formula (11) for the power density in the
form: ∑ ν⋅Δε= i i e( k0iN0Ui + k0mN0Um + kmiNmUmi) .
Using the i expression (6) for the metastable
atoms’ density N m , it is evident that:
∑ ν⋅Δε= i i e⎡⎣( k0i + k0m) N0Um +νadUmi⎤⎦.
i
The losses on the direct iomization and atoms’
excitation into metastable state without the step
ionization process are described by the expression:
∑ ν⋅Δε= i i e( k0iUi + k0mUm) N0.
i It is possible to make it clear that:
k + k N U +ν U ≥ k U + k U N , if
( ) ( )
0i 0m 0 m ad mi 0i i 0m m 0
νad ≥ν 0i
.
The results of the numeric solution of the equation
(10) for the discharge in He are presented at
Fig.2 — 4. The partial dependencies on the gas
pressure and capillary radius are presented as they
in contrary to the solutions of equations (7) and

(8), from the equation (10) the solution’s dependence
on the product pR 0 , and Te≠f( pR0)
doesn’t
follow. We have used the following constants:
−17
Ci
= 0.12⋅10 cm2 −17
/eV, Cm
= 0.45⋅10 cm2 /eV,
−14
Cmi
= 6.5⋅10 cm2 /eV, eU 0i = 24.6 eV, eU 0m = 20 eV,
eU mi = 4.6 eV. Besides, it is assumed that the gas temperature
equals to that of the outer walls’ one. For
this latter parameter we have used the experimentally
0 0
0
measured value of TC= 20 C+ 7 ⋅ Ir,
where 20 C is
the temperature of the ambient, I r — the discharge
current in mA.
The numeric calculations have shown that the
electronic temperature in the real situation with the
account of both the direct and step ionization takes
the value which doesn’t coincide with any limit value
determined by equations (7) and (8). At the figures
presented, it is seen that the electronic temperature’s
value obtained as the solution of the equation (10), is
smaller than the temperature obtained from the equation
(7), but the greater than that obtained from equation
(8). Only at small pressures and not significant
discharge currents and in thin tubes, the real electronic
temperature is almost the same as the electronic
temperature obtained from Schottky’s condition (7)
(see, please, the curves at Fig.2à). With the increase of
the pressure, the step ionization plays the greater role
and the solution of the equation (10), even for thin
tubes, differs slightly from the solution of the modified
Schottky equation (8) (see, please, the curves at
Figs.2, 3).
In the present paper, in the framework of the assumptions
taken, the electronic temperature depends
only on the temperature of the ambient and is proportional
to the discharge current value. The proportionality
quotient is a constant determined from the
experiment. Really, according to the results of [7],
the temperature of the working gas is the function
of the discharge inner parameters such as: the electronic
temperature, longitudinal electric field strength
and electrons’ concentration. As it is seen from Fig.4
(curves 1), with the increase of discharge current the
metastable atoms’ concentration increases as well and
the electronic temperature decreases as a result. But,
afterwards, under the following growth of the discharge
current and of the gas temperature, the gas density decreases
due to the termal gas expansion to the ballast
volume. This effect is accompanied by the increase of
the electronic temperature. The placement of the discharge
tube into the thermostat causes the decrease of
the electronic temperature which could be explained
by the growing role of the step ionization due to the
gas pressure increase (see, please, Fig.4, curves 2).
Thus, under the taken assumptions, the working gas
temperature T remains stable and the solutions of the
equations (7b) and (8b) do not dependent on the discharge
current as it is seen at Fig.4 (horizontal lines).
Fig. 2. The results of the numeric solution of the equation
(10). The solid lines represent the dependencies of the electronic
temperature during the gas pressure changes. Punctured and
pin-stripe ones correspond to the solutions of the equations (7)
and (8). The discharge current Ir= 10mA
, gas temperature
0
T = 20 C+ 7 ⋅ Ir,
à) discharge capillary radius R0= 0.05cm,
b) discharge capillary radius R0= 0.5cm
Fig. 3. The results of the numeric solution of the equation
(10). The solid line represents the dependence of the electronic
on the capillary radius. The punctured and pin-stripe ones correspond
to the solution of the equations (7) è (8). Discharge current
Ir= 10mA
, gas pressure p = 10Torr
, gas temperature
0
T = 20 C+ 7 ⋅
Ir
b
�
109

Fig. 4. The results of the numeric solution of the equation
(10). The solid lines – dependencies of the electronic temperature
on the discharge current. Gas pressure p = 10Torr
, capillary
0
radius R0= 0.05cm,
1 – gas temperature T = 20 C+ 7 ⋅ Ir,
0
2 – gas temperature T = 20 C .
110
CONCLUSIONS
As a result, we would like to make the following
conclusions:
1. The performed theoretical analysis has shown
that it is impossible to calculate the electronic temperature
in the positive column of the gaseous discharge
using only the Schottky equation (7) which takes into
account the processes of direct ionization (limiting
case of small discharge currents Ir → 0 ) or the equation
(8) which operates only the processes of step ion-
UDC 633.9
L.V. Mikhaylovskaya, A.S. Mykhaylovska
ization (limiting case of extremely high discharge currents
Ir →∞). In the intermediate
2. In the intermediate case of the medium values
of discharge currents, the electronic temperature is determined
by the equation (10) obtained in the present
paper, which accounts both direct and step ionization.
3. As a result of this equation solution, the dependencies
of electronic temperature on gas pressure, discharge
current value as well as the capillary radius value.
4. It is shown that in the real range of discharge
parameters changes such as gas pressure, discharge
current and capillary radius, for the physical processes
in positive column plasma adequate description it is
necessary to take into account all possible ways of atoms
excitation and ionization.
REFERENCES
1. Ýíöèêëîïåäèÿ íèçêîòåìïåðàòóðíîé ïëàçìû. Ò.ÕI-4. Ãàçîâûå
è ïëàçìåííûå ëàçåðû. (Ïîä ðåä. Â.Å.Ôîðòîâà) Ì.:
Ôèçìàòëèò. 2005 ã.396 ñòð.
2. Ðàéçåð Þ.Ï. Ôèçèêà ãàçîâîãî ðàçðÿäà. — Ì.: Íàóêà,
1997. — 592ñ.
3. Ñìèðíîâ Á.Ì. Ôèçèêà ñëàáîèîíèçîâàííîãî ãàçà (â çàäà-
÷àõ ñ ðåøåíèÿìè). — Ì.: Íàóêà, 1999. — 423ñ.
4. Ìèëåíèí Â.Ì., Òèìîôååâ Í.À. Ïëàçìà ãàçîðàçðÿäíûõ
èñòî÷íèêîâ ñâåòà íèçêîãî äàâëåíèÿ. — Ë.:Ýíåðãîèçäàò,
1999. — 240 ñ.
5. Ãðàíîâñêèé Â.Ë. Ýëåêòðè÷åñêèé òîê â ãàçå– Ì.: Íàóêà,
1994. — 544ñ.
6. Å. A. Áîãäàíîâ, À. À. Êóäðÿâöåâ, Ë. Ä. Öåíäèí, Ð. Ð. Àðñëàíáåêîâ,
Â. È. Êîëîáîâ, Â. Â. Êóäðÿâöåâ. Âëèÿíèå ìåòàñòàáèëüíûõ
àòîìîâ è íåëîêàëüíîãî ýëåêòðîííîãî ðàñïðåäåëåíèÿ
íà õàðàêòåðèñòèêè ïîëîæèòåëüíîãî ñòîëáà â
àðãîíå.//ÆÒÔ. — 2004. — Ò.74, âûï.6. — Ñ.35-42.
7. Mikhailovskaya L.V. Energy balance and gas temperature in
plasma of positive column in gas discharge narrow tubes. //
Proc. SPIE. — 1999. — V. 3686. — P. 62-69.
INFLUENCE OF THE STEP IONIZATION PROCESSES ON THE ELECTRONIC TEMPERATURE IN THIN
GAS-DISCHARGE TUBES
Abstract
The theoretical analysis of dependence of the steady-stated electron temperature on the external parameters of discharge, such,
as a value of discharge current, pressure of working gas and size of radius of discharge capillary, has been done taking into account the
simultaneous processes of direct and stepped ionization. This analysis has been done on the basis of solution of the closed system of the
balance equations. Conditions at which a determining role in formation of the charged particles plays stepped ionization are found.
Key word: step ionization, processes, gas discharge tubes.
ÓÄÊ 633.9
Ë. Â. Ìèõàéëîâñêàÿ, À. Ñ. Ìèõàéëîâñêàÿ
ÂËÈßÍÈÅ ÏÐÎÖÅÑÑΠÑÒÓÏÅÍ×ÀÒÎÉ ÈÎÍÈÇÀÖÈÈ ÍÀ ÝËÅÊÒÐÎÍÍÓÞ ÒÅÌÏÅÐÀÒÓÐÓ Â ÓÇÊÈÕ
ÃÀÇÎÐÀÇÐßÄÍÛÕ ÒÐÓÁÊÀÕ
Ðåçþìå
Ñ ó÷åòîì ïðîöåññîâ ïðÿìîé è ñòóïåí÷àòîé èîíèçàöèè íà îñíîâå ðåøåíèÿ çàìêíóòîé ñèñòåìû áàëàíñíûõ óðàâíåíèé
ïðîâåäåí òåîðåòè÷åñêèé àíàëèç çàâèñèìîñòè óñòàíîâèâøåéñÿ òåìïåðàòóðû ýëåêòðîíîâ îò âíåøíèõ ïàðàìåòðîâ ðàçðÿäà, òàêèõ,
êàê âåëè÷èíà òîêà ðàçðÿäà, äàâëåíèå ðàáî÷åãî ãàçà è ðàçìåðà ðàäèóñà ðàçðÿäíîãî êàïèëëÿðà. Íàéäåíû óñëîâèÿ, ïðè
êîòîðûõ îïðåäåëÿþùóþ ðîëü â îáðàçîâàíèè çàðÿæåííûõ ÷àñòèö èãðàåò ñòóïåí÷àòàÿ èîíèçàöèÿ.
Êëþ÷åâûå ñëîâà: ñòóïåí÷àòàÿ èîíèçàöèÿ, ïðîöåññ, ãàçîðàçðÿäíàÿ òðóáêà.

ÓÄÊ 633.9
Ë. Â. Ìèõàéëîâñüêà, À. Ñ. Ìèõàéëîâñüêà
ÂÏËÈ ÏÐÎÖÅѲ ÑÒÓϲÍ×ÀÑÒί ²ÎͲÇÀÖ²¯ ÍÀ ÅËÅÊÒÐÎÍÍÓ ÒÅÌÏÅÐÀÒÓÐÓ Â ÂÓÇÜÊÈÕ
ÃÀÇÎÐÎÇÐßÄÍÈÕ ÒÐÓÁÊÀÕ
Ðåçþìå
Ç óðàõóâàííÿì ïðîöåñ³â ïðÿìî¿ òà ñòóï³í÷àñòî¿ ³îí³çàö³¿ íà ï³äñòàâ³ ð³øåííÿ çàìêíóòî¿ ñèñòåìè áàëàíñíèõ ð³âíÿíü ïðîâåäåíî
òåîðåòè÷íèé àíàë³ç çàëåæíîñò³ óñòàëåíî¿ òåìïåðàòóðè åëåêòðîí³â â³ä çîâí³øí³õ ïàðàìåòð³â ðîçðÿäó, òàêèõ, ÿê âåëè÷èíà
ðîçðÿäíîãî ñòðóìó, òèñê ðîáî÷îãî ãàçó òà ðîçì³ð ðàä³óñà ðîçðÿäíîãî êàï³ëÿðó. Çíàéäåí³ óìîâè, ïðè ÿêèõ âèçíà÷àëüíó ðîëü â
óòâîðåíí³ çàðÿäæåíèõ ÷àñòèíîê ãðຠñòóï³í÷àñòà ³îí³çàö³ÿ.
Êëþ÷îâ³ ñëîâà: ñòóï³í÷àñòà ³îí³çàö³ÿ, ïðîöåñ, ãàçîðàçðÿäíà òðóáêà.
111

112
UDÑ 539.184
E. V. MISCHENKO
Odessa National Polytechnical University, Odessa
QUANTUM MEASURE OF FREQUENCY AND SENSING THE COLLISIONAL
SHIFT AND BROADENING OF Rb HYPERFINE LINES IN MEDIUM
OF HELIUM GAS
New theoretical data regarding the collisional shift and broadening of the hyperfine spectral lines
for Rb in the atmosphere of the buffer inert He gas within relativistic perturbation theory formalism
are presented.
1. INTRODUCTION
Studying the collisional shifts and broadening of
the hyperfine structure lines for heavy elements (alkali,
alkali-earth, lanthanides, actinides and others) in
an atmosphere of inert gases is one of the important
and actual topics of the modern atomic and molecular
optics, quantum and photo-electronics etc. [1-8].
It should be mentioned also that the heavy atoms are
interesting from the point of view of studying a role of
weak interactions in atomic optics and heavy-elements
chemistry. Besides, calculation of the hyperfine structure
line shift and broadening allows one to check the
quality of wave functions and study a contribution of
relativistic effects in two-center (multi-center) atomic
systems . From the applied science point of view, the
mentioned physical effects form a basis for creating
an atomic quantum measure of frequency [2,8]. For
a long time the corresponding phenomenon for thallium
atom attracted a special attention because of
possibility to create the thallium quantum frequency
measure. Alexandrov and co-workers [8] have realized
the optical pumping of the thallium atoms on the line
of 21GHz, which corresponds to transition between
the components of hyperfine structure for the ground
state, and have measured the collisional shift of this
line due to buffer (bath) gas. Naturally, the inert buffer
gases (He, Ar etc.) were used. The detailed non-relativistic
theory of the collisional shift and broadening of
the hyperfine structure lines for simple elements (light
alkali elements etc.) has been developed by many authors
(see discussions in refs. [1-8]). However, consideration
of heavy elements faces serious difficulties
related with account for the relativistic and correlation
corrections. It is very curious that until now a consistent,
accurate quantum mechanical approach for
calculating main characteristics of the collisional processes
was not developed though many different simplified
models have been proposed (see, for example
[6-13]). The most widespread approach is based on the
calculation of the corresponding collision cross-section,
in particular, in a case of the van der Waals interaction
between colliding particles [2]. However, such
an approach does not factually define any difference
between the Penning process and resonant collisional
one and gives often non-correct results for cross-sections.
More consistent method requires data on the
process probability (cross-section, collision strength)
G(R) as a function of internuclear distance. It should
be noted that these data for many physically interesting
tasks are practically absent at present time. In ref.
[6,13] a new relativistic optimized approach, based on
the gauge-invariant perturbation theory with using the
optimized wave functions basis’s, is developed in order
applied to calculating the inter atomic potentials,
hyper fine structure collision shift for heavy atoms in
an atmosphere of inert gases. In this paper we present
some new theoretical data regarding the collision shift
and broadening the hyperfine spectral lines for Rb
atom in an atmosphere of the inert gas He.
2. THE SPECTRAL BROADENING OF
THE ATOMIC HYPERFINE LINES IN THE
BUFFER GAS
To calculate the collision shift of hyperfine structure
spectral lines one could use the following expression
known from kinetic theory of spectral line form
(see, for example, [2,5]):
( ) ( ( ) ) 2
0
∞
D 4πw
fp= = w R exp U R kT R dR
p kT ∫ δ −
(1)
0
where U(R) is the effective potential of the interatomic
interaction, which has a central symmetry in a case of
the systems A—B (in our case, for example, B=He;
A=Rb); T is a temperature, w is a frequency of the
0
hyperfine structure transition in the isolated active
atom; Δω(R)=Dw(R)/w is the relative local shift of
0
the hyperfine structure lines, which is arisen due to the
disposition of the active atoms (say, atom of Rb and
helium He) on a distance R. To calculate an effective
potential of the interatomic interaction we use a method
of the exchange perturbation theory (the modified
version ÅL-ÍÀV) [1,5]. Within exactness to second
order terms on potential of Coulomb interaction of
the valent electrons and atomic cores one can write:
S0 C ⎛ 6 2 1 ⎞
δω ( R)
= + Ω 1+ Ω2 − ,
6 ⎜ + ⎟ (2)
1− S0 R ⎜Ea Ea + E ⎟
⎝ B ⎠
Here Ñ is the van der Waals constant for interac-
6
tion À-Â (e.g., a pair of Rb-Íå); I, Å are the ioniza-
1a,b
tion potential and excitation energy on the first level
for atoms A, B correspondingly; S is the overlapping
0
© E. V. Mischenko, 2009

integral; The value of E α ,b can be simply defined as
follows:
( )
Eα , b = Ia, b+ E1
a, b 2,
The values Ω , Ω in the expression (2) are the
1 2
non-exchange and exchange non-perturbation sums
of the first order correspondingly, which are defined
as follows:
( 1 )
() 1 () 1
2 〈Φ H Φ 〉 V
Ω= 1
N −S ρ E −E
( 1 )
' ' '
'
∑
0 CT k k 0
(3)
0 0 k 0 k
() 1 () 1
2 〈Φ H Φ 〉 U
'
Ω 2=
∑
N −S ρ E −E
' ' '
0 CT k k 0
0 0 k 0 k
() 1 () 1 / () 1 () 1
с =

method and determination of Cs atomic properties// Phys.
Rev. A. — 2005. — Vol.71. — P.032509.
15. Ivanov L.N.,Ivanova E.P. Extrapolation of atomic ion energies
by model potential method: Na-like spectra // Atom.
Data Nucl Tabl. — 1999-Vol.24,N2. — p.95-101.
16. Bekov G.I., Vidolova-Angelova E., Ivanov L.N., Letokhov
V.S., Mishin V.I., Laser spectroscopy of narrow two-timely
excited autoionization states for ytterbium atom// JETP. —
1991. — Vol.80,N3. — P.866-878.
17. Basar Gu., Basar Go., Acar G., Ozturk I.K., Kroger S., Hyperfine
structure investigations of MnI: Experimental and
theoretical studies of the hyperfine structure in the even configurations//
Phys.Scripta. — 2003. — Vol.67. — P.476-484.
18. Dorofeev D.L., Zon B.A., Kretinin I.Y., Chernov V.E.,
Method of the Quantum Defect Green’s Function for Calculation
of Dynamic Atomic Polarizabilities// Optics and
Spectroscopy. — 2005. — Vol. 99, N4. — P.540-548.
19. Mischenko E.V., Transition energies and oscillator strengths
in helium within equation of motion approach with density
functional method for effective account of correlation’s//
Photoelectronics. — 2006 . — N15. — P.58-60.
114
UDÑ 539.184
E. V. Mischenko
20. The Fundamentals of Electron Density, Density Matrix and
Density Functional Theory in Atoms, Molecules and the
Solid State. Series: Progress in Theoretical Chemistry and
Physics. Eds. Gidopoulos N.I. and Wilson S. — Springer,
2004. — Vol.14. — 244P.
21. Kolachevsky N.N., Precise laser spectroscopy of cold atoms
and search of drift of the fine structure constant//Physics Uspekhi.
— 2008. — Vol.178. — P.1225-1230.
22. Courade E., Anderlini M., Ciampini D. Etal, Two-photon
ionization of cold rubidiun atoms with near resonant intermediate
state//J.Phys.B. At.Mol.Opt.Phys. — 2004. —
Vol.37. — P.967-979.
23. Singer K., Reetz-Lamour M., Amthor T., Marcassa L.G.,
Weidemuller M., Spectral broadening and suppression of
excitation induced by ultralong-range interactions in a cold
gas of Rydberg atoms //Phys. Rev. Lett. — 2004. — Vol.93. —
P.163001.
24. Loboda A.V., Mischenko E.V. et al, Spectral Broadening of
excitation induced by ultralong-range interaction in a cold gas
of Rydberg atoms// Spectral Line Shapes (AIP). — 2008. —
Vol.15. — P.260-264.
QUANTUM MEASURE OF FREQUENCY AND SENSING THE COLLISIONAL SHIFT AND BROADENING OF RB
HYPERFINE LINES IN MEDIUM OF HELIUM GAS
Abstract
New theoretical data regarding the collisional shift and broadening of the hyperfine spectral lines for Rb in the atmosphere of the
buffer inert He gas within relativistic perturbation theory formalism are presented.
Key words: atoms of Rb, spectral shift, inert gas He.
ÓÄÊ 539.184
E. Â. Ìèùåíêî
ÊÂÀÍÒÎÂÀß ÌÅÐÀ ×ÀÑÒÎÒÛ È ÄÅÒÅÊÒÈÐÎÂÀÍÈÅ ÑÒÎËÊÍÎÂÈÒÅËÜÍÎÃÎ ÑÄÂÈÃÀ È ÓØÈÐÅÍÈß ËÈÍÈÉ
ÑÂÅÐÕÒÎÍÊÎÉ ÑÒÐÓÊÒÓÐÛ RB Â ÀÒÌÎÑÔÅÐÅ ÃÅËÈß È ÕÎËÎÄÍÎÌ ÃÀÇÅ ÀÒÎÌÎÂ RB
Ðåçþìå
Ïðèâåäåíû íîâûå òåîðåòè÷åñêèå äàííûå ïî ñòîëêíîâèòåëüíîìó ñäâèãó è óøèðåíèþ ñïåêòðàëüíûõ ëèíèé ñâåðõòîíêîé
ñòðóêòóðû àòîìîâ Rb â àòìîñôåðå èíåðòíîãî ãàçà Íå, ïîëó÷åííûå â ðàìêàõ ôîðìàëèçìà ðåëÿòèâèñòñêîé òåîðèè âîçìóùåíèé.
Êëþ÷åâûå ñëîâà: àòîìû Rb, ñïåêòðàëüíûé ñäâèã, èíåðòíûé ãàç Íå.
ÓÄÊ 539.184
Î. Â. ̳ùåíêî
ÊÂÀÍÒÎÂÀ ̲ÐÀ ×ÀÑÒÎÒÈ ² ÄÅÒÅÊÒÓÂÀÍÍß ÇÑÓÂÓ ÒÀ ÓØÈÐÅÍÍß Ë²Í²É ÍÀÄÒÎÍÊί ÑÒÐÓÊÒÓÐÈ RB ÇÀ
ÐÀÕÓÍÎÊ Ç²ÒÊÍÅÍÜ Â ÀÒÌÎÑÔÅв ÃÅ˲ß
Ðåçþìå
Íàâåäåí³ íîâ³ òåîðåòè÷í³ äàí³ ïî çñóâó òà óøèðåííþ ñïåêòðàëüíèõ ë³í³é ïîíàäòîíêî¿ ñòðóêòóðè àòîì³â Rb çà ðàõóíîê
ç³òêíåíü â àòìîñôåð³ ³íåðòíîãî ãàçó Íå, îòðèìàí³ ó ìåæàõ ôîðìàë³çìó ðåëÿòèâ³ñòñüêî¿ òåî𳿠çáóðåíü.
Êëþ÷îâ³ ñëîâà: àòîìè Rb , ñïåêòðàëüíèé çñóâ, ³íåðòíèé ãàç Íå.

UDC 621.315.592
O. O. PTASHCHENKO 1 , F. O. PTASHCHENKO 2 , N. V. MASLEYEVA 1 , O. V. BOGDAN 1
1 I. I. Mechnikov National University of Odessa, Dvoryanska St., 2, Odessa, 65026, Ukraine
2 Odessa National Maritime Academy, Odessa, Didrikhsona St., 8, Odessa, 65029, Ukraine
SURFACE CURRENT IN GaAs P-N JUNCTIONS, PASSIVATED BY
SULPHUR ATOMS
1. INTRODUCTION
P-n junctions on wide-band III–V semiconductors
can be used as gas sensors [1, 2]. Such sensors
have low background currents, are sensitive at room
temperature, have a response time of 100 s [3]. The gas
sensitivity of these sensors is due to forming of a surface
conducting channel in the electric field induced
by the ions adsorbed on the surface of the natural oxide
layer [1, 2].
The threshold gas partial pressure of a sensor on
p-n junction depends on the surface states density in
the semiconductor [3]. The results of calculations [3]
predict rise of the sensitivity to low concentrations of
a donor gas when the surface states density in the p-n
junction is diminished.
The surface states density in GaAs can be lowered
by sulphur atoms deposition from some solutions [4].
The sulphur-passivation reduces the excess forward
current and reverse current in GaAs p-n junctions,
enhances the photosensitivity in the spectral region
of strong absorption, substantially increases the sensitivity
to ammonia vapors [5]. However the stability of
the characteristics of sulphur-passivated p-n junctions
was not investigated.
The aim of this work is a study of the influence of
the storage in a neutral gas on the surface currents in
sulphur-passivated GaAs p-n junctions. Effect of the
storage in helium atmosphere at room temperature on
I-V characteristics of forward and reverse currents in
sulphur-passivated GaAs p-n structures was studied.
2. EXPERIMENT
Influence of the storage (low-temperature annealing) of sulphur-passivated GaAs p-n structures
in a neutral (helium) atmosphere at room temperature on I-V characteristics of forward and reverse
currents was studied. The storage strongly reduces the excess forward current and the reverse current
in p-n junctions. The ideality coefficient of I-V characteristics decreases with the storage. This effect
has two stages. It is showed that all these phenomena can be explained by lowering of the surface
recombination centers density and reduction of the electrically active centers concentration in the
surface depletion layer.
I-V characteristics were measured on GaAs pn
junctions with the structure described in previous
works [1, 2]. The sulphur atoms deposition (passivation)
was carried out by a treatment of different durations
in 30% water solutions of Na 2 S . H 2 O [5].
I-V characteristics of the forward current in a typical
p-n structure are presented in Fig. 1.
Curve 1 was measured before the treatment. Over
the current range between 1μA and 1mA the I–V curve
can be described with the expression
IV ( ) = I0exp( qV/ nkT t ) , (1)
where I is a constant; q is the electron charge; V de-
0
notes bias voltage; k is the Boltzmann constant; T is
temperature; nt ≈ 2 is the ideality constant. Such I-V
curves can be ascribed to recombination on deep levels
in p-n junction and (or) at the surface [6]. And the
corresponding current is known as a recombination
current.
10 -5
© O. O. Ptashchenko, F. O. Ptashchenko, N. V. Masleyeva, O. V. Bogdan, 2009
10 -6
10 -7
10 -8
I,A
– 1
– 2
– 3
–4
– 5
– 6
– 7
0 0,2 0,4 0,6 0,8
V, Volts
Fig. 1. I–V characteristics of the forward current of a p-n
structure: initial (1) and after S-treatment and subsequent storage
in helium: 2 – 2.4 . 103 s; 3 – 7.2 . 103 s; 4 – 1.7 . 105 s; 5 – 5.2 . 105 s;
6 – 2.6 . 106 s; 7 – 7.8 . 106 s
At lower biases curve 1 has a section of an excess
current, which has an ideality constant n >2 and cor-
t
responds to the phonon-assisted tunnel recombination
at deep centers [6]. This recombination is located
at the p-n junction non-homogeneities, which cause
local increase of the electric field [6].
Curves 2 to 7 in Fig. 1 were obtained after passivation
of 40 s duration. Curve 2, measured after subsequent
40 min storage, exhibits an increase of the
115

excess current. And the further storage leads to a substantial
decrease of the excess current, as illustrated by
curves 3 to 7. After the storage during one month the
excess current disappears, and the I–V characteristic
corresponds to (1) over the current range from 10-8 A
≈ 2 .
to 10 -3 A with ideality constant n t
116
10 -5
10 -6
10 -7
10 -8
I, �
10 3
2
1
10 4
10 5
3
3A
10
t, s
6 10 7
Fig. 2. Effect of the storage duration on the forward current at
V=0.4 V (1) and at V=0.7 V (2) and on the reverse current at V=-4
V (3, 3A). Curve 3A is shifted down by 0.7
Curve 1 in Fig. 2 represents the dependence of the
excess current (at the voltage of 0.4 V) on the storage
duration. Curve 2 illustrates such dependence for
the recombination current (at the voltage of 0.7 V). A
comparison between curves 1 and 2 shows that the influence
of passivation and the subsequent storage on
the recombination current is much weaker than on the
excess current.
The effect of the passivation and the subsequent
storage on the I–V characteristic of reverse current in
the same p-n junction is illustrated by Fig. 3. Curve
1 was obtained before passivation. Curve 2, measured
after subsequent storage during 40 min, exhibits an
increase of the reverse current. And further storage
decreases the reverse current, as is seen from curves 3
to 6. Curve 3 in Fig. 2 presents the dependence of the
reverse current, measured at a voltage of –4 V, on the
storage duration. Curve 3A is obtained from curve 3 by
a shift down by 0.7. This curve practically coincides
with curve 1. It means that the time-dependences of
the excess forward current and the reverse current are
identical.
3. DISCUSSION
The presented experimental results show that
storage in helium atmosphere at room temperature
substantial reduces recombination and excess forward
currents, as well as reverse current in sulphur-passivated
GaAs p-n junctions. The storage time dependence
of the excess forward current and the reverse current
are identical. It suggests that decrease of these currents
has the same nature. It is known [6] that the excess
current in GaAs p-n structures is localized in nonhomogeneities
of the p-n unction. A strong influence
of the passivation and the subsequent storage on the
excess current suggests that these non-homogeneities
are placed on the surface of our structures. And the
same can be concluded about the localization of the
reverse current in our samples.
10 -5
10 -6
10 -7
10 -8
I,A
1
2
3
0 1 2 3 4 5
V, Volts
Fig. 3. I–V characteristics of the reverse current of a p-n
structure: initial (1) and after S-treatment and subsequent storage
in helium: 2 – 2.4 . 103 s; 3 – 1.7 . 105 s; 4 – 1.2 . 106 s; 5 – 2.6 . 106 s;
6 – 7.8 . 106 s
Curve 2 in Fig. 2 illustrates the time dependence of
the recombination current during the storage. The surface
component of this current can be expressed [6] as
1 1 1
s p s s
2 2
ns
2
ps
I = ql n(0)( C N / 2) ( D + D ) . (2)
Here l is the perimeter of the p-n junction; n(0) is
p
the surface electron concentration at the point, where
the surface recombination centers are half-occupied;
N and C are the density of surface recombination
s s
centers and their electron capture coefficient, correspondingly;
D and D are the diffusion coefficients
ns ps
for electrons and holes at the surface, respectively.
Sulphur-passivation of GaAs reduces the density
of surface recombination centers [4]. Therefore the
decrease in the recombination current, illustrated by
curve 2 in Fig. 2, can be ascribed to the lowering of the
density N of surface recombination centers in (2).
s
An analysis of curve 2 in Fig. 2 with the help of relation
(2) gives the time-dependence N /N (0), where
s s
N (0) is the concentration of surface recombination
s
centers before storage. This dependence is represented
by curve 1 in Fig. 4.
Some information about the concentration N of
electrically active centers at the surface of a p-n structure
gives an analysis of ideality coefficient n of I–V
t
characteristics [6]. This coefficient is related to N by
expression [6]
5
4

where
N = N (1 − 2 / n ) , (3)
t t
N m kT q
ε is the permittivity; m denotes the tunnel effective
t
mass of charge carriers.
1,2
0,8
0,4
0
Ns / Ns0, N/Nt
10 3
2
3
2 2
t = 12 ε t(
) /( h ) , (4)
10 4
10 5
3A
1
10
t, s
6 10 7
Fig. 4. Effect of the storage duration on the concentrations:
1 – N s /N s (0); 2 – N/N t in surface non-homogeneities; 3, 3A – average
of N/N t in surface. Ordinates of curve 3A are normalized at
t=7.2 . 10 3 s
Curves 1 and 2 in Fig. 5 present the time-dependences
of the ideality coefficients at low and high injection
levels, respectively. An analysis of curve 1 by
using formula (3) gives the change of electrically active
centers concentration N in the surface depletion
layer of non-homogeneities, which are responsible for
the excess current. N(t) dependence during the storage
for these centers is depicted as curve 2 in Fig. 4. The
dependence N(t) for the homogeneous region of the
surface, obtained from analogous analysis of curve 2 in
Fig. 5, is represented by curve 3 in Fig. 4.
A comparison between curves 2 and 3 in Fig. 4
shows that the storage much stronger reduces the concentration
of electrically active centers (non-compensated
acceptors) in surface non-homogeneities, than
in average at the surface of p-n structure. After a storage
for one month curve 2 in Fig. 4 trends to curve 2.
It means that the non-homogeneities at the surface,
which are responsible for the excess current, disappear.
The main defects that increase the excess current
in p-n junctions on III–V semiconductors are dislocations
[6]. And sulphur atoms are donors in GaAs.
It permits to conclude that during the storage S atoms
at the surface diffuse to dislocations and compensate
their charge.
As mentioned, curves 1 and 3 in Fig. 4 represent
the time-dependences of the surface recombination
centers concentration N s (normalized to initial its
value N s (0)) and the electrically active centers at the
surface N (normalized to the quantity N t , defined
by Eq. (4)). Curve 3A was obtained from curve 3 by
normalization to its value at t=2 h. The courses of
curves 1 and 3A at t>10 4 s are similar. It means that
the density of surface recombination centers and the
concentration of electrically active centers vary identically
during the storage. However, at the beginning,
at t

The forward current at high injection level (at
I>1μA) also decreases with the storage, due to lowering
of both the density of surface recombination centers
and the concentration of electrically active centers
in the surface depletion layer.
All these effects can be ascribed to compensation
of acceptors (perhaps, related to dislocations)
by sulphur atoms in the surface depletion layer and
to destroying of surface states, acting as recombination
centers.
References
1. Ïòàùåíêî Î. Î., Àðòåìåíêî Î. Ñ., Ïòàùåíêî Ô. Î.
Âïëèâ ãàçîâîãî ñåðåäîâèùà íà ïîâåðõíåâèé ñòðóì â pn
ãåòåðîñòðóêòóðàõ íà îñíîâ³ GaAs–AlGaAs // Ô³çèêà ³
õ³ì³ÿ òâåðäîãî ò³ëà . — 2001. — Ò. 2, ¹ 3. — Ñ. 481 — 485.
2. Ptashchenko O. O., Artemenko O. S., Dmytruk M. L. et al.
Effect of ammonia vapors on the surface morphology and
118
UDC 621.315.592
O. O. Ptashchenko, F. O. Ptashchenko, N. V. Masleyeva, O. V. Bogdan
SURFACE CURRENT IN GaAs P-N JUNCTIONS, PASSIVATED BY SULPHUR ATOMS
surface current in p-n junctions on GaP // Photoelectronics. —
2005. — No. 14. — P. 97 — 100.
3. Ïòàùåíêî À. À., Ïòàùåíêî Ô. À. P-n — ïåðåõîäû íà îñíîâå
GaAs è äðóãèõ ïîëóïðîâîäíèêîâ À III B V êàê ãàçîâûå
ñåíñîðû // Äåâÿòàÿ êîíôåðåíöèÿ “Àðñåíèä ãàëëèÿ è ïîëóïðîâîäíèêîâûå
ñîåäèíåíèÿ ãðóïïû III-IV”: Ìàòåðèàëû
êîíôåðåíöèè/ — Òîìñê: Òîìñêèé ãîñóíèâåðñèòåò,
2006. — Ñ. 496 — 499.
4. Äìèòðóê Í. Ë., Áîðêîâñêàÿ Î. Þ., Ìàìîíîâà Ë. Â. Ñóëüôèäíàÿ
ïàññèâàöèÿ òåêñòóðèðîâàííîé ãðàíèöû ðàçäåëà
ïîâåðõíîñòíî-áàðüåðíîãî ôîòîïðåîáðàçîâàòåëÿ íà îñíîâå
àðñåíèäà ãàëëèÿ // Æóðíàë òåõíè÷åñêîé ôèçèêè. —
1999. — Ò. 69, ¹6. — Ñ. 132 — 134.
5. Ptashchenko O. O., Ptashchenko F. O., Masleyeva N. V. et
al. Effect of sulfur atoms on the surface current in GaAs p-n
junctions. // Photoelectronics. — 2007. — No 17. — P. 36 —
39.
6. Ptashchenko A. A., Ptashchenko F. A. Tunnel surface recombination
in optoelectronic device modelling // Proc.
SPIE. — 1997. — V. 3182. — P. 145 — 149.
Abstract
Influence of the storage (low-temperature annealing) of sulphur-passivated GaAs p-n structures in a neutral (helium) atmosphere
at room temperature on I-V characteristics of forward and reverse currents was studied. The storage strongly reduces the excess forward
current and the reverse current in p-n junctions. The ideality coefficient of I-V characteristics decreases with the storage. This effect has
two stages. It is showed that all these phenomena can be explained by lowering of the surface recombination centers density and reduction
of the electrically active centers concentration in the surface depletion layer.
Key words: influence, surface current, P — N junctions.
ÓÄÊ 621.315.592
À. À. Ïòàùåíêî, Ô. À. Ïòàùåíêî, Í. Â. Ìàñëååâà, Î. Â. Áîãäàí
ÏÎÂÅÐÕÍÎÑÒÍÛÉ ÒÎÊ Â P-N ÏÅÐÅÕÎÄÀÕ ÍÀ ÎÑÍÎÂÅ GaAs, ÏÀÑÑÈÂÈÐÎÂÀÍÍÛÕ ÀÒÎÌÀÌÈ ÑÅÐÛ
Ðåçþìå
Èññëåäîâàíî âëèÿíèå õðàíåíèÿ (íèçêîòåìïåðàòóðíîãî îòæèãà) ïàññèâèðîâàííûõ àòîìàìè ñåðû p-n ïåðåõîäîâ íà îñíîâå
GaAs â íåéòðàëüíîé àòìîñôåðå (â ãåëèè) ïðè êîìíàòíîé òåìïåðàòóðå íà ÂÀÕ ïðÿìîãî è îáðàòíîãî òîêîâ. Ïðè õðàíåíèè
ñóùåñòâåííî óìåíüøàþòñÿ ïðÿìîé èçáûòî÷íûé òîê è îáðàòíûé òîê â p-n ïåðåõîäàõ. Êîýôôèöèåíò èäåàëüíîñòè ÂÀÕ óìåíüøàåòñÿ
â ïðîöåññå õðàíåíèÿ. Ýòîò ïðîöåññ äâóõñòàäèéíûé. Ïîêàçàíî, ÷òî âñå ýòè ÿâëåíèÿ ìîæíî îáúÿñíèòü óìåíüøåíèåì
ïëîòíîñòè ïîâåðõíîñòíûõ öåíòðîâ ðåêîìáèíàöèè è óìåíüøåíèåì êîíöåíòðàöèè ýëåêòðè÷åñêè àêòèâíûõ öåíòðîâ â ïîâåðõíîñòíîì
îáåäíåííîì ñëîå.
Êëþ÷åâûå ñëîâà: ïîâåðõíîñòíûé òîê, P-N — ïåðåõîä, èññëåäîâàíèÿ.
ÓÄÊ 621.315.592
Î. Î. Ïòàùåíêî, Ô. Î. Ïòàùåíêî, Í. Â. Ìàñ뺺âà, Î. Â. Áîãäàí
ÏÎÂÅÐÕÍÅÂÈÉ ÑÒÐÓÌ Ó P-N ÏÅÐÅÕÎÄÀÕ ÍÀ ÎÑÍβ GaAs, ÏÀÑÈÂÎÂÀÍÈÕ ÀÒÎÌÀÌÈ Ñ²ÐÊÈ
Ðåçþìå
Äîñë³äæåíî âïëèâ çáåð³ãàííÿ (íèçüêîòåìïåðàòóðíîãî â³äïàëó) ïàñèâîâàíèõ àòîìàìè ñ³ðêè p-n ïåðåõîä³â íà îñíîâ³ GaAs
ó íåéòðàëüí³é àòìîñôåð³ (â ãå볿) ïðè ê³ìíàòí³é òåìïåðàòóð³ íà ÂÀÕ ïðÿìîãî ³ çâîðîòíîãî ñòðóì³â. Ïðè çáåð³ãàíí³ çíà÷íî
çìåíøóþòüñÿ íàäëèøêîâèé ïðÿìèé ñòðóì òà çâîðîòíèé ñòðóì ó p-n ïåðåõîäàõ. Êîåô³ö³ºíò ³äåàëüíîñò³ ÂÀÕ çìåíøóºòüñÿ â
ïðîöåñ³ çáåð³ãàííÿ. Äàíèé ïðîöåñ º äâîñòàä³éíèé. Ïîêàçàíî, ùî âñ³ ö³ ÿâèùà ìîæíà ïîÿñíèòè çìåíøåííÿì ù³ëüíîñò³ ïîâåðõíåâèõ
öåíòð³â ðåêîìá³íàö³¿ òà çìåíøåííÿì êîíöåíòðàö³¿ åëåêòðè÷íî àêòèâíèõ öåíòð³â ó ïîâåðõíåâîìó çá³äíåíîìó øàð³.
Êëþ÷îâ³ ñëîâà: ïîâåðõíåâèé ñòðóì, Ð-N — ïåðåõ³ä, äîñë³äæåííÿ.

UDÑ 539.19+539.182
A. V. GLUSHKOV, YA. I. LEPIKH, A. P. FEDCHUK, A. V. LOBODA
I. I. Mechnikov Odessa National University, Odessa
Odessa National Polytechnical University
THE GREEN’S FUNCTIONS AND DENSITY FUNCTIONAL APPROACH
TO VIBRATIONAL STRUCTURE IN THE PHOTOELECTRON SPECTRA
OF MOLECULES
We present the basis’s of the new combined theoretical approach to vibrational structure in photoelectron
spectra of molecules. The approach is based on the Green’s function method and quasiparticle
density functional theory (DFT). The density of states, which describe the vibrational structure in
photoelectron spectra, is defined with the use of combined DFT-Green’s-functions approach and is
well approximated by using only the first order coupling constants in the one-particle approximation.
Using the DFT theory leads to significant simplification of the calculation.
I. INTRODUCTION
A number of phenomena, provided by interaction
of electrons with vibrations of the atomic nuclei
in molecules or solids is manifested in the molecular
photoelectron spectra. Indeed, the physics of the
interaction of electrons with vibrations of the atomic
nuclei in molecules or solids is more richer (c.f.[1-
16]). One could mention here a great field of the resonant
collisions of electrons with molecules, which are
one of the most efficient pathways for the transfer of
energy from electronic to nuclear motion. While the
corresponding theory has been refined over the years
with sophisticated and elaborate non-local treatments
of the reaction dynamics, such studies have
for the most part treated the nuclear dynamics in one
dimension. This situation has resulted from the fact
that, as the field of electron-molecule scattering developed,
both experimentally and theoretically, the
phenomena of vibrational excitation and dissociative
attachment were first understood for diatomics,
and it seemed natural to extend that understanding
to polyatomic molecules using one-dimensional or
single-mode models of the nuclear motion. However
a series of experimental measurements of these phenomena
in small polyatomic molecules have proven
to be uninterpretable in terms of atomic motion with
a single degree of freedom. Primary among these are
potential-energy surfaces which describe the behavior
of the electronic energy with respect to the locations
of the nuclei, subject to the underlying Born-Oppenheimer
or clamped nuclei approximation. From the
ground- and excited-state wave functions one could
in principle obtain all properties that arise from a solution
to the vibrational Schrödinger equation that
gives the frequencies, and, with the derivatives of the
dipole moment, the infrared intensities [1-6]. Electronic
excited states are also accessible along with
electronic and photoelectron spectra.
As it is often takes a place, the old multi-body
quantum theoretical approaches, which have been
primarily developed in a theory of superfluity and superconductivity,
and generally speaking in a theory
of solids, became by the powerful tools for develop-
© A. V. Glushkov, Ya. I. Lepikh, A. P. Fedchuk, A. V. Loboda, 2009
ing new conceptions in a theory of molecules [7-11].
Many of them offers a synthesis of cluster expansions,
Brueckner’s summation of ladder diagrams, the summation
of ring diagrams Gell-Mann and an infinite-order
generalization of many-body perturbation
theory (MBPT). Using the quantum-field methods in
molecular theory allowed to obtain a very powerful approach
for correlation in many-electron systems.
The Green’s method is very well known in a
quantum theory of field, quantum theory of solids
(c.f.[7,8]). Naturally, an attractive idea was to use
it in the molecular theory. Returning to problem of
description of the vibrational structure in photoelectron
spectra of molecules, it is easily understand that
this approach has great perspective (c.f.[12,13]). One
could note that the experimental photoelectron (PE)
spectra usually show a pronounced vibrational structure.
Usually the electronic Green’s function is defined
for fixed position of the nuclei. As result, only
vertical ionization potentials (V.I.P.’s) can be calculated
[14]. The cited method, however, requires as
input data the geometries, frequencies, and potential
functions of the initial and final states. Since in most
cases at least a part of these data are unavailable, the
calculations have been carried out with the objective
of determining the missing data by comparison
with experiment. Naturally, the Franck-Condon
factors are functions of the derivatives of the difference
between the potential curves of the initial and
final states with respect to the normal coordinates.
To avoid the difficulty and to gain additional information
about the ionization process, the Green’s
functions approach has been extended to include the
vibrational effects in the photoelectron spectra. Nevertheless,
there are well known great difficulties of
the correct interpretation of the photoelectron spectra
for any molecules.
Further let us remember that for larger molecules
and solids, far more approximate but more easily
applied methods such as density-functional theory
(DFT) [15-17] or from the wave-function world the
simplest correlated model MBPT are preferred [3].
Indeed, in the last decades DFT theory became by a
great, quickly developing field of the modern quan-
119

tum computational chemistry of molecules, solids.
Naturally, this approach does not allow to reach a
spectroscopic accuracy in description of the different
molecular properties, nevertheless, the key idea is very
attractive and can be used in new combined theoretical
approaches.
Here we present the basis’s of the new combined
theoretical approach to vibrational structure in photoelectron
spectra of molecules. The approach is
based on the Green’s function method (Cederbaum-
Domske version) [12,13] and Fermi-liquid DFT formalism
[11,14] (see also [18-23,25]). The density of
states, which describe the vibrational structure in molecular
photoelectron spectra, is calculated with the
help of combined DFT-Green’s-functions approach.
In addition to exact solution of one-bode problem
different approaches to calculate reorganization and
many-body effects are presented. The density of states
is well approximated by using only the first order coupling
constants in the one-particle approximation.
It is important that the calculational procedure is
significantly simplified with using the quasiparticle
DFT formalism. Thus quite simple method becomes
a powerful tool in interpreting the vibrational structure
of photoelectron spectra for different molecular
systems.
2. The Hamiltonian of the system. The density of
states in one-body and many-body solution
The quantity which contains the information
about the ionization potentials and the molecular vibrational
structure due to quick ionization is the density
of occupied states [12]:
120
−1
ihº t t
k( ) (1/2 h)
0 a (0) k(
)
k
0
N º = π ∫ dte 〈ψ a t ψ 〉 , (1)
where Ψ〉 0 is the exact ground state wavefunction of
the reference molecule and ak() t is an electron destruction
operator, both in the Heisenberg picture.
For particle attachment the quantity of interest is the
density of unoccupied states:
1
ihº t
t
k ( ) (1/ 2 h)
0 a k(t)a (0) k 0
N dte −
º = π ∫ 〈ψ ψ 〉 (2)
Usually in order to calculate the value (1) states
for photon absorption one should express the Hamiltonian
of the molecule in the second quantization formalism
(see [12,13]). The corresponding Hamiltonian
is as follows:
H = TΕ( ∂/ ∂ x) + TΝ( ∂/ ∂ X) + U( x, X)
, (3)
where TΕ is the kinetic energy operator for the electrons,
TΝ is the kinetic energy operator for the nuclei,
and U represents the interaction
U( x, X) = UΕΕ ( x) + UΝΝ ( X) + UΕΝ ( x, X)
, (4)
where x denotes electron coordinates, X denotes nuclear
coordinates, UΕΕ represents the Coulomb interaction
between electrons, etc. Introducing the field
operator:
Ψ( R, θ , x) = ∑ φi( x, R, θ) ai( R,
θ)
(5)
i
where the ô are Hartree-Fock (HF) one–particle
i
functions and the a are destruction operators for a HF
i
particle in the “i” state, them the Hamiltonian in a occupation
number representation is given as
H = H ( R, θ ) + U ( R, θ ) + T ( ∂/ ∂ R)
, (6)
ΕΝ 0 ΝΝ 0 Ν
H
t 1
= ∑º ( Raa ) + ∑V
i
2
t t
( Raaaa )
[ V
t
( R)] a a ,
EN i i i ijkl i j l k
−∑ ∑ (7)
ikkj i j
ij k∈ f
Vijkl 2
ij e r
'
r
−1
kl
=〈 − 〉
The i ( ) R ∈ are the one-particle HF energies and f
denotes the set of orbitals occupied in the HF ground
state. As usually in the adiabatic approximation one
could write the eigenfunctions to H as products
xR , , θ〉 0 E × R〉
N ,and further expand i ( ) R ∈ , Vijkl ( R ) ,
and UNN ( R, θ ) about R leaving the operators a 0 i and
a unchanged [13]:
t
i
H= ∑
i
t 1
t t
º i ( R0) aa i i + ∑ Vijkl ( R0) aaaa i j l k −
2
− [ V ( R ) − V ( R )] a a +
∑∑
ij k∈ f
ikjk 0 ikkj 0
t
i j
⎛∂∈ ⎞
M
1
+ ∑ [ ∑ ⎜ ⎟ ( R− Rso
) +
i s= 1 ⎝ ∂Rs
⎠0
2
⎛ ∂ ∈ ⎞ i
M 1
+ ∑ ∑ ⎜ ⎟ ( Rs − Rso)
×
2 ⎝∂R ∂R
⎠
i s, s'=
1 s s'0
t
⎛ ∂ ⎞
× ( Rs' − Rs'0) ] aiai + ... + UNN( R0, θ 0)
+ ... + TN
⎜ ⎟
, (8)
⎝∂R⎠ where M is the number of normal coordinates.
Choosing R as the equilibrium geometry on the
0
HF level and introducing dimensionless normal coordinates
Q one can write the following Hamiltonian
s
(the subscript 0 stands for R ) [13]:
0
H = H + H + H + H ,
(1) (2)
E N EN EN
1
H = º ( R) aa + V ( R) aaaa −
∑ ∑
t t t
E
i
i 0 i i
2
ijkl 0 i j l k
t
−∑∑ [ Vikjk ( R0) −Vikkj
( R0)] aiaj, i, j k∈f M
t 1
HN = h ∑ ω s( bsbs + ),
s=
1 2
⎛ ∂є
⎞
M
(1) −1/
2
i
t t
HEN = 2 ∑ ⎜ ⎟ ( bs+ bs)[ aiai− ni]
+
s= 1 ⎝∂Qs⎠0 i
M
s, s'=
1
2
⎛ ∂ є ⎞ i
⎜ ⎟
⎝∂Qs∂Qs'⎠0 bs t
bs bs' t
bs' t
aiai ni
1
+ ∑ ∑
( + )( + )[ − ],
4
⎛∂V⎞ H b b
M
(2) −3/2
EN = 2 ∑∑
s= 1
ijkl
⎜ ⎟ (
⎝ ∂Qs
⎠0
s +
t
s ) ×
t t
vaaa 1 i j k
t t
vaaaa 2 l k i j
t t
vaaaa
3 j k l i
×δ [ +δ + 2 δ ]
1 ⎛ ∂ V ⎞
+ ∑ ∑
( + ) ×
8
M 2
ss , '= 1
ijkl
⎜ ⎟
⎜ QsQ ⎟ '' ⎝
∂ ∂ s ⎠0
bs t
bs
t t t
× ( bs' + bs'[ δ v1aiajak +
2 l k
t
i
t
j 2 3
t
j k l
t
i],
+δ vaaaa + δvaaaa
(9)

ni = 1 i ∈ f , δσ f = 1 ( ijkl)
∈σ,
= 0, i ∉ f , = 0 ( ijkl)
∉σ ,
where the index set v means that at least 1 k
or i φ and j φ are unoccupied, v2 the orbitals is unoccupied, and v that 3 k
φ and l φ
that at most one of
φ and j φ or l φ
and φ j are unoccupied. Besides, here for simplicity all
terms leading to anharmonicities are neglected. The
t
ωs are the HF frequencies and the b s and b s are destruction
and creation operators for vibrational quanta
defined by
t
Q = (1/ 2)( b + b ),
s s s
f
/ (1/ 2)( )
t
∂ ∂ Qs = bs − bs
(10)
The first term H E describes the electronic motion
for nuclei fixed at the HF ground state geometry. The
second term H N describes the motion of the nuclei in
the harmonic HF potential (the extension to anhar-
(1)
monic terms can easily be done). H EN represents the
coupling of the HF particles with the nuclear motion.
The coupling constants are the normal coordinate
derivatives of the HF one-particle energies. The first
(1)
sum in the expression for H EN is responsible for the
geometry shifts and the second one for the charge of
frequencies due to electrons. There is also a modification
of the interaction between electrons through the
(2)
coupling to the nuclear motion. The term H EN , which
describes this modification, is due to its nature less im-
(1)
portant than H EN .
The exact solution of the one-body HF problem
has been given in ref.[12]. Correspondingly in the
one-particle picture the density of occupied states is
given by
1
1
0 1
iє є( t )
i H
k
0
t
Nk( ) dte 0 e 0 ,
2
−
∞
−
−
±
= 〈 〉
π −∞
∫
×〈ψ0 T
t
ak() t ak(0)
ψ 0〉
(12)
where T is Wick’s time ordering operator and the function
Nє k ( ) then follows from the relation
π Nk( º ) = aIm Gkk( º −aiη) , (13)
a =− signº
k ,
where η is a positive infinitesimal. Choosing the unperturbed
Hamiltonian H 0 to be
t
H0= ∑ º i aiai + HN
(14)
one finds for the corresponding Green’s functions
0
Gkk ( º ) =δkk ' /( º −º k −aiη) (15)
The Dyson equation
0 0
Gkk ' = Gkk ' + ∑ GkkΣ kk ''Gk'' k ' (16)
k ''
h %
h
º (11)
h
with
relates the Green’s functions to the free ones introducing
a new function kk '' ( ) є Σ called the (proper) self-energy
part. In in order to calculate Σ kk ' , a well-known
diagrammatic method is used. The sum of Feynman
diagrams leading to the self-energy part is shown in
Fig. 1. All notations are standard.
The one-body problem treated above results in the
exact solution of the Dyson equation with the selfenergy
part given by the infinite number of diagrams
shown in the first row of Fig. 1 and the corresponding
Green’s function is as follows [12-14]:
g
0
M
∑ s
t
s s
M
∑
k
s s
t
s
s= 1 s=
1
M
k t t
∑ γ ss '( bs+ bs)( bs' + bs')
ss , '= 1
H% = h ω b b + g ( b + b ) +
1 ⎛ ∂є ⎞
1⎛
∂ є ⎞
.
2
i i i
i
s =± ⎜ ⎟ , γ ss'=±
⎜ ⎟
2 ⎝∂Qs ⎠ 4 Q 0 ⎝∂ s∂Qs'⎠0 In a diagrammatic method in order to obtain the
function N k ( º ) one should calculate the Green’s
function G kk ' ( º ) first:
kk '
Fig. 1. The sum of diagrams contributing to the self-energy part
−1
ih
h ∫−∞
{ }
−1º
t
G ( º ) =− i dte ×
∞
( m )
OB
−1
Gkk′ () t =±δkk′ iexp⎡ ⎣−in εk Δε t⎤
⎦×
∑
n
2
n$ k Uk 0 exp(
ink kt)
× ± ⋅ω
(17)
121

The corresponding Dyson-like equation is as follows:
OB OB
Gkk′ () ∈ = Gkk′ () ∈ + ∑Gkk () ∈Ô kk′′ Gk′′
k′
() ∈ (18)
122
kk′
The expression for a sum of the first 2 diagrams
appearing in Fig. 2 are written by a standard way:
Ф
kk′
where
()
( − )
Vklij Vklij Vk′ lijUniiUnj jUnll ∈ = ∑ ∑
+
∈+ E −E −E
+
i, j∈F ni, nj, nl l i j
l∉F ( Vklij −Vklij
) Vk′ lijUniiUnj jUnll ∑ ∑ (19)
∈+ E −E −E
i, j∈F ni, nj, nl l i j
l∉F 2
U $
ni i 0
i = n Ui
and E $
i =∈i mΔ∈i m hni
⋅ωi
The direct method for calculation of N (∈) as the
k
imaginary part of the corresponding Green’s function
implicitly includes the determination of the V. I. P. s of
the reference molecule and then of Nk() ∈ . The zeros
of the functions
op () ∈ =∈− ∈ +Σ() ∈
D ⎡ k ⎣
⎤
⎦ , (20)
k
op
where ( ∈ +Σ) denotes the kth eigenvalue of the di-
k
agonal matrix of the one-particle energies added to the
matrix of the self-energy part, are the negative V. I. P. ‘s
for a given geometry. Further it is easily to write [12]:
( VIP) ( F)
.. . k k k
=− ∈ + ,
1
Fk =Σkk( −( V.. I P.
) ) ≈ Σkk( ∈k)
. (21)
k
1 −∂Σkk ( ∈k ) / ∂∈
N 1
Expanding the ionic energy Ek − about the equilibrium
geometry of the reference molecule in a power
series of the normal coordinates of this molecule:
where
( F )
⎛∂∈ + ⎞
E = E − Q −
M
N−1 N−1
k k
k k () 0 ∑ ⎜ ⎟ s
s= 1 ⎝ ∂Qs
⎠0
q
k
=
∑
Fig. 2. Perturbation expansion of Ô kk
2
( V V )
where kk Ф ′ , is equal to Σ kk′ , less the diagrams of the
first row in Fig.1. The perturbation expansion of Ô is
OB
shown in Fig. 2 where iG kk′
, is symbolized by a double
solid line.
N ( k Fk E0)
2 ⎛ ⎞
M 1 ∂ ∈ + −
− ∑ ⎜ ⎟ QQ s s′
(22)
2! ss , ′= 1⎜
∂Qs∂Q ⎟
s′
⎝ ⎠0
leads to a set of linear equations in the unknown normal
coordinate shifts ΔQ , S
2
( k Fk) ( k Fk)
∑
⎛∂∈ + ⎞ ⎛∂∈ + ⎞
− ⎜ ⎟ = ⎜ ⎟ δQs′
, (23)
∂Q ⎜ ∂Q ∂Q
⎟
⎝ ⎠ ⎝ ⎠
s 0
s′≠ s s s′
0
( F )
⎡ 2
⎛∂ ∈ k + ⎞ ⎤
k
⎢⎜ 2 ⎟ s⎥ s
⎢
⎜ Q ⎟
⎝ ∂ 3 ⎠0⎥
+ −hω δ Q , s = 1... M,
⎣ ⎦
where ω s are frequencies of the reference molecule.
The new coupling constants are then:
( ) ( )
g =± 1/ 2 ⎡⎣∂∈ + F / ∂Q
⎤⎦
(24)
1 k k l 0
⎛1⎞ 2
γ ll′ = ± ⎜ ⎟⎣
⎡∂ ( ∈ k + Fk) / ∂Ql/ ∂Ql′
⎤
4
⎦0
⎝ ⎠
Thee coupling constants l g and ll y ′ are calculated
by the well-known perturbation expansion of the selfenergy
part using the Hamiltonian H of Eq. (6). In
EN
second order one obtains:
( − )
V V V
∈ = +
() 2
ksij ksji ksij
∑ kk () ∑
i, j ∈+∈s −∈i −∈j
s∉F ( − )
V V V
+
∈+∈ −∈ −∈
and the coupling constant g , can be written as
l
g
ksij − ksji ⎡∂∈s ∂∈ ∂∈ i j ⎤
2 ⎢ − − ⎥
( VIP .. . )
∂Q s i j
l ∂Ql ∂Ql
⎣
⎡− +∈ −∈ −∈ ⎤ ⎣ ⎦
k
⎦
l
∑
ksij ksji ksij
(25)
i, j
s∉F s i j
k( ) ∑ kk ( ) k
( ) ∑ ( )
1 ∂∈ 1 + q ∂/ ∂∈ ⎡− V. I. P.
⎤
k
≈±
⎣ ⎦
, (26)
2 ∂Ql 1 − ∂/ ∂∈ ⎡ kk ⎣− VIP . . . ⎤
k ⎦
2
( Vksij −Vksji
)
∂∈
∑ ∂ ⎡ ⎤
k
2
Ql ⎣− ( VIP .. . ) +∈ k s −∈i −∈j⎦
(27)

It is suitable to use further the pole strength of the
corresponding Green’s function
[ ] 1 −
VIP
⎧ ∂
⎫
ρ k = ⎨1 − ∑ kk −( . . .) k ⎬ ;1≥ρk ≥0,
(28)
⎩ ∂∈
⎭
and then
( )
0
0 −1/2
gl ≈ gl ⎡⎣ρ k + qk
ρk −1
⎤⎦
, gl =± 2 ∂∈k / ∂ Ql
(29)
Below we firstly give the DFT definition of the pole
strength corresponding to V. I. P.’s and confirm earlier
data [13,14]: p ≈0,8-0,95. The closeness of p to 1 in
k k
fact means that a role of the multi-body correlation
0
effects is small ( gl ≈ gl
). The above presented results
can be usefully treated in the terms of the correlation
and reorganization effects. Usually it is introduced the
following expression for an I.P.:
( IP . . )
k
( Vkikj −Vkijk
)
∑
=−∈k − −
∈ −∈
j∉, i∈F j i
( Vkijl −Vkilj
)
1
− −δ
2 ∈ +∈ −∈ −∈
∑ ( 1 ik ) (30)
i∈F k i j l
jl , ∉F
2
( Vkjpq −Vkjqp
)
1
− ∑ ( 1−δkp )( 1−δkq
)
2 pq , ∈F∈
k +∈i −∈p −∈q
j∉F The first correction term is due to reorganization,
the remaining correction terms are due to correlation
effects. Then the coupling constant g , can be written as
l
gl ⎧
0 ⎪
gl
⎨1
⎪⎩
2
( Vkkkj
)
∑
2
j∉F( ∈j −∈k)
2
( Vkijl −Vkilj
)
∑
1 2
( ∈ k +∈i −∈j −∈l)
≈ + −
⎡
1
− ⎢
( −δ ki ) +
2 ⎢i∈F
⎢⎣ jl , ∉F
2
⎫
( Vkjpq −V ⎤
kjqp )
⎪
+ 2 ( 1 kq )( 1 kp ) ⎥
∑ −δ −δ ⎬ (31)
pq , ∈F(
∈
⎥ ) j, ∉F
k +∈i −∈p −∈q ⎥⎦⎭
⎪
The second coupling constant can be written
γ = γ
⎛ g
⎜
⎝
⎞ 1
⎟+ ⎠
2g
∂ ⎛ g
⎜
Q ⎝
⎞
⎟
⎠
γ , is defined analogously
0
ll
0 l 0
l
ll ll 0
gl 4
l
∂ l
0
gl
0
g l .
(32)
3. QUASIPARTICLE DENSITY FUNCTIONAL
THEORY
The quasiparticle Fermi-liquid version of the DFT
theory has been presented in ref. [11,14] (see also [18-
23,25]), starting from the problem of searching for the
optimal one-electron representation [2-5]. One of the
simplified recipes represents the Kohn-Sham DFT
theory [15]. Earlier new QED DFT version, based on
the formally exact QED perturbation theory (energy
approach), has been developed and a new approach
to construction of the optimized one-quasiparticle
representation has been proposed (look details in ref.
[11]). The energy approach uses the adiabatic Gell-
Mann and Low formula for the energy shift ΔE with
electrodynamic scattering matrice. In a modern theory
of molecules there is a number of tasks, where an
accurate account for the complex exchange-correlation
effects, including the continuum pressure, energy
dependence of a mass operator etc., is critically important.
It includes also the calculation of the vibration
structure for the molecular systems. In this case it
can be very useful the quasiparticle DFT [11,14].
In order to get the master equations and construct
an optimal basis of the one-particle wave functions
ϕ λ one could use the Green’s function method. Let
us define the one-particle Hamiltonian for functions
ϕ λ so that the Greens’ function pole part in the ( λ ϕ
) representation is diagonal on λ . Starting equation
is the Dyson equation for multi-electron (for example
atom or molecule):
∑
∑
2 /
( p /2 Zα / rα) G( x, x , )
ε− + ⋅ ε −
/ / /
∫ dx ( x, x , ) ( x x ) (33)
− ε =δ −
where x = (,) r s are the spatial and spin variables, ∑
is the mass operator; Z , as usually, a charge of a nucleus
(nuclei) “ α ”, G is the Green’s function. In the
/
representation of auxiliary functions ϕ λ the equation
(67) has the following form:
p Z
( ε⋅δ −[ − + ( , , ε )] ) =δ
λλ1 2
2
α
rα
/
xx λλ1 G /
λλ
/
λλ
∑ ∑ (34)
where λ 1 is an index of summation. It is natural to
choose ϕ λ so that the following expression will be diagonal:
∑ ∑ (35)
2 /
[ p /2 − Zα / rα + ( x, x , ε )] λλ = E ( )
1 λ ε ⋅δλλ1
α
Then the Green’s function is diagonal on λ :
G / = G ⋅δ /, G = 1/[ ε−E ( ε )] (36)
λλ λ λλ λ λ
/
and the functions ϕ λ , which diagonalizes G , satisfy to
equation as follows: :
∑
2
( p /2 −
/
Zα / rα) ϕλ( x,
ε ) +
/
∫ ∑(
xx , , )
α
/
λ( x1, ) dx1 Eλ( )
/
λ(
x,
) (37)
+ ε ϕ ε − ε ϕ ε
One could introduce the mixed representation for
a mass operator as follows:
∑ ∑
∫ 1 1 1 (38)
( x, p, ε ) = ( x, x , ε)exp[ i( r−r) p] dr
Then equation (37) with account for of the expression
(38) can be written as follows:
2 /
[ p /2 − Z / r + ( x, p, ε)] ϕ ( x,
ε ) =
∑ ∑
α
α α λ
/
= Eλ() ε ϕλ(,) x ε
(39)
It can be shown that an operator p = iv in (33) acts
on functions which are on the right of ∑ ( x, p, ε)
. So,
in order to find the one-particle energies, defined by
the pole part of the Green’s function G, it is sufficient
/
to know the functions ϕ λ under ε=ε λ . The Greens’
function pole part is as follows:
λ
G / = a δ / /( ε−ε + iγ
) (40)
λλ λλ
λ λ
123

where
124
λ
a = 1/(1 − ∂E / δε)| ,( ∂E/ ∂ε )| = ( ∂E/ ∂ε )|
λ ε=ε /
λ ε=ελ λλ
∑ ∑ (41)
ε = ε = − + ε
λ Eλ() 2
{ p /2 Zα / rα (, x p,)}|
λλ
α
/
λ( x) /
λ( x,
λ)
The functions ϕ
following equation:
=ϕ ε are satisfying to
∑ ∑ (42)
2
[ p /2 − Zα / rα + ( x, p, ελ)] ϕ λ =ελϕλ( x)
α
Introducing an expansion for self-energy part ∑
2 2
into set on degrees x, ε−εF, p − pF
(here ε F and F p
are the Fermi energy and pulse correspondingly):
∑ ∑
( x, p, ε ) = ( x)
+
+∂∑ ∂ − + ∂∑ ∂εε−ε +
then equation (42) is rewritten as follows:
2
[ p /2 − Z / r + ( x)
+
0
(
2 2
/ p )( p
2
pF)
( / )( F)
...
∑ ∑
∑ ∑ (43)
α α 0
( /
2
) ]
α
λ( ) (1 / ) λ λ(
)
+ p ∂ ∂p p Φ x = −∂ ∂ε ε Φ x
The functions Φ λ in (77) are orthogonal with a
-1 1
weight ρ = a [1 / ]
k
− = −∂∑ ∂ε . Now one can introduce
1/2
the wave functions of the quasiparticles a −
ϕ λ = Φ λ ,
which are, as usually, orthogonal with weight 1. For
complete definition of { ϕ λ}
it should be determined
2
the values 0 , / , / p ∑ ∂∑ ∂ ∂∑ ∂ε.
Naturally, the equations
(43) can be obtained on the basis of the variational
principle, if we start from a Lagrangian of a system
L q (density functional). It should be defined as a
functional of the following quasiparticle densities:
∑
0 () r nλ |
2
λ()|,
r
1()
r
λ
∑ nλ |
λ
2
λ()|,
r
2 () r ∑ nλ[
λ
*
λ λ
*
λ λ].
ν = Φ
ν = ∇Φ
ν = Φ Φ −Φ Φ
(44)
The densities 0 ν and ν 1 are similar to the HF electron
density ρ ( ρ=ν⋅ a ) and kinetical energy density
correspondingly; the density ν 2 has no an analog in the
HF or standard Kohn-Sham theory and appears as result
of account for the energy dependence of the mass
operator. A Lagrangian L q can be written as a sum of a
free Lagrangian and Lagrangian of interaction:
0 int
Lq = Lq + Lq
,
0
where a free Lagrangian L q has a standard form:
0 *
Lq = ∫ dr∑nλΦλ( i∂/ ∂t−εp) Φλ,
(45)
λ
And an interaction Lagrangian is defined in the
form, which is characteristic for a standard Kohn-
Sham DFT theory (as a sum of the Coulomb and exchange-correlation
terms), however, it takes into account
for the energy dependence of a mass operator:
1
L L F r r r r drdr
2
int
q = K −
2 ik , = 0
βik ( 1, 2) νi( 1) νk(
2) 1 2
∑ ∫ (46)
where β ik are some constants (look below), F is an effective
potential of the exchange-correlation interaction. Let
us explain here the essence of the introduced constants.
Indeed, in some degree they have the same essence as the
similar constants in the well-known Landau Fermi-liquid
theory and Migdal finite Fermi-systems theory. The
Coulomb interaction part LK looks as follows:
1
LK=− [1 − 2( r1)] ν0( r1)[1−
2 ∫ ∑
− ν −
∑ 2( r2)] 0( r2)/| r1 r2 | dr1dr (47)
2
∑ ∑ . Regarding the exchange-cor-
where 2 =∂ / ∂ε
relation potential F, it should be noted the there are
many possible approximations (directly in the density
–functional theory and its modern generalizations).
One of the suitable forms for this potential is the Ivanov-Ivanova
potential (look details in ref. [11]):
∫
F( r , r ) = X ( drρ ( r)/ r −rr−r− 1 2
(0)1/3
c
1 2
' (0)1/3 / /
−( ∫ dr ρc( r )/ r1 −r⋅ //
dr
(0)1/ 3 //
c r
//
r r2 dr
(0)1/ 3
c r
∫ ∫ (48)
⋅ ρ ( )/ − )/ ρ ( )
where X is the numerical coefficient. It has been
obtained on the basis of calculating the Rayleigh-
Schrödinger perturbation theory Feynman diagrams
of the second and higher order (so called polarization
diagrams) in the Thomas-Fermi approximation [26].
The relativistic generalization of the potential (48) is
obtained in ref.[11].
In the local density approximation in the density
functional the potential F can be expressed through
the exchange-correlation pseudo-potential V XC as follows
[15,]:
Frr ( 1, 2 ) =δVXC / δν0⋅δ( r1− r2).
(49)
Further, one can get the following expressions for
int
i q / 1 L ∑ =−δ δν :
ex
∑ 0 = (1 − ∑ e) VK
+ ∑ 0 +
1 2 2 2
+ β00δ VXC / δν ⋅ν 0 +β00δVXC / δν0⋅ν 0 +
2
2 2
+β01δVXC / δν0⋅ν 1 +β01δ VXC
/ δν0⋅ν0ν 1 +
2 2
+β δ V / δν ⋅ν ν + β δV / δν ⋅ν (50)
02 XC 0 0 2 02 XC 0 2
∑
1 =β01δVXC / δν0⋅ν 0 +
+β δV / δν ⋅ν + β δV / δν ⋅ν ;
12 XC 0 2 11 XC 0 1
∑
2 =β02δVXC / δν0⋅ν 0 +
+β12δVXC / δν0 ⋅ν 1 + β22δVXC / δν0 ⋅ν 2;
ex
Here V K is the Coulomb term (look above), ∑ 0 is the
exchange term. Using the known canonical relation-
* *
ship Hq =ΦλδLq / δΦ λ +ΦλδLq / δΦλ − Lq
after some
transformations one can receive the expression for the
quasiparticle Hamiltonian, which is corresponding to
a Lagrangian L q :
0 int 0 1
2
Hq = Hq + Hq = Hq − LK + β00δVXC / δν0⋅ν 0 +
2
1
2
+β01δVXC / δν0⋅ν0⋅ν 1 + β11δVXC / δν0⋅ν1− 2
1
2
− β22δVXC / δν0⋅ν 2
(51)
2

In further applications as potential V XC it is suitable
to use the exchange-correlation pseudo-potential
which contains the correlation (Gunnarsson-Lundqvist)
potential and exchanger Kohn-Sham one
[11]:
1/3
VXC ( r) = f( θ) VX( r) −0,0333⋅ ln[1+ 18,376 ⋅ρ ( r)]
(52)
where
2 1/3
VX=−(1/ π)[3 π ⋅ρ ( r)]
2 1/3
is the Kohn-Sham exchange potential, θ= [3 πρ ] / c ,
and function f ( θ ) is some function. Using the above
written formula, one can simply define the values (46),
(50).
Further let us give the corresponding comments
regarding the constants β . First of all, it is obvi-
ik
ous that the terms with constants β01, β11, β12, β 22 give
omitted contribution to the energy functional (at
least in the zeroth approximation in comparison
with others), so they can be equal to zero. The value
for a constant β 00 in some degree is dependent upon
the definition of the potential V XC . If as V XC it is use
one of the correct exchange-correlation potentials
from the standard density functional theory, then
without losing a community of statement, the constant
β 00 can be equal to 1. The constant β 02 can
be in principle calculated by analytical way, but it is
very useful to remember its connection with a spectroscopic
factor Fsp of the molecular system (it is
usually defined from the ionization cross-sections)
[11,14]:
⎧ ∂
⎫
Fsp = ⎨1 − ∑ kk[ −(
V. I. P.)
k ] ⎬ (53)
⎩ ∂∈
⎭
The term ∂∑ / ∂ε is defined above. It is easily to
understand the this definition is in fact corresponding
to the pole strength of the corresponding Green’s
function. It is interesting to discuss the possible
analogous universality of β and the constants in the
ik
well-known Landau Fermi-liquid theory and Migdal
finite Fermi-systems theory. Indeed, as we know
now, the entire universality of the constants in the
last theories is absent, though a range of its changing
is quite little. Without a detailed explanation, we note
here that the corresponding constants in our theory
possess the same universality as ones in the Landau
Fermi-liquid theory and Migdal finite Fermi-systems
theory. More detailed explanation requires a careful
check. Further it is obvious that omitting the energy
dependence of the mass operator (i.e. supposing
β 02 = 0 ) the quasiparticle density functional theory
can be resulted in the standard Kohn-Sham theory.
In this essence presented approach to definition of
the functions basis { Φ λ}
of Hamiltonian H q can be
treated as an improved in comparison with similar
basise’s of other one-particle representations (HF,
Hatree-Fock-Slater, Kohn-Sham etc.). Naturally,
this advancement can be manifested during studying
those properties of the multi-electron systems, when
an accurate account for the complex exchange-correlation
effects, including a continuum pressure, energy
dependence of a mass operator etc., is critically
important.
4. APPLICATION OF THE COMBINED
METHOD TO DIATOMICS
PHOTOELECTRON SPECTRA
As an object of studying we choose the diatomic
molecule of N for application of the combined
2
Green’s function method and quasiparticle DFT approach.
The nitrogen molecule has been naturally discussed
in many papers. The valence V. I. P. ‘s of N2 have been calculated [1,13,14,24] by the method of
Green’s functions and therefore the pole strengths pk are known and the mean values q can be estimated. It
k
should be reminded that the N molecule is the clas-
2
sical example where the known Koopmans’ theorem
even fails in reproducing the sequence of the V. I. P. ‘s
in the PE spectrum. From the HF calculation of Cade
et al.[24] one finds that including reorganization the
V. I. P. ‘s assigned by g σ and σu improve while for π V.
I. P. the good agreement between the Koopmans value
and the experimental one is lost, leading to the same
sequence as given by Koopmans’ theorem. Earlier
[13,14] it has been shown that the nitrogen spectra can
be in principle reproduced by applying a one-particle
theory with account of the correlation and reorganization
effects. The above-mentioned Green’s functions
calculation which takes account of reorganization and
correlation effects leads to the experimental sequence
of V. I. P.’s. In Table 1 the experimental V. I. P. ‘s (a),
the one-particle HF energies (b), the V. I. P. ‘s calculated
by Koopmans’ theorem plus the contribution
of reorganization (c), the V. I. P. ‘s calculated with
Green’s functions method (d), the combined Green
functions and DFT approach (e) and the corresponding
pole strengths (d,e) are listed.
Table 1
The experimental and calculated V. I. P.’s (in eV) of N . R is the
2 k
contribution of reorganization; p stands for pole strength
k
Orbital
Exptla V.I.P. , s - b
∈k
(
−∈ +
+ R
k
k
c
)
Calc d
V.I.P. , s
d
ρk
Calc e
V.I.P. , s
e
ρk
3 σg 15,60 17,36 16,01 15,50 0,91 15,52 0,913
1 πu 16,98 17,10 15,67 16,83 0,94 16,85 0,942
2 σu 18,78 20,92 19,93 18,59 0,87 18,63 0,885
Analysis shows that the data, obtained within the
standard Green functions approach and combined
method are very much close. Taking into account a
simplification of the method scheme within the DFT
approach, the standard Green’s function theory ( in
particular the Cederbaum-Domske theory [12]) looks
more attractive else. As it is known, of the three bands
in the experimental low-energy spectrum of the N 2
molecule ( Fig. 3), only the lπ u band exhibits a strong
vibrational structure.
When the change of frequency due to ionization is
small, the density of states can be well approximated
using only one parameter g:
∞ n
−s
S
() ∈ = ∑ δ( ∈−∈ +Δ∈ + ⋅h ω)
,
N e n
k k k
n=
0 n!
S g
( ) 2 −
2
= ω
h (54)
125

Fig. 3. Experimental and calculated PE spectra of N 2 . The
uppermost spectrum is calculated with S 0 and Eq. (54). The middle
spectrum is calculated with values of S from (29) (see text and
[12,14]).
In case the frequencies change considerably, the
intensity distribution of the most intensive lines can
analogously be well approximated by an effective parameter
S. In fig.1 the experimental and calculated
photoelectron spectra for the N 2 .molecule are presented.
The uppermost spectrum is calculated with
S 0 (i.e. the constant S calculated with g 0 ) and Eq.
(54). The middle spectrum is calculated with values
of S from Eq. (29). It is important to note that
the original Green’s functions and combined Green
functions +DFT approach coincide in the scale of
the figure. In a whole the agreement between the
calculated spectrum (the corrected g ) and the experimental
one is improved. Regarding the inclusion
of the anharmonicites it should be mentioned
that a theory can be generalized by means a standard
normal coordinate expansion of the Hamiltonian to
third and higher orders.
126
5. CONCLUSIONS
So, firstly we present a new combined theoretical
approach to vibrational structure in molecular photoelectron
spectra, which is based on the Green’s function
method and DFT approach. The density of states,
which describe the vibrational structure in molecular
photoelectron spectra, is calculated with the help of
combined DFT-Green’s-functions approach. It is
important that the calculational procedure is significantly
simplified with using the quasiparticle DFT formalism.
In result, we believe that quite simple theory
become a powerful tool in interpreting the vibrational
structure of the molecular photoelectron spectra.
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THE GREEN’S FUNCTIONS AND DENSITY FUNCTIONAL APPROACH TO VIBRATIONAL STRUCTURE IN THE
PHOTOELECTRON SPECTRA OF MOLECULES
Abstract
We present the basis’s of the new combined theoretical approach to vibrational structure in photoelectron spectra of molecules. The
approach is based on the Green’s function method and density functional theory (DFT). The density of states, which describe the vibrational
structure in photoelectron spectra, is defined with the use of combined DFT-Green’s-functions approach and is well approximated
by using only first order coupling constants in the one-particle approximation. It is important that the calculational procedure is
significantly simplified with using the DFT.
Key words: photoelectron spectra, Green’s functions method, density functional theory.
ÓÄÊ 539.19+539.182
A. Â. Ãëóøêîâ, ß. È. Ëåïèõ, A. Ï. Ôåä÷óê, A. Â. Ëîáîäà
ÌÅÒÎÄ ÔÓÍÊÖÈÉ ÃÐÈÍÀ È ÔÓÍÊÖÈÎÍÀËÀ ÏËÎÒÍÎÑÒÈ Â ÎÏÐÅÄÅËÅÍÈÈ ÊÎËÅÁÀÒÅËÜÍÎÉ
ÑÒÐÓÊÒÓÐÛ ÔÎÒÎÝËÅÊÒÐÎÍÍÛÕ ÑÏÅÊÒÐÎÂ ÌÎËÅÊÓË
Ðåçþìå
Èçëîæåíû îñíîâû íîâîãî êîìáèíèðîâàííîãî òåîðåòè÷åñêîãî ìåòîäà îïèñàíèÿ êîëåáàòåëüíîé ñòðóêòóðû äëÿ ôîòîýëåêòðîííûõ
ñïåêòðîâ ìîëåêóë, êîòîðûé áàçèðóåòñÿ íà ìåòîäå ôóíêöèé Ãðèíà è òåîðèè ôóíêöèîíàëà ïëîòíîñòè (ÒÔÏ). Ïëîòíîñòü
ñîñòîÿíèé, îïèñûâàþùàÿ êîëåáàòåëüíóþ ñòðóêòóðó ñïåêòðà, îïðåäåëÿåòñÿ ñ èñïîëüçîâàíèåì ìåòîäà ôóíêöèé Ãðèíà
è êâàçè÷àñòè÷íîé ÒÔÏ è ïðèåìëåìî àïïðîêñèìèðóåòñÿ ñ èñïîëüçîâàíèåì êîíñòàíò ñâÿçè òîëüêî ïåðâîãî ïîðÿäêà óæå â
îäíî÷àñòè÷íîì ïðèáëèæåíèè.
Êëþ÷åâûå ñëîâà: ôoòoýëåêòðîííûé ñïåêòð, ìåòîä ôóíêöèé Ãðèíà, òåîðèÿ ôóíêöèîíàëà ïëîòíîñòè.
ÓÄÊ 539.19+539.182
Î. Â. Ãëóøêîâ, ß. ². Ëåï³õ, Î. Ï. Ôåä÷óê, A. Â. Ëîáîäà
ÌÅÒÎÄ ÔÓÍÊÖ²É ÃвÍÀ ² ÔÓÍÊÖ²ÎÍÀËÓ ÃÓÑÒÈÍÈ Ó ÂÈÇÍÀ×ÅÍͲ ²ÁÐÀÖ²ÉÍί ÑÒÐÓÊÒÓÐÈ
ÔÎÒÎÅËÅÊÒÐÎÍÍÈÕ ÑÏÅÊÒв ÌÎËÅÊÓË
Ðåçþìå
Âèêëàäåí³ îñíîâè íîâîãî êîìá³íîâàíîãî òåîðåòè÷íîãî ìåòîäó îïèñó â³áðàö³éíî¿ ñòðóêòóðè äëÿ ôîòîåëåêòðîííèõ ñïåêòð³â
ìîëåêóë, ÿêèé áàçóºòüñÿ íà ìåòîä³ ôóíêö³é Ãð³íà ³ òåî𳿠ôóíêö³îíàëó ãóñòèíè (ÒÔÃ). Ãóñòèíà ñòàí³â, ùî îïèñóº â³áðàö³éíó
ñòðóêòóðó ñïåêòðà, âèçíà÷àºòüñÿ ç âèêîðèñòàííÿì ìåòîäó ôóíêö³é Ãð³íà òà êâàç³÷àñòèíêîâî¿ ÒÔà ³ ïðèéíÿòíî àïðîêñèìóºòüñÿ
ç âèêîðèñòàííÿì ñòàëèõ çâ’ÿçêó ò³ëüêè ïåðøîãî ïîðÿäêó íàâ³òü ó îäíî÷àñòèíêîâîìó íàáëèæåíí³.
Êëþ÷îâ³ ñëîâà: ôoòoåëåêòðîííèé ñïåêòð, ìåòîä ôóíêö³é Ãð³íà, òåîð³ÿ ôóíêö³îíàëà ãóñòèíè.
127

128
UDC 621.315.592
A. V. TYURIN, A. YU. POPOV, S. A. ZHUKOV, YU. N. BERCOV
Scientific Research Institute of Physics, I.I. Mechnikov National Odesa University,
27 Paster str., 27, Ukraine, 65082 E-mail: zhukov@onu.edu.ua, bercov@gmail.com
MECHANISM OF SPECTRAL SENSITIZING OF THE EMULSION
CONTAINING HETEROPHASE “CORE –SHELL” MICROSYSTEMS
The new approach to the process of spectral sensitizing of emulsions created on base of heterophase
microcrystals of “non- photosensitive core — photosensitive silver-haloid shell” structure is
offered. The distinctive feature of the given system is a possibility of sensitizer dye introduction on the
“core-shell” border. Considering such spatial separation of dye adsorbed on a core by the shell of silver
halide, the mechanism of sensitization, which provides the expansion of emulsion spectral sensitivity
area, is offered.
INTRODUCTION
Holographic emulsions based on silver halide till
now are the most sensitive among all recording media
and it attracts the permanent interest to them. These
emulsions are suitable for recording of the reflecting
and transmitting transparent volume holograms possessing
both high diffraction efficiency, and high angular
and spectral selectivity [1,2]. Nevertheless, in
this sphere till now there are problems demanding the
solution, one of which is expansion of emulsion spectral
sensitivity range. In the given work the new approach
to spectral sensitization of holographic emulsions
is considered, which allows to expand a range
of their spectral sensitivity considerably and to obtain
single-layer emulsions, suitable for color and infrared
holography.
PROBLEM STATEMENT
In some cases, for example for recording of color
holograms it is necessary to expand emulsion spectral
sensitivity to all visible range. Moreover, for the solution
of some technical problems it is necessary to have
emulsion, which is sensitive to infrared (IR) area of
spectrum. The latter problem is solved by introduction
of the dyes absorbing light in near infrared area of a
spectrum with generation of non-equilibrium charge
carriers. However, used dyes are unstable even during
storage at low temperatures, and they decompose to
components, therefore such emulsions are insensitive
and tend to fogging and degradation of the latent image.
Besides in usual AgHal emulsions, especially at
exceeded concentration of dye, the IR sensitivity decreases
because of so-called dyes self-desensitizing
phenomenon of the second kind [3]. In this case, illumination
quanta interaction with dye molecules excited
by light with non- excited ones happens, and as
the result, the luminescence of the nearest dye appears
instead of generation of the free charge carrier. The
solving of the problem could be achieved through spatial
division of dyes interacting this way.
The similar situation arises also while using two or
more dyes absorbing light in different areas of a spec-
trum. They also can interact with each other and desensitize
the emulsion. For solution of this problem,
the multilayered emulsions are used, each layer of
which is sensitized by its dye, but such solution in the
case of holographic emulsion is not optimal.
To solve both problems described above, it is possible
to apply the model of emulsions based on heterophase
micro-crystals of “non-photosensitive core —
photosensitive silver-halide shell” structure [4].
Due to special features of hetero-phase microcrystals
structure the dyes — sensitizers could be absorbed
not only on an external surface of silver-halide
shell (as it is done traditionally), but also on the internal
surface on the border core — shell surface [5],
what allows to solve a problem of spatial separation of
various dyes, and to increase their storage stability as
well.
The goal of the given work is to study the features
of the described above spectral sensitizing of photosensitive
hetero-phase micro-crystals emulsions (including
the holographic ones), and to create the working
model of the electron-hole processes occurring in
the emulsion when the latent image is created.
MATERIALS AND METHODS
General scheme of synthesis process of emulsion
with hetero-phase micro-crystals “core CaF 2 — AgBr
shell” is described in detail in [5]. Depending on purpose
of emulsion the average size of microcrystals in
them is:
~0.35 microns — emulsion intended for the photographic
purposes (“photographic” emulsion); ~0.05
microns — emulsion intended for record of holograms
(“holographic” emulsion).
For spectral sensitization of such emulsions we
used three various dyes:
I — natrium salt of 3,3 3,3’-di-γ-sulfopropyl-1,1’diethyl-5,5’-dicarboethoximid-carbocyaninebetaine
II — pyridine salt of 3,3’-di-γ-sulfopropyl-9-ethyl-4,5,4’,5’-dibenzothiacarbocyaninebetaine
III — 1,1 ‘-diethyl-quini-2,2 ‘-cyaniniodide.
Infusion of such dyes in emulsion occurs as in molecular
(Ì) and aggregated phases (J and H aggregates
[6]). Wavelengths of absorption maxima of molecular
© A. V. Tyurin, A. Yu. Popov, S. A. Zhukov, Yu. N. Bercov, 2009

M and aggregated J and H phases of dyes I-III adsorbed
on a surface of micro-crystals in halogen-silver
emulsion are specified in the Table.
Table
Dye Í-band (nm) M-band(nm) J-band (nm)
I 508 519 -
II - 630 680-690
III - 545 578
It has to be marked that the long-wave part of absorption
band of J-aggregates of dyes often extends up
to 900 nm.
Spectral sensitization of hetero-phase emulsions
using marked dyes was carried out stage by stage. Therefore,
for experimental research three types of sensitized
emulsion were prepared (symbolically a,b,c):
à) emulsion with hetero-phase micro-crystals “
CaF 2 core — AgBr shell ”, prepared under the procedure
described in work [5], was sensitized with dyes II
or III in concentration 10 -4 mole of dye for mole CaF 2 ,
by traditional way (control emulsion);
b) to suspension containing homogeneous calcium
fluoride particles of given size we added 10 -4 mole
of dye II or III for mole on ìîëü CaF 2 . These conditions
provided practically full adsorption of dye on a
surface of core CaF 2 . Then an AgBr shell was grown
up on core CaF 2 with adsorbed dye II or III under the
procedure [5];
c) “b” emulsion but additionally sensitized with
the dye I in concentration 10 -4 mole of dye for mole
CaF 2 ;
For developing of obtained emulsions surface and
deep developers [7] were used. Such ways of developing
allow us to observe position of the centers of the
latent image all over volume of halogen-silver shell
of composite system. Surface developer –only those
hetero-phase micro-crystals in which centers of the
latent image are on external surface of AgBr shell can
be developed. Deep developer provides partial dissolution
of AgBr shell top layers. So thus we can develop
those hetero-phase micro-crystals in which centers of
the latent image are in volume of AgBr shell up to the
surface of non-photosensitive core.
RESULTS
On Fig. 1 results of the spectral sensitometric tests
are presented, which are concerned to three mentioned
above types (“a”, “b”, “c”) of “photographic” emulsions,
containing dye II. Concentration of dye was
high enough for the existence in emulsion not only a
molecular phases of dye, but also its J-aggregates. Exposure
and processing of layers of the specified types
of emulsions was carried out in spectral-sensitometer
ISP-3 with the help of a standard technique [8].
As it follows from the data submitted on Fig. 1.A,
for exposed emulsion “a” optical density after processing
with the help of both surface and deep developers
(curves 1, 1’) in comparison with non-exposed emulsion
“a” (curve 3) are practically equal, both in the
absorption area of molecular dye II (λ max = 630 nm)
and in the absorption area of the J-aggregate of dye II
(λ max = 690 nm).
° — developed in surface developer
• — developed in deep developer
Fig. 1. A. Spectral distribution of optical density (D) of exposed
layers of “photographic” emulsions “à” (1,1’) and “b” (2,2 ‘)
containing the dye II after development in surface (1,2) and deep
(1’, 2’) developers. Bar line (3) marks the fog optical density of
non-exposed and developed samples of emulsion “à” and “b” both
in surface and deep developers. B. Spectral distribution of optical
density (D-D ) of exposed layers of “photographic” emulsion “c”
0
after developing in surface (1) and deep (1 ‘) developers, D — fog
0
optical density of non-exposed and developed both in surface and
deep developers of emulsion samples “c”.
For the exposed emulsion “b” developed with surface
developer (curve 2) in comparison with non-exposed
emulsion “b” (curve 3), on wavelengths λ > 600
nm, the reduction of optical density (enlightenment)
occurs and main part of this enlightenment falls on
the absorption area of J-aggregate of dye II (λ max = 690
nm). Application of deep developer in a case of exposed
emulsion “a” (curve 2’), in comparison with non-exposed
emulsion after processing with deep developer
(curve 3), shows an increase of optical density in the absorption
band of both molecular dye II (band M, λ max =
630 nm) and in the absorption area of J-aggregate of
dye II (band J, λ max = 690 nm). However, if for emulsion
“a” this increase occurs almost equally both in a band
M and in band J, in case of emulsion “b” an increase of
absorption in band J occurs in the much greater degree
than in band M. If we compare between each other exposed
emulsions “a” and “b” with sensitized dye II, in a
case of emulsion “b”, the expansion of a spectral range
of a photosensitivity in long-wave area (see curves 1 and
2’ in long-wave area) is observed.
For “photographic” emulsion “c” Fig. 1 B, after
processing in surface developer (curve 1) the increase
of the optical density in the absorption field of a molecular
band of dye I (λ max = 519 nm) is observed as well
as small increase of the optical density in the absorption
field of dye II both in molecular (λ max = 630 nm)
and in J-aggregated (λ max = 690 nm) phases. Application
of deep developer results in reduction of absorption
in M band of dye I and essential increase of optical
density in absorption band of J-aggregates of dye II
(λ max = 690 nm) (curve 1’).
The same spectral sensitometric tests were carried
out for “holographic” emulsions (types “à” and “b”).
Experimental data of such researches are presented at
Fig. 2.
129

Fig. 2 A. Spectral distribution of optical density (D-D ) of ex-
0
posed layers of “holographic” emulsions “à” (1) and “b” (1’) with
dye II after development in deep developer. B. Spectral distribution
of optical density (D-D ) of exposed layers of “holographic”
0
emulsion “à” (1) and “b” (1’) with dye III after development in
deep developer
D is the optical density of a fog of non-exposed
0
and developed in deep developer emulsion samples
“a” and “b”.
From Fig. 2 one could see, that the sensitization
both with dye II and dye III of “holographic” emulsion
of “b” type in comparison with emulsions of “a”
130
type sensitized by the same dyes results in expansion of
emulsion sensitivity spectral area in long-wave part of a
spectrum. If for dye II this displacement is insignificant,
for dye III it is essential. It should be mentioned that for
“photographic” emulsion of “b” type the expansion of
the spectral sensitivity in long-wave region in comparison
with to emulsion of “a” type is also observed.
Observed spectral sensitivity displacement both
for “photographic” and “holographic” emulsions occurs
up to 900 nm and it is natural to assume that it is
caused by absorption of J-aggregates of dye. The reason
of this effect (in case of emulsion of type “b”) is
the greater efficacy of generated in J-aggregates nonequilibrium
carriers of charge use for latent image
creating. It could occur due to the spatial division of
molecular dye and J-aggregates of dye by AgBr cover
because molecular dye is basically adsorbed on external
surface of a cover and J-aggregate of dye — on
internal surface. Spatial division of various phases of
dye eliminates interaction at photo-excitation of the
J-aggregate, which leads only to a recombination luminescence
of molecular dye, instead of charge free
carriers generation in silver halogenide [9].
Increase of CaF 2 dye concentration adsorbed on
core at spatial division of the molecular and aggregated
dye by AgBr cover is accompanied, besides the
expansion of spectral sensitivity area, by decrease of
fog level on the cover external surface (see Fig. 3).
Fig. 3 Spectral sensitograms of emulsions developed by deep developer containing dye II in different concentrations (a mole dye
/mole AgBr): À-2∙10 -5 ; B — 4∙10 -5 ; C — 6∙10 -5
Seen fogging decrease on an outer surface of AgBr
shell results from reaction [10]
0 + Ag + p → Agm → Agm-1
m
0Ag + 0 + → Ag + Agi . (1)
m-1
Occurrence of the holes on an outer surface of a
shell is caused by the following reason. Adsorption of
J-aggregate of dye II on an interior surface of a shell is
accompanied by reaction
+ 0 0 + Ag + J → Agn + J (2).
n
As it has been established by us in [11], the main
level of the J-aggregate of dye II lays below the level of
a valence band top of AgBr, therefore the hole is localized
on J + transfers in valence band AgBr
J + → J0 + p (3),
Then the hole in valence band migrates to an outer
surface of AgBr shell and provides the reaction (1).
To prove our assumption, we carried out the lowtemperature
research of the luminescence of these
emulsions. On Fig. 4, one could see the spectra of
low-temperature (Ò = 77 Ê) luminescence and excitation
of a luminescence not only in “holographic”
emulsions of type “b” but also as an intermediate stage
of its preparation: — before we cover CaF core with
2

adsorbed on them dye II with a AgBr shell. These luminescent
studies were performed under such conditions:
time of sample excitation and time of its luminescence
registration are equal, and they equal to 10 -4
s and dark interval is 1.1∙10 -3 s at the modulation frequency
of 400 Hz.
As it follows from the mentioned luminescent
data, the phosphorescence of molecular dye II (λ max =
800 nm) (curve 1) is excited by light not from the absorption
area of molecular dye (λ max = 630 nm), but
from absorption area of J-aggregate of dye II (λ max =
630 nm) (curve 1’). This fact proves the presence of
the interaction between excited dyes, which result in
emulsion desensitization. After AgBr shell is created,
the phosphorescence of molecular dye II under excitation
of the J-aggregate of dye disappears, and there
emerges a luminescence with λ max = 700 nm (curve 2).
Excitation of this luminescence (curve 2’) is both
caused by absorption AgBr of a shell (λ max = 430-450
nm) and absorption of molecular dye (λ max = 630 nm)
as the excitation of the luminescence from absorption
area of the J-aggregate of dye II is absent.
Fig. 4. Spectra of low-temperature Ò 77 K luminescence (À)
and excitation of luminescence (B) of “holographic” emulsion of
“b” type at the intermediate stage of its preparation: curves 1,1’ —
when we do not create AgBr shell on CaF core with adsorbed on
2
them dye II; curves 2,2 ’ — “holographic” emulsion of type “b”
with dye II
Spectra of a luminescence (À) were obtained at
the excitation with λ = 690 nm — curve 1 and with
λ = 450, 630 nm — curve 2; Spectra of excitation (B)
were given for a luminescence at λ = 800 nm — curve
1’ and on λ = 700 nm — curve 2’.
As after AgBr shell creation, the luminescence of
molecular dye at excitation of the J-aggregate of dye
has disappeared, hence, it testifies that self- desensitizing
action of dye caused by their interaction is eliminated
and thus, it provides the significant displacement
of spectral sensitivity of emulsion of type “b” in
the long-wave area.
DISCUSSION
Earlier in [12], it was shown the basic opportunity
of covering of the dye adsorbed on non-silver CaF 2
core by AgBr shell without specification of a aggregate
phases of dye and its role in the process of an spectral
sensitization. The comparison of the luminescent and
sensitometric results, proves the existence of interaction
between the molecular and J-aggregated dye on
core CaF 2 . For a case of hetero-phase micro-crystal,
we assumed that the shell divides interaction among
the molecular and aggregated phases of dye that results
in observable expansion of area of spectral sensitivity of
various composite of the system.
It should also be noted that for the case of holographic
emulsions with hetero-phase micro-crystals
spatial separation of the molecular and aggregated
dye by shell contributes to the effective separation of
photo-excited non-equilibrium charge carriers. Separation
of non-equilibrium charge carriers, in the case
of composite system, could be illustrated by occurrence
of a enlightenment in spectral area λ > 600 nm
for emulsion “b” , when we develop it in the surface
developer (Fig.1, curve 2). Observed enlightenment
testifies that the quantity of the centers of the latent
image located on AgBr shell surface of emulsion “b”
micro-crystals after the exposure and development in
surface developer, decreases in comparison with nonexposed
emulsion. The greatest reduction takes place
when illumination is made in an absorption band of
J-aggregates of dye. As to our opinion, such reduction
could proceed under the schemes, offered in reactions
(1) — (3). As far as we have already determined, Jaggregates
of dye are located basically on an internal
surface of AgBr shell adjoining micro-crystals’ core,
when absorbing the light by J-aggregates, the generated
holes migrate through a AgBr shell to its surface
and there they result in destruction (reduction, neutralization)
of the centers of the latent image, i.e. in
“enlightenment”. The AgBr shell presence provides
translation of free holes of the J-aggregate of dye,
adsorbed on core CaF 2 through all thickness of the
shell, leads to reduction of a fogging and causes the
substantial increase of the diffraction efficacy of such
emulsions. It could be used for the creation of “direct
positive” images.
The ability of hetero-phase micro-crystals halogen
silver shell to separate interacting phases of the
dye can be used for spatial separation of different sensitizer
dyes, which application earlier was complicated
because of their interaction resulting in emulsion desensitization.
Such dyes’ separation allows to replace
the multilayered emulsions with single-layered emulsions,
which spectral sensitivity is determined by the
dyes, which are located on different surfaces of a AgBr
shell without desensitization effect.
CONCLUSIONS
As a result of the studies of the newly modified
emulsions and discussion of the e3xperimentral results
we can state the follows:
1. The spectral sensitization of composite system
“non-photosensitive core — halogen silver shell” allows
adsorbing the sensitizer dye not only on external,
but also on an internal surface of halogen silver shell.
2. It is determined, that halogen silver shell effectively
separates the aggregated and interacting molecular
dye phases (aggregated dye on non-photosensitive
core and molecular dye on a surface of halogen silver
shell), that eliminates effect of dye self-desensitization
and results in expansion of area of emulsions with hetero-phase
micro-crystals spectral sensitization.
131

3. Dyes’ spatial separation allows to replace the
multilayer emulsions with the single layer one with the
spectral sensitivity determined by dyes at different surfaces
of AgBr shell without desensitization effect.
References
1. Á.È. Øàïèðî Òåîðåòè÷åñêèå íà÷àëà ôîòîãðàôè÷åñêîãî
ïðîöåññà. Ì.: Ýäèòîðèàë ÓÐÑÑ. 2000, 209 ñ.
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ôîòîãðàô³÷íî¿ åìóëüñ³¿. Â.Ì. Á³ëîóñ, Ä.Ã. ͳæíåð,
Â.Ï. ×óðàøîâ.
3. Â.Ì. Áåëîóñ, Ë.È. Ìàí÷åíêî, À.Þ. Ïîïîâ, À.Â. Òþðèí,
Â.Ï. ×óðàøîâ, Þ.Á. Øóãàéëî Ôîòîãðàôè÷åñêàÿ ýìóëüñèÿ
ñ ãåòåðîôàçíûìè ìèêðîêðèñòàëëàìè — íîâàÿ ñðåäà
äëÿ çàïèñè ãëóáîêèõ òðåõìåðíûõ ïðîïóñêàþùèõ ãîëîãðàìì//
Îïòèêà è ñïåêòðîñêîïèÿ. 1999, ò.86, ¹2, ñ. 344-
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4. À.Þ. Ïîïîâ, Ë.È. Ìàí÷åíêî, À.Â. Òþðèí, Þ.Á. Øóãàéëî
Ðåãèñòðàöèÿ è âîñïðîèçâåäåíèå ñâåòîâûõ ïó÷êîâ
ñ òîïîëîãè÷åñêèìè äåôåêòàìè // Ñáîðíèê “Ôîòîýëåêòðîíèêà”
âûï.9, Îäåññà 2000, “Àñòðîïðèíò”, c.126-129.
5. D.G. Nizhner, V.M. Belous, V.P. Churashov Preparation and
Properties of Photographic Emulsions with Heterophase Microcrystals
Comprising Nonsilver Cores and Silver Halide
Shells// Imaging Science and Technology. 1999, v. 39, N 1,
p. 56-66.
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UDC 621.315.592
Tyurin A. V., Popov A. Yu., S. A. Zhukov, Yu.N.Bercov
6. F. Dietz Zum stand der Theorie der spektralen Sensibilisierung
//J. für Signalsufzeichnungsmaterialien. 1998, bd. 6, N 4,
s. 245-266; N5, s. 341-361.
7. Ê.Â. ×èáèñîâ Ôîòîãðàôè÷åñêîå ïðîÿâëåíèå. Ìîñêâà.
1999. “Íàóêà”.Ñ 208
8. Þ.Í. Ãîðîõîâñêèé Ñïåêòðàëüíûå èññëåäîâàíèÿ ôîòîãðàôè÷åñêîãî
ïðîöåññà. Ìîñêâà. 1960. Èçä. ôèç. — ìàò.
ëèòåðàòóðû. Ñ 390
9. À.Â. Òþðèí, Â.Ï. ×óðàøîâ, Ñ.À. Æóêîâ, Ë.È. Ìàí÷åíêî,
Ò.Ô. Ëåâèöêàÿ, Î.È. Ñâèðèäîâà Âçàèìîäåéñòâèå ìîëåêóëÿðíûõ
è ïîëèìîëåêóëÿðíûõ ôîðì êðàñèòåëÿ// Îïòèêà
è ñïåêòðîñêîïèÿ. 2008, ò. 104, ¹ 1, ñ. 97-103.
10. À.Â. Òþðèí, Â.Ï. ×óðàøîâ, Ñ.À. Æóêîâ, Î.Â. Ïàâëîâà
Ìåõàíèçì àíòèñòîêñîâîé ëþìèíåñöåíöèè ãàëîãåíñåðåáðÿíîé
ýìóëüñèè ñåíñèáèëèçèðîâàííîé êðàñèòåëåì//
Îïòèêà è ñïåêòðîñêîïèÿ. 2008, ò. 104, ¹ 2, ñ.237-244.
10. James,T.H. The Theory of the Photographic Process. // 1997,
New York: Editorial Macmillan, 456 pp.
11. Â.Ì. Áåëîóñ, Ä.Ã. Íèæíåð, Í.À. Îðëîâñêàÿ, Ï.Ã. Õåðñîíñêàÿ
Çàðàùèâàíèå àäñîðáèðîâàííîãî êðàñèòåëÿ îáîëî÷êîé
ãàëîãåíèäà ñåðåáðà â ãåòåðîôàçíûõ ìèêðîêðèñòàëëàõ//
Æóðí. íàó÷í. è ïðèêë. ôîòî- è êèíåìàòîãðàôèè.
1999, ò. 34, ¹ 4, ñ. 299-301.
12. Belous V.M., Nizhner D.G., Orlovskaya N.A., Khersonskaya
P.G. Growth of the Adsorbed Dye by Halogen-Silver Core in
Hetero-Phase Micro-crystals//Journal of Scientific and Applied
Photo-and Cinematography 1999. v. 34. ¹ 4. p. 299
MECHANISM OF SPECTRAL SENSITISATION OF EMULSION CONTAINING HETEROPHASE “CORE –SHELL”
MICROSYSTEMS
The new approach to the process of spectral sensitization of emulsions created on a base of hetero-phase micro-crystals of “non-
photosensitive core — photosensitive silver-halide shell” structure is offered. Distinctive feature of the given systems is a possibility of
sensitizer dye introduction to “core-shell” border. Considering such spatial separation of dye adsorbed on a core by the shell of silver
halide, the mechanism of sensitization which provides the expansion of emulsion spectral sensitivity area is offered.
Key words: sensitisation, heterophase microsystems, emulsion.
ÓÄÊ 621.315.592
À. Â. Òþðèí, À. Þ. Ïîïîâ, Ñ. À. Æóêîâ, Þ. Í. Áåðêîâ
ÌÅÕÀÍÈÇÌ ÑÏÅÊÒÐÀËÜÍÎÉ ÑÅÍÑÈÁÈËÈÇÀÖÈÈ ÝÌÓËÜÑÈÈ, ÑÎÄÅÐÆÀÙÅÉ ÃÅÒÅÐÎÔÀÇÍÛÅ
ÌÈÊÐÎÑÈÑÒÅÌÛ “ßÄÐÎ — ÎÁÎËÎ×ÊÀ”
Ïðåäëîæåí íîâûé ïîäõîä ê ïðîöåññó ñïåêòðàëüíîé ñåíñèáèëèçàöèè ýìóëüñèé, ñîçäàííûõ íà îñíîâå ãåòåðîôàçíûõ ìèêðîêðèñòàëëîâ
ñîñòàâà “íåñâåòî÷óâñòâèòåëüíîå ÿäðî — ñâåòî÷óâñòâèòåëüíàÿ ñåðåáðÿíî-ãàëîèäíàÿ îáîëî÷êà”. Îòëè÷èòåëüíîé
òåõíîëîãè÷åñêîé îñîáåííîñòüþ äàííîãî ïðîöåññà ÿâëÿåòñÿ ââåäåíèå êðàñèòåëÿ ñåíñèáèëèçàòîðà íà ãðàíèöó ðàçäåëà “ÿäðîîáîëî÷êà”.
Ñ ó÷åòîì ýòîé îñîáåííîñòè — ïðîñòðàíñòâåííîãî îòäåëåíèÿ îáîëî÷êîé ãàëîãåíèäà ñåðåáðà êðàñèòåëÿ àäñîðáèðîâàííîãî
íà ÿäðå — ïðåäëîæåí ìåõàíèçì ñåíñèáèëèçàöèè, îáåñïå÷èâàþùèé ðàñøèðåíèå îáëàñòè ñïåêòðàëüíîé ÷óâñòâèòåëüíîñòè
ýìóëüñèè.
Êëþ÷åâûå ñëîâà: ñåíñèáèëèçàöèÿ ýìóëüñèè, ãåòåðîôàçíûå ìèêðîñèñòåìû.
ÓÄÊ 621.315.592
Î. Â. Òþðèí, À. Þ. Ïîïîâ, Ñ. Î. Æóêîâ, Þ. Ì. Áåðêîâ
ÌÅÕÀͲÇÌ ÑÏÅÊÒÐÀËÜÍί ÑÅÍÑÈÁ²Ë²ÇÀÖ²¯ ÅÌÓËÜѲ¯, ßÊÀ Â̲ÙÓª ÃÅÒÅÐÎÔÀÇͲ ̲ÊÐÎÑÈÑÒÅÌÈ
“ßÄÐÎ — ÎÁÎËÎÍÊÀ”
Çàïðîïîíîâàíî íîâèé ï³äõ³ä äî ïðîöåñó ñïåêòðàëüíî¿ ñåíñèá³ë³çàö³¿ åìóëüñ³é, ñòâîðåíèõ íà îñíîâ³ ãåòåðîôàçíèõ ì³êðîêðèñòàë³â
ñêëàäó “íåñâ³òëî÷óòëèâå ÿäðî — ñâ³òëî÷óòëèâà ñð³áíî-ãàëî¿äíà îáîëîíêà”. Òåõíîëîã³÷íîþ îñîáëèâ³ñòþ äàíîãî
ïðîöåñó º ââåäåííÿ áàðâíèêà ñåíñèá³ë³çàòîðà íà ãðàíèöþ ðîçïîä³ëó “ÿäðî — îáîëîíêà”. Ç óðàõóâàííÿì ö³º¿ îñîáëèâîñò³
— ïðîñòîðîâîãî ðîçïîä³ëó îáîëîíêîþ ãàëîãåí³äà ñð³áëà áàðâíèêà àäñîðáîâàíîãî íà ÿäð³ — çàïðîïîíîâàíèé ìåõàí³çì ñåíñèá³ë³çàö³¿,
ùî çàáåçïå÷óº ðîçøèðåííÿ îáëàñò³ ñïåêòðàëüíî¿ ÷óòëèâîñò³ åìóëüñ³¿.
Êëþ÷îâ³ ñëîâà: ñåíñèá³ë³çàö³ÿ åìóëüñ³¿, ãåòåðîôàçí³ ì³êðîñèñòåìè.

UDC 530.145+678.9
V. V. KOVALCHUK, O. V. AFANAS’EVA, O. I. LESHCHENKO, O. O. LESHCHENKO
Odessa State Institute of the Measuring Technique
SIZE DISTRIBUTIONS OF CLUSTERS ON PHOTOLUMINESCENCE FROM
ENSEMBLES OF SI-CLUSTERS
The quantum confinement model to obtain the photoluminescence (PL) spectra from ensembles
of Si-clusters was used. The size of Si-clusters in ensembles are considered with a Gaussian distribution.
The work demonstrates that a PL peak spectrum in the red-shift region is in agreement with
experiments; a red-shift in the PL peak can be determine due to the size distribution and thus used to
obtain the physically reasonable information about binding energy.
The observations of visible photoluminescence
(PL) in silicon clusters (Si-clusters) suggest that the
Si clusters may become a material for optical applications
if their electronic and optical properties are well
understood [1-9]. The quantum confinement model
[10] has been used to determine the origin and mechanism
of visible PL in Si-clusters.
To explain the effect of the size distributions on
the PL spectra from the Si nanocluster ensembles is
an alternative.
The aim of this work is to report a simple theoretical
framework with a minimal set of parameters to
explain the PL spectra of Si-cluster ensembles.
Our work is based on the quantum confinement
model [10], which has been generally used to determine
the novel electronic and optical properties of
semiconductor clusters. We sugested that disorder
plays a key role and model Si-cluster sizes by a Gaussian
size distribution.
From the experiments [11], it appears reasonable
to assume Si-clusters with a Gaussian distribution of
diameter d centered around a mean d Q ,
( ) 2
d − d
C
0
Рd exp
2
2
2
N ⎛ ⎞
= ⎜− ⎟ (1)
πσ ⎜ σ ⎟
⎝ ⎠
The number of carriers (N ) in a cluster of diam-
C
eter d participating in the PL process is proportional
to d3 : N =ad c 3 , where a is a constant.
For a Si-cluster sample consisting of varying diameters
the probability of carriers participating in the
PL process is given by a product of the above two expressions,
( ) 2
d − d
1 ⎛ ⎞
3
0
Pcd = bd exp⎜−
⎟ (2)
2
2
2πσ
⎜ 2σ
⎟
⎝ ⎠
where b is a suitable normalization constant.
In the quantum confinement model the PL process
is attributed to an energy shift of the carriers
(electrons and holes) and is proportional to l/d2 . The
PL energy hω is given by
h E E c d
where E is the bulk silicon gap, E the exciton binding
b
energy, and c an appropriately dimensioned constant.
The energy shift due to confinement ΔE is
2
ω= g − b + , (3)
© V. V. Kovalchuk, O. V. Afanas’eva, O. I. Leshchenko, O. O. Leshchenko, 2009
( g b)
Δ E = hω− E − E , (4)
2
Δ E0= c d , (5)
where we have also defined a shift 0 E Δ related to the
mean nanocluster diameter d . 0
The PL line shape is approximately Gaussian if σ
is small. For limited σ the factor (ΔE) -1/2 in the exponential
outweighs the polynomial dependence in the
prefactor, resulting in an asymmetric curve with the
shoulder on the short-wavelength (high-energy) side,
which is in agreement with the results of experiments
[11].
In the following, we shall present calculations
based upon our expressions and compare them with
experimentally reported PL sjpectra. We have selected
a representative set associated with the natural theoretical
framework [3-5,10]. In the comparison with the
experimental data, we have faithfully transformed λ to
the energy hω (eV)= 12.4/ λ, where λ is in nm. Recall
that hω=Δ E+ ( Eg − Eb)
from the Gaussian shape. We
compare the theoretical spectra with the one experimentally
obtained at low-power density by Zhang et
al. [11]. We note that the asymmetric line shape, with
the shoulder on the short-wavelength (high-energy)
side, is in agreement with the experimental spectra.
It can be found obviously that the line shapes of PL
spectra deviate from the Gaussian shape. The theoretical
spectra are obtained with a mean diameter d = 0
55 A and σ = 6 A and with a mean diameter d = 45 A
0
and σ = 5 A. Our results show the positions of the PL
peaks if we neglect the effect of the size distribution of
Si-clusters and use the mean energy upshift ΔE in the
0
calculations. A further noteworthy feature is an energy
downshift in the PL peak due to the distribution of
cluster sizes. This enables us to predict the physically
reasonable exciton binding energy E = E + ΔE -hω b g p p
other than E = E + ΔE -hω . For example, we can
b g 0 p
obtain the exciton binding energy of the Si-cluster
with mean diameter 55 A, E = 0.10 eV, in which the
b
peak of the PL is hω =1.48 eV [11], ΔE is obtained E p p t
from bulk band gap of silicon [7,8].
By using the quantum confinement model in neglecting
size distributions of Si -clusters, the exciton
binding energy E , based on experiment [11], is higher
b
than that of the theoretical calculations [15]. In general,
the quantum confinement model only uses the
average size of Si-clusters to obtain the confinement
133

energy. In neglecting the size distributions of Si nanoclusters,
the confinement energy is overestimated. The
exciton binding energy ( E b < 0.10 eV) is more reasonable
when excluding the overestimated part of the
confinement energy from the size distributions of Si
nanoclusters. Thus, the exciton binding energy (E b <
0.10 eV) is small and physically more reasonable.
Our calculation shows that the experimental PL
spectra have a peak at 1.48 eV and a peak at 1.59 eV
in agreement with the quantum conmement model in
combination with the Gaussian size distributions of
Si-clusters.
Indeed, the quantum confinement model, in
combination with the Gaussian distribution of Sicluster
sizes, very well explains the blue shift of the PL
spectra from the Si-cluster-based materials, but still
slightly overestimates the confinement energy. The
widths of the theoretical curves are slightly narrower
compared with the experimental ones. This reflects a
tempera ture effect similar to statistical distribution of
the shapes of the Si-clusters.
We would like to stress, that a whole new class of
materials called clathrates can be generated by altering
the bond angles from their ideal tetrahedral value
in the diamond structure [4,5]. Importantly, the band
gaps of these structures are substantially larger than
that of Si in the diamond structure and well into the
visible region. It is worth noting that the high pressure
phases of bulk Si such as β -Sn, on the other hand, are
metallic with no gap.
When the temperature effect is considered, the
PL spectra as a function of the energy will involve the
temperature distribution function of the electronic
and hole states in the Si nanocluster ensembles. The
statistical average effect results in a broadening of the
PL spectra. The temperature effect results in a thermal
broadening ~ 50 meV at room temperature, which is
not enough to explain the reported broadening of the
PL spectra.
Next, we discuss the shape effect of the Si-clusters
in the ensembles on the PL spectra. Clusters with the
same volume but different shapes can result in different
confinement energies. For example, Si-clusters in
a simple ometry, like spheres, cubes and cylinders, etc.
have different confinement energies [4]. The carriers
with different confinement energies participate in the
PL process and cause the broadening of the PL spectra.
Therefore, the shape effect may also partially contribute
to the broadening of the PL spectra; but the
broadening of the PL spectra (for example, ~ 50 meV
in sphere and cylinder shape Si-clusters) can explain
the experimental results (Fig.1)
On the other hand, the effect of the electron-phonon
interaction on the PL features of the ensembles
of Si nanoclusters as the natural line-width broadening.
In the excitonic state the lattice vibration occurs
because an electron has been transferred from a bonding-like
(valence) to an antibonding-like (conduction)
state, which tends to weaken the bonds [5].
The local amplitude of the lattice vibration is directly
connected to the exciton density. The atomic
displacements are obtained by minimization on the
total energy using PDFT-scheme, for examle [4]. The
variation of the exiton energy gap with respect to the
134
lattice vibration arising from the electron-phonon
interaction is the deformation potentials. It seems as
if the natural line-width broadening is caused by the
electron-phonon interaction. In fact, the hypothesis
that the electron-phonon interaction is responsible for
the broadening of the PL spectra is not plausible.
Fig. 1. Model (up) [4] and STM images [2] acquired from the
same region of the cluster deposited Si(111) 7x7 surface (down).
The image represents an empty state image with bias of 1,5 V
The electron-phonon interaction gives a typical
broadening ( ~ kT < 25 meV), which is too small to
explain the reported full width at half maximum (~
200-300 meV) of the PL spectra of me ensembles of
Si-clusters.
An explanation of this broadening based on the
electron-phonon interaction would involve unphysical
considerations.
Therefore, to obtain more accurate results for the
electron-phonon interaction, it would be necessary,
for instance, to make a very careful theoretical calculation
[4] on the Si-clusters.
In the present work, our aim is mainly to, obtain
the size of Si-clusters from the PL spectra. We only
want to give a method of explaining the PL spectra
from the ensembles of Si-clusters by neglecting me
electron-phonon interaction, the temperature effect
and the shape distributions of Si-clusters.
The problem will be worth further studying in experimental
observations and theoretical calculations.
However, the novel features (width broadening) of me
PL-spectra may be partially due to ubese effects; the
size distributions of the Si-clusters in the ensembles
would influence physical phenomena other than the
PL spectra.
In summary, the method of the quantum confinement
model are used to describe the PL spectra from
an ensembles of Si nanoclusters. The diameters d of
the Si -clusters in the ensembles are considered with a
Gaussian distribution.
This our work demonstrates a PL spectrum with a
line-shape asymmetry on the wavelength (or energy)
scale, in agreement with experiments; a downshift in
the PL peak due to the size distribution.

Cluster approach allows formulating in a new fashion
material sciences concept, it is essential to expand
its possibilities for the decision of modern problems of
nanoelectronics.
We would like to express our deep thanks to Prof.
Dr. M. Drozdov for the helpful comments of the calculation
results.
References
1. Ho M.S, Hwang I.S., Tsong T.T. Direct Observation of Electromigration
of Si Magic Clusters on Si() Surfaces // Phys.
Rev.Lett. — V.84, N25. — 2000. — P.5792-5795
2. M. O. Watanabe, T. Miyazaki, T. Kanayama Deposition of
Hydrogenated Si Clusters on Si(111) — (7 x 7) Surfaces //
Phys.Rev.Lett. — 1998. — v.81,N24. — P. 5362- 5365
3. Drozdov V.A., Êîvalchuk V.V. Electronic processes in nanostructures
with silicon subphase // J.of Phys.Studies. —
2003. — v.4, ¹ 7. — p.393-401
UDC 530.145+678.9
V. V. Kovalchuk, O. V. Afanas’eva, O. I. Leshchenko, O. O. Leshchenko
4. Kovalchuk V.V. Cluster modification semiconductor’s heterostructures.
— : Hi-Tech Press, 2007. — 309 p.
5. Jarrold M.F. Nanosurface chemistry on size-selected silicon
clusters // Science. — 1999. — v. 252. — Ð. 1085-1092
6. Êîvalchuk V.V., Drozdov V.A., Moiseev L.M., Moiseeva V.O.
Optical spectra of polyhedral clusters: influence of the matrix
surroundings // Photoelectronics. — 2005. — ¹ 14. — p.12-18
7. Delerue C., Allan G., Lannoo M. Optical band gap of Si
nanoclusters// J. Lum. — 1999. — v.80. — p.65-73
8. Pavesi L., Dal Negro L., Mazzoleni C., Franzo G., Priolo
F. Optical gain in silicon nanocrystals // Nature. — 2000. —
v.408. — ð.440-444
9. Kamenutsu Y., Suzuki K., Kondo M. Luminescence properties
of a cubic silicon cluster octasilacubane // Phys.Rev. —
1999. — B 51. — P.10666–10669
10. Drozdov V.A., Êîvalchuk V.V., Ìîiseev L.Ì., Osipenko
O.V.Quantum Confinement and Optical Properties of Clusters
// Photoelectronics, 2007. — No 16. — Ð.3-6
11. Zhang R.M., Kozbas P.D. Gaussian distribution of Silicon clusters//
Appl.Phys.Lett.,2004. — 165. — P. 2684-2689
SIZE DISTRIBUTIONS OF CLUSTERS ON PHOTOLUMINESCENCE FROM ENSEMBLES OF SI-CLUSTERS
Abstract
The quantum confinement model to obtain the photoluminescence (PL) spectra from ensembles of Si-clusters was used. The size
of Si-clusters in ensembles are considered with a Gaussian distribution. The work demonstrates that a PL peak spectrum in the red-shift
region is in agreement with experiments; a red-shift in the PL peak can be determine due to the size distribution and thus used to obtain
the physically reasonable information about binding energy.
Key words: clusters, photoluminescence, distributions.
ÓÄÊ 530.145+678.9
Â. Â. Koâaëü÷óê, O. Â. Àôàíàñüåâà, À. Î. Ëåùåíêî, Î. È. Ëåùåíêî
ÐÀÑÏÐÅÄÅËÅÍÈÅ ÏÎ ÐÀÇÌÅÐÀÌ ÊËÀÑÒÅÐÎÂ ÏÐÈ ÔÎÒÎËÞÌÈÍÅÑÖÅÍÖÈÈ, ÎÁÓÑËÎÂËÅÍÍÎÉ
ÑÓÙÅÑÒÂÎÂÀÍÈÅÌ ÀÍÑÀÌÁËß SI-ÊËÀÑÒÅÐÎÂ
Ðåçþìå
Èñïîëüçîâàíà êâàíòîâàÿ ìîäåëü êîíôàéìåíòà ñ öåëüþ ïîëó÷åíèÿ ñïåêòðîâ ôîòîëþìèíåñöåíöèè (ÔË), âûçâàííîé íàëè÷èåì
àíñàìáëÿ Si-êëàñòåðîâ. Ðàçáðîñ ðàçìåðîâ Si-êëàñòåðîâ â àíñàìáëå àïðîêñèìèðîâàí â ðàìêàõ ðàñïðåäåëåíèÿ Ãàóññà. Â
ðàáîòå ïîêàçàíî, ÷òî ñïåêòðû ÔË èìåþò àñèììåòðèþ ïèêà â îáëàñòü êðàñíîãî ñìåùåíèÿ, ÷òî ñîãëàñóåòñÿ ñ ýêñïåðèìåíòîì;
êðàñíûé ñäâèã ïèêà ñïåêòðà ÔË îïðåäåëÿåòñÿ ðàñïðåäåëåíèåì ïî ðàçìåðàì êëàñòåðîâ, ÷òî ïîçâîëÿåò ïîëó÷èòü ôèçè÷åñêè
ðàçóìíóþ èíôîðìàöèþ îá ýíåðãèè ñâÿçè.
Êëþ÷åâûå ñëîâà: êëàñòåðû, ôîòîëþìèíåñöåíöèÿ, ðàñïðåäåëåíèå.
ÓÄÊ 530.145+678.9
Â. Â. Koâaëü÷óê, Î. Â. Àôàíàñüºâà, Î. ². Ëåùåíêî, Î. Î. Ëåùåíêî
ÐÎÇÏÎÄ²Ë ÏÎ ÐÎÇ̲ÐÀÕ ÊËÀÑÒÅв ÏÐÈ ÔÎÒÎËÞ̲ÍÅÑÖÅÍÖ²¯, ÎÁÓÌÎÂËÅÍί ²ÑÍÓÂÀÍÍßÌ
ÀÍÑÀÌÁËÞ SI-ÊËÀÑÒÅвÂ
Ðåçþìå
Âèêîðèñòàíà êâàíòîâà ìîäåëü êîíôàéìåíòà ç ìåòîþ îäåðæàííÿ ñïåêòð³â ôîòîëþì³íåñöåíö³¿ (ÔË), ùî âèêëèêàíà íàÿâí³ñòþ
àíñàìáëþ Si-êëàñòåð³â. Ðîçïîä³ë ðîçì³ð³â Si-êëàñòåð³â â àíñàìáë³ àïðîêñèìîâàíèé ó ðàìêàõ ðîçïîä³ëó Ãàóññà. Ó ðîáîò³
ïîêàçàíî, ùî ñïåêòðè ÔË ìàþòü àñèìåòð³þ ï³êà â îáëàñòü ÷åðâîíîãî çñóâó, ùî óçãîäæóºòüñÿ ç åêñïåðèìåíòîì; ÷åðâîíèé çñóâ
ï³êà ñïåêòðà ÔË âèçíà÷àºòüñÿ ðîçïîä³ëîì ïî ðîçì³ðàõ êëàñòåð³â, ùî äîçâîëÿº îäåðæàòè ô³çè÷íî ðîçóìíó ³íôîðìàö³þ ïðî
åíåðã³þ çâ’ÿçêó.
Êëþ÷îâ³ ñëîâà: êëàñòåðè, ôîòîëþì³íåñöåíö³ÿ, ðîçïîä³ë.
135

136
UDC 621.382
I. M. VIKULIN, 1 SH. D. KURMASHEV, P. YU. MARKOLENKO, 1 P. P. GECHEV
Odessa A.S.Popov National Academy of Communications
1 Odessa I.I.Mechnicov National University
Odessa, 65026, Ukraine, e-mail: kurm@mail.css.od.ua. Tel. (0482) — 746-66-58.
RADIATION IMMUNITY OF THE PLANAR n-p-n-TRANSISTORS
Influence of streams of electrons, neutrons and γ–quantum is investigational on the amplification
factor of bipolar planar-epitaxial transistors. It is shown that a preliminary thermal-electric-train
allows to increase of radiation immunity in 2–3 times.
1. INTRODUCTION
The action of radiation around to solids brings to
the origin of a number of effects: excitation of atoms
and their ionization, nuclear transmutation birth of
pair, is an electron-positron, displacement of atoms
from the knots of crystalline grate in interstice space
and other The change of electrophysics properties of
silicon under the action of radiation (this, as a rule,
compensation of conductivity [1]) associates both
with the process of origin of initially-stable defects
(divacancies, tetravacancies and other is similar defects)
and second — as a result of quasi-chemical reactions
(complexes of vacancies with admixtures by
the alloying and concomitant admixtures of oxygen,
carbon and other[2]). In particular, in n-Si, alloyed
phosphorus, non-equilibrium vacancies, entering
into the quasi-chemical reaction with alloying (phosphorus)
or with base-line (oxygen, carbon) admixtures,
and also between itself, form the second radiation
defects[3].
Most effectively the reactions take place in the
conditions of irradiation of γ–quantum Ñî 60 , by electrons
with energy 1 MeV, low-energy protons and
other by particles energy of which in order of size is
comparable with energy of origin of defects (by different
estimations she makes for silicon 145-250 keV).
In scientific literature in detail all sides of work of
bipolar transistors are lighted up at the irradiation. It is
shown that none of parameters characteristic for them
remains here unchanging. Nevertheless, distinctions
appear substantial in the change of properties at the
irradiation of alloyed transistors and structures got a
diffusive method, in particular, planar-epitaxial transistors.
In the real work the comparative change of amplifying
properties of the planar transistors of the same
type is considered at influence of radiation by fast
electrons, γ–quantum, fast neutrons.
2. METHOD OF EXPERIMENT
The experimental samples silicon n-p-n-transistors
were made on planar-epitaxial technology. Specific
resistance of initial epitaxial film ρ= 0.5 Ω∙cm.
Before the leadthrough of thermal operations silicon
epitaxial structures 15KEP was processed by boiling
5 min. in solution of Í Î + Í ÎÍ + Í Î (4:1:1).
2 2 2 2
Then conducted oxidization of standards in a stove at
Ò=(1200±3) 0Ñ. . Thickness of the growth layer SiO2 it was 0.6 μ. This layer served as a mask at diffusion
of the boron. After creation of oxyde masking film
photolithography was conducted for diffusion of the
coniferous boron (base). Boron spin-on was carried
out at Ò=9400Ñ in the atmosphere of argon for the receipt
of sheet resistivity R =60 Ω/�. For forming of
s
base layer with the necessary distributing of concentration
of dopant the drivi-in of dopant of the boron
was conducted at Ò=11500Ñ. Concentration of alloy-
ing dopant in a base ~1.5∙10 18 cm 2
− , depth of diffusive
transition was ~3.5 μ. Photolithography was further
conducted under the emitter of transistor. The region
of emitter was created by diffusion of phosphorus from
PCl 3 at Ò=1050 0 Ñ in the atmosphere of oxygen. Depth
of emitter diffusion was 2-3 μ. The thickness of base
made ~1.5 μ. For forming of contact in area of base
and emitter photolithography was conducted under
the contacts. After it on the plate of silicon by cathode-ray
evaporation coating the layer of aluminium
in thick 1.5 μ. After lithography on metallization aluminium
was firing at Ò=550 0 Ñ in the atmosphere of
argon during 15 min. The got structures were pressurized
in a glass-to-metal corps.
The irradiation of structures was made by the
stream of fast electrons Fe on the linear accelerating
”Electronics” as ELU-4. Energy of electrons 5.0
MeV, current of irradiation 0.1-1.0 mA. The irradiation
of samples was made at Ò=60 0 Ñ.
The irradiation by the streams of neutrons F n with
Å=1.5 MeV was made in the horizontal channel of reactor
of ÂÂÐ-M. The thermal-neutron were chopped
off by a cadmium filter. The fluence was 10 11 -10 15
n∙cm -2 .
The irradiation of γ–quantum was made from the
source of Ñî 60 . Intensity of γ–quantum (dose of D γ )
was 3500 R/s, middle energy of quantum — 1.25 MeV.
The temperature of samples in the process of irradiation
changed in an interval (293-330) 0 C.
Alloying of single-crystals planar-epitaxial of silicon
by the ions of the boron with energy 30-100 keV
to the doses 10 14 -10 18 i∙cm -2 it was conducted on the
accelerating setting “Vesuvius-1À” with the division
on the masses.
© I. M. Vikulin, Sh. D. Kurmashev, P. Yu. Markolenko, P. P. Gechev, 2009

3. RESULTS AND DISCUSSION
On descriptions of semiconductor elements determination
of maximum streams is the practical purpose
of any research of influencing of radiations at which
an element falls out. There is a research task also development
of technological methods of increase of
these maximum values.
Amplifying properties of transistor are characterized
by h 21e , the transfer coefficient of current h 21e
equal to attitude of change of output current toward
the change of entrance in a scheme common-emitter
( h 21e = Ic I b ). In this case we examine a transfer coefficient
exactly h 21e , as it answers most amplification
factor of power of transistor. As is generally known,
it concernes by efficiency of emitter, coefficient of
transfer and efficiency of collector.
In a scheme common-emitter h 21e measured a
transfer (strengthening) current h21e at tension on a
collector U с = 3V and current of collector I c =3 A.
Temperature of measurings T = 293K . Measurings
were conducted for three parties of transistors (for
three types of transfer got out with the identical value
h 21e , each of which was exposed to the rays by a certain
stream in a range 10 12 - 10 15 cm 2 − , whereupon
extracted a transistor from the chamber of irradiation
and measured the value h 21e .
It was studied to dependence of mobility (fig.1),
time of life of charge curriers (fig.2), and also specific
resistance of collector, base and emitter (fig.3) from a
radiation stream.
Fig. 1. Dependence of mobility of electrons in epitaxial layer
of silicon with ρ= 0.5 Ω∙cm from the stream of electrons (1), fast
neutrons (2) and γ–quantum (3)
The slump of mobility and of life time of charge
curriers under the action of radiation decreases length
of diffusion L , and accordingly the transfer coeffi-
n,p
cient of current of transistor, as 21e
h ~ L n,p /w 2 . At the
same time the thickness of base w changes at the irradiation.
The growth of specific resistance of collector,
base and emitter (fig. 3) corresponds to decreases of
concentration of charge curriers in a semiconductor
at the irradiation [1]. It results in displacement of collector
deep into semiconductor, i.e. increase w. It is
special shows up in structures with a thin base, as in
our case (w≈1.5 μ).
Fig. 2. Change of life time of electrons in the p-base (1) and
holes in the n-collector (2)
Fig. 3. Change of specific resistance collector, base and emitter
at the irradiation by neutrons: 1– n-collector ( ρ= 10 Ω⋅cm),
2 — p-base ( ρ=10 –2 Ω⋅cm), 3 — n-emitter ( ρ=10 –3 Ω⋅cm)
On a fig. 4 dependence of the transfer coefficient
of current h 21e of planar transistors is shown on the
stream of electrons, neutrons and γ–quantum. It ensues
from the graphs, that thresholds values of radiation
streams which the sharp decreasing of strengthening
of transistor is after, make accordingly: for the
14
2
stream of electrons 5 ∙10
e ∙ cm − , for the neutrons of
10 13 2
n cm − , for γ–quantum 10 6 R . Physical reason
of decreasing h 21e under the action of radiation is the
origin of defects in the crystalline structure of semiconductor,
which shunt emitter p-n-junctions and reduce
its coefficient of injection, and also decreasing of
life time of charge curriers in the base of transistor.
The graphs of fig. 4 correlates with the dependencis
of pictures 1, 2 and 3. It ensues from these dataes, that
with the increase of maximum frequency of transistors
their radiation immunity is increased. We will remind,
that maximum decreased is frequency on which the
transfer coefficient of current h 21e diminishes in 2
one times. In the scheme of including common-emitter
maximum frequency concernes by effective time of
life of transmitters of charge (inversely proportional).
At planar, i.e. diffusive transistor of n-p-n-type maximum
frequency higher, than at driveable, therefore
and radiation immunity higher.
137

Fig. 4. Influencing of streams of electrons, neutrons and
γ–quantum on the transfer coefficient of current h 21e
For the increase of radiation immunity of transistors
we used the method of thermal-electric-train
(ÒEÒ). Co-operation of radiation streams with a
semiconductor it is possible to examine by consisting
of two stages. On the first stage (at small energies of
stream) a radiation operates on technological defects
appearing in material at creation of transistor, and on
the second (at large energies) the own defects of crystalline
structure are created. The creature of method
consists of that at ÒÝÒ technological defects and parameters
of transistor collapse at the small streams of
radiation does not change.
138
UDC 621.382
I. M. Vikulin, Sh. D. Kurmashev, P. Yu. Mfrkolenko, P. P. Gechev
RADIATION IMMUNITY OF THE PLANAR n-p-n-TRANSISTORS
Experimental verification of method of ÒEÒ was
carried out as follows. Transistors were heated to
0
125 C and was simultaneously exposed to periodic
electric influence with power in 2.5 time greater, than
passport maximal power. Self-control was conducted
at maximal influence about 5 min. with a period 20
min. Research of influencing of radiation streams on
the parameters of transistors, that after ÒEÒ during
40–60 hours thresholds values of radiation streams resulting
in the sharp decreased h 21e , is increased more
than in 2 times. The got results talk about the change
of terms of second radiation residual damage as a result
preliminary thermal and ÒEÒ treatments of transistors
structures.
As the structure of investigational transistors does
not differ from transistors in the integrated circuits,
phototransistors and etc, the considered method of
increase of radiation immunity is applicable to these
semiconductor devices.
4. CONCLUSIONS
The thresholds streams of electrons, neutrons, γ–
14
quantum for a planar n-p-n-transistor make 5 ∙10
e
2
cm − , 10 13 2
n cm − and 10 6 R , accordingly. For the increase
of radiation immunity of transistors the method
of thermal-electric-train can be used.
References
1. Áðóäíûé Â.Í. Ìîäåëü ñàìîêîìïåíñàöèè è ñòàáèëèçàöèÿ
óðîâíÿ Ôåðìè â îáëó÷åííûõ ïîëóïðîâîäíèêàõ/
Â.Í.Áðóäíûé, Í.Ã.Êîëèí, Ë.Ñ.Ñìèðíîâ// Ôèçèêà è òåõíèêà
ïîëóïðîâîäíèêîâ. — 2007. — Ò.41, ¹9. — Ñ. 1031-
1040.
2. Ìóðèí Ë.È. Áèñòàáèëüíîñòü è ýëåêòðè÷åñêàÿ àêòèâíîñòü
êîìïëåêñà âàêàíñèÿ-äâà àòîìà êèñëîðîäà â
êðåìíèè/Ë.È.Ìóðèí, Â.Ï.Ìàðêåâè÷, È.Ô.Ìåäâåäåâà,
Ë.Äîáî÷åâñêèé // Ôèçèêà è òåõíèêà ïîëóïðîâîäíèêîâ.
— 2006. — Ò.40, ¹11. — Ñ. 1316-1320.
3. Ïàãàâà Ò.À. Âëèÿíèå òåìïåðàòóðû îáëó÷åíèÿ íà ýôôåêòèâíîñòü
ââåäåíèÿ ìóëüòèâàêàíñèîííûõ äåôåêòîâ â
êðèñòàëëàõ n-Si/ Ò.À.Ïàãàâà // Ôèçèêà è òåõíèêà ïîëóïðîâîäíèêîâ.
— 2006. — Ò.40, ¹8. — Ñ. 919-921.
Abstract
Influence of streams of electrons, neutrons and γ–quantum is investigational on the amplification factor of bipolar planar-epitaxial
transistors. It is shown that a preliminary thermal-electric-train allows to increase of radiation immunity in 2–3 times.
Key words: neytrons, radiation immuniti, transistors.
ÓÄÊ 621.382
È. Ì. Âèêóëèí, Ø. Ä. Êóðìàøåâ, Ï. Þ. Ìàðêîëåíêî, Ï. Ï. Ãå÷åâ
ÐÀÄÈÀÖÈÎÍÍÀß ÑÒÎÉÊÎÑÒÜ ÏËÀÍÀÐÍÛÕ n-p-n-ÒÐÀÍÇÈÑÒÎÐÎÂ
Ðåçþìå
Èññëåäîâàëîñü âëèÿíèå ïîòîêîâ ýëåêòðîíîâ, íåéòðîíîâ è γ-êâàíòîâ íà êîýôôèöèåíò óñèëåíèÿ áèïîëÿðíûõ ïëàíàðíîýïèòàêñèàëüíûõ
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ÓÄÊ 621.382
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ÐÀIJÀÖ²ÉÍÀ ÑÒ²ÉʲÑÒÜ ÏËÀÍÀÐÍÈÕ n-p-n -ÒÐÀÍÇÈÑÒÎвÂ
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139

140
UDC.539.125.5
K. V. AVDONIN
The Kiev national university of technologies and design,
01011, Ukraine, Kiev, Nemirovich’s street, 2,
Ph. 256-29-27, 419-32-59
E-mail: info@izdo-knutd.com.ua
BUILD-UP OF WAVE FUNCTIONS OF THE PARTICLE
IN THE MODELLING PERIODIC FIELD
A movement pattern of charged free particles inside of a crystal is proposed in this work. Effective
potential field of interaction between particles and crystal lattice point is considered in two presentations:
as three-dimensional Fourier series and as the presentation of effective field, in which its periodicity
is made by Heviside’s function. Wave functions are found by composition of individual solutions
of Schrödinger equation in the form of functional series. A possibility of existence of energy levels of
foreign particle’s condition in crystal appropriate to them is researched.
1. INTRODUCTION
The Overall objective of paper was examination of
an opportunity to find particular solutions of a steadystate
Schrodinger equation: ϕ (r)
2
⎛ ⎞
h
⎜− Δ+ W(r) ⎟ψ
(r) = Eϕ(r).
(1)
⎝ 2μ
⎠
In the form of functional numbers by means of a
method created in paper [1], for a derived periodic field
(2) and a modelling field (38), research of existence of
corresponding power levels, and also opportunities of
reception of distribution of probability for directions
of movement of a particle. One of last papers devoted
to the general features of a power spectrum of a particle
in a periodic field, is paper [2] which result confirms
the character of the power spectrum received in given
paper. Advantage of an offered method of search is its
relative simplicity and besides it gives new opportunities
for a computer simulation of processes occuring
in real crystals.
2. SEARCH OF WAVE FUNCTIONS
OF A PARTICLE IN THE PERIODIC FIELD
WHICH HAS BEEN RESOLVED
IN A FOURIER SERIES
The most often the periodic field is represented in
the form of a Fourier series:
W(r) = a +∑ a exp( ikr).
(2)
0 k
k≠0 After substitution of potential energy in a Schrodinger
equation (1) in the form of a Fourier series (2)
it would be:
{ } 2
m
Δ+
Or in the other form:
ϕ (r),
(3)
Δϕ (r) = f (r) ϕ (r),
Where the labels are used as follows:
(4)
f(r) = A +
2 2μ
m = 2 ( E−a0) ,
h
2μ
Ak = a 2 k,
h
A exp( ikr) = A exp( ikr),
0 k k
k≠0 k
(5)
∑ ∑ (6)
Let’s choose function, too periodic, with a Fourier
analysis: h (r)
h(r) = ∑ Hнexp( ivr),
н≠0 Satisfying to a requirement:
Δ h(r) = A0h(r), Then the particular solution of the equation (6)
can be constructed in such form:
Where:
1
n
∑ ( ) n (7)
ϕ (r) = h(r) −D (r, ν ) + −1 D (r, ν),
D
∑∑
∞
n=
2
н k00 1
н k0≠0 2
k0
+ν
{ ( +ν)
}
H A exp i k r
;
sα = k0 + k 1+
... + k α.
In fact, we shall work functional Laplassa on function
(7):
Δϕ (r) =Δh−Δ D1+ΔD2 −Δ D3 +ΔD4 − ... (8)
As:
∑
н≠0 { } ∑
k0≠0 0 { }
h(r) ∑ Ak exp{ ik}
0
0r
;
ΔD (r, ν ) = − H exp iνrA exp ikr−
1н k 0
−
k0≠0 ⎧⎪ ⎫⎪
ΔDn(r, ν ) = − ⎨∑Ak exp{ ik}
1
1r
n−
n−⎬×
⎪⎩kn−1⎪⎭ × ∑∑∑
н k0≠0 k1 Hн∏ n−1exp{ i(
sn−2 +ν)
r}
... ∑
=
2 2 2
kn−2
s0 +ν s 1+ν ⋅... ⋅ sn−
2 +ν
=−f(r) D (r, ν).
n−1
© K. V. Avdonin, 2009

{ i 0( − 0)
+ i ( − ) }
That of expression (8) follows, that:
Δϕ (r) = h(r) A0 + h(r) ∑ Ak exp{ ik}
0
0r−
k≠0 − f(r) D1(r) + f(r) D2(r) − f(r) D3(r)
+ ... =
= f(r) ( h− D1+ D2 − D3 + ... ) = f(r)
ϕ(r).
For an important special case:
h(r) = exp( imr
) .
The solution (7) will look like:
Ak exp{ i(
k ) }
0
0 + m r
ϕ (r) = exp{ imr}
− ∑
+
2
k≠0
k0+ m
(9)
n
∞
( −1) ∏ n−1exp{ i(
sn−1+ m) r}
+ ∑∑∑ ... ∑
.
2 2 2
n=
2 k0≠0 k1 kn−1
s0 + m s1+ m ⋅... ⋅ sn−1+ m
Grouping addends on degrees of coefficient (see
appendix A), we have: 0 A
⎧ ⎪ Ak exp{ i(
k ) }
0
0 + m r
ϕ= exp{ imr}
−⎨1− ∑
+
2
⎪⎩ k≠0
k0 + m + A0
∏ n−1exp{ i(
sn + m) r
⎫ } ⎪
+ ∑ ∑ −... .
2 2 ⎬ (10)
k0≠0 k1≠0( s0 + m + A0)( s1+ m + A0)
⎪
⎭
A series (10) has a singularity at, that impedes
search of wave functions generally. s j = 0 Let Fourier
analysis of a wave function looks like:
ϕ (r) =∑ Bkexp( ikr).
k
Then the functional series (10) will be iteration of
a relation:
Ak B { ( ) }
0 k exp i k0 + k r
ϕ= exp( imr
) −∑
. 2
k 0 ,k k0+ k −m
(11)
By a direct substitution it is possible to prove (see
addition), that the relation (11) satisfies the equation
(5). Substituting in expression of a Fourier analysis
(13) coefficients in the form of:
λ0
1
Ak = u( с ) { }
0
0 exp ik0с0 dс
0.
V ∫
0 0
(12)
Where: 0 0 0 0 ;
1 exp с k r с
Ω= ∑
=
2 2
VV 0 kk 0 k-k0
− m
⎛ 1 ⎞ 1 exp с { ik0(
r − 0)
}
= ⎜ ∑exp с { ik0(
r − 0) }
2 2
V
⎟ ∑
=
⎝ k ⎠V0k
k 0 0 − m
1 exp с { ik0(
r − 0)
}
=δ(
с - с 0 ) ∑ . (14)
2 2
V0 k k 0 0 − m
Substituting the integrand total in the form of (14)
in the equation (13) we have:
λ
imr
ϕ (r) = e + ∫ G0( r, ρ) u( ρ) ϕ( ρ) dρ.
0
V =λ xλyλ z V =λxλyλ z and — a vector
of translation for functions that accordingly, we shall
gain:
λ0 λ
ϕ (r) = exp{ imr } −∫∫ Ωu( ρ0) ϕ( ρ) dρ0dρ. (13)
0 0
Where:
1 exp{ ik0( r −ρ 0)
+ ik(
r −ρ)
}
Ω= ∑
.
2 2
VV 0 kk 0 k-k0
− m
It is obvious, that translations vectors and should
multiple. λλ 0 Here two cases are possible: 1);
λ 0 = nλ
2), where — natural number n. In the first
case for the integrand total of expression (13) there is
an opportunity to shift the beginning of summation
on a vector to a vector then the integrand total would
be equal:
% (15)
Where:
1 exp{ ik
0 (r }
G%
−ρ
0 (r, ρ ) = − ∑
. (16)
2 2
V0 k k 0 0 − m
In the second case for the integrand total of expression
(13) there is an opportunity to shift the beginning
of summation on a vector to a vector then the
integrand total is as follows: Ω kk0
1 exp с { i k k0( r − с 0)
+ i ( − ) }
Ω= ∑
=
2 2
VV 0 kk 0 k-k0
− m
⎛ 1 ⎞ 1 exp с { ik(
r − ) }
= ⎜ ∑exp с с{
ik0(
− 0) } ⎟
2 2
V ⎟ ∑
=
⎝ 0 k V 0
⎠ k k − m
1 exp с { ik(
r − 0 ) }
=δ( с−с 0 ) ⋅ ∑ . (17)
2 2
V k k − m
Substituting the integrand total in the form of (17)
in the equation (13) we have:
λ0
imr
ϕ (r) = e + ∫ G(r, ρ) u() ρ ϕ( ρ) dρ.
0
% Where:
(18)
1 exp{ ik(r
}
G%
−ρ
0 (r, ρ ) = − ∑
. (19)
2
V k k0−m By a direct substitution we can convince, that functional
action on functions (16) and (19) gives a Dirac
delta function. ( ) 2
Δ+ m Thus, functions also play a
role of source functions for the equation (3). Spectral
decompositions of a source function (16), (19) are already
known (for example, from [4]). A vector and a
wave function as arise from the equations (15); (18)
have an identical translation vector, that is:
⎛2π 2π 2π
⎞
m = ⎜ lx; ly; lz
.
⎜
⎟
⎝λx λy λz
⎠
(20)
Where: lx, ly, l z — integers.
Let’s view a boundary case, in other words, we
shall change Fourier series by a Fourier integral in expressions
(16), (19). After Integrating, by means of the
calculus of residues, we gain:
1 exp { ik(r
−ρ)
}
G(r,
ρ ) = − ∑ . (21)
2 2
V k k − m
Expression (21) coincides with a source function
for the acyclic field, found in paper [5]. Source func-
141

tions in the equations (15), (18) have a singularity at,
accordingly k0= m k = m . Let — the complete set
of the vectors equal to a vector modulo. We can put out
singularity for source functions in expressions (16),
(19) by transducing source functions as follows:
N 1 imr%
j
G(r, ρ ) = − ∑ exp 2 { imj(r
−ρ) } −
V j=
1 2m
1 exp{ ik(r
−ρ)
}
− ∑
.
(22)
2 2
V k k − m
k ≠ m
N 1 imr%
j
G0(r, ρ ) = − ∑ exp 2 { imj(r
−ρ) } −
V0 j=
1 2m
1 exp{ ik
0 (r −ρ)
}
− ∑
. (23)
2 2
V0 k k0−m k ≠ m
Where:
r% = r −λn;
л n = { nzλx; nyλy; nzλ
z}
— the peak translation
vector, contained in radius-vector.
As is shown in appendix D, the functions, definiendums
by (22), (23) satisfied relations:
142
2 ( m ) G(
)
Δ+ r, ρ =δ(r −ρ ). (24)
Thus, the transduced source functions (22), (23)
can be used in integral representations of a Schrodinger
equation (15); (18), that is:
λ
ϕ (r) = exp imr + G (r, ρ) u ρ ϕ( ρ) dρ.
{ } ( )
∫
0
0
(25)
λ0
{ } ( )
ϕ (r) = exp imr + ∫ G(r, ρ) u
0
ρ ϕ( ρ) dρ.
(26)
The homogeneous equations corresponding the
equations (25); (26), can be presented in the form
of:
N imr%
j
ϕ (r) = −∑ exp 2 { imjr} P(
m j)
−
j=
1 2m
exp{ ikr}
− ∑ P(k).
2 2
k − m
(27)
k
k ≠ m
N imr%
j
ϕ (r) = −∑ exp 2 { imjr} P0(
m j)
−
j=
1 2m
exp{ ik0r}
− ∑ P(k).
2 2
k k − m
k ≠ m
Where:
λ0
0
(28)
1
P(k) = u() ρ ϕ( ρ)exp( −ik ρ) dρ.
V ∫ (29)
λ0
1
P (k) = ∫ u() ρ ϕ( ρ)exp( −ik ρ) dρ.
(30)
0 0
V0
0
After both parts of the equations (27), (28) were
multiplied on functions:
1
u(r)exp{ − ik′
r } .
V
Accordingly, and having integrated, we shall gain
systems of the homogeneous linear equations:
Where:
( ( ′ ) +δk,k′
)
k
( ( ′ ) +δ ′ )
∑ Q k,k P(k).
(31)
∑ Q0 k,k 0 0 k 0,k P
0 0(k). 0 (32)
k0
N
N
⎛ Ck,k ′ ⎞ A%
k,k ′
Q = ∑⎜δ k,m 2 2 2 { 1 k,m } .
j ⎟+
∏ −δ (33)
j
j= 1 ⎝ 2m
⎠ k − m j=
1
N
N
⎛ Ck 0′ ,k⎞ A%
0 k 0′ ,k0
Q0
= ∑⎜δ k { }
0 ,m 1 2 ⎟+
2 2
k,m .
j ∏ −δ (34)
j
j= 1 ⎝ 2m
⎠ k0−m j=
1
λ0
1
A% k,k′
= u() r exp{ −i( k −k′
) r} dr.
V ∫
0
λ0
i
Ck,k′ = kru() r exp{ i( k k′ ) r} dr.
V ∫ − −
0
Then, according to the general theory of integral
equations, the discrete energy distribution can be found,
putting to sero systems determinants (31), (32):
( ) k,k
k,k′ +δ = 0.
(35)
Q ′
Q ( 0 0) k 0,k0′ k,k′ +δ = 0.
(36)
Except for relations (35), (36) for finding of a discrete
spectrum we can use a requirement of equality to
zero of a determinant of Fredholm corresponding the
equations (25), (26). If a determinant of systems (31),
(32) or a determinant of Fredholm of the equations
(25), (26) are not equal to zero, that, by consecutive
iterations, from integral equations (25), (26) it is possible
to find the wave functions corresponding an ionization
continuum.
3. WAVE FUNCTIONS OF A PARTICLE
IN A MODELLING PERIODIC FIELD
The modelling periodic field can be constructed
as follows: all space should be broken into unit cells
⎛a b c⎞
with the size ⎜ ; ; ⎟.
To put to each cell two vec-
⎝2 2 2⎠
tors in conformity: n = { nx; ny; nz}
— an integer vector
which defines a position of a cell in space and a vector
which defines a potential energy of a particle in the
given cell:
{ α }
б б
wn(r) = h0 +θn(r) ⋅hexp β
б
Rn
. (37)
Where: h 0 And — the real constants;
α1 α1
R = x− T R = y− T .
α1 α1
n ;
x nx
ny ny
The set of values of a vector is defined by equalities:
б
⎧+
1
α=⎨ .
⎩−1
Components of a vector for all cells are equal on
absolute size, but different on a sign, that is: б в
в б = { α1βx, α2βy, α3β z}
, äå βx, βy, β z — the real
stationary values.

The translation vector provides a value set identical
to all cells for exponential curve argument in expression
(37), and Heaviside vector function chooses
for each unit cell an exponential curve with a corre-
б б
sponding vector T nбθn(r) β . The obvious view of vectors
is given in addition C. Particle potential energy
can be written down in the form of:
∞
W(r) = ∑∑ w (r).
(38)
n=
0б
The characteristic feature of the created model of
a field is that the field in each cell consists only of one
exponential curve and a constant component h 0 . At
transition to the next cell the sign of one of components
of vectors changes on opposite, and the module
of component does not change в б . The exponent of
exponential curve in expression (37) is a real number.
However if to resolve function (38) in a Fourier series
we shall gain the real translation vector for a reciprocal
lattice that will be coordinated with the standard
theory. Thus, there is no necessity to write down a
Schrodinger equation for all space, it is enough to
write it down for one cell and to impose corresponding
boundary condition on its solutions. We shall write
down a Schrodinger equation for one cell:
б
n
2
⎛ h
б ⎞ б б
− Δ+ wn ϕ n = Eϕn
⎜ (r) ⎟ (r) (r). (39)
⎝ 2μ
⎠
Let’s substitute potential energy (38) in the equation
(39) and write down it in the form of:
б б
Δϕ n(r) = f (r) ϕ n(r).
(40)
Where such table of symbols are used:
2 2μ
2μ
m = 2 ( E−h0) , A0 =− 2 ( E−h0) ,
h
h
2μ
α
A= hf 2 () r = A0 + Aexp(
βαRn)
(41)
h
Particular solution of the equation (40) can
be found using the solution (10) if to figure:
k0 = k1 = k 2 = ... = −iβ α .
It will be such:
∞
αα , ′ imбr
ϕ n = e + ∑
k = 1
α { ( α′ α n ) }
k k
( −1) A exp i m r −ikβ R
k
∏(
mα′
−ilβα) l = 1
Where: m б′ ( ′ 1m , ′ x 2my, ′ 3mz)
.
2
.
(42)
= α α α With the view of
satisfying the wave function found from the equation
(40), to boundary conditions it is necessary to choose
it in the form of such linear combination of particular
solutions (42) as follows:
б б,б′
ϕ n = ∑ ϕn
.
б′
Boundary conditions look like:
(43)
( na yz) ( na yz)
ϕ ± , , =ϕ ± , , ;
α1, α2, α3 −α1, α2, α3
n x n
x
α1, α2, α⎛ na 3 x ⎞ −α1, α2, α⎛
na
3 x ⎞
ϕ n ⎜± yz , =ϕ n ± yz , ;
2
⎟ ⎜
2
⎟
⎝ ⎠ ⎝ ⎠
( x, nyb, z) ( x, nyb, z)
;
ϕ ± =ϕ ±
α1, α2, α3 α1, −α2, α3
n n
nb
1, 2, y nb
α α α⎛ ⎞ 3 α1, −α2, α⎛
y ⎞
3
ϕ n ⎜x, ± , z⎟=ϕ n ⎜x, ± , z⎟;
⎝ 2 ⎠ ⎝ 2 ⎠
α1, α2, α3 ϕ xy , , ± nc
α1, α2, −α3
=ϕ xy , , ± nc;
( ) ( )
n z n
z
α1, α2, α⎛ nc 3 z ⎞ α1, α2, −α⎛
nc
3
z ⎞
ϕ n ⎜xy , , ± =ϕ n xy , , ± ;
2
⎟ ⎜
2
⎟
⎝ ⎠ ⎝ ⎠
We gain the next expressions from them:
⎧1⎫ sin ⎨ ( α 1ma x +α 2mb
y ) ⎬=
0;
⎩2⎭ ⎧1⎫ sin ⎨ ( α 2mb y +α 3mc
z ) ⎬=
0;
⎩2⎭ ⎧1⎫ sin ⎨ ( α 3mc z +α 1ma
z ) ⎬=
0; (44)
⎩2⎭ From which arises, that builders of a wave vector
are real numbers, which quantize as follows:
2πN
2πN
x
y 2πN
z
mx
= ; my
= ; mz
= . (45)
a b c
Where: N x — the arbitrary integers.
Then the energy distribution corresponding the
constructed wave function will be discrete:
2 2 2 2 2
2π
h ⎛ N N x y N ⎞
z
EN= h0+
⎜ + + .
2 2 2 ⎟ (46)
μ ⎜ a b c ⎟
⎝ ⎠
There is shown in appendix A, that the functional
series of type (10) converge under condition of:
A < m −iβ .
(47)
0
2
α′ α
The inequality (47) can be copied in the form of:
2 2
h β
h0 < E < h0
+ . (48)
2
4μ( 1−2cos θ)
Where: θ — It is a corner between vectors that m б .
From a relation (48) arises existence of the forbidden
and allowed directions of a particle wave vector
so as the corner cannot accept value for which
1
θ cos θ ≥ . Thus, the particle can transfer in one
2
of the next cells with different probability. We can see
from figure 1, that if the particle has energy in an interval:
2 2
h β
h0 < E < .
(49)
4μ
That the greatest quantity of the allowed moving
directions exists for it . If value of energy will exceed
critical value, that, with magnification of energy, the
quantity of possible trajectories of a motion will sharply
decrease and will aspire to zero for the energy considerably
exceeding critical value.
2 2
h β
E = .
4μ
Thus, in a modelling field, the particle actually
has a narrow band , with degree of, a band of the allowed
values of energy, definiendums (46) and (49)
−1 −1
~10 − 10 eB . In paper [6] on the basis of the ob-
143

servational effects the possible model of energy states (46). It is shown, that a discrete series of energy levels
of an amorphous cadmium diphosphide has been de- has a upper bound which depends on a direction of a
veloped which will be coordinated with effects of ex- wave vector. In the created modelling potential field
periment. The approach was used at build-up of this there is an opportunity of search of probability distri-
model according to which the amorphous substance is bution for possible trajectories of a particle motion.
considered as a crystal periodic field of which gets new The constructed modelling field is useful for exami-
properties, owing to rather major concentration of nation of features of electromigration mechanisms in
flaws. Infringement of stehiometry in (surplus) leads
to formation of donor type centre in which the electron
simultaneously is both in a field of flaws, and in a
amorphous semiconductors.
periodic field of a crystal CdP2Cd . Volumetric periodicity
of an arrangement of such centres as experiment
5. ADDITIONS
has proved, leads to occurrence of the new periodic
field, one of main features is existence of periodically
located planes of reflecting symmetry that is characteristic
for the modelling potential created in given
paper. It enables to explain, leaning on an energy distribution
of a particle in a modelling field, occurrence
of the non-local energy levels in a forbidden region
A. Expression transformation (9)
Let’s group summands of series (9) on degrees of
coefficient: 0
amorphous CdP 2 . The flaws related to surplus, are the
double donors, capable to donate one or two electrons
Cd. They should create very narrow bands that will be
coordinated with the effect gained from created model.
Besides prompt diminution of quantity of the allowed
particle mechanical trajectory, with increasing of its
energy, can explain occurrence of conductance channels
of in amorphous CdP 2 . The motion of particles
with high energy on rather small fields of substance
volume raises their temperature and as consequence,
can cause local changes of structure amorphous CdP 2 .
That is, the created modelling field gives one of possible
explanations to a switching effect in amorphous
semiconductors, supplementing the principal causes
of its occurrence viewed in paper [7].
E
A
⎧⎪ Ak exp{ ik}
0
0r
imr ϕ= e ⎨1−
∑
+ 2
⎪⎩ k0≠0 k+m 0
Ak exp{ ik} { }
0 0l Ak A
0 k1exp is1r
+ A0
∑ + 2 ∑ ∑
−
2 2
k0≠0 k+m 0
k0≠0 k1≠0 k+m 0 s+m 1
Ak exp{ ik} { }
0 0r Ak A
0 k1exp is
2
1r
−A0∑ − A
6 0∑
∑ r 2 r − 4
k0≠0 k+m 0
k0≠0 k1≠0 k+m 0 s+m 1
Ak A { }
0 k1exp is1r
−A0∑ ∑ r 4 r − 2
k0≠0 k1≠0 k+m 0 s+m 1
∏ 2exp{ is2r}
⎫⎪
− ∑ ∑ ∑
+ ...
2 2 2 ⎬ =
k0≠0 k1≠0 k2≠0 k+m 0 s+m 1 s+m 2 ⎪⎭
Ak exp{ ik} ( )
0
0rS1 k0
= exp{ imr}{
1−
∑
+
2
k ≠0
k+m
−π
144
3π
−
4
π
−
2
π
−
4
2 2
β
h0
+
4μ
�
h0
0
π
4
π 3π
π
2 4
Fig. 1. Dependence of the greatest possible energy of a particle
on a corner, a definiendum (40). θ
4. EFFECTS
For search of the particle wave functions having
an ionization continuum in a modelling periodic field,
from integral equations of Fredholm type (25) and
(26), source functions (22), (23) are offered, which allow
to carry out search of wave functions with a continuance
not only equal but also multiple to a continuance
of a potential field. The possible discrete energy
distribution can be defined from relations (35), (36).
The modelling periodic field for which wave functions
of a particle in an analytical view are gained is
constructed. The energy distribution of a particle, in
a modelling potential field, is defined by expression
θ
∑ ∑
k0≠0 k1≠0 0
∏
0
( )
isr 1
1e S2
k 0,k1 2 2
+ −
k +m k +k +m
0 0 1
∏ 2exp{ is3r} S3(
k 0,k 1,k2) ⎫⎪
∑ ∑ ∑ ... (50)
2 2 2
− + ⎬
k0≠0 k1≠0 k2≠0 k+m 0 s+m 1 s+m 2 ⎪⎭
Let’s find quantities: S j( k 0,k 1,..,k j−
1)
S
A A
= − + −
1( k0) 1
0
2
k0 + m
2
0
4
k0 + m
3 4
A0 A0
− + −...
6 8
k0 + m k0 + m
(51)
A series (51) is a geometrical progression which
will converge under condition of:
A 0 < k0 + m .
(52)
If the requirement (52) is carried out, quantity will
k S
be equal: ( )
1 0
S
2
k0+ m
1( 0) =
2
k0 + m + A0
k .
2
(53)
Assumed, that the condition (52) is satisfied, we
S
k,k
shall evaluate a value: ( )
2 0 1

S
A A A
= − − + +
1( k,k 0 1) 1
0
2
k0 + m
0
2
s1+ m
2
0
4
k0 + m
2 3 3
A0 A0 A0
+ − − + ... +
4 6 6
s1+ m s1+ m k0 + m
A ⎡ A A ⎤
+ × ⎢1 − − + ... ⎥ =
k m s m ⎢⎣ k m s m ⎥⎦
0 +
2
0
2
1+ 2
0
0 +
2
0
r 2
1+
2
s1+ m A0
= − +
2 2
s1+ m + A0 k0 + m + A0
2
A0
+
S
2 2 2( k,k 0 1)
.
k0 + m s1+ m
There is the linear algebraic equation for finding
S k,k
of it: ( )
2 0 1
S2(
k,k 0 1) 2
s1+ m
2
s1+ m + A0
A0 2
A0
0 +
2
+ A0
0 +
2
1+
2
= −
( )
−
k m
+
k m s m
S2
k,k 0 1 . (54)
We have from the equation (54) as follows:
II
k,k .
0 1
S2(
0 1)
=
FF 0 1
2
Ij = s j + m
Where:
Similarly we find other values of sequence:
j−1
Il
S j( k 0,k 1,...,k j−1)
= ∏ . (55)
l = 0 Fl
Substituting expression (55) in (50) we gain:
{ }
⎛ Ak exp ik
0
0r
ϕ= exp{ imr}
⎜1−
+
⎜ ∑
⎝ k0
≠0
F0
∏ 1exp{ is1r}
⎞
∑ ∑ ... . (56)
+ − ⎟
k0≠0 k1≠0
FF ⎟⎠
0 1
B. Relation check (13)
Acting on both parts of expression (13) by func-
2
Δ+ m
tional we have: ( )
( )
k 0 ,k
k 0 ,k
∑
{ ( + ) }
2 2 k0k 0
Δ+ m ϕ=−m −
2 2
k 0 ,k k0+ k −m
( Δ exp{ ( k + k)
} )
k0k 0
2 2
k0+ k −m
{ ( + ) }
2 k0k 0
k 0 ,k
2 2
k0+ k −m
k0k 0 +
2
0 +
2 2
−m
{ ( ) }
k0k 0
A B exp i k k r
A B i
− =
∑
A B exp i k k r
=− m
+
∑
A B k
+ ∑
k 0 ,kk
k
k
exp{ i(
k0 + k) r}
=
= A B exp i k + k r = u(r)
ϕ(r).
∑
C. The functions used in model of a periodic field
The label θξ () — corresponds to function of
Heaviside. The table of symbols — corresponds to
Heaviside function.
⎧+
1
б = ( α1; α2; α 3)
; α i = ⎨ ;
⎩−1
б б б
w (r) =θ (r) Aexp β R (r) ;
б
n
( α )
n n n
α1 α2
α3
( Rn x R )
x n y R
y n z
z
R (r) = ( ); ( ); ( ) ;
( x y z)
б α1 α2
α3
в = α β , α β , α β ; θ (r) =θ ( x) θ ( y) θ ( z);
б 1 2 3
n
( 1+α
)
nx ny nz
α ⎛
1
1 ⎞
Tn =γ 1 ( ) ;
x xa⎜nx + −αθx
⎟
⎝ 2 ⎠
α ⎛ ( 1+α
)
2
2 ⎞
Tn =γ 2 ( ) ;
y yb⎜ny + −αθ y ⎟
⎝ 2
⎠
α ⎛ ( 1+α
)
3
3 ⎞
Tn =γ 3 ( ) ;
z zc⎜nz + −αθ z ⎟
⎝ 2
⎠
γ x , are functions of a coordinates sign, accordingly;
( 1−α
)
α ⎧⎪ 1
1 ⎫⎪
θ n ( x) = ⎨ +α1θ( x) ⎬θ(
x − an )
x
x ×
⎪⎩ 2 ⎪⎭
( 1+α
)
⎛ ⎛ 1 ⎞ ⎞ ⎧⎪ 1 ⎫⎪
×θ ⎜a⎜nx+ ⎟−
x ⎟+
⎨ − α1θ ( x)
⎬×
⎝ ⎝ 2⎠ ⎠ ⎪⎩ 2 ⎪⎭
⎛ ⎛ 1 ⎞⎞
×θ⎜ x − a⎜nx + ⎟⎟θ
( a( nx + 1 ) − x)
;
⎝ ⎝ 2 ⎠⎠
α ⎧⎪( 1−α
)
2
2 ⎫⎪
θ n ( y) = ⎨ +α2θ( y) ⎬θ(
y − bn )
y
y ×
⎪⎩ 2
⎪⎭
⎛ ⎛ 1 ⎞ ⎞ ⎧⎪( 1+α2)
⎫⎪
×θ ⎜b⎜ny+ ⎟−
y ⎟+
⎨ − α2θ ( y)
⎬×
⎝ ⎝ 2⎠ ⎠ ⎪⎩ 2
⎪⎭
⎛ ⎛ 1 ⎞⎞
×θ⎜ y − b⎜ny + ⎟⎟θ
( b( ny + 1 ) − y)
;
⎝ ⎝ 2 ⎠⎠
( 1−α
)
α ⎧⎪ 3
3 ⎫⎪
θ n ( z) = ⎨ +α3θ( z) ⎬θ(
z − cn )
z
z ×
⎪⎩ 2 ⎪⎭
( 1+α
)
⎛ ⎛ 1 ⎞ ⎞ ⎧⎪ ×θ ⎜c⎜nz+ ⎟−
z ⎟+
⎨
⎝ ⎝ 2⎠ ⎠ ⎪⎩ 2
3 ⎫⎪
− α3θ ( z)
⎬×
⎪⎭
⎛ ⎛ 1 ⎞⎞
×θ⎜ z − c⎜nz + ⎟⎟θ
( c( nz + 1 ) − z)
.
⎝ ⎝ 2 ⎠⎠
D. The proof of relations (24)
(57)
Operating with the functional on function (22) we
2
Δ+ m
gained: ( )
G
( r, )
( mrexp % j { im
j(
r ) } )
N Δ −ρ
ρ = − −
∑
0
j=
1
2
2Vm
N
2
( mrexp %
j { m j(
r−ρ)
} )
m
−∑ j=
1
i
2
2Vm
−
⎛ 2
⎞
1 ⎜ Δexp{ ik( r −ρ) } m exp{ ik(
r −ρ)
} ⎟
− 2 2 2 2
V ⎜ ∑ + ∑
k k m k k m ⎟
=
⎜ − − ⎟
⎝ k ≠ m k ≠ m
⎠
145

146
N 1 1
= ∑exp{ im j { r −ρ } + ∑ exp{ ik(
r −ρ ) } =
V V
j=
1 k
k ≠ m
1
= ∑exp{
ik(
r −ρ ) } =δ( r −ρ)
.
V k
Similarly we can gain a relation (24) for function
G ρ .
( )
0 r,
References
1. Àâäîí³í Ê. Â. Çíàõîäæåííÿ ðîçâ’ÿçê³â ³íòåãðàëüíèõ òà
äèôåðåíö³àëüíèõ ð³âíÿíü çà äîïîìîãîþ îïåðàòîð³â
çì³ùåííÿ // Ìàòåð³àëè ì³æíàðîäíî¿ íàóêîâî-òåõí³÷íî¿
êîíôåðåíö³¿, ïðèñâÿ÷åí³é 90 — ð³÷÷þ ç äíÿ íàðîäæåííÿ
Ã. À. ϳñêîðñüêîãî, 2003., Ñ. 139 — 142.
2. Áîðèñîâ Ä. È., Ãàäûëüøèí Ð. Ð. Î ñïåêòðå îïåðàòîðà
Øðåäèíãåðà ñ áûñòðî îñöèëëèðóþùèì ïîòåíöèàëîì //
ÒÌÔ, ò.147, ¹1, 2006.
3. Äæîíñ Ã. Òåîðèÿ çîí Áðèëëþýíà è ýëåêòðîííûå
ñîñòîÿíèÿ â êðèñòàëëàõ. — Ì., Ìèð, 2000. — 564 ñ.
4. Ìåíòêîâñêèé Þ. Ë. ×àñòèöà â ÿäåðíî-êóëîíîâñêîì
ïîëå. — Ì., Íàóêà, 2002. — 216 ñ.
5. Áîãîëþáîâ Í. Í., Øèðêîâ Ä. Â. Ââåäåíèå â òåîðèþ
êâàíòîâàííûõ ïîëåé. — Ì., 2001. — 442 ñ.
6. Àâäîí³í Ê. Â., Êëèìåíêî À. Ï., Ëàïøèí Â. Ô., Â. Ê.
Ìàêñèìîâ Â. Ê. Åëåêòðîíí³ ÿâèùà ïåðåíîñó â øàð³
óëüòðàäèñïåðñíîãî äèôîñô³äó êàäì³ÿ // Òåçè äîïîâ³äåé
XXII íàóêîâî¿ êîíôåðåíö³¿ êðà¿í ÑÍÄ “Äèñïåðñí³
ñèñòåìè”, Îäåñà, 2006., Ñ.25 — 26.
7. Êîñòûë¸â Ñ. À., Øêóò Â. À. Ýëåêòðîííîå ïåðåêëþ÷åíèå â àìîðôíûõ ïîëóïðîâîäíèêàõ. — Ê., Íàóêîâà äóìêà, 1999. — 204
ñ.
UDC.539.125.5
K. V. Avdonin
BUILD-UP OF WAVE FUNCTIONS OF THE PARTICLE IN THE MODELLING PERIODIC FIELD
Abstract
A movement pattern of charged free particles inside of a crystal is proposed in this work. Effective potential field of interaction
between particles and crystal lattice point is considered in two presentations: as three-dimensional Fourier series and as the presentation
of effective field, in which its periodicity is made by Heviside’s function. Wave functions are found by composition of individual solutions
of Schrödinger equation in the form of functional series. A possibility of existence of energy levels of foreign particle’s condition in
crystal appropriate to them is researched.
Key words: individual solutions, periodic field.
ÓÄÊ.539.125.5
Ê. Â. Àâäîíèí
ÏÎÑÒÐÎÅÍÈÅ ÂÎËÍÎÂÛÕ ÔÓÍÊÖÈÉ ×ÀÑÒÈÖÛ Â ÌÎÄÅËÜÍÎÌ ÏÅÐÈÎÄÈ×ÅÑÊÎÌ ÏÎËÅ
Ðåçþìå
 äàííîé ðàáîòå ðàññìàòðèâàåòñÿ äâèæåíèå ÷àñòèöû â ìîäåëüíîì ïåðèîäè÷åñêîì ïîëå, êîòîðîå ðàññìàòðèâàåòñÿ â òðàäèöèîííîì
âèäå, òî åñòü â ïðåäñòàâëåíèè ðÿäà Ôóðüå, è â òàêîì ïðåäñòàâëåíèè, â êîòîðîì åãî ïåðèîäè÷íîñòü ñîçäà¸òñÿ ôóíêöèÿìè
Õåâèñàéäà. Ðàññìîòðåíà âîçìîæíîñòü íàõîæäåíèÿ âîëíîâûõ ôóíêöèé ÷àñòèöû ïóò¸ì ïîñòðîåíèÿ ÷àñòíûõ ðåøåíèé
êëàññè÷åñêîãî âîëíîâîãî óðàâíåíèÿ â âèäå ôóíêöèîíàëüíûõ ðÿäîâ.
Êëþ÷åâûå ñëîâà: âîëíîâûå ôóíêöèè, ìîäåëüíîå ïåðèîäè÷åñêîå ïîëå.
ÓÄÊ.539.125.5
Ê. Â. Àâäîí³í
ÏÎÁÓÄÎÂÀ ÕÂÈËÜÎÂÈÕ ÔÓÍÊÖ²É ÄËß ×ÀÑÒÈÍÊÈ Ó ÌÎÄÅËÜÍÎÌÓ ÏÅвÎÄÈ×ÍÎÌÓ ÏÎ˲
Ðåçþìå
 äàí³é ðîáîò³ ðîçãëÿäàºòüñÿ ðóõ çàðÿäæåíî¿ ÷àñòèíêè ó ìîäåëüíîìó ïåð³îäè÷íîìó ïîë³, ÿêå ïðåäñòàâëåíå ó òðàäèö³éíîìó
âèãëÿä³, òîáòî ó âèãëÿä³ ðÿäó Ôóð’º, òà ó òàêîìó ïðåäñòàâëåíí³, â ÿêîìó éîãî ïåð³îäè÷í³ñòü ñòâîðþºòüñÿ ôóíêö³ÿìè Õåâ³ñàéäà.
Ðîçãëÿíóòà ìîæëèâ³ñòü çíàõîäæåííÿ õâèëüîâèõ ôóíêö³é ÷àñòèíêè ó ìîäåëüíîìó ïîë³ øëÿõîì ïîáóäîâè ÷àñòèííèõ
ðîçâ’ÿçê³â êëàñè÷íîãî õâèëüîâîãî ð³âíÿííÿ ó âèãëÿä³ ôóíêö³îíàëüíèõ ðÿä³â.
Êëþ÷îâ³ ñëîâà: õâèëüîâ³ ôóíêö³¿, ìîäåëüíå ïåð³îäè÷íå ïîëå.

UDC 621.315.59
V. A. ZAVADSKY, G. S. POPIK
Odessa National Maritime Academy, 8, Didrikhsona, Odessa, Ukraine.
e-mail: vaaz@ukr.net
MODIFICATION OF PARAMETERS IR-FOTODETECTORS BY HIGH-
ENERGY PARTICLES
Irradiation influence by high-energy particles, by γ-quantums and fast electrons on parameters
of IR-photodetectors on the basis of triple semi-conductor compound cadmium-mercury-tellurium
(CMT) is investigated.
Radiating firmness and modification possibility electro- and photo-electric parameters are investigated:
the Hall constant, photosensitivity, dark resistance and current of photoconductive cell by
CMT.
INTRODUCTION
The development and prospective trends of solid
state electronics are concerned with mulicomponent
single and polycrystalline materials. Mulicomponent
materials can be prepared as blocks and films
with different thickness. CdHgTe is one of above
mentioned materials. The most useful application of
CdHgTe is fabrication of IR- detectors, what forms
the base of optoelectronics. This material is also
prospective compound for fabrication of semiconductor
image signal devices and charge connection
devices [1].
Electrical properties of CdHgTe are affected by
biographic point defects (vacancies, complexes, and
interstate atoms), longing (dislocations, grain boundaries,
metal inclusions) and non desirable admixtures.
Because of strong interactions and non ideal control
all defect parameters CdHgTe has great deviation of
properties. At the same time, the devices, based on
CdHgTe, have non stable parameters what decreases
their reliability and working time.
Mulicomponent materials can be prepared as
blocks and films with different thickness. The fabrication
methods, their electrical and structural properties
have been deeply studied. The applications of
mulicomponent materials in quantum and nano electronics,
optoelectronics and electro technique have
also been worked out. However, radiation physics and
technology of mulicomponent materials are under the
level of their practical applications.
EXPERIMENTAL
Investigation of n-type Cd x Hg 1-x Te solid state solutions
treated by electron and γ-radiation showed
that Hall’s mobility and resistivity temperature dependences
didn’t change at 77-300 Ê after irradiation with
electrons, having enegry 4,5 ÌeV on linear accelerator
with intensity 10 12 cm -2 with streams 10 15 — 5∙10 16
cm -2 . Treatment with γ-radiation from Co 60 source
with doze of 10 6 — 10 7 rentgen led to binding of the
Hall’s mobility curve at 100-110 Ê. Additional irra-
© V. A. Zavadsky, G. S. Popik, 2009
diation shifted the binding to the higher temperature
range.
The objects of research were IR-photresistors
based on single crystalline CdHgTe. Taking in account
the quality of bulk single crystals on structural parameters
(dislocation density, Hg vacancy concentration)
and conductivity (charge carriers concentration, their
mobility) is better than the quality of epitaxial layers,
bulk n-type single crystals with x=0,2 have been chosen
for photo resistor fabrication [2].
The source of high energy electrons (3,5 MeV)
was linear accelerator Electronica ELA-4. Integral
electrons stream was calculated according to [2]:
Ô = 6,2∙1012I t ý
where I — current of high energy electrons stream,
ý
μÀ, t — exposition time, sec.
The treatment profile has been chosen with restriction
of samples heating up to 600Ñ. The investigation of γ-radiation influence to Cd-
HgTe lattice constant resulted to conclusion that the
most radiative stable compound is the one with the
lowest Hg vacancy concentration, i.e. having Hg limit
of homogeniousity [3].
Investigation of natural and radiative ageing of
CdHgTe epitaxial layers (by means of Hall’s mobility
temperature dependence measurements) showed
that the maximum of this dependence enhanced and
shifted to higher temperatures for samples, naturally
aged for 1,5 years (fig.1) [4].
Treatment with 3,6 . 108 rentgen γ-radiation
changed the material properties in a such way that
in 7 hour of ageing after irradiation the maximum of
R (1/T) shifted to lower temperatures and in 30 hours
x
it position was almost constant (fig.2). Ageing of the
irradiated samples during 1-7 days entailed with decreasing
resistivity and deterioration of photo electrical
parameters (fig.3) [4].
Under investigation of non stability and hysteretic
phenomena in MOS structures based on CdHgTe
it was found that the change of their characteristics
is tailored by the oxide-semiconductor interface and
neighbor regions where surface states and traps in
semiconductor band gap are located [5].
147

148
Rx, cm 3 , C -1
Fig. 1. Temperature dependence of R x epitaxial layers CdHgTe
[4]: 1 — before ageing; 2 — after ageing during 1,5 years
Rx, cm 3 , C -1
Fig. 2. Temperature dependence of R x for epitaxial layers after
3,6 . 10 8 rentgen irradiation with γ-radiation [4]: 1- before irradiation;
2 — in 7 hours after iradiation; 3 — in 31 hours after iradiation;
4 — in 55 hours after iradiation ÷åðåç
Fig. 3. Phot response of the samples befor and after 3,6 . 10 8
rentgen irradiation with γ-radiation: 1 — before irradiation; 2 — in
1 day; 3 — in 2 days; 4 — in 7 days
RESULTS AND DISCUSSION
The influence of high energy electrons (25 ÌeV)
on electro physical properties of n and p-type Cd Hg x 1-
Te (x = 0,2) has been investigated. Irradiation of pxtype
samples with 1019 m-2 stream resulted in inversion
point shift to lower temperatures approximately to
10 0C what points to the increase of donor concentration.
The n-type samples with initial concentration
of charge carriers 2∙1021 m-3 have been exposed
consequently to 1019 è 1020 m-2 at 77 K. Annealing
was observed at room temperature. It was found that
with increase of irradiation doze electron concentration
increased and resistivity decreased. The mobility
decreased at the initial point but it increased starting
with stream 1019 m-2 . The charge carrier concentration
increased proportionally to square root from electron
stream. The annealing at room temperature pointed to
the fact that charge carrier concentration changed exponentially
with time, i.e. according to the first order
reaction [8, 9].
The irradiation of the same samples with stream
3∙1019 m-2 showed that electro physical parameters of
the samples have not been changed up to stream 1019 m-2 as in the first case, but then the charge carrier
concentration sharply increased. It says about thermal
stability of some defects, formed under irradiation.
The Hall’s constant increased after 15 hours annealing.
Its temperature dependence pointed to the
presence of admixture conductance band. Temperature
dependence of charge carrier mobility μ(T) was
also changed, and its decline in low temperature region
pointed to stronger scattering than as for point
defects. The dependence R(T) has not been changed
in 10 days after irradiation whereas admixture conductance
band disappeared. Next changes of parameters
at room temperature have not been found, so additional
20 minutes annealing in vacuum at 100 and
1500Ñ has been performed. After that charge carrier
concentration was restored and the mobility restored
partially [8].
Under irradiation of Cd Hg Te with low en-
0,2 0,8
ergy radiation Frenkel’s pair formation is the post
possible process. The initial defect structure restored
immediately because of Frenkel’s pairs after
the irradiation off. Their concentration is compared
with interstate Hg atoms concentration, what can
be recognized as increase of electron concentration.
The structure restore rate is defined by diffusion
coefficient of the most mobile defect (Hg ), which
i
depends on temperature and material structure perfection
[6].
The increase of irradiation stream and temperature
can bring to Frenkel’s pairs concentration growth
and point defect complexes formation. The recombination
of the latest needs higher temperatures.
Investigation of γ-radiation influence on lattice
constant of powder materials (CdHg)Te showed that
the most radioactive stable material is the solution of
those components on Hg — the boundary of homogeneity
region, i.e. with minimal concentration of
Hg vacancies. The change of solid state properties
can be concerned with radioactive defect formation,
similar to high temperature defects. They represent

difficult Te x complexes with concentration, proportional
Hg vacancy concentration. The separation Te x
phase takes place with the increase of Hg vacancy
concentration [7].
It has been studied for photo resistors the modification
of two main parameters dark current I T and
dark resistivity with fast electrons irradiation.
Measurement errors of the above mentioned parameters
of photo resistors were up to ± 5%, with
probability P=0,95. The results of measurements and
calculations are presented in fig.4. Those results show
following statements:
– fast electron irradiation with 10 13 -10 15 cm -2 doze
led to decrease of dark resistivity and increase of dark
current ;
– relative changes of dark resistivity and dark current
bigger at 80 K;
– For doze higher 10 15 cm -2 relative changes of
photo resistors parameters differ little.
Fig. 4. Doze dependence of photo resistor’s dark current (�)
and dark resistivity (�) at 120 K (---) and at 80K (—)
UDC 621.315.59
V. A. Zavadsky, G. S. Popik
CONCLUSION
Irradiation of photo detectors based on CdHgTe
changes their parameters: sensitivity limit (for its enhance
it is necessary to decrease charge carrier concentration
and increase effective quantum efficiency),
recovery time (for its decrease it is worth to decline
charge carrier life time ) and photo resistor spectral
sensitivity range.
References
1. Ëåíêîâ Ñ. Â., Ìîêðèöêèé Â. À., Ãàðêàâåíêî À. Ñ., Çóáàðåâ
Â. Â., Çàâàäñêèé Â. À. Ðàäèàöèîííîå óïðàâëåíèå
ñâîéñòâàìè ìàòåðèàëîâ è èçäåëèé îïòî- è ìèêðîýëåêòðîíèêè.
Ìîíîãðàôèÿ. — Îäåññà: 2003. — 345ñ.
2. Çàâàäñêèé Â. À., Ìàñåíêî Á. Ï. Âëèÿíèå îáëó÷åíèÿ íà
ïàðàìåòðû êðåìíèåâûõ ýëåìåíòîâ/ Â ñá.: Ìîëîäåæü
òðåòüåãî òûñÿ÷åëåòèÿ: ãóìàíèòàðíûå ïðîáëåìû è ïóòè
èõ ðåøåíèÿ. Ñåð. Ýêîíîìèêà, ìîäåëèðîâàíèå òåõíè-
÷åñêèõ è îáùåñòâåííûõ ïðîöåññîâ, èíôîðìàöèîëîãèÿ,
ýêîëîãèÿ. — Îäåññà: 2003. — Ò. Ç. — Ñ. 236-241.
3. Èíäåíáàóì Ã.Â. è äð. Âëèÿíèå îáëó÷åíèÿ ãàììà-êâàíòàìè
íà ïåðèîä ðåøåòêè òâåðäûõ ðàñòâîðîâ Cd Hg Te // Òåç.
x 1-x
äîêë. I Âñåñîþçí. íàó÷í.-òåõí. êîíô. “Ïîëó÷åíèå è ñâîéñòâà
ïîëóïðîâîäíèêîâûõ ñîåäèíåíèé òèïà ÀÏÂYI è AIYBYI è
òâåðäûõ ðàñòâîðîâ íà èõ îñíîâå. — Ì., 1997. — Ñ. 115.
4. Îòðàáîòêà íàó÷íûõ îñíîâ òåõíîëîãèè è ïàðàìåòðîâ
ïðîöåññà ãëóáîêîé î÷èñòêè èñõîäíûõ âåùåñòâ, ñèíòåçà
ñîåäèíåíèé è âûðàùèâàíèÿ ñîâåðøåííûõ ìîíîêðèñòàëëîâ
è ïëåíîê õàëüêîãåíèäîâ è îêèñëîâ òÿæåëûõ
öâåòíûõ ìåòàëëîâ: Îò÷åò î ÍÈÐ (/ Ìîñêîâñêèé èí-ò
ñòàëè è ñïëàâîâ Ðóê. Âàíþêîâ À.Â. — ¹ ÃÐ 77067934;
Èíâ. ¹ Â787041. — Ì., 1999.
5. Ëèòîâ÷åíêî Â.Ã. Òðåõñëîéíàÿ ìîäåëü ñòðóêòóð ïîëóïðîâîäíèê-äèýëåêòðèê
// Ïîëóïðîâîäíèêîâàÿ òåõíèêà è
ìèêðîýëåêòðîíèêà. — 1998. — Âûï. 12. — Ñ. 3-15.
6. Êðåãåð Ô. Õèìèÿ íåñîâåðøåííûõ êðèñòàëëîâ. — Ì.:
Ìèð, 1999. — 218 ñ.
7. Çàèòîâ Ô.À. è äð. Ïîëóïðîâîäíèêè ñ óçêîé çàïðåùåííîé
çîíîé è ïîëóìåòàëëû // Ìàòåðèàëû IY Âñåñîþçíîãî ñèìïîçèóìà.
— Ëüâîâ: Âèùà øêîëà, 1995. — 4.5. — Ñ. 14-17.
8. Çàèòîâ Ô.À., Ìóõèíà Î.Â., Ïîëÿêîâ À.ß. Îáëó÷åíèå
òâåðäîãî ðàñòâîðà CdTe — HgTe ýëåêòðîíàìè ñ ýíåðãèåé
25 ÌýÂ.: Ñá. “Òåõíèêà ðàäèàöèîííîãî ýêñïåðèìåíòà”.
— Ì.: Àòîìèçäàò, 1997. — Âûï. 5. — Ñ. 34.
9. Çàèòîâ Ô.À. è äð. Äåéñòâèå ïðîíèêàþùåé ðàäèàöèè íà
ýëåêòðîôèçè÷åñêèå ïàðàìåòðû ïîëóïðîâîäíèêîâîãî
ñïëàâà Cd Hg Te– Ê.: 1996. — 56 ñ. (Ïðåïð. Ðàäèàöè-
x 1-x
îííûå ýôôåêòû â ïîëóïðîâîäíèêîâûõ ñîåäèíåíèÿõ
ÊÈßÈ ÀÍ Óêðàèíû, 76-22).
MODIFICATION OF PARAMETERS IR-FOTODETECTORS BY HIGH-ENERGY PARTICLES
Abstract
Irradiation influence by high-energy particles, by γ-quantums and fast electrons on parameters of IR-photodetectors on the basis
of triple semi-conductor compound cadmium-mercury-tellurium (CMT) is investigated.
Radiating firmness and modification possibility electro- and photo-electric parameters are investigated: the Hall constant, photosensitivity,
dark resistance and current of photoconductive cell by CMT.
Key words: high energy particles, three elements compound, photo resistor, modification of parameters, irradiation influence.
149

150
ÓÄÊ 621.315.59
Â. À. Çàâàäñêèé, Ã. Ñ. Ïîïèê
ÌÎÄÈÔÈÊÀÖÈß ÏÀÐÀÌÅÒÐΠÈÊ-ÔÎÒÎÏÐÈÅÌÍÈÊΠÂÛÑÎÊÎÝÍÅÐÃÅÒÈ×ÅÑÊÈÌÈ ×ÀÑÒÈÖÀÌÈ
Ðåçþìå
Èññëåäîâàíî âëèÿíèå îáëó÷åíèÿ âûñîêîýíåðãåòè÷åñêèìè ÷àñòèöàìè, γ-êâàíòàìè è áûñòðûìè ýëåêòðîíàìè íà ïàðàìåòðû
ÈÊ-ôîòîïðèåìíèêîâ íà îñíîâå òðîéíîãî ïîëóïðîâîäíèêîâîãî ñîåäèíåíèÿ êàäìèé-ðòóòü-òåëëóð (ÊÐÒ).
Èññëåäîâàíû ðàäèàöèîííàÿ ñòîéêîñòü è âîçìîæíîñòü ìîäèôèêàöèè ýëåêòðî- è ôîòîýëåêòðè÷åñêèõ ïàðàìåòðîâ: ïîñòîÿííîé
Õîëëà, ôîòî÷óâñòâèòåëüíîñòè, òåìíîâûõ ñîïðîòèâëåíèé è òîêà ôîòîðåçèñòîðîâ íà ÊÐÒ.
Êëþ÷åâûå ñëîâà: âûñîêîýíåðãåòè÷åñêèå ÷àñòèöû, òðîéíîå ñîåäèíåíèå, ôîòîðåçèñòîð, ìîäèôèêàöèÿ ïàðàìåòðîâ, âëèÿíèå
îáëó÷åíèÿ.
ÓÄÊ 621.315.59
Â. À. Çàâàäñüêèé, Ã. Ñ. Ïîï³ê
ÌÎÄÈÔ²ÊÀÖ²ß ÏÀÐÀÌÅÒв ²×-ÔÎÒÎÏÐÈÉÌÀײ ÂÈÑÎÊÎÅÍÅÐÃÅÒÈ×ÍÈÌÈ ×ÀÑÒÊÀÌÈ
Ðåçþìå
Äîñë³äæåíî âïëèâ îïðîì³íåííÿ âèñîêîåíåðãåòè÷íèìè ÷àñòêàìè, γ-êâàíòàìè òà øâèäêèìè åëåêòðîíàìè íà ïàðàìåòðè
²×-ôîòîïðèéìà÷³â íà îñíîâ³ ïîòð³éíîãî íàï³âïðîâ³äíèêîâîãî ç’ºäíàííÿ êàäì³é-ðòóòü-òåëóð (ÊÐÒ).
Äîñë³äæåíà ðàä³àö³éíà ñò³éê³ñòü ³ ìîæëèâ³ñòü ìîäèô³êàö³¿ åëåêòðî- òà ôîòîåëåêòðè÷íèõ ïàðàìåòð³â: ïîñò³éíî¿ Õîëëà,
ôîòî÷óòëèâîñò³, òåìíîâèõ îïîð³â ³ ñòðóìó ôîòîðåçèñòîð³â íà ÊÐÒ.
Êëþ÷îâ³ ñëîâà: âèñîêîåíåðãåòè÷í³ ÷àñòèíêè, ïîòð³éíå ç’ºäíàííÿ, ôîòîðåçèñòîð, ìîäèô³êàö³ÿ ïàðàìåòð³â, âïëèâ îïðîì³íåííÿ.

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íå áóäåò óêàçàí íè îäèí øèôð, ðåäàêöèÿ æóðíàëà
óñòàíàâëèâàåò øèôð ñòàòüè ïî ñâîåìó âûáîðó.
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ïî÷òû äëÿ êàæäîãî èç àâòîðîâ.
4. Íàçâàíèå ñòàòüè.
151

5. Ðåçþìå îáúåìîì äî 200 ñëîâ ïèøåòñÿ íà àíãëèéñêîì,
ðóññêîì ÿçûêàõ è (äëÿ àâòîðîâ èç Óêðàèíû)
— íà óêðàèíñêîì.
Òåêñò äîëæåí ïå÷àòàòüñÿ øðèôòîì 14 ïóíêòîâ
÷åðåç äâà èíòåðâàëà íà áåëîé áóìàãå ôîðìàòà À4.
Íàçâàíèå ñòàòüè, à òàêæå çàãîëîâêè ïîäðàçäåëîâ
ïå÷àòàþòñÿ ïðîïèñíûìè áóêâàìè è îòìå÷àþòñÿ
ïîëóæèðíûì øðèôòîì.
Óðàâíåíèÿ íåîáõîäèìî ïå÷àòàòü â ðåäàêòîðå
ôîðìóë MS Equation Editor. Íåîáõîäèìî äàâàòü
îïðåäåëåíèå âåëè÷èí, êîòîðûå ïîÿâëÿþòñÿ â òåêñòå
âïåðâûå.
Òàáëèöû ïîäàþòñÿ íà îòäåëüíûõ ñòðàíèöàõ.
Äîëæíû áûòü âûïîëíåíû â ñîîòâåòñòâóþùèõ
òàáëè÷íûõ ðåäàêòîðàõ èëè ïðåäñòàâëåíû â òåêñòîâîì
âèäå ñ èñïîëüçîâàíèåì ðàçäåëèòåëåé (òî÷êà,
çàïÿòàÿ, çàïÿòàÿ ñ òî÷êîé, çíàê òàáóëÿöèè).
Ññûëêè íà ëèòåðàòóðó äîëæíû ïå÷àòàòüñÿ
÷åðåç äâà èíòåðâàëà, íóìåðîâàòüñÿ â êâàäðàòíûõ
ñêîáêàõ (â íîðìàëüíîì ïîëîæåíèè) ïîñëåäîâàòåëüíî,
â ïîðÿäêå èõ ïîÿâëåíèÿ â òåêñòå ñòàòüè.
Ññûëàòüñÿ íåîáõîäèìî íà ëèòåðàòóðó, êîòîðàÿ èçäàíà
ïîçäíåå 2000 ãîäà. Äëÿ ññûëîê èñïîëüçóþòñÿ
ñëåäóþùèå ôîðìàòû:
Êíèãè. Àâòîð(û) (èíèöèàëû, ïîòîì ôàìèëèè),
íàçâàíèå êíèãè êóðñèâîì, èçäàòåëüñòâî, ãîðîä
è ãîä èçäàíèÿ. (Ïðè ññûëêå íà ãëàâó êíèãè, óêàçûâàåòñÿ
íàçâàíèå ãëàâû, íàçâàíèå êíèãè êóðñèâîì,
íîìåðà ñòðàíèö). Ïðèìåð, J. A. Hall, Imaging
tubes, Chap 14 ø The Infrared Handbook, Eds W. W.
 æóðíàë³ “Ôîòîåëåêòðîí³êà” äðóêóþòüñÿ
ñòàòò³ òà êîðîòê³, ÿê³ ì³ñòÿòü â³äîìîñò³ ïðî íàóêîâ³
äîñë³äæåííÿ òà òåõí³÷í³ ðîçðîáêè ó íàïðÿìêàõ:
* ô³çèêà íàï³âïðîâ³äíèê³â;
* ãåòåðî- òà íèçüêîâèì³ðí³ ñòðóêòóðè;
* ô³çèêà ì³êðîåëåêòðîííèõ ïðèëàä³â;
* ë³í³éíà òà íåë³í³éíà îïòèêà òâåðäîãî ò³ëà;
* îïòîåëåêòðîí³êà òà îïòîåëåêòðîíí³ ïðèëàäè;
* êâàíòîâà åëåêòðîí³êà;
* ñåíñîðèêà.
Æóðíàë “Ôîòîåëåêòðîí³êà” âèäàºòüñÿ àíãë³éñüêîþ
ìîâîþ. Ðóêîïèñ ïîäàºòüñÿ àâòîðîì ó
äâîõ ïðèì³ðíèêàõ àíãë³éñüêîþ ìîâîþ. Äî ðóêîïèñó
äîäàºòüñÿ äèñêåòà ç òåêñòîâèì ôàéëîì ³ ìàëþíêàìè
Åëåêòðîííà êîï³ÿ ìàòåð³àëó ìîæå áóòè
íàä³ñëàíà äî ðåäàêö³¿ åëåêòðîííîþ ïîøòîþ.
Åëåêòðîííà êîï³ÿ ñòàòò³ ïîâèííà â³äïîâ³äàòè
íàñòóïíèì âèìîãàì:
1. Åëåêòðîííà êîï³ÿ (àáî äèñêåòà) ìàòåð³àëó
íàäñèëàºòüñÿ îäíî÷àñíî ç òâåðäîþ êîﳺþ òåêñòó
òà ìàëþíê³â.
2. Äëÿ òåêñòó ïðèïóñòèì³ íàñòóïí³ ôîðìàòè —
MS Word (rtf, doc).
3. Ìàëþíêè ïðèéìàþòüñÿ ó ôîðìàòàõ — EPS,
TIFF, BMP, PCX, JPG, GIF, CDR, WMF, MS Word
² MS Giaf, Micro Calc Origin (opj). Ìàëþíêè, âèêîíàí³
ïàêåòàìè ìàòåìàòè÷íî¿ òà ñòàòèñòè÷íî¿
152
²ÍÔÎÐÌÀÖ²ß ÄËß ÀÂÒÎвÂ
ÇÁ²ÐÍÈÊÀ “ÔÎÒÎÅËÅÊÒÐÎͲÊÀ”
Wolfe, Î J’ Zissis. pp. 132-176, ERIM, Arm Arbor, MI
(1978).
Æóðíàëû. Àâòîð(û) (èíèöèàëû, ïîòîì ôàìèëèè),
íàçâàíèå ñòàòüè, íàçâàíèå æóðíàëà êóðñèâîì
(èñïîëüçóþòñÿ àááðåâèàòóðû òîëüêî äëÿ èçâåñòíûõ
æóðíàëîâ), íîìåð òîìà è âûïóñêà, íîìåð
ñòðàíèö è ãîä èçäàíèÿ. Ïðèìåð, N. Blutzer and
A. S. Jensen, Current readout of infrared detectors //
Opt Eng 26(3), pp. 241-248.
Ïîäïèñè ê ðèñóíêàì è òàáëèöàì ïå÷àòàþòñÿ â
ðóêîïèñè ïîñëå ëèòåðàòóðíûõ ññûëîê ÷åðåç äâà
èíòåðâàëà.
Èëëþñòðàöèè áóäóò ñêàíèðîâàòüñÿ öèôðîâûì
ñêàíåðîì. Ïðèíèìàþòñÿ â ïå÷àòü òîëüêî âûñîêîêà÷åñòâåííûå
èëëþñòðàöèè. Ïîäïèñè è ñèìâîëû
äîëæíû áûòü âïå÷àòàíû. Íå ïðèíèìàþòñÿ â ïå-
÷àòü íåãàòèâû, ñëàéäû, òðàíñïîðàíòû.
Ðèñóíêè äîëæíû èìåòü ñîîòâåòñòâóþùèé ê
ôîðìàòó æóðíàëà ðàçìåð — íå áîëüøå 160x200 ìì.
Òåêñò íà ðèñóíêàõ äîëæåí âûïîëíÿòüñÿ øðèôòîì
12 ïóíêòîâ. Íà ãðàôèêàõ åäèíèöû èçìåðåíèÿ
óêàçûâàþòñÿ ÷åðåç çàïÿòóþ (à íå â ñêîáêàõ). Âñå
ðèñóíêè (èëëþñòðàöèè) íóìåðóþòñÿ â ïîðÿäêå èõ
ðàçìåùåíèÿ â òåêñòå. Íå äîïóñêàåòñÿ âíîñèòü íîìåð
è ïîäïèñü íåïîñðåäñòâåííî íà ðèñóíêàõ.
Ðåçþìå îáúåìîì äî 200 ñëîâ ïèøåòñÿ íà àíãëèéñêîì,
ðóññêîì ÿçûêàõ è íà óêðàèíñêîì (äëÿ
àâòîðîâ èç Óêðàèíû). Ïåðåä òåêñòîì ðåçþìå ñîîòâåòñòâóþùèì
ÿçûêîì óêàçûâàþòñÿ ÓÄÊ, ôàìèëèè
è èíèöèàëû âñåõ àâòîðîâ, íàçâàíèå ñòàòüè.
îáðîáêè ïîâèíí³ áóòè êîíâåðòîâàí³ ó âèùåâêàçàí³
ãðàô³÷í³ ôîðìàòè ³ ðîçòàøîâàí³ ó òåêñò³ ñòàòò³,
çã³äíî çì³ñòó.
Ðóêîïèñè íàäñèëàþòüñÿ íà àäðåñó:
³äï. ñåêð. Êóòàëîâ³é Ì. ²., âóë. Ïàñòåðà, 42,
ô³ç. ôàê. ÎÍÓ, ì.Îäåñà, 65026 Å-mail: wadz@mail.
ru, òåë. 0482-266356.
Äî ðóêîïèñó äîäàºòüñÿ:
1. Êîäè ÐÀÑ òà ÓÄÊ. Äîïóñêàºòüñÿ âèêîðèñòàííÿ
äåê³ëüêîõ øèôð³â, ùî ðîçä³ëÿþòüñÿ êîìîþ.
Ó âèïàäêó, êîëè àâòîðîì (àâòîðàìè) íå áóäå
âêàçàíî æîäåí øèôð, ðåäàêö³ÿ æóðíàëó âñòàíîâëþº
øèôð ñòàòò³ çà ñâî¿ì âèáîðîì.
2. Ïð³çâèùå òà ³í³ö³àëè àâòîðà.
3 Óñòàíîâà, ïîâíà ïîøòîâà àäðåñà, íîìåð òåëåôîíó,
íîìåð ôàêñó, àäðåñà åëåêòðîííî¿ ïîøòè
äëÿ êîæíîãî ç àâòîð³â.
4. Íàçâà ñòàòò³.
Ðåçþìå îá’ºìîì äî 200 ñë³â ïèøåòüñÿ àíãë³éñüêîþ,
óêðà¿íñüêîþ òà ðîñ³éñüêîþ ìîâàìè. Ïåðåä
òåêñòîì ðåçþìå â³äïîâ³äíîþ ìîâîþ âêàçóþòüñÿ
êîä, íàçâà ñòàòò³, ïð³çâèùà òà ³í³ö³àëè âñ³õ àâòîð³â.
Òåêñò ïîâèíåí äðóêóâàòèñÿ øðèôòîì 12 ïóíêò³â
÷åðåç äâà ³íòåðâàëè íà á³ëîìó ïàïåð³ ôîðìàòó
À4. Íàçâà ñòàòò³, à òàêîæ çàãîëîâêè ï³äðîçä³ë³â
äðóêóþòüñÿ ïðîïèñíèìè ë³òåðàìè ³ â³äçíà÷àþòüñÿ
íàï³âæèðíèì øðèôòîì.

гâíÿííÿ íåîáõ³äíî äðóêóâàòè ó ðåäàêòîð³
ôîðìóë MS Equation Editor. Íåîáõ³äíî äàâàòè
âèçíà÷åííÿ âåëè÷èí, ùî ç’ÿâëÿþòüñÿ â òåêñò³
âïåðøå.
Òàáëèö³ ïîäàþòüñÿ íà îêðåìèõ ñòîð³íêàõ. Ïîâèíí³
áóòè âèêîíàí³ ó â³äïîâ³äíèõ òàáëè÷íèõ ðåäàêòîðàõ
àáî ïðåäñòàâëåí³ ó òåêñòîâîìó âèãëÿä³ ç
âèêîðèñòàííÿì ðîçä³ëüíèê³â (êðàïêà, êîìà, êîìà
ç êðàïêîþ, çíàê òàáóëÿö³¿).
Ïîñèëàííÿ íà ë³òåðàòóðó ïîâèíí³ äðóêóâàòèñÿ
÷åðåç äâà ³íòåðâàëè, íóìåðóâàòèñü â êâàäðàòíèõ
äóæêàõ (ó íîðìàëüíîìó ïîëîæåíí³) ïîñë³äîâíî ó
ïîðÿäêó ¿õ ïîÿâè â òåêñò³ ñòàòò³.
Êíèãè. Àâòîð(è) (³í³ö³àëè, ïîò³ì ïð³çâèùà),
íàçâà êíèãè êóðñèâîì, âèäàâíèöòâî, ì³ñòî ³ ð³ê âèäàííÿ.
(Ïðè ïîñèëàíí³ íà ãëàâó êíèãè, âêàçóºòüñÿ
íàçâà ãëàâè, íàçâà êíèãè êóðñèâîì, íîìåðè ñòîð³íîê).
Ïðèêëàä: J. A. Hall, Imaging tubes, Chap 14 ø
The Infrared Handbook, Eds W. W. Wolfe, Î J’ Zissis.
pp. 132-176, ERIM, Arm Arbor, MI (1978).
Æóðíàëè ( ×àñîïèñè). Àâòîð(è) (³í³ö³àëè, ïîò³ì
ïð³çâèùà), íàçâà ñòàòò³, íàçâà æóðíàëó êóðñèâîì
(âèêîðèñòîâóþòüñÿ àáðåâ³àòóðè ò³ëüêè äëÿ
â³äîìèõ æóðíàë³â), íîìåð òîìó ³ âèïóñêó, íîìåð
ñòîð³íîê ³ ð³ê âèäàííÿ. Ïðèêëàä: N. Blutzer and
A. S. Jensen, Current readout of infrared detectors //
Opt Eng 26(3), pp. 241-248 (1987).
²ëþñòðàö³¿ áóäóòü ñêàíóâàòèñÿ öèôðîâèì ñêàíåðîì.
Ïðèéìàþòüñÿ äî äðóêó ò³ëüêè âèñîêîÿê³ñí³
³ëþñòðàö³¿. ϳäïèñè ³ ñèìâîëè ïîâèíí³ áóòè
âäðóêîâàí³. Íå ïðèéìàþòüñÿ äî äðóêó íåãàòèâè,
ñëàéäè, òðàíñïàðàíòè.
Ðèñóíêè ïîâèíí³ ìàòè â³äïîâ³äíèé äî ôîðìàòó
æóðíàëó ðîçì³ð íå á³ëüøå 160x200 ìì. Òåêñò
íà ðèñóíêàõ ïîâèíåí âèêîíóâàòèñü øðèôòîì
10 ïóíêò³â. Íà ãðàô³êàõ îäèíèö³ âèì³ðó âêàçóþòüñÿ
÷åðåç êîìó (à íå â äóæêàõ). Óñ³ ðèñóíêè (³ëþñòðàö³¿)
íóìåðóþòüñÿ â ïîðÿäêó ¿õ ðîçì³ùåííÿ â
òåêñò³. Ðåêîìåíäîâàíî ïîñèëàòèñü íà ë³òåðàòóðó,
ÿêà íàäðóêîâàíà ç 2000 ïî 2009 ð³ê.
153

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̳æâóç³âñüêèé íàóêîâèé çá³ðíèê
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¹ 18’2009
Àíãë³éñüêîþ ìîâîþ
Ãîëîâíèé ðåäàêòîð Â. À. Ñìèíòèíà
³äïîâ³äàëüíèé ñåêðåòàð Ì. ². Êóòàëîâà
Çäàíî ó âèðîáíèöòâî 26.06.2009. ϳäïèñàíî äî äðóêó 17.08.2009.
Ôîðìàò 60õ84/8. Ïàï³ð îôñåòíèé. Ãàðí³òóðà «Newton». Äðóê îôñåòíèé.
Óì. äðóê. àðê. 17,90. Òèðàæ 100 ïðèì. Çàì. ¹ 324.
Âèäàâíèöòâî ³ äðóêàðíÿ «Àñòðîïðèíò»
65091, ì. Îäåñà, âóë. Ðàçóìîâñüêà, 21
Òåë.: (0482) 37-07-95, 37-24-26, 33-07-17, 37-14-25
www.astroprint.odessa.ua; www.fotoalbom-odessa.com
Ñâ³äîöòâî ñóá’ºêòà âèäàâíè÷î¿ ñïðàâè ÄÊ ¹ 1373 â³ä 28.05.2003 ð.