V - Positron Annihilation in Halle

Defect Characterization in Crystalline y Solids 

R. Krause-Rehberg 

Univ. Halle 

• Why are nano-defects important at all? 

• Defects in metals and semiconductors 

• Positron beam applications 

Martin-Luther-Universität RK 

Halle 

R

Point defects determine properties of materials 

Galliumphosphide 

• Point defects determine 

electronic and optical 

properties 

without vacancies with 00.001% 001% vacancies 

• electric conductivity 

strongly influenced 

transparent opaque 

1 vacancy in 100000 atoms 

• Point defects are generated by irradiation, by plastic deformation or by 

diffusion, … 

• Metals in high radiation environment -> > formation of voids -> > embrittlement 

• -> Properties of vacancies and other point defects must be known 

• Analytical tools are needed to characterize point defects 

Martin-Luther-Universität Halle 

1 cm

• Vacancy concentration in 

thermal equilibrium: 

• in metals H F 1...4 eV 

at T m [1v] 10 -4...-3 /atom 

• fits well to the sensitivity 

range of positron annihilation 

(Ziegler, 1979) 


Vacancies in thermal Equilibrium 

meter 

W param 

Tungsten 

H F = (4.0 0.3) eV 

temperature (K) 

fit to trapping model

Defects in Iron after tensile strength and fatigue treatment 

• extensive i study d of f defects d f in i mechanically h i ll ddamaged d i iron and d steel l 

• Positrons are very sensitive: detection of defects already in the Hooks range of the 

stress-strain experiment 

• Vacancy cluster and dislocations are detectable in both cases 


Somieski et al., J. Physique IV 5, C1/127-134 (1995)

Defects in electron-irradiated electron irradiated Ge 

• Electron irradiation (2 MeV @ 4K) induces Frenkel pairs (vacancy - interstitial pairs) 

• steep annealing stage at 200 K 

• at high irradiation dose: divacancies are formed (thermally stable up to 400 K) 

(Polity et al., 1997) 


GGe 

e - irr. at 4K

Electron irradiation of Si 

• low-temperature electron irradiation 

was performed at 4K (Ee-=2 MeV) 

• annealing stage of monovacancies at 

about 170 K 

• moving V Si partly form divacancies 

• divacancies anneal at about 550…650 K 


PPolity lit et t al., l Ph Phys. RRev. B 58 (1998) 10363

GaAs: annealing under defined As As-partial partial pressure 

• two-zone-furnace: Control of sample 

temperature and As partial pressure 

allows to navigate freely in phase 

diagram (existence area of compound) 

• Measurements near equilibrium after 

quenching of samples 

T Tsample: l : 1100 1100° C T d t i A H W l t l J C t G th 109 191 (1991) 

As: determines Aspartial 

pressure 


H. Wenzl et al., J. Cryst. Growth 109, 191 (1991).

ation (cm -3 Vacanccy 

concentra ) 

10 17 

GaAs: Annealing under defined As pressure 

Si Ga-V Ga 

GaAs:Si 

Linear fit 

001 0,01 01 0,1 1 10 

Arsenic pressure (bar) 

Thermodynamic reaction: 

1/4 As gas 

4 ↔ AsAs As As + V Ga 

Mass action law: 

[V [VG ] = KVG × p 1/4 

Ga] KVG × pAAs Martin-Luther-Universität Halle 

tration (cm ) 

-3 Vacanncy 

concent ) 

10 18 

10 17 

10 

10 16 

-3 

[T [Te] ] in i cm -3 

6x10 18 

2x10 18 

17 

4x10 17 

9x10 16 

GaAs:Te 

Te As-V Ga 

0,1 1 10 

Arsenic pressure (bar) 

Fit: [V Ga-Dopant] ~ p As n 

→ n = 1/4 

250 

245 

240 

235 

231 

K (ps) 

τ at 550 K 

av 

J. Gebauer et al., 

Physica y B 273-274, 705 (1999) ( )

Comparison of doped and undoped GaAs 

Bondarenko et al., 2003 


Thermodynamic y reaction: 

As As ↔ VAs + 1/4As gas 

4 

Mass action law: 

[V As] = K VAs × p As -1/4 

Fit: [V-complex] [V complex] ~ p n 

As 

→ n = -1/4 

undoped GaAs: As vacancy

Vacancy clusters in semiconductors 

• vacancy clusters were observed after ion/neutron irradiation, ion 

implantation and plastic deformation 

• due to lar large e open volume (low electron density) -> > positron lifetime 

increases distinctly 

• example: plastically deformed Ge 

• lifetime: τ = 525 ps 

• reason for void formation: jog 

dragging mechanism 

• trapping rate of voids disappears 

during annealing experiment 


Krause-Rehberg et al., 1993

Theoretical Calculation of Vacancy Clusters in Si 


• there are cluster configurations 

with a large energy gain 

• „Magic Magic Numbers“ Numbers with 6, 6 10 und 

14 vacancies 

• positron lifetime increases 

distinctly with cluster size 

• for n > 10 saturation effect, i.e. 

size cannot be determined 

T.E.M. Staab et al., 

Physica B 273-274 (1999) 501-504

Height H [nm] ] 

02 0.2 

0.1 

0.0 

Identification of V VGa Ga-Si SiGa Ga-Complexes Complexes in GaAs:Si 

occupied empty states 

-2.0 V +1.4 V 

1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 

lattice spacing in [110] direction 

• Scanning tunneling microscopy at GaAs (110)- 

cleavages l planes l (by (b Ph Ph. Ebert, Eb t Jülich) Jüli h) 

• Defect complex identified as VGa-SiGa Martin-Luther-Universität Halle 

cm -3 Defect 

conceentration 

(c ) 

10 19 

10 19 

10 18 

10 17 

10 18 

Positrons - c vac 

STM - [Si Ga -V Ga ] 

10 19 

Si concentration (cm -3 ) 

• Quantification → Agreement 

Mono-Vacancies in GaAs:Si are V Ga- Si Ga-complexes 

Gebauer et al., Phys. Rev. Lett. 78 (1997) 3334

Defects after high energy Si self self-implantation 

implantation -the the Rp/2 Effect 

on (cm -3 Cu conncentratio 

) 

• After high-energy self-implantation of Si (3.5 MeV; 5 ×10 

2 15 cm -2 ) and RTA (900°C, 30s): two 

new getter zones appear at Rp and Rp /2 (Rp = projected range of Si + ) 

• Zones become visible after Cu in-diffusion from rear side of sample (Cu implantation and 

diffusion annealing at 600°C) 

10 17 

10 16 

TEM image by P. Werner, MPI Halle 

SIMS 

10 

0 1 2 3 4 

15 


R p/2 

DDepth th( (μm) 

) 

R p 

• at Rp : gettering by interstitial type 

dislocation loops 

• Formed due to interstial excess Si after 

iimplantation l t ti and dRTA RTA annealing li 

• Although gettering appears, no defects 

visible by TEM at Rp /2 

• What is the nature of these defects?

positron 

lifetime (pss) 

Improved depth resolution by using a positron microbeam 

τ defect 

τ bulk 

positron 

microbeam 

E = 8 keV 

• We used Munich positron 

microscope p 

• Sample polished wedge-like 

scan direction (wedge angle 0.5…2°) 

• Defect depth profile of 10 µm 

μ 

α = 0.6° lateral resolution 

1 ... 2 μm 

becomes as long as 1 mm 

• Thus, depth resolution con be 

optimized by wedge angle 

defect depth 

10 m 


0 1 mm 

scan width

First defect-depth defect depth profile using a 

0,6 

positron microprobe 

0,4 

• 45 lifetime spectra were recorded along 

wedge d 

• Because of beam diameter - depth resolution 

of 155 nm is obtained at α = 0.81° 

• Positron implantation energy: 8 keV ⇒ mean 

information depth 400 nm 

• OOptimum i ddepth h resolution l i 

• Both defected regions well visible 

• Vacancy clusters with increasing density 

down to 2 µm (Rp/2 region) 

• At R p region: lifetime τ2 = 330 ps; open 

volume corresponds to a divacancy; must 

be stabilized or being part of dislocation 

loops 

R. Krause-Rehberg et al., Appl. Phys. Lett. 77 (2000) 3932 


η 

τ 2 (ps) 

averagee 

lifetime (ps) ( 

0,8 

450 

400 

350 

380 

360 

340 

320 

300 

260 

0 1 2 3 4 5 6 

microvoids 

R p /2 R p 

fraction of 

trapped positrons 

defect-related 

lifetime 

divacancy-type 

defect 

Silicon self-implantation 

- 3.5 MeV, 5×10 15 cm -2 

- annealed 30s 900°C 

- Cu contaminated 

Cu SIMS-Profil 

280 surface bulk silicon 

0 1 2 3 4 5 6 

ddepth th( (µm) )

Diffusion of Cu in GaAs 

280 

• Positron experiment: 

• 30 nm Cu-layer deposited by 

• 

evaporation evapo at o 

Annealing at 1100°C (under defined 

270 

• 

• 

As-pressure) for Cu in-diffusion 

Quenching to RT 

then annealing with growing 

260 

• 

temperature 

Positron lifetime measurement 

250 

• Cu is completely solved at 1100°C 

• But it is oversaturated at RT 

• Precipitation starts very slowly (slow 

diffusion) 

• However: at elevated temperatures – diffusion 

240 

bbecomes faster: f out-diffusion diff i process 

• Result: formation of vacancy-type defects 

when out-diffusion starts 

• Not compatible with ith current c rrent diffusion diff sion models 

230 


averrage 

positrron 

lifetimee 

(ps) 

400 K 

500 K 

550 K 

600 K 

650 K 

700 K 

750 K 

800 K 

850 K 

900 K 

0 100 200 300 400 500 

measurement temperature (K)

Determination of Defect Type 280 

• Formation of these clusters is almost 

independent of doping / conduction type 

• Identical behavior in undoped p GaAs 

• In beginning of defect formation: defectrelated 

lifetime is about 250 ps – a 

monovacancy 

• In course of annealing: lifetime growth to 

averagee 

lifetime (pps) 

defect-relaated 

lifetime (pps) 

270 

260 

250 

240 

230 

500 

450 

400 

350 

300 

320-350 ps corresponding to a divacancy 250 

• at 800 K: τ 2 > 450 ps: rather large vacancy 

clusters (n > 10) 


intensitty 

I2 1,0 

05 0,5 

0,0 

undoped GaAs 

GaAs:Te 

measurement temperature: 466 K 

500 600 700 800 900 

annealing temperature (K)

Voids in GaAs 

• Molecular-dynamic cluster 

calculations give energy gain 

compared to sum of monovacancies 

• Relaxation was taken into account 

• Energetically favored: 12 vacancies 

• Positron lifetime was calculated 

• stable 12-atom cluster exhibit positron 

lifetime of about 450 ps 

• Found in experiment 


TEM Staab et al., Physica B 273-274 (1999) 501-504

Coincidence 

Coincidence-Doppler Doppler Spectroscopy at GaAs:Cu 

• In high-momentum region (>10-2 2 

m m0c) c) annihilation with Coreelectrons 

dominate 

0 

• Electron momentum distribution of 

core electrons almost not changed 

compared to individual atoms 

1,00 

• Rlti Relatively l easy to t calculate l lt 

• In example: the detected vacancies 

have Cu atoms in closest vicinityy 075 0,75 

• Vacancies are obviously stabilized 

by Cu 


Raatio 

to bulkk 

GaAs 

4 

Cu 

V Ga -Si Ga 

SI-GaAs:Cu (annealed, at 500 K) 

SI-GaAs:Cu (as quenched, at 30 K) 

0 10 20 

p (10 L 

30 

-3 m c) 0 

V. Bondarenko, K. Petters, R. Krause Krause-Rehberg, Rehberg, J. Gebauer, H.S. Leipner, 

Physica B 308-310 (2001)792-795

Conclusions 

• Positrons are a useful tool 

• For characterization of vacancy-type defects in crystalline solids 

• Unique for mono-vacancies 

• V Very sensitive iti for f vacancy clusters l t for f n < 10 (below (b l TEM sensitivity) iti it ) 

• Sensitivity limit for monovacancies ≈ 10 15 /ccm 

R. Krause-Rehberg, H.S. Leipner 

„Positron Annihilation in Semiconductors“ 

Springer Springer-Verlag, Verlag 1999

V - Positron Annihilation in Halle

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