Substitutional B in Si: Accurate lattice parameter ... - Matis - Cnr
Substitutional B in Si: Accurate lattice parameter ... - Matis - Cnr
Substitutional B in Si: Accurate lattice parameter ... - Matis - Cnr
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JOURNAL OF APPLIED PHYSICS 101, 093523 2007<br />
<strong>Substitutional</strong> B <strong>in</strong> <strong>Si</strong>: <strong>Accurate</strong> <strong>lattice</strong> <strong>parameter</strong> determ<strong>in</strong>ation<br />
G. Bisogn<strong>in</strong>, a D. De Salvador, E. Napolitani, M. Berti, and A. Carnera<br />
MATIS CNR-INFM and Dipartimento di Fisica, Università di Padova, via Marzolo 8, 35131 Padova, Italy<br />
S. Mirabella, L. Romano, M. G. Grimaldi, and F. Priolo<br />
MATIS CNR-INFM and Dipartimento di Fisica ed Astronomia, Università di Catania, via S. Sofia 64,<br />
95123 Catania, Italy<br />
Received 13 December 2006; accepted 23 February 2007; published onl<strong>in</strong>e 14 May 2007<br />
In this work the <strong>lattice</strong> deformation <strong>in</strong>duced by substitutional B <strong>in</strong> <strong>Si</strong> is carefully determ<strong>in</strong>ed by<br />
us<strong>in</strong>g different experimental techniques. The <strong>in</strong>vestigated <strong>Si</strong> 1−x B x /<strong>Si</strong> layers x=0.0012÷0.005 are<br />
grown by solid phase epitaxy of B-implanted preamorphized <strong>Si</strong> and by molecular beam epitaxy.<br />
Nuclear reaction analysis both <strong>in</strong> random and <strong>in</strong> channel<strong>in</strong>g geometry, secondary ion mass<br />
spectrometry and high resolution x-ray diffraction allow to quantify the total amount of B and its<br />
<strong>lattice</strong> location, the B depth profile and the B-doped <strong>Si</strong> <strong>lattice</strong> <strong>parameter</strong>, respectively. The reasons<br />
for the large spread present <strong>in</strong> the data reported so far <strong>in</strong> literature are discussed. Our results, thanks<br />
to the synergy of the earlier techniques, lead to a significantly more accurate stra<strong>in</strong> determ<strong>in</strong>ation,<br />
that is <strong>in</strong> agreement with very recent ab <strong>in</strong>itio theoretical calculations. © 2007 American Institute<br />
of Physics. DOI: 10.1063/1.2720186<br />
I. INTRODUCTION<br />
<strong>Si</strong>licon is the key material <strong>in</strong> the field of semiconductor<br />
device <strong>in</strong>dustry and boron is its primary p-type dopant. In the<br />
last decades B attracted a lot of cont<strong>in</strong>uous scientific and<br />
technological <strong>in</strong>terest. Recently, the ultrahigh B dop<strong>in</strong>g of<br />
silicon, i.e., the <strong>in</strong>corporation of B at concentrations well<br />
over an order of magnitude higher than its equilibrium solubility<br />
limit, became an issue of primary importance for the<br />
future generation devices. Unfortunately B solubility <strong>in</strong> <strong>Si</strong> is<br />
quite low 210 19 at./cm 3 at 700 °C 1 and its implantation<br />
<strong>in</strong> <strong>Si</strong>, the widely used nonequilibrium strategy for p-type<br />
dop<strong>in</strong>g of <strong>Si</strong>, is accompanied by a lot of <strong>in</strong>tensively <strong>in</strong>vestigated<br />
detrimental effects like cluster<strong>in</strong>g and anomalous<br />
diffusion. 2 The latter severely limit the electrical activity and<br />
the sharpness of the B implanted profile. For these reasons<br />
alternative approaches to <strong>in</strong>corporate B <strong>in</strong>to substitutional<br />
sites are <strong>in</strong>vestigated ma<strong>in</strong>ly based on the capability of<br />
reach<strong>in</strong>g high metastable <strong>in</strong>corporation dur<strong>in</strong>g phase transformation<br />
such as epitaxy. Due to its compatibility with ion<br />
implantation technology, solid phase epitaxy SPE is one of<br />
the most <strong>in</strong>vestigated way to obta<strong>in</strong> substitutionally B-doped<br />
<strong>Si</strong>. The earlier issues represent only part of motivations that<br />
made boron probably the most studied impurity <strong>in</strong> <strong>Si</strong>.<br />
However, despite the great amount of scientific work<br />
devoted to this dopant <strong>in</strong> the last 20 years, a satisfactory<br />
characterization of one of its basic <strong>parameter</strong>s, the <strong>lattice</strong><br />
<strong>parameter</strong> of the silicon crystal doped with B, i.e., the<br />
amount of contraction <strong>in</strong>duced by substitutional B <strong>in</strong> <strong>Si</strong>, is<br />
still lack<strong>in</strong>g. The accurate determ<strong>in</strong>ation of this <strong>parameter</strong> is<br />
important not only from a fundamental po<strong>in</strong>t of view, but<br />
also because it would allow x-ray diffraction techniques to<br />
a Author to whom correspondence should be addressed1; electronic mail:<br />
bisogn<strong>in</strong>@padova.<strong>in</strong>fm.it<br />
quantify the amount of substitutional B <strong>in</strong> <strong>Si</strong> <strong>in</strong> a nondestructive<br />
and fast way simply by means of <strong>in</strong>terplanar distances<br />
measurement.<br />
The aim of this work is twofold: first of all we will<br />
review the experimental and theoretical work till now performed<br />
to determ<strong>in</strong>e the stra<strong>in</strong> <strong>in</strong>duced by substitutional B <strong>in</strong><br />
<strong>Si</strong>, while <strong>in</strong> the second part we will describe how the comb<strong>in</strong>ed<br />
use of nuclear reaction analyses NRA, secondary ion<br />
mass spectrometry SIMS, and high resolution x-ray diffraction<br />
HRXRD represents an effective strategy which can<br />
lead to an accurate and reliable quantification of B-<strong>in</strong>duced<br />
stra<strong>in</strong>.<br />
II. REVIEW OF LITERATURE DATA<br />
Several studies were carried out <strong>in</strong> the past with the aim<br />
of quantify<strong>in</strong>g the relation between the <strong>lattice</strong> <strong>parameter</strong> of a<br />
B doped <strong>Si</strong> layer and the substitutional B concentration. The<br />
concentration level of substitutional B x B that can be usually<br />
reached is not higher than 1–2 at. %. In this case a l<strong>in</strong>ear<br />
relation between the <strong>lattice</strong> <strong>parameter</strong> of the B-doped <strong>Si</strong><br />
a <strong>Si</strong>1−x B x<br />
and x B is very reasonably assumed<br />
a <strong>Si</strong>1−x B x<br />
= a B − a <strong>Si</strong> x B + a <strong>Si</strong> .<br />
1<br />
This is the well known Vegard’s rule. 3 The slope of the<br />
l<strong>in</strong>ear relation is determ<strong>in</strong>ed by the <strong>lattice</strong> <strong>parameter</strong>s a <strong>Si</strong> and<br />
a B . In the case of <strong>Si</strong> 1−x B x alloy the limit structure for x=1,<br />
i.e., a diamond crystal of pure B, does not exist and a B is<br />
simply a conventional <strong>parameter</strong> that fixes the trend of the<br />
slope of a <strong>Si</strong>1−x B x<br />
. Another possible convention that describes<br />
the relation between the <strong>lattice</strong> <strong>parameter</strong> and the concentration<br />
makes use of the <strong>parameter</strong> , that is the proportionality<br />
constant between the relative variation of the <strong>lattice</strong> <strong>parameter</strong><br />
and the B concentration per unit volume c B ,<br />
a <strong>Si</strong> − a <strong>Si</strong>1−x B x<br />
= c B . 2<br />
a <strong>Si</strong><br />
0021-8979/2007/1019/093523/8/$23.00<br />
101, 093523-1<br />
© 2007 American Institute of Physics<br />
Downloaded 15 May 2007 to 192.84.150.51. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp
093523-2 Bisogn<strong>in</strong> et al. J. Appl. Phys. 101, 093523 2007<br />
FIG. 1. Literature fictious cubic B <strong>lattice</strong> <strong>parameter</strong>s a B organized accord<strong>in</strong>g<br />
the <strong>Si</strong> B-dop<strong>in</strong>g strategy closed symbols. Also a theoretical prediction<br />
is reported open symbol.<br />
The two descriptions 1 and 2 are fully equivalent, as<br />
a B and are related by the expression: a B =1−Na <strong>Si</strong> ,<br />
where N is the density of silicon 510 22 at./cm 3 . However,<br />
<strong>in</strong> the follow<strong>in</strong>g, even if description 2 is adopted by<br />
the majority of literature papers, we will report all the results<br />
<strong>in</strong> terms of a B , which is the <strong>parameter</strong> more easily implemented<br />
<strong>in</strong> HRXRD simulation codes.<br />
In Fig. 1 we report the literature experimental closed<br />
symbols and theoretical open diamond determ<strong>in</strong>ations of<br />
a B <strong>in</strong> Table I a schematic description of each a B determ<strong>in</strong>ation<br />
can be found. Accord<strong>in</strong>g to the strategy exploited to<br />
dope <strong>Si</strong>, the experimental data were divided <strong>in</strong>to three<br />
groups: the first group squares refers to melted material,<br />
while the second circles and the third triangles groups<br />
refer to <strong>Si</strong> 1−x B x samples obta<strong>in</strong>ed by means of B diffusion <strong>in</strong><br />
<strong>Si</strong> or grown by epitaxial techniques molecular beam epitaxy<br />
MBE or chemical vapor deposition CVD, respectively.<br />
In the lower part of Table I the mean values and the<br />
standard deviation of each group of data are also reported. It<br />
is clear that a B determ<strong>in</strong>ations obta<strong>in</strong>ed by melted and diffused<br />
materials are affected by a large spread. This spread is<br />
smaller for epitaxial materials. Moreover, the mean value of<br />
the last group is different from that of the other two, while it<br />
is <strong>in</strong> agreement with the value obta<strong>in</strong>ed by Dunham and<br />
co-workers 15 by ab <strong>in</strong>itio calculations.<br />
The large spread<strong>in</strong>g <strong>in</strong> the first group of data melted<br />
material might be due to the material itself. In fact the <strong>in</strong>vestigated<br />
samples were <strong>in</strong> many cases highly B-doped polycrystall<strong>in</strong>e<br />
silicon samples up to 1% of B that suffer for B<br />
segregation at gra<strong>in</strong> boundaries. As a consequence, the determ<strong>in</strong>ed<br />
percentage of electrical active B is mislead<strong>in</strong>g, <strong>in</strong> particular<br />
if determ<strong>in</strong>ed by Hall measurements, be<strong>in</strong>g the mobility<br />
of the carriers affected by the scatter<strong>in</strong>g due to B<br />
present at the gra<strong>in</strong> boundaries.<br />
On the contrary diffused materials, that are obta<strong>in</strong>ed by<br />
equilibrium diffusion of B <strong>in</strong>side the bulk from a surface<br />
deposition, are <strong>in</strong> pr<strong>in</strong>ciple samples of higher quality be<strong>in</strong>g<br />
proved that B diffuses <strong>in</strong>to the <strong>lattice</strong> by occupy<strong>in</strong>g substitutional<br />
sites. Such group of works all use electrical measurements<br />
to evaluate B content but, also <strong>in</strong> this case, the possible<br />
presence of defects might lead to an uncorrect<br />
evaluation of substitutional B. Moreover B-doped samples<br />
prepared by B diffusion are difficult to analyze by x-ray diffraction,<br />
s<strong>in</strong>ce the B depth profile is not flat and can generate<br />
a complicate x-ray spectrum. This effect can be deconvoluted<br />
by a fitt<strong>in</strong>g procedure based on dynamical simulation codes<br />
or by the help of a profil<strong>in</strong>g technique, but such k<strong>in</strong>d of<br />
approaches were not exploited <strong>in</strong> literature papers. Furthermore,<br />
the absence of contam<strong>in</strong>ations should be carefully<br />
checked <strong>in</strong> diffused samples s<strong>in</strong>ce, unless high care is used <strong>in</strong><br />
sample preparation, they might strongly affect the stra<strong>in</strong> if<br />
<strong>in</strong>troduced dur<strong>in</strong>g diffusion. In pr<strong>in</strong>ciple the problem of contam<strong>in</strong>ants<br />
could be overcome by epitaxial material, even if it<br />
should be directly checked for each particular grow<strong>in</strong>g system.<br />
In spite of this, also data com<strong>in</strong>g from epitaxial samples<br />
show a certa<strong>in</strong> spread, which <strong>in</strong>duces an error of 11% <strong>in</strong> the<br />
determ<strong>in</strong>ation of x if HRXRD <strong>lattice</strong> <strong>parameter</strong> measurements<br />
and Eq. 1 are used.<br />
Several reasons can be responsible for the spread <strong>in</strong> the<br />
a B values, even <strong>in</strong> the most recent articles based on epitaxial<br />
works. First of all, s<strong>in</strong>ce most B concentration determ<strong>in</strong>ations<br />
were performed by SIMS, an approximate knowledge<br />
of B dose of the B calibration standard samples could expla<strong>in</strong><br />
this discrepancy. As a matter of fact, when <strong>in</strong>dicated,<br />
the error on the standard sample dose is of about 10%. 11,14<br />
Furthermore, it is <strong>in</strong>terest<strong>in</strong>g to note that <strong>in</strong> the literature<br />
works no check of the B <strong>lattice</strong> location was performed:<br />
however, full substitutionality is not automatically true, be<strong>in</strong>g<br />
the substitutional <strong>in</strong>corporation of B <strong>in</strong> <strong>Si</strong> strongly dependent<br />
on growth conditions. Even <strong>in</strong> the works which reported<br />
B electrical measurements 12,14 one cannot be sure<br />
about B substitutional amount, s<strong>in</strong>ce the presence of defects<br />
can strongly affect the results. Furthermore, <strong>in</strong> these works<br />
the possible stra<strong>in</strong> contribution given by electrically <strong>in</strong>active<br />
B was neglected, while it was recently demonstrated that<br />
clustered B <strong>in</strong>duces non-negligible compressive 16 or tensile 17<br />
stra<strong>in</strong>, depend<strong>in</strong>g on the particular conditions that orig<strong>in</strong>ates<br />
the B off-<strong>lattice</strong> displacement.<br />
As a summary we th<strong>in</strong>k that an accurate evaluation of<br />
substitutional B <strong>in</strong>duced <strong>lattice</strong> contraction can be performed<br />
if: a particular care is devoted to the concentration measurements<br />
by the use of an appropriate standard, b a control<br />
is made on the contam<strong>in</strong>ants that might be <strong>in</strong>troduced dur<strong>in</strong>g<br />
the growth process, c a direct measurement of B substitutional<br />
fraction is performed, and d the stra<strong>in</strong> contribution<br />
associated to nonsubstitutional B is taken <strong>in</strong>to account. In the<br />
follow<strong>in</strong>g we will describe an approach based on the comb<strong>in</strong>ed<br />
use of NRA both <strong>in</strong> random and <strong>in</strong> channel<strong>in</strong>g geometry,<br />
SIMS and HRXRD, which enable us to study the stra<strong>in</strong><br />
given only by the fraction of B substitutionally dissolved <strong>in</strong><br />
<strong>Si</strong>. Either SPE or MBE samples were analyzed and an accurate<br />
evaluation of a B is presented. The value found resulted<br />
to be <strong>in</strong> agreement with two experimental MBE epitaxial <strong>in</strong><br />
pr<strong>in</strong>ciple the CVD material is purer than the MBE one, but<br />
very probably the datum of Ref. 10 is affected by the earlier<br />
listed problems 11,12 and very recent ab <strong>in</strong>itio 15 results.<br />
III. EXPERIMENTAL PROCEDURE<br />
A. SPE and MBE growth of the samples<br />
The follow<strong>in</strong>g special procedure was used <strong>in</strong> order to<br />
produce the SPE samples. We first grew, by means of MBE,<br />
Downloaded 15 May 2007 to 192.84.150.51. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp
TABLE I. Summary of literature experimental values and theoretical calculations of a B and lower part of the average values and standard deviation of literature data grouped by <strong>Si</strong> B-dop<strong>in</strong>g strategy.<br />
Cubic <strong>lattice</strong> <strong>parameter</strong><br />
a B Å<br />
Growth<br />
technique<br />
Characterization techniques<br />
4.75 Melted mat. Powder X-Ray Diffraction XRD, electrical activity ¯ Polycrystall<strong>in</strong>e material: B segregation 4<br />
at the gra<strong>in</strong> boundaries is possible<br />
3.91 Melted mat. XRD, Concentration gradient<br />
¯<br />
Polycrystall<strong>in</strong>e material: B segregation 5<br />
measurements<br />
at the gra<strong>in</strong> boundaries is possible<br />
4.81 Diffused mat. Double crystal diffraction<br />
¯ ¯ 6<br />
and electrical measurements<br />
4.02 Diffused mat. Curvature and sheet resistance, Transmission Electron Microscopy TEM ¯ Only electrical measurements<br />
7<br />
for B concentration<br />
4.21 Melted mat. XRD, colorimetry, Hall<br />
Characterization of the<br />
Homogeneity and quality<br />
8<br />
and four-po<strong>in</strong>t measurements<br />
contam<strong>in</strong>ations:<br />
C, N410 17<br />
O10 18<br />
of the materials are questionable<br />
4.07 Diffused mat. XRD, sheet resistance ¯ ¯ 9<br />
4.07 CVD XRD, curvature measurements,<br />
¯ ¯ 10<br />
topography<br />
3.77 MBE XRD, SIMS ¯ Low B concentrations, the Bragg peak 11<br />
of the film is hardly dist<strong>in</strong>guishable<br />
3.72 MBE XRD,SIMS, electrical activity ¯ ¯ 12<br />
3.99 MBE ¯ ¯ ¯ 13<br />
4.08 Gas source MBE XRD, SIMS, electrical activity, TEM Characterization of the<br />
¯ 14<br />
contam<strong>in</strong>ants:<br />
C and O are absent<br />
3.66 Ab <strong>in</strong>itio calculations 15<br />
Type of material Mean value Å Standard deviation Å<br />
Melted 4.29 0.43<br />
Diffused 4.30 0.44<br />
Epitaxial 3.92 0.17<br />
Strong<br />
po<strong>in</strong>t<br />
Weak<br />
po<strong>in</strong>t<br />
Reference<br />
093523-3 Bisogn<strong>in</strong> et al. J. Appl. Phys. 101, 093523 2007<br />
Downloaded 15 May 2007 to 192.84.150.51. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp
093523-4 Bisogn<strong>in</strong> et al. J. Appl. Phys. 101, 093523 2007<br />
FIG. 2. Schematic representation of the SPE samples: epitaxial growth of a<br />
<strong>Si</strong> 1-y C y alloy barrier and of a <strong>Si</strong> cap layer, followed by amorphiz<strong>in</strong>g <strong>Si</strong><br />
implants, multiple B implants, and solid phase regrowth. The dashed l<strong>in</strong>e<br />
marks the amorphous/crystal a/c <strong>in</strong>terface.<br />
a 550 <strong>Si</strong> layer on a <strong>Si</strong> 001 substrate with a 50 nm thick<br />
<strong>Si</strong> 1−y C y alloy layer 390 nm below the surface, with a substitutional<br />
C concentration of 1.110 20 at./cm 3 . In Fig. 2 a<br />
schematic picture of the SPE sample structure is shown. All<br />
the samples were amorphized from the surface up to a depth<br />
of 550 nm by a 250 keV <strong>Si</strong> implantation at a dose of 3<br />
10 15 <strong>Si</strong>/cm 2 at liquid nitrogen temperature. The samples<br />
were subsequently implanted with 40 keV 10 15 <strong>Si</strong>/cm 2 . This<br />
last <strong>Si</strong> implantation was performed <strong>in</strong> order to completely<br />
amorphize the samples up the surface. In order to obta<strong>in</strong> a<br />
smooth box-like B profile, three different 11 B implants were<br />
performed on the same sample 26, 43, and 68 keV, respectively.<br />
Different sets of B doses were chosen <strong>in</strong> order to<br />
produce five samples with different B maximum concentrations<br />
0.60, 1.00, 1.25, 1.50, and 2.5010 20 B/cm 3 . After B<br />
implantation, preanneal<strong>in</strong>g at 450 °C was carried out <strong>in</strong> <strong>in</strong>ert<br />
nitrogen atmosphere <strong>in</strong> order to avoid po<strong>in</strong>t defect <strong>in</strong>troduction<br />
for 30 m<strong>in</strong> to produce a good amorphous/crystal <strong>in</strong>terface.<br />
Then, the samples were fully recrystallized by SPE by<br />
perform<strong>in</strong>g N 2 atmosphere anneal<strong>in</strong>gs for several m<strong>in</strong>utes <strong>in</strong><br />
the temperature range 550–600 °C. Dur<strong>in</strong>g such anneal<strong>in</strong>g<br />
the residual damage formed just below the amorphization<br />
depth end of range defects EOR might <strong>in</strong>ject self<strong>in</strong>terstitials<br />
Is above the equilibrium concentration 18,19 so<br />
<strong>in</strong>duc<strong>in</strong>g an unwanted B cluster<strong>in</strong>g. Nevertheless, the presence<br />
of the <strong>Si</strong> 0.9978 C 0.0022 alloy layer stops such Is flux toward<br />
the surface, so prevent<strong>in</strong>g nonsubstitutional B<br />
formation. 20 The presence of substitutional C both after SPE<br />
and MBE growth was verified with HRXRD measurements.<br />
Due to the <strong>in</strong>terferometric structure of the sample, the low C<br />
content of the <strong>Si</strong> 1−y C y layer and its reduced thickness,<br />
HRXRD C contribution is not a separate Bragg peak, but a<br />
shoulder located at the right of the substrate <strong>Si</strong> peak modulated<br />
by <strong>in</strong>terference fr<strong>in</strong>ges. 16 On the contrary, the thicker<br />
<strong>Si</strong> 1−x B x alloy is able to produce a Bragg peak well separated<br />
by the <strong>Si</strong> one and it is the ma<strong>in</strong> feature of our HRXRD<br />
spectra. Other <strong>Si</strong> samples were grown directly with a B-rich<br />
layer by MBE as described <strong>in</strong> Ref. 16. This allowed us to<br />
make a comparison between the two materials and have further<br />
confidence on the results.<br />
B. NRA and Rutherford backscatter<strong>in</strong>g spectrometry<br />
measurements<br />
We performed simultaneous Rutherford backscatter<strong>in</strong>g<br />
spectroscopy RBS and NRA analyses at a scatter<strong>in</strong>g angle<br />
of 170° with a 650-keV proton beam. At this energy the<br />
11 Bp, 8 Be reaction has a strong and broad resonance<br />
=300 keV produc<strong>in</strong>g particles of about 8 MeV. 21 At the<br />
resonance energy the reaction probability is approximately<br />
constant from the surface to the maximum depth where B is<br />
located <strong>in</strong> the samples 300–400 nm. Two silicon solid-state<br />
detectors were mounted <strong>in</strong> the scatter<strong>in</strong>g chamber and connected<br />
with two <strong>in</strong>dependent acquisition electronic cha<strong>in</strong>s,<br />
allow<strong>in</strong>g the simultaneous collection of NRA and RBS spectra.<br />
S<strong>in</strong>ce the cross section of the nuclear reactions is much<br />
lower than the Rutherford one, the NRA detector was<br />
mounted very close to the sample, <strong>in</strong> order to maximize the<br />
solid angle and hence the count<strong>in</strong>g rate of the nuclear reaction<br />
products.<br />
As the backscattered proton flux is orders of magnitude<br />
higher than the flux of particles from the p, reaction,<br />
an absorber foil of suitable thickness i.e., 10 m mylar is<br />
used to prevent high count<strong>in</strong>g rates and the pileup of proton<br />
pulses. Moreover, the absorber foil is useful also to slow<br />
down the energy of the produced particles that can be fully<br />
stopped <strong>in</strong> the 300 m thick detector.<br />
NRA was used <strong>in</strong> order to check the total dose of B <strong>in</strong><br />
the standard used for SIMS analysis see later. This was<br />
possible thanks to four ma<strong>in</strong> facts: i the solid angle of the<br />
NRA detector was accurately determ<strong>in</strong>ed by geometrical<br />
construction of the detection chamber with a value of<br />
0.1073±0.0016 strad and a relative error of about 1.5%;<br />
ii charge collection was as accurate as 1%, be<strong>in</strong>g the whole<br />
chamber used as an isolated Faraday cup; iii the cross section<br />
of 11 Bp, 8 Be reaction is accurately known 2.4%, as<br />
reported <strong>in</strong> the recent work of Liu and co-workers; 22 iv no<br />
spurious signal due to reactions with impurities contam<strong>in</strong>ates<br />
the 11 Bp, 8 Be reaction, as demonstrated by measur<strong>in</strong>g a<br />
bare <strong>Si</strong> sample. This allows to convert the NRA yield <strong>in</strong>to B<br />
dose with an overall error of about ±3%.<br />
Furthermore, by align<strong>in</strong>g the proton beam along ma<strong>in</strong><br />
axial directions channel<strong>in</strong>g conditions, we can obta<strong>in</strong> <strong>in</strong>formation<br />
about the location of B atoms <strong>in</strong> the <strong>Si</strong> <strong>lattice</strong>. The<br />
basic idea is to compare the m<strong>in</strong>imum yield i of the given<br />
impurity def<strong>in</strong>ed as the ratio between its channel<strong>in</strong>g and<br />
random yields to the M of the matrix, through the equation<br />
f = 1− i<br />
1− M<br />
,<br />
where f is the substitutional fraction. While i can be obta<strong>in</strong>ed<br />
by the NRA signal, M comes from the <strong>Si</strong> signal obta<strong>in</strong>ed<br />
from contemporary collected RBS spectra.<br />
However, NRA technique suffers from the lack of depth<br />
resolution for the reduced energy loss of p <strong>in</strong>to the <strong>Si</strong>, the<br />
nonmonocromaticity <strong>in</strong> the energy of the emitted particles<br />
the reaction product 8 Be decays successively <strong>in</strong>to two <br />
particles and energy straggl<strong>in</strong>g suffered by particles <strong>in</strong> the<br />
absorber mylar foil. To overcome this problem and to quan-<br />
3<br />
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093523-5 Bisogn<strong>in</strong> et al. J. Appl. Phys. 101, 093523 2007<br />
tify the concentration of substitutional B <strong>in</strong> the samples, we<br />
used channel<strong>in</strong>g <strong>in</strong> comb<strong>in</strong>ation with the SIMS technique.<br />
C. SIMS measurements<br />
SIMS was used to measure the concentration profiles of<br />
B, and also to measure the concentration of contam<strong>in</strong>ants<br />
such as C and O <strong>in</strong> the B-doped region. We restricted our<br />
contam<strong>in</strong>ant analyses to carbon and oxygen because they are<br />
the most common <strong>Si</strong> impurities. We used a 3 keV O + 2 beam<br />
to detect 10 B + and 11 B + and a 14.5 keV Cs + beam to detect<br />
16 O − and 12 C − the other isotopes were not considered <strong>in</strong><br />
these latter cases as they are of negligible natural abundance.<br />
The B, C, and O detection limits were of 110 14 ,<br />
110 16 , and 110 17 at./cm 3 , respectively.<br />
In order to perform a quantitative measurement of the<br />
earlier three elements, calibration standards were used. For B<br />
we used a bulk-doped C B =1.3210 19 at./cm 3 silicon<br />
commercial standard with known<br />
10 B and<br />
11 B<br />
concentrations, 23 traceable to the National Institute of Standards<br />
and Technology NIST SRM 2137 standard, and certified<br />
with an accuracy of ±3%. As an additional check, the<br />
dose of a 11 B implanted secondary standard was measured<br />
by NRA assum<strong>in</strong>g tabulated cross section 22 as described earlier,<br />
f<strong>in</strong>d<strong>in</strong>g a value <strong>in</strong> agreement with<strong>in</strong> 3% with the B dose<br />
estimated us<strong>in</strong>g SIMS and the bulk-doped <strong>Si</strong> NIST standard<br />
B dose. This excellent agreement between NRA and SIMS B<br />
determ<strong>in</strong>ations confirms the reliability <strong>in</strong> the use of the bulkdoped<br />
<strong>Si</strong> NIST standard to quantify samples B amount. The<br />
overall error of the total B concentration calculated as the<br />
sum of 10 B and 11 B isotopes <strong>in</strong> SIMS measurements is<br />
about 3%. For O, we used a 18 O implanted <strong>Si</strong> commercial<br />
standard, 23 with a dose of 510 14 at./cm 2 , certified with an<br />
accuracy of 5%. For C, we used a MBE grown sample with<br />
a<strong>Si</strong> 0.9947 C 0.0053 layer with C concentration known with an<br />
accuracy of ±10%. 24<br />
D. HRXRD measurements<br />
Lattice <strong>parameter</strong>s of the samples were obta<strong>in</strong>ed by<br />
means of high resolution x-ray diffraction. HRXRD measurements<br />
were collected with a Philips X’Pert PRO MRD<br />
diffractometer equipped with a Bartels Ge 220 four-crystal<br />
monochromator and a parabolic mirror. The Cu K 1 radiation<br />
8 keV was selected as the probe. By us<strong>in</strong>g a<br />
channel-cut Ge 220 analyzer before the detector the angular<br />
acceptance was reduced up to 12 arc sec triple axis configuration.<br />
Symmetrical and asymmetrical reflections 004 and<br />
224, respectively were chosen to measure the <strong>in</strong>-plane and<br />
out of plane <strong>Si</strong> 1−x B x film <strong>lattice</strong> <strong>parameter</strong>s also 113 reciprocal<br />
space map RSM was performed on selected samples,<br />
confirm<strong>in</strong>g the results obta<strong>in</strong>ed by us<strong>in</strong>g 224 reflection. In<br />
order to extract the perpendicular stra<strong>in</strong> =a −a rel /a rel ,<br />
where a is the out-of plane <strong>lattice</strong> <strong>parameter</strong> and a rel is the<br />
relaxed <strong>lattice</strong> <strong>parameter</strong> profiles of the samples and therefore<br />
the <strong>lattice</strong> <strong>parameter</strong> of the material as a function of the<br />
depth, −2 scan rock<strong>in</strong>g curves RCs were performed<br />
and simulated with the help of RADS code, 25 a program<br />
which takes <strong>in</strong> account the x-ray diffraction dynamical<br />
theory.<br />
TABLE II. Maximum B concentrations of the SPE samples, their B substitutional<br />
fractions, and the correspond<strong>in</strong>g a B values.<br />
B top concentration<br />
10 20 at./cm 3 B substitutional<br />
fraction f<br />
IV. RESULTS AND DISCUSSION<br />
a B Å<br />
0.60 100±2 3.75±0.07<br />
1.00 98±2 3.77±0.07<br />
1.25 95±2 3.80±0.07<br />
1.50 94.5±2 3.83±0.07<br />
2.50 90.5±2 3.76±0.07<br />
The B concentration of our samples both SPE regrown<br />
and MBE grown materials resulted to vary <strong>in</strong> depth with<strong>in</strong><br />
±5% only. The C and O concentrations resulted to be lower<br />
than 110 18 at./cm 3 <strong>in</strong> all the samples. This maximum level<br />
has to be compared to the lowest plateau of B concentration<br />
of the samples, that is 610 19 at./cm 3 . The presence of C at<br />
this low concentration can be neglected: its contribution to<br />
the tensile stra<strong>in</strong> of the <strong>lattice</strong> is very small, s<strong>in</strong>ce the <strong>lattice</strong><br />
<strong>parameter</strong> of a <strong>Si</strong> 1−y C y alloy 26 with y=210 −5 is 5.4306 Å,<br />
while the <strong>lattice</strong> <strong>parameter</strong> of bare <strong>Si</strong> is 5.4307 Å. Also <strong>in</strong> the<br />
oxygen case, as its level it is at least a factor of 60 lower than<br />
the level of B, we can neglect its compressive stra<strong>in</strong><br />
contribution 27 to the overall <strong>lattice</strong> stra<strong>in</strong>.<br />
Another important <strong>in</strong>formation comes from NRAchannel<strong>in</strong>g<br />
measurements: B <strong>lattice</strong> location measurements<br />
along the 001 axial direction were performed <strong>in</strong> order to<br />
quantify the amount of substitutional B atoms. Strictly<br />
speak<strong>in</strong>g, this procedure of evaluat<strong>in</strong>g the substitutional fraction<br />
does not take <strong>in</strong>to account the possible presence of B<br />
po<strong>in</strong>t defects <strong>in</strong> which the <strong>in</strong>terstitial B atoms are aligned<br />
along the 001 growth direction. In order to give a more<br />
complete characterization of the samples, channel<strong>in</strong>g measurements<br />
were also repeated on selected specimens along<br />
110 and 111 direction, confirm<strong>in</strong>g the data com<strong>in</strong>g from<br />
001 channel<strong>in</strong>g analyses. The results are summarized <strong>in</strong><br />
Table II.<br />
By look<strong>in</strong>g at Table II we can observe that after SPE the<br />
majority of B atoms occupies substitutional sites the B substitutional<br />
fraction f is close to 100%. Nevertheless, a small<br />
fraction of B atoms <strong>in</strong>creas<strong>in</strong>g with B concentrations is out<br />
of site. This off-site B small percentage is not due to the<br />
<strong>in</strong>teraction between B and Is released by the EOR region<br />
s<strong>in</strong>ce, as previously described, the substitutional C box acts<br />
as a barrier for the Is flux. The non-null B <strong>in</strong>terstitial fraction<br />
is consistent with B-B dimers formation <strong>in</strong> the amorphous<br />
phase dur<strong>in</strong>g the SPE regrowth, as theoretically predicted <strong>in</strong><br />
Ref. 28 and very recently experimentally demonstrated <strong>in</strong><br />
Ref. 29. Moreover, these B-B complexes could be the same<br />
which form <strong>in</strong> room temperature RT B-implanted <strong>Si</strong>. 30<br />
Once determ<strong>in</strong>ed the B concentration depth profile and<br />
the B <strong>lattice</strong> location, we performed HRXRD measurements<br />
<strong>in</strong> order to quantify the B <strong>in</strong>duced stra<strong>in</strong>. RSMs around 004<br />
and 224 reciprocal <strong>lattice</strong> po<strong>in</strong>ts ensure us that the whole<br />
set of <strong>in</strong>vestigated layers are pseudomorphic to the <strong>Si</strong> substrate.<br />
The perfect alignment between the substrate and the<br />
B-doped reciprocal space nodes along the 00l direction <strong>in</strong><br />
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093523-6 Bisogn<strong>in</strong> et al. J. Appl. Phys. 101, 093523 2007<br />
FIG. 3. 004 a and 224 b RSMs<br />
of the 1.510 20 at./cm 3 B doped<br />
sample. Note the perfect alignment between<br />
the substrate and the B-doped<br />
layer nodes <strong>in</strong> both RSMs.<br />
the 004 and 224 RSMs mean that no tilt and no stra<strong>in</strong><br />
relaxation of the SPE layer occurred, respectively see as<br />
example Fig. 3. The broaden<strong>in</strong>g present around the substrate<br />
peak is very probably due to a nonexcellent quality of the<br />
substrate depth zone, while RBS-channel<strong>in</strong>g analyses testified<br />
a very good quality of the <strong>Si</strong> surface region.<br />
The absence of tilt and the pseudomorphicity of the layers<br />
allow us to simulate only a 004 symmetrical RC to<br />
know the <strong>lattice</strong> <strong>parameter</strong>s of the samples. In Fig. 4a the<br />
004 RC of the 1.510 20 B/cm 3 is reported circles, together<br />
with its best simulation l<strong>in</strong>e. The presence of<br />
Pendellösung fr<strong>in</strong>ges confirms the pseudomorphicity of the<br />
layer previously detected by RSM. The best simulation is<br />
obta<strong>in</strong>ed <strong>in</strong> the follow<strong>in</strong>g way: profile was generated on<br />
the basis of the SIMS concentration profile, the relation 1<br />
among the B-doped <strong>Si</strong> <strong>lattice</strong> <strong>parameter</strong> and the B concentration<br />
and the elasticity theory. In particular, the equation<br />
that connects with the parallel stra<strong>in</strong> =a −a rel /a rel is<br />
= a − a rel<br />
a rel<br />
=− a − a rel <br />
a rel<br />
=− , 4<br />
where a and a are the perpendicular and the <strong>in</strong>-plane <strong>lattice</strong><br />
<strong>parameter</strong>s, respectively, a rel is the relaxed <strong>lattice</strong> <strong>parameter</strong><br />
of the layer, i.e., the <strong>lattice</strong> <strong>parameter</strong> of the material after the<br />
epitaxial constra<strong>in</strong>t is removed, and =0.77. Moreover, Eq.<br />
4 can be rewritten with the help of Eq. 1 as a function of<br />
B concentration x B ,<br />
= a − a <strong>Si</strong>1−x B x<br />
a <strong>Si</strong>1−x B x<br />
a B − a <strong>Si</strong> x B<br />
a <strong>Si</strong><br />
, 5<br />
where <strong>in</strong> the second equality a <strong>Si</strong>1−x B x<br />
is approximated to a <strong>Si</strong> at<br />
the denom<strong>in</strong>ator, <strong>in</strong>troduc<strong>in</strong>g a relative error of less than<br />
0.1% and the pseudomorphicity of the B-doped layer is exploited<br />
a =a <strong>Si</strong> .<br />
As a result of the comb<strong>in</strong>ation of Eqs. 4 and 5, a<br />
l<strong>in</strong>ear relation between the concentration profile and the<br />
stra<strong>in</strong> profile is obta<strong>in</strong>ed, where the only undeterm<strong>in</strong>ed quantity<br />
is the a B <strong>parameter</strong>. The cont<strong>in</strong>uous l<strong>in</strong>e of Fig. 4a is<br />
the best simulation obta<strong>in</strong>ed by fitt<strong>in</strong>g the a B <strong>parameter</strong> alone<br />
and tak<strong>in</strong>g <strong>in</strong>to account the stra<strong>in</strong> contribution given by the<br />
buried <strong>Si</strong> 1−y C y layer. In Fig. 4b the B concentration profile<br />
and the profile of the B-doped region are reported. The<br />
perfect agreement between simulation and experimental data<br />
<strong>in</strong> Fig. 4a demonstrates that the l<strong>in</strong>ear relation holds true<br />
and that the approach is much reliable.<br />
In Fig. 5 we reported the experimental a B determ<strong>in</strong>ations<br />
for the exam<strong>in</strong>ed samples obta<strong>in</strong>ed by SPE as a function of<br />
the layer B-top concentration. With the open squares we reported<br />
the a B values neglect<strong>in</strong>g the stra<strong>in</strong> contribution of the<br />
nonsubstitutional fraction 1−f. As can be noted these a B<br />
values does not have a common value, but they clearly <strong>in</strong>crease<br />
as a function of B concentration. This fact is related to<br />
the decrease of B substitutional fraction f <strong>in</strong>creas<strong>in</strong>g B-top<br />
concentration, demonstrat<strong>in</strong>g that the off-<strong>lattice</strong> B fraction<br />
does not give the same stra<strong>in</strong> of substitutional B. In order to<br />
account the specific <strong>lattice</strong> stra<strong>in</strong> given both by off-<strong>lattice</strong><br />
and substitutional B, Eq. 5 can be generalized as follows:<br />
= a B − a <strong>Si</strong> x B<br />
f + a B Cl<br />
− a <strong>Si</strong> x B<br />
1−f, 6<br />
a <strong>Si</strong><br />
a <strong>Si</strong><br />
where the <strong>parameter</strong> a BCl takes <strong>in</strong>to account the specific stra<strong>in</strong><br />
due to off-<strong>lattice</strong> B. It is clear that a B can be estimated only<br />
if a BCl is considered. Different hypotheses about a BCl can be<br />
made: i the off-<strong>lattice</strong> B gives no stra<strong>in</strong>, i.e., a BCl =a <strong>Si</strong> Fig.<br />
5, open circles; ii nonsubstitutional B gives the same compressive<br />
stra<strong>in</strong> as the clustered B studied <strong>in</strong> Ref. 16 Fig. 5,<br />
open stars; iii it gives a tensile stra<strong>in</strong> contribution as B-B<br />
dimers <strong>in</strong>vestigated <strong>in</strong> Ref. 17 open triangles. The last two<br />
cases are relative to very different conditions <strong>in</strong> which non-<br />
FIG. 4. a RC of the 1.5<br />
10 20 B/cm 3 sample circles with its<br />
best simulation cont<strong>in</strong>uous l<strong>in</strong>e. b<br />
Correspond<strong>in</strong>g perpendicular stra<strong>in</strong><br />
profile used to generate the best simulation<br />
cont<strong>in</strong>uous l<strong>in</strong>e and B chemical<br />
profile dashed l<strong>in</strong>e of the same<br />
sample.<br />
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093523-7 Bisogn<strong>in</strong> et al. J. Appl. Phys. 101, 093523 2007<br />
V. CONCLUSIONS<br />
FIG. 5. a B determ<strong>in</strong>ations for the SPE samples neglect<strong>in</strong>g open squares or<br />
tak<strong>in</strong>g <strong>in</strong>to account the f correction open circles: a BCl =a <strong>Si</strong> ; open triangles:<br />
a BCl ⇒stra<strong>in</strong> of Ref. 17; open stars: a BCl ⇒stra<strong>in</strong> of Ref. 16. The dashed<br />
l<strong>in</strong>e represents the correspond<strong>in</strong>g a B mean value of open triangles . Literature<br />
data about epitaxial materials are also reported closed star see Ref.<br />
15, cross see Ref. 12, closed circle see Ref. 11, closed diamond see Ref.<br />
13, closed up triangle see Ref. 14, and closed down triangle see Ref.<br />
10.<br />
In this article we have presented an accurate determ<strong>in</strong>ation<br />
of the fictious B <strong>lattice</strong> <strong>parameter</strong> a B which results to be<br />
3.78±0.07 Å. Most of the previously published data, which<br />
are <strong>in</strong> disagreement with our results, suffer for the lack of B<br />
<strong>lattice</strong> location measurements, of a check of the presence of<br />
contam<strong>in</strong>ants, of a suitable SIMS B calibration standard, and<br />
of the knowledge of the stra<strong>in</strong> <strong>in</strong>duced by off-site B. On the<br />
contrary, we performed an accurate and complete characterization<br />
of the samples: by means of NRA we measured B<br />
substitutional fraction and with the use of a well characterized<br />
SIMS B standard we determ<strong>in</strong>ed B total amount with an<br />
error of 3%. Moreover, we checked the presence of impurities<br />
found<strong>in</strong>g very low C and O background levels<br />
10 18 at./cm 3 for both dopants. F<strong>in</strong>ally, we took <strong>in</strong>to account<br />
also the stra<strong>in</strong> contribution given by non substitutional<br />
B accord<strong>in</strong>g to the value reported <strong>in</strong> Ref. 17. The reliability<br />
of our a B determ<strong>in</strong>ation is confirmed also by the agreement<br />
with some recent experimental works 11,12 and theoretical ab<br />
<strong>in</strong>itio calculations. 15<br />
substitutional B is <strong>in</strong>vestigated. For the case ii of Ref. 16<br />
large B clusters are produced by substitutional B <strong>in</strong>teraction<br />
with a flux of Is, while <strong>in</strong> the case iii B-B pairs are produced<br />
by RT irradiation of substitutional B with He high<br />
energy beam. As can be noted the data hav<strong>in</strong>g the most costant<br />
trend for a B are those where this last hypothesis for<br />
nonsubstitutional B stra<strong>in</strong> is exploited. This fact is very reasonable<br />
s<strong>in</strong>ce it the same B-B dimer was demonstrated to be<br />
formed after He irradiation or room temperature B implantation<br />
<strong>in</strong> crystall<strong>in</strong>e <strong>Si</strong>, 30 and reasonably this small B complex<br />
is the same formed also dur<strong>in</strong>g SPE processes. 29<br />
This reason<strong>in</strong>g makes us to conclude that the most reliable<br />
value for a B <strong>parameter</strong>, that describe the stra<strong>in</strong> of substitutional<br />
B is: a B =3.78±0.03 Å, that is the average value<br />
and the standard deviation of data extracted under hypothesis<br />
iii.<br />
In order to further check the reliability of our a B determ<strong>in</strong>ation<br />
and to rule out any possible dependence on the<br />
B-dop<strong>in</strong>g epitaxial technique, we also measured MBE material,<br />
and a perfect agreement with the SPE results was found.<br />
Furthermore, tak<strong>in</strong>g <strong>in</strong>to account the possible systematic error<br />
ma<strong>in</strong>ly due to the concentration determ<strong>in</strong>ation, we estimated<br />
an overall error of 0.07 Å. As a consequence if<br />
HRXRD determ<strong>in</strong>ation of stra<strong>in</strong> profile is used to obta<strong>in</strong> B<br />
concentration profile an uncerta<strong>in</strong>ty of 4% is obta<strong>in</strong>able on<br />
the basis of this data, much less than what was previously<br />
possible on the basis of literature data.<br />
At this po<strong>in</strong>t, we can compare our a B determ<strong>in</strong>ation with<br />
literature data: <strong>in</strong> Fig. 5 all the experimental data com<strong>in</strong>g<br />
from experiments on epitaxial materials and theoretical<br />
closed symbols, see Fig. 5 caption values of a B are reported<br />
together with our a B determ<strong>in</strong>ation dashed l<strong>in</strong>e. If error<br />
bars are taken <strong>in</strong>to consideration, our a B determ<strong>in</strong>ation is <strong>in</strong><br />
excellent agreement with the work of Baribeau et al. 11 and<br />
Sardela et al., 12 who studied MBE samples. Moreover, a<br />
good agreement is evident also with the theoretical prediction<br />
of Dunham et al. 15<br />
ACKNOWLEDGMENTS<br />
The authors wish to acknowledge A. Sambo, R. Storti<br />
Padova University, C. Percolla, S. Tatì MATIS CNR-<br />
INFM, and A. Mar<strong>in</strong>o CNR-IMM for expert technical assistance.<br />
This work was partially supported by the MIUR<br />
Project No. PRIN 2004.<br />
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