Substitutional B in Si: Accurate lattice parameter ... - Matis - Cnr

JOURNAL OF APPLIED PHYSICS 101, 093523 2007 

Substitutional B in Si: Accurate lattice parameter determination 

G. Bisognin, a D. De Salvador, E. Napolitani, M. Berti, and A. Carnera 

MATIS CNR-INFM and Dipartimento di Fisica, Università di Padova, via Marzolo 8, 35131 Padova, Italy 

S. Mirabella, L. Romano, M. G. Grimaldi, and F. Priolo 

MATIS CNR-INFM and Dipartimento di Fisica ed Astronomia, Università di Catania, via S. Sofia 64, 

95123 Catania, Italy 

Received 13 December 2006; accepted 23 February 2007; published online 14 May 2007 

In this work the lattice deformation induced by substitutional B in Si is carefully determined by 

using different experimental techniques. The investigated Si 1−x B x /Si layers x=0.0012÷0.005 are 

grown by solid phase epitaxy of B-implanted preamorphized Si and by molecular beam epitaxy. 

Nuclear reaction analysis both in random and in channeling geometry, secondary ion mass 

spectrometry and high resolution x-ray diffraction allow to quantify the total amount of B and its 

lattice location, the B depth profile and the B-doped Si lattice parameter, respectively. The reasons 

for the large spread present in the data reported so far in literature are discussed. Our results, thanks 

to the synergy of the earlier techniques, lead to a significantly more accurate strain determination, 

that is in agreement with very recent ab initio theoretical calculations. © 2007 American Institute 

of Physics. DOI: 10.1063/1.2720186 

I. INTRODUCTION 

Silicon is the key material in the field of semiconductor 

device industry and boron is its primary p-type dopant. In the 

last decades B attracted a lot of continuous scientific and 

technological interest. Recently, the ultrahigh B doping of 

silicon, i.e., the incorporation of B at concentrations well 

over an order of magnitude higher than its equilibrium solubility 

limit, became an issue of primary importance for the 

future generation devices. Unfortunately B solubility in Si is 

quite low 210 19 at./cm 3 at 700 °C 1 and its implantation 

in Si, the widely used nonequilibrium strategy for p-type 

doping of Si, is accompanied by a lot of intensively investigated 

detrimental effects like clustering and anomalous 

diffusion. 2 The latter severely limit the electrical activity and 

the sharpness of the B implanted profile. For these reasons 

alternative approaches to incorporate B into substitutional 

sites are investigated mainly based on the capability of 

reaching high metastable incorporation during phase transformation 

such as epitaxy. Due to its compatibility with ion 

implantation technology, solid phase epitaxy SPE is one of 

the most investigated way to obtain substitutionally B-doped 

Si. The earlier issues represent only part of motivations that 

made boron probably the most studied impurity in Si. 

However, despite the great amount of scientific work 

devoted to this dopant in the last 20 years, a satisfactory 

characterization of one of its basic parameters, the lattice 

parameter of the silicon crystal doped with B, i.e., the 

amount of contraction induced by substitutional B in Si, is 

still lacking. The accurate determination of this parameter is 

important not only from a fundamental point of view, but 

also because it would allow x-ray diffraction techniques to 

a Author to whom correspondence should be addressed1; electronic mail: 

bisognin@padova.infm.it 

quantify the amount of substitutional B in Si in a nondestructive 

and fast way simply by means of interplanar distances 

measurement. 

The aim of this work is twofold: first of all we will 

review the experimental and theoretical work till now performed 

to determine the strain induced by substitutional B in 

Si, while in the second part we will describe how the combined 

use of nuclear reaction analyses NRA, secondary ion 

mass spectrometry SIMS, and high resolution x-ray diffraction 

HRXRD represents an effective strategy which can 

lead to an accurate and reliable quantification of B-induced 

strain. 

II. REVIEW OF LITERATURE DATA 

Several studies were carried out in the past with the aim 

of quantifying the relation between the lattice parameter of a 

B doped Si layer and the substitutional B concentration. The 

concentration level of substitutional B x B that can be usually 

reached is not higher than 1–2 at. %. In this case a linear 

relation between the lattice parameter of the B-doped Si 

a Si1−x B x 

and x B is very reasonably assumed 


= a B − a Si x B + a Si . 

1 

This is the well known Vegard’s rule. 3 The slope of the 

linear relation is determined by the lattice parameters a Si and 

a B . In the case of Si 1−x B x alloy the limit structure for x=1, 

i.e., a diamond crystal of pure B, does not exist and a B is 

simply a conventional parameter that fixes the trend of the 

slope of a Si1−x B x 

. Another possible convention that describes 

the relation between the lattice parameter and the concentration 

makes use of the parameter , that is the proportionality 

constant between the relative variation of the lattice parameter 

and the B concentration per unit volume c B , 

a Si − a Si1−x B x 

= c B . 2 

a Si 

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093523-2 Bisognin et al. J. Appl. Phys. 101, 093523 2007 

FIG. 1. Literature fictious cubic B lattice parameters a B organized according 

the Si B-doping strategy closed symbols. Also a theoretical prediction 

is reported open symbol. 

The two descriptions 1 and 2 are fully equivalent, as 

a B and are related by the expression: a B =1−Na Si , 

where N is the density of silicon 510 22 at./cm 3 . However, 

in the following, even if description 2 is adopted by 

the majority of literature papers, we will report all the results 

in terms of a B , which is the parameter more easily implemented 

in HRXRD simulation codes. 

In Fig. 1 we report the literature experimental closed 

symbols and theoretical open diamond determinations of 

a B in Table I a schematic description of each a B determination 

can be found. According to the strategy exploited to 

dope Si, the experimental data were divided into three 

groups: the first group squares refers to melted material, 

while the second circles and the third triangles groups 

refer to Si 1−x B x samples obtained by means of B diffusion in 

Si or grown by epitaxial techniques molecular beam epitaxy 

MBE or chemical vapor deposition CVD, respectively. 

In the lower part of Table I the mean values and the 

standard deviation of each group of data are also reported. It 

is clear that a B determinations obtained by melted and diffused 

materials are affected by a large spread. This spread is 

smaller for epitaxial materials. Moreover, the mean value of 

the last group is different from that of the other two, while it 

is in agreement with the value obtained by Dunham and 

co-workers 15 by ab initio calculations. 

The large spreading in the first group of data melted 

material might be due to the material itself. In fact the investigated 

samples were in many cases highly B-doped polycrystalline 

silicon samples up to 1% of B that suffer for B 

segregation at grain boundaries. As a consequence, the determined 

percentage of electrical active B is misleading, in particular 

if determined by Hall measurements, being the mobility 

of the carriers affected by the scattering due to B 

present at the grain boundaries. 

On the contrary diffused materials, that are obtained by 

equilibrium diffusion of B inside the bulk from a surface 

deposition, are in principle samples of higher quality being 

proved that B diffuses into the lattice by occupying substitutional 

sites. Such group of works all use electrical measurements 

to evaluate B content but, also in this case, the possible 

presence of defects might lead to an uncorrect 

evaluation of substitutional B. Moreover B-doped samples 

prepared by B diffusion are difficult to analyze by x-ray diffraction, 

since the B depth profile is not flat and can generate 

a complicate x-ray spectrum. This effect can be deconvoluted 

by a fitting procedure based on dynamical simulation codes 

or by the help of a profiling technique, but such kind of 

approaches were not exploited in literature papers. Furthermore, 

the absence of contaminations should be carefully 

checked in diffused samples since, unless high care is used in 

sample preparation, they might strongly affect the strain if 

introduced during diffusion. In principle the problem of contaminants 

could be overcome by epitaxial material, even if it 

should be directly checked for each particular growing system. 

In spite of this, also data coming from epitaxial samples 

show a certain spread, which induces an error of 11% in the 

determination of x if HRXRD lattice parameter measurements 

and Eq. 1 are used. 

Several reasons can be responsible for the spread in the 

a B values, even in the most recent articles based on epitaxial 

works. First of all, since most B concentration determinations 

were performed by SIMS, an approximate knowledge 

of B dose of the B calibration standard samples could explain 

this discrepancy. As a matter of fact, when indicated, 

the error on the standard sample dose is of about 10%. 11,14 

Furthermore, it is interesting to note that in the literature 

works no check of the B lattice location was performed: 

however, full substitutionality is not automatically true, being 

the substitutional incorporation of B in Si strongly dependent 

on growth conditions. Even in the works which reported 

B electrical measurements 12,14 one cannot be sure 

about B substitutional amount, since the presence of defects 

can strongly affect the results. Furthermore, in these works 

the possible strain contribution given by electrically inactive 

B was neglected, while it was recently demonstrated that 

clustered B induces non-negligible compressive 16 or tensile 17 

strain, depending on the particular conditions that originates 

the B off-lattice displacement. 

As a summary we think that an accurate evaluation of 

substitutional B induced lattice contraction can be performed 

if: a particular care is devoted to the concentration measurements 

by the use of an appropriate standard, b a control 

is made on the contaminants that might be introduced during 

the growth process, c a direct measurement of B substitutional 

fraction is performed, and d the strain contribution 

associated to nonsubstitutional B is taken into account. In the 

following we will describe an approach based on the combined 

use of NRA both in random and in channeling geometry, 

SIMS and HRXRD, which enable us to study the strain 

given only by the fraction of B substitutionally dissolved in 

Si. Either SPE or MBE samples were analyzed and an accurate 

evaluation of a B is presented. The value found resulted 

to be in agreement with two experimental MBE epitaxial in 

principle the CVD material is purer than the MBE one, but 

very probably the datum of Ref. 10 is affected by the earlier 

listed problems 11,12 and very recent ab initio 15 results. 

III. EXPERIMENTAL PROCEDURE 

A. SPE and MBE growth of the samples 

The following special procedure was used in order to 

produce the SPE samples. We first grew, by means of MBE, 


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 Si B-doping strategy. 

Cubic lattice parameter 

a B Å 

Growth 

technique 

Characterization techniques 

4.75 Melted mat. Powder X-Ray Diffraction XRD, electrical activity ¯ Polycrystalline material: B segregation 4 

at the grain boundaries is possible 

3.91 Melted mat. XRD, Concentration gradient 

¯ 

Polycrystalline material: B segregation 5 

measurements 

at the grain boundaries is possible 

4.81 Diffused mat. Double crystal diffraction 

¯ ¯ 6 

and electrical measurements 

4.02 Diffused mat. Curvature and sheet resistance, Transmission Electron Microscopy TEM ¯ Only electrical measurements 

7 

for B concentration 

4.21 Melted mat. XRD, colorimetry, Hall 

Characterization of the 

Homogeneity and quality 

8 

and four-point measurements 

contaminations: 

C, N410 17 

O10 18 

of the materials are questionable 

4.07 Diffused mat. XRD, sheet resistance ¯ ¯ 9 

4.07 CVD XRD, curvature measurements, 

¯ ¯ 10 

topography 

3.77 MBE XRD, SIMS ¯ Low B concentrations, the Bragg peak 11 

of the film is hardly distinguishable 

3.72 MBE XRD,SIMS, electrical activity ¯ ¯ 12 

3.99 MBE ¯ ¯ ¯ 13 

4.08 Gas source MBE XRD, SIMS, electrical activity, TEM Characterization of the 

¯ 14 

contaminants: 

C and O are absent 

3.66 Ab initio calculations 15 

Type of material Mean value Å Standard deviation Å 

Melted 4.29 0.43 

Diffused 4.30 0.44 

Epitaxial 3.92 0.17 

Strong 

point 

Weak 

point 

Reference 




FIG. 2. Schematic representation of the SPE samples: epitaxial growth of a 

Si 1-y C y alloy barrier and of a Si cap layer, followed by amorphizing Si 

implants, multiple B implants, and solid phase regrowth. The dashed line 

marks the amorphous/crystal a/c interface. 

a 550 Si layer on a Si 001 substrate with a 50 nm thick 

Si 1−y C y alloy layer 390 nm below the surface, with a substitutional 

C concentration of 1.110 20 at./cm 3 . In Fig. 2 a 

schematic picture of the SPE sample structure is shown. All 

the samples were amorphized from the surface up to a depth 

of 550 nm by a 250 keV Si implantation at a dose of 3 

10 15 Si/cm 2 at liquid nitrogen temperature. The samples 

were subsequently implanted with 40 keV 10 15 Si/cm 2 . This 

last Si implantation was performed in order to completely 

amorphize the samples up the surface. In order to obtain a 

smooth box-like B profile, three different 11 B implants were 

performed on the same sample 26, 43, and 68 keV, respectively. 

Different sets of B doses were chosen in order to 

produce five samples with different B maximum concentrations 

0.60, 1.00, 1.25, 1.50, and 2.5010 20 B/cm 3 . After B 

implantation, preannealing at 450 °C was carried out in inert 

nitrogen atmosphere in order to avoid point defect introduction 

for 30 min to produce a good amorphous/crystal interface. 

Then, the samples were fully recrystallized by SPE by 

performing N 2 atmosphere annealings for several minutes in 

the temperature range 550–600 °C. During such annealing 

the residual damage formed just below the amorphization 

depth end of range defects EOR might inject selfinterstitials 

Is above the equilibrium concentration 18,19 so 

inducing an unwanted B clustering. Nevertheless, the presence 

of the Si 0.9978 C 0.0022 alloy layer stops such Is flux toward 

the surface, so preventing nonsubstitutional B 

formation. 20 The presence of substitutional C both after SPE 

and MBE growth was verified with HRXRD measurements. 

Due to the interferometric structure of the sample, the low C 

content of the Si 1−y C y layer and its reduced thickness, 

HRXRD C contribution is not a separate Bragg peak, but a 

shoulder located at the right of the substrate Si peak modulated 

by interference fringes. 16 On the contrary, the thicker 

Si 1−x B x alloy is able to produce a Bragg peak well separated 

by the Si one and it is the main feature of our HRXRD 

spectra. Other Si samples were grown directly with a B-rich 

layer by MBE as described in Ref. 16. This allowed us to 

make a comparison between the two materials and have further 

confidence on the results. 

B. NRA and Rutherford backscattering spectrometry 

measurements 

We performed simultaneous Rutherford backscattering 

spectroscopy RBS and NRA analyses at a scattering angle 

of 170° with a 650-keV proton beam. At this energy the 

11 Bp, 8 Be reaction has a strong and broad resonance 

=300 keV producing particles of about 8 MeV. 21 At the 

resonance energy the reaction probability is approximately 

constant from the surface to the maximum depth where B is 

located in the samples 300–400 nm. Two silicon solid-state 

detectors were mounted in the scattering chamber and connected 

with two independent acquisition electronic chains, 

allowing the simultaneous collection of NRA and RBS spectra. 

Since the cross section of the nuclear reactions is much 

lower than the Rutherford one, the NRA detector was 

mounted very close to the sample, in order to maximize the 

solid angle and hence the counting rate of the nuclear reaction 

products. 

As the backscattered proton flux is orders of magnitude 

higher than the flux of particles from the p, reaction, 

an absorber foil of suitable thickness i.e., 10 m mylar is 

used to prevent high counting rates and the pileup of proton 

pulses. Moreover, the absorber foil is useful also to slow 

down the energy of the produced particles that can be fully 

stopped in the 300 m thick detector. 

NRA was used in order to check the total dose of B in 

the standard used for SIMS analysis see later. This was 

possible thanks to four main facts: i the solid angle of the 

NRA detector was accurately determined by geometrical 

construction of the detection chamber with a value of 

0.1073±0.0016 strad and a relative error of about 1.5%; 

ii charge collection was as accurate as 1%, being the whole 

chamber used as an isolated Faraday cup; iii the cross section 

of 11 Bp, 8 Be reaction is accurately known 2.4%, as 

reported in the recent work of Liu and co-workers; 22 iv no 

spurious signal due to reactions with impurities contaminates 

the 11 Bp, 8 Be reaction, as demonstrated by measuring a 

bare Si sample. This allows to convert the NRA yield into B 

dose with an overall error of about ±3%. 

Furthermore, by aligning the proton beam along main 

axial directions channeling conditions, we can obtain information 

about the location of B atoms in the Si lattice. The 

basic idea is to compare the minimum yield i of the given 

impurity defined as the ratio between its channeling and 

random yields to the M of the matrix, through the equation 

f = 1− i 

1− M 

, 

where f is the substitutional fraction. While i can be obtained 

by the NRA signal, M comes from the Si signal obtained 

from contemporary collected RBS spectra. 

However, NRA technique suffers from the lack of depth 

resolution for the reduced energy loss of p into the Si, the 

nonmonocromaticity in the energy of the emitted particles 

the reaction product 8 Be decays successively into two 

particles and energy straggling suffered by particles in the 

absorber mylar foil. To overcome this problem and to quan- 

3 



tify the concentration of substitutional B in the samples, we 

used channeling in combination with the SIMS technique. 

C. SIMS measurements 

SIMS was used to measure the concentration profiles of 

B, and also to measure the concentration of contaminants 

such as C and O in the B-doped region. We restricted our 

contaminant analyses to carbon and oxygen because they are 

the most common Si impurities. We used a 3 keV O + 2 beam 

to detect 10 B + and 11 B + and a 14.5 keV Cs + beam to detect 

16 O − and 12 C − the other isotopes were not considered in 

these latter cases as they are of negligible natural abundance. 

The B, C, and O detection limits were of 110 14 , 

110 16 , and 110 17 at./cm 3 , respectively. 

In order to perform a quantitative measurement of the 

earlier three elements, calibration standards were used. For B 

we used a bulk-doped C B =1.3210 19 at./cm 3 silicon 

commercial standard with known 

10 B and 

11 B 

concentrations, 23 traceable to the National Institute of Standards 

and Technology NIST SRM 2137 standard, and certified 

with an accuracy of ±3%. As an additional check, the 

dose of a 11 B implanted secondary standard was measured 

by NRA assuming tabulated cross section 22 as described earlier, 

finding a value in agreement within 3% with the B dose 

estimated using SIMS and the bulk-doped Si NIST standard 

B dose. This excellent agreement between NRA and SIMS B 

determinations confirms the reliability in the use of the bulkdoped 

Si NIST standard to quantify samples B amount. The 

overall error of the total B concentration calculated as the 

sum of 10 B and 11 B isotopes in SIMS measurements is 

about 3%. For O, we used a 18 O implanted Si commercial 

standard, 23 with a dose of 510 14 at./cm 2 , certified with an 

accuracy of 5%. For C, we used a MBE grown sample with 

aSi 0.9947 C 0.0053 layer with C concentration known with an 

accuracy of ±10%. 24 

D. HRXRD measurements 

Lattice parameters of the samples were obtained by 

means of high resolution x-ray diffraction. HRXRD measurements 

were collected with a Philips X’Pert PRO MRD 

diffractometer equipped with a Bartels Ge 220 four-crystal 

monochromator and a parabolic mirror. The Cu K 1 radiation 

8 keV was selected as the probe. By using a 

channel-cut Ge 220 analyzer before the detector the angular 

acceptance was reduced up to 12 arc sec triple axis configuration. 

Symmetrical and asymmetrical reflections 004 and 

224, respectively were chosen to measure the in-plane and 

out of plane Si 1−x B x film lattice parameters also 113 reciprocal 

space map RSM was performed on selected samples, 

confirming the results obtained by using 224 reflection. In 

order to extract the perpendicular strain =a −a rel /a rel , 

where a is the out-of plane lattice parameter and a rel is the 

relaxed lattice parameter profiles of the samples and therefore 

the lattice parameter of the material as a function of the 

depth, −2 scan rocking curves RCs were performed 

and simulated with the help of RADS code, 25 a program 

which takes in account the x-ray diffraction dynamical 

theory. 

TABLE II. Maximum B concentrations of the SPE samples, their B substitutional 

fractions, and the corresponding a B values. 

B top concentration 

10 20 at./cm 3 B substitutional 

fraction f 

IV. RESULTS AND DISCUSSION 

a B Å 

0.60 100±2 3.75±0.07 

1.00 98±2 3.77±0.07 

1.25 95±2 3.80±0.07 

1.50 94.5±2 3.83±0.07 

2.50 90.5±2 3.76±0.07 

The B concentration of our samples both SPE regrown 

and MBE grown materials resulted to vary in depth within 

±5% only. The C and O concentrations resulted to be lower 

than 110 18 at./cm 3 in all the samples. This maximum level 

has to be compared to the lowest plateau of B concentration 

of the samples, that is 610 19 at./cm 3 . The presence of C at 

this low concentration can be neglected: its contribution to 

the tensile strain of the lattice is very small, since the lattice 

parameter of a Si 1−y C y alloy 26 with y=210 −5 is 5.4306 Å, 

while the lattice parameter of bare Si is 5.4307 Å. Also in the 

oxygen case, as its level it is at least a factor of 60 lower than 

the level of B, we can neglect its compressive strain 

contribution 27 to the overall lattice strain. 

Another important information comes from NRAchanneling 

measurements: B lattice location measurements 

along the 001 axial direction were performed in order to 

quantify the amount of substitutional B atoms. Strictly 

speaking, this procedure of evaluating the substitutional fraction 

does not take into account the possible presence of B 

point defects in which the interstitial B atoms are aligned 

along the 001 growth direction. In order to give a more 

complete characterization of the samples, channeling measurements 

were also repeated on selected specimens along 

110 and 111 direction, confirming the data coming from 

001 channeling analyses. The results are summarized in 

Table II. 

By looking at Table II we can observe that after SPE the 

majority of B atoms occupies substitutional sites the B substitutional 

fraction f is close to 100%. Nevertheless, a small 

fraction of B atoms increasing with B concentrations is out 

of site. This off-site B small percentage is not due to the 

interaction between B and Is released by the EOR region 

since, as previously described, the substitutional C box acts 

as a barrier for the Is flux. The non-null B interstitial fraction 

is consistent with B-B dimers formation in the amorphous 

phase during the SPE regrowth, as theoretically predicted in 

Ref. 28 and very recently experimentally demonstrated in 

Ref. 29. Moreover, these B-B complexes could be the same 

which form in room temperature RT B-implanted Si. 30 

Once determined the B concentration depth profile and 

the B lattice location, we performed HRXRD measurements 

in order to quantify the B induced strain. RSMs around 004 

and 224 reciprocal lattice points ensure us that the whole 

set of investigated layers are pseudomorphic to the Si substrate. 

The perfect alignment between the substrate and the 

B-doped reciprocal space nodes along the 00l direction in 



FIG. 3. 004 a and 224 b RSMs 

of the 1.510 20 at./cm 3 B doped 

sample. Note the perfect alignment between 

the substrate and the B-doped 

layer nodes in both RSMs. 

the 004 and 224 RSMs mean that no tilt and no strain 

relaxation of the SPE layer occurred, respectively see as 

example Fig. 3. The broadening present around the substrate 

peak is very probably due to a nonexcellent quality of the 

substrate depth zone, while RBS-channeling analyses testified 

a very good quality of the Si surface region. 

The absence of tilt and the pseudomorphicity of the layers 

allow us to simulate only a 004 symmetrical RC to 

know the lattice parameters of the samples. In Fig. 4a the 

004 RC of the 1.510 20 B/cm 3 is reported circles, together 

with its best simulation line. The presence of 

Pendellösung fringes confirms the pseudomorphicity of the 

layer previously detected by RSM. The best simulation is 

obtained in the following way: profile was generated on 

the basis of the SIMS concentration profile, the relation 1 

among the B-doped Si lattice parameter and the B concentration 

and the elasticity theory. In particular, the equation 

that connects with the parallel strain =a −a rel /a rel is 

= a − a rel 

a rel 

=− a − a rel 

a rel 

=− , 4 

where a and a are the perpendicular and the in-plane lattice 

parameters, respectively, a rel is the relaxed lattice parameter 

of the layer, i.e., the lattice parameter of the material after the 

epitaxial constraint is removed, and =0.77. Moreover, Eq. 

4 can be rewritten with the help of Eq. 1 as a function of 

B concentration x B , 

= a − a Si1−x B x 


a B − a Si x B 


, 5 

where in the second equality a Si1−x B x 

is approximated to a Si at 

the denominator, introducing a relative error of less than 

0.1% and the pseudomorphicity of the B-doped layer is exploited 

a =a Si . 

As a result of the combination of Eqs. 4 and 5, a 

linear relation between the concentration profile and the 

strain profile is obtained, where the only undetermined quantity 

is the a B parameter. The continuous line of Fig. 4a is 

the best simulation obtained by fitting the a B parameter alone 

and taking into account the strain contribution given by the 

buried Si 1−y C y layer. In Fig. 4b the B concentration profile 

and the profile of the B-doped region are reported. The 

perfect agreement between simulation and experimental data 

in Fig. 4a demonstrates that the linear relation holds true 

and that the approach is much reliable. 

In Fig. 5 we reported the experimental a B determinations 

for the examined samples obtained by SPE as a function of 

the layer B-top concentration. With the open squares we reported 

the a B values neglecting the strain contribution of the 

nonsubstitutional fraction 1−f. As can be noted these a B 

values does not have a common value, but they clearly increase 

as a function of B concentration. This fact is related to 

the decrease of B substitutional fraction f increasing B-top 

concentration, demonstrating that the off-lattice B fraction 

does not give the same strain of substitutional B. In order to 

account the specific lattice strain given both by off-lattice 

and substitutional B, Eq. 5 can be generalized as follows: 

= a B − a Si x B 

f + a B Cl 

− a Si x B 

1−f, 6 



where the parameter a BCl takes into account the specific strain 

due to off-lattice B. It is clear that a B can be estimated only 

if a BCl is considered. Different hypotheses about a BCl can be 

made: i the off-lattice B gives no strain, i.e., a BCl =a Si Fig. 

5, open circles; ii nonsubstitutional B gives the same compressive 

strain as the clustered B studied in Ref. 16 Fig. 5, 

open stars; iii it gives a tensile strain contribution as B-B 

dimers investigated in Ref. 17 open triangles. The last two 

cases are relative to very different conditions in which non- 

FIG. 4. a RC of the 1.5 

10 20 B/cm 3 sample circles with its 

best simulation continuous line. b 

Corresponding perpendicular strain 

profile used to generate the best simulation 

continuous line and B chemical 

profile dashed line of the same 

sample. 



V. CONCLUSIONS 

FIG. 5. a B determinations for the SPE samples neglecting open squares or 

taking into account the f correction open circles: a BCl =a Si ; open triangles: 

a BCl ⇒strain of Ref. 17; open stars: a BCl ⇒strain of Ref. 16. The dashed 

line represents the corresponding a B mean value of open triangles . Literature 

data about epitaxial materials are also reported closed star see Ref. 

15, cross see Ref. 12, closed circle see Ref. 11, closed diamond see Ref. 

13, closed up triangle see Ref. 14, and closed down triangle see Ref. 

10. 

In this article we have presented an accurate determination 

of the fictious B lattice parameter a B which results to be 

3.78±0.07 Å. Most of the previously published data, which 

are in disagreement with our results, suffer for the lack of B 

lattice location measurements, of a check of the presence of 

contaminants, of a suitable SIMS B calibration standard, and 

of the knowledge of the strain induced by off-site B. On the 

contrary, we performed an accurate and complete characterization 

of the samples: by means of NRA we measured B 

substitutional fraction and with the use of a well characterized 

SIMS B standard we determined B total amount with an 

error of 3%. Moreover, we checked the presence of impurities 

founding very low C and O background levels 

10 18 at./cm 3 for both dopants. Finally, we took into account 

also the strain contribution given by non substitutional 

B according to the value reported in Ref. 17. The reliability 

of our a B determination is confirmed also by the agreement 

with some recent experimental works 11,12 and theoretical ab 

initio calculations. 15 

substitutional B is investigated. For the case ii of Ref. 16 

large B clusters are produced by substitutional B interaction 

with a flux of Is, while in the case iii B-B pairs are produced 

by RT irradiation of substitutional B with He high 

energy beam. As can be noted the data having the most costant 

trend for a B are those where this last hypothesis for 

nonsubstitutional B strain is exploited. This fact is very reasonable 

since it the same B-B dimer was demonstrated to be 

formed after He irradiation or room temperature B implantation 

in crystalline Si, 30 and reasonably this small B complex 

is the same formed also during SPE processes. 29 

This reasoning makes us to conclude that the most reliable 

value for a B parameter, that describe the strain of substitutional 

B is: a B =3.78±0.03 Å, that is the average value 

and the standard deviation of data extracted under hypothesis 

iii. 

In order to further check the reliability of our a B determination 

and to rule out any possible dependence on the 

B-doping epitaxial technique, we also measured MBE material, 

and a perfect agreement with the SPE results was found. 

Furthermore, taking into account the possible systematic error 

mainly due to the concentration determination, we estimated 

an overall error of 0.07 Å. As a consequence if 

HRXRD determination of strain profile is used to obtain B 

concentration profile an uncertainty of 4% is obtainable on 

the basis of this data, much less than what was previously 

possible on the basis of literature data. 

At this point, we can compare our a B determination with 

literature data: in Fig. 5 all the experimental data coming 

from experiments on epitaxial materials and theoretical 

closed symbols, see Fig. 5 caption values of a B are reported 

together with our a B determination dashed line. If error 

bars are taken into consideration, our a B determination is in 

excellent agreement with the work of Baribeau et al. 11 and 

Sardela et al., 12 who studied MBE samples. Moreover, a 

good agreement is evident also with the theoretical prediction 

of Dunham et al. 15 

ACKNOWLEDGMENTS 

The authors wish to acknowledge A. Sambo, R. Storti 

Padova University, C. Percolla, S. Tatì MATIS CNR- 

INFM, and A. Marino CNR-IMM for expert technical assistance. 

This work was partially supported by the MIUR 

Project No. PRIN 2004. 

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Substitutional B in Si: Accurate lattice parameter ... - Matis - Cnr

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