Journal of Minerals & Materials Characterization & Engineering, Vol. 5, No.2, pp 143-153, 2006
jmmce.org Printed in the USA. All rights reserved
143
Structural and microstructural characteristics of B-doped
PbTe semiconductor
Jovica N. Stojanovic
Institute for Technology of Nuclear and Other Raw Mineral Materials, Applied
Mineralogy Unit, Franche d‘Eperey 86, P.O. Box 390, 11000 Belgrade, Serbia
Abstract: The main task of this paper was accurate determination of structural and
microstructural parameters of B-doped PbTe semiconductor (“p” type). Four
samples (undoped PbTe, and three doped with initial B contents: 1 %, 3 % and 8 %)
were synthesized using the Bridgman method and analysed using X-ray powder
diffraction (XRD) technique. Structural features were obtained using the Rietveld
method and microstructural by diffraction-line broadening methods. Microstructural
measurements contain both crystallite domain sizes and microstrain calculations
obtained by the Warren-Averbach and the simplified integral-breadth methods.
Keywords: B-doped PbTe semiconductor, the Rietveld method, microstructural
measurements.
INTRODUCTION
PbTe is a narrow-gap semiconductor. The research in doping of semiconductor
materials and hereby modified properties is one of the most significant tasks of
modern semiconductor physics. Great consideration is given to optical, photoelectric
and magnetic features of AIVBVI compounds doped with some elements from the III
group (B, Al, Ga, In, Tl). The most studied compounds, thus far, are In, Ga and Tl-
doped AIVBVI compounds. B-doped PbTe is one serial semiconductor material,
important in manufacturing of laser and detector infrared (IR) optoelectronics within
wavelength from 1 to 40 µm.

144 Stojanovic Vol.5,
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The scope of the paper is to give an answer with the reference to the issues of
how and where B atoms have sited into PbTe structure. Rietveld refinement method
was used for structural and crystallite domain-size as well as crystal lattice
microstrain calculations for microstructural determinations. Both crystallite domain
size and microstrain measurements were calculated towards obtaining the
crystallographic direction distributions of B atoms.
The Warren-Averbach method and corresponding microstrain calculations were
applied in diffraction-line broadening measurements for surface-weighted (<D>S) and
volume-weighted <D>V), crystallite domain sizes. The referred measurements were
also done by applying “simplified” integral-breadth methods: 1) broadenings
originated due to both crystallite domain sizes and microstrains, which correspond to
the Cauchy function, 2) the Gauss function and 3) both broadenings originated due to
crystallite domain sizes that correspond to the Cauchy function and microstrains that
correspond to the Gauss function. The last one provides for an excellent theoretical
basis and it is widely applied in various Rietveld analysis softwares intended to
microstructural calculations.
EXPERIMENT AND ANALY TICAL METHODS
B-doped PbTe samples were synthesized using the Bridgman method. Pb and Te
were applied in an ingot form, of a normal 99.99 wt% purity. So derived samples
were further powdered for XRD analyses. Four samples were synthesized in the
Institute of Technical Sciences of the Serbian Academy of Sciences and Arts:
undoped PbTe, PbTe doped with B (1 at.%, 3 at.% and 8 at.%). X-ray intensity
measurements were carried out on a PHILIPS PW 1710 automated diffractometer.
The powder diffraction data are given in Table 1. The FULLPROF software [2] was
used for the Rietveld structure refinement and BREADTH [1] for the diffraction-line
broadening measurements.
RESULTS AND DISCUS SI ON
Rietveld structure refinement
PbTe is cubic, space group mFm3 with Z=4. Both Pb and Te atoms are in fixed
positions at ½½½ and 000 respectively, and both atoms are in octahedral

Vol.5, No.2 Structural and Microstructural Characteristics 145
coordination.
Table 1. Rietveld powder diffraction data for B-doped PbTe.
Sample characterization
Name (chemical, mineral) Lead telluride (altaite)
Empirical formula PbTe
Source/preparation synthetic
Technique
Radiation type, source X-rays, Cu λ value used 1.54060Å Kα1/1.54439 Kα2
Monochromator diffracted beam graphite
monochromator
Detector (film, scint. etc)
Instrument description
(type, slits)
proportional
vertical diffractometer
divergence slit 1o
receiving slit 0.1 mm
soller slit 1o
Instrumental profile
breadth
0.10 o2θ temp. (oC) 25
± 1
Specimen form/particle
size
Range of 2θ
Specimen motion
edge loaded powder/ <10 µm particle size
from 20 o to 140 o2θ, 4 s per step
none
There were no other phases except PbTe during the treatments. Even the
reflection displacements did not occur. Therefore, the conclusion is that B atoms
haven’t deranged the PbTe structure when sited in it. (200) reflection showed strong,
while (220) and (222) reflection showed appreciably weaker preferred orientation
effects in all sample. The observed (circles), calculated (continuous line) and
difference powder diffraction profiles for all analysed samples are shown in Figure 1.
The Rietveld agreement factors are presented in Table 2.
Table 2. Rietveld refinement agreement factors
PbTe PbTe+B (1%) PbTe+B (3%) PbTe+B (8%)
Rexp 11.4 10.7 11.3 10.5
Rp 13.3 12.7 14.2 12.4
Rwp 14.3 14.1 14.9 14.8
RB 6.12 5.58 5.69 5.82
RF 6.47 5.55 5.28 6.48
GofF 1.6 1.7 1.6 1.7
The unit-cell parameter of pure PbTe is in a good agreement with all B-doped

146 Stojanovic Vol.5,
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samples and literature data [4] as well. The isotropic displacement parameters of
Figure 1. The observed (circles), calculated (continuous line) and difference powder
diffraction profiles for: a) undoped PbTe, b) PbTe doped with B 1 at%, c)
PbTe doped with B 3 at% and d) PbTe doped with B 8 at%.

Vol.5, No.2 Structural and Microstructural Characteristics 147
Pb atoms have been observed to be larger than those of Te atoms, which can indicate
thermal vibration increment of the Pb sublattice to that of the Te sublattice, especially
in samples doped with 1 and 8 %. However, this is not an unusual phenomenon. Even
in pure PbTe crystals, the relatively large anharmonic thermal vibrations of Pb lattice
to that of the Te sublattice along the [hhh] direction were observed [3]. According to
the same data these thermal vibrations of Pb atoms are enhanced by the alloying
elements Ge or Sn and make a lattice unstable. Unit-cell and isotropic displacement
parameters in comparison to the literature data [4] are given in Table 3.
Table 3. Rietveld refinement unit-cell and isotropic displacement parameters in
comparison to the literature data.
PbTe
PbTe+B
(1%)
PbTe+B
(3%)
PbTe+B
(8%)
YASUTOSHI
et al. (1987)
Biso Pb (Å2) 2.037(2) 2.661(1) 2.109(7) 2.648(1) 1.61(2)
Biso Te (Å2) 1.126(2) 1.319(2) 1.267(1) 1.426(6)
1.11(1)
BisoPb/BisoTe 1.809 2.017 1.665 1.856 1.45
a (Å) 6.4603(2) 6.4605(2) 6.4601(7) 6.4605(2) 6.4541(9)
V (Å3) 269.62(1) 269.65(2) 269.60(5) 269.65(1) 268.85
Microstructural measurements
Microstructural parameter calculations were measured in crystallographic
directions as follows: [h00]-(200), (400), (600); [hh0]-(220) (440); [hhh]-(111), (222),
(333) (444); [hkk]-(311), (622) [h00] and [hh0] layers consist of both Pb and Te atoms
while [hhh] and [hkk] layers consist of either Pb or Te atoms. So, the (311) layer
consists entirely of Te atoms and the (622) one of Pb atoms. Likewise, (111) and
(333) layers consist entirely of Te atoms; the (222) and (444) layers consist entirely of
Pb atoms. Diffraction-line broadening measurements containing both crystallite
domain sizes and microstrain parameters obtained by the Warren-Averbach and the
simplified integral-breadth methods are given in Tables 4-7.

148 Stojanovic Vol.5,
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Table 4. Crystallite domain sizes obtained by the Warren-Averbach method.
D (Å)
h 0 0 h h 0 h h h h k k
PbTe <D>s* 480 ± 36 357 ± 29 466 ± 64 163 ± 82
<D>v** 484 ± 14 443 ± 19 484± 27 315 ±113
PbTe+B(1%) <D>s 498 ± 43 428 ± 38 476 ± 46 312 ± 25
<D>v 543 ± 20 482 ± 20 546 ± 24 421 ± 20
PbTe+B(3%) <D>s 417 ± 46 339 ± 30 394 ± 63 235 ± 18
<D>v 406 ± 17 362 ± 14 407 ± 26 314 ± 14
PbTe+B(8%) <D>s 554 ± 38 430 ± 54 448 ± 51 330 ± 41
<D>v 583 ± 16 536 ± 36 545 ± 46 479 ± 38
* Surface-weighted domain size. ** Volume- weighted domain size.
Table 5. Microstrain parameters obtained by the Warren-Averbach method.
2/1
2
ε (10-3)
h 0 0 h h 0 h h h h k k
2/1
2/
2
S
D
ε * 0.89 ± 0.03 0.99 ± 0.05 0.66 ± 0.05 0.72 ± 0.02
PbTe
2/1
2/
2
V
D
ε ** 0.88 ± 0.02 0.89 ± 0.04 0.68 ± 0.05 0.75 ± 0.02
2/1
2/
2
S
D
ε 0.95 ± 0.03 1.05 ± 0.03 0.77 ± 0.03 0.84 ±0.05
PbTe+B(1%)
2/1
2/
2
V
D
ε 0.91 ± 0.02 0.94 ± 0.03 0.72 ± 0.03 0.73 ± 0.04
2/1
2/
2
S
D
ε 1.18 ± 0.04 1.33 ± 0.04 0.91 ± 0.06 0.99 ± 0.07
PbTe+B(3%)
2/1
2/
2
V
D
ε 1.19 ± 0.04 1.29 ± 0.04 0.89 ± 0.06 0.86 ± 0.06
2/1
2/
2
S
D
ε 0.80 ± 0.02 0.89 ± 0.06 0.64 ± 0.01 0.68 ± 0.08
PbTe+B(8%)
2/1
2/
2
V
D
ε 0.78 ± 0.02 0.80 ± 0.05 0.53 ± 0.01 0.56 ± 0.07
* Root-mean-square microstrain (RMSM) averaged over the distance <D>s.
** RMSM averaged over the distance <D>v.

Vol.5, No.2 Structural and Microstructural Characteristics 149
Table 6. Crystallite domain sizes obtained by the simplified integral-breadth methods.
D (Å)
h 0 0 h h 0 h h h h k k
<DC-C>* 524 491 467 271
<DC-G>** 454 446 446 323
PbTe
<DG-G> *** 451 443 443 319
<DC-C> 652 619 569 454
<DC-G> 523 509 463 421
PbTe+B(1%)
<DG-G> 506 493 460 420
<DC-C> 469 441 403 317
<DC-G> 384 374 366 311
PbTe+B(3%)
<DG-G> 375 368 361 311
<DC-C> 672 638 617 502
<DC-G> 562 551 539 479
PbTe +B(8%)
<DG-G> 555 544 538 478
Volume-averaged domain size from the simplified integral-breadth methods: *
Cauchy-Cauchy function, ** Cauchy-Gauss function, *** Gauss-Gauss function.
Microstrain parameters of both the Warren-Averbach and the simplified integral-
breadth methods increase up to the sample doped with 3 %, to be followed by a rapid
decrease in the sample doped with 8% of B. This trend is noticeable along each
measured crystallographic direction. The referred phenomenon can be explained by B
atoms, sited in PbTe structure, in two different manners. Besides, microstrain parameters
in the directions, consisting of layers with homogeneous atoms, are much lower in
comparison to the parameters with heterogeneous atoms. Taking into consideration all
these facts, the basic assumption is that high microstrain values appear as the result of
vacancy arrangements in the directions where the layers consist of heterogeneous atoms
(Pb and Te). The point to be emphasised is that the values of the kind were measured in
all samples, meaning they are not resulting from B atoms disposition. If so, such values

150 Stojanovic Vol.5,
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would not be measured in the sample doped with 8 %.
Table 7. Microstrain parameters obtained by the simplified integral-breadth methods.
ε (10-3)
h 0 0 h h 0 h h h h k k
CC −
ε
* 0.468 0.394 0.093 -
GC−
ε ** 0.648 0.656 0.122 -
PbTe
GG−
ε *** 0.874 0.875 0.189 -
CC −
ε 0.793 0.768 0.543 0.268
GC −
ε 0.963 0.979 0.637 0.499
PbTe+B(1%)
GG−
ε 1.210 1.240 0.873 0.674
CC −
ε 0.896 0.845 0.358 0.085
GC −
ε 1.120 1.150 0.546 0.304
PbTe+B(3%)
GG−
ε 1.430 1.470 0.736 0.426
CC −
ε 0.551 0.508 0.320 0.152
GC −
ε 0.714 0.716 0.440 0.342
PbTe +B(8%)
GG−
ε 0.921 0.929 0.612 0.469
Upper limit of microstrain from the simplified integral-breadth methods: * Cauchy-
Cauchy function, ** Cauchy-Gauss function, *** Gauss-Gauss function.
Generally, crystallite domain sizes both for the Warren-Averbach and the
simplified integral-breadth methods show higher crystallinity degree in the samples
doped with 1 and 8 % (these two samples have also the highest isotropic displacement
parameters) and lower one in a pure sample and the sample doped with 3 %.
Therefore, the crystallinity degree increases up to the sample doped with 1 % of B;
aftermath it decreases in the sample doped with 3% of B, and increases again in the
sample doped with 8% of B. Likewise, this trend may be noticed in microstrain
parameter calculations, along each measured crystallographic direction. Graphic

Vol.5, No.2 Structural and Microstructural Characteristics 151
illustrations of diffraction-line broadening measurements are shown in Figures 2 and
3.
Figure 2. Graphic illustrations of crystallite: a) surface-weighted domain sizes, b)
volume-weighted domain sizes, and c) RMSM averaged over the distance
<D>s, d) RMSM averaged over the distance <D>v obtained by Warren-
Averbach method.
CONCLUSION
The achieved results of structural and microstructural measurements, par
exellence unit-cell and microstrain parameters indicate that B atoms embedding did
not generate disorder in PbTe-type structure. The disorder increases until the sample
has been doped with 3 % and then rapidly falls down with the sample doped with 8 %
of B. So, if contents of B atoms in the PbTe structure were limited they would be
expelled as an

152 Stojanovic Vol.5,
No.2
Figure 3. Graphic illustrations of volume-averaged domain sizes: a) Cauchy-Cauchy
function, b) Cauchy-Gauss function, c) Gauss-Gauss function, and upper
limit of microstrains: d) Cauchy-Cauchy function, e) Cauchy-Gauss
function, f) Gauss-Gauss function obtained by the simplified integral-
breadth methods.
extra phase in the sample doped with 8 %. Have B atoms occupied interstitial
site-positions or filled-up vacancies or maybe both? Since these are real crystals, the
crystal lattice defects are expected to appear. Schottky-type defects appear when
atoms or ions are of approximate dimensions; consequently, the atom distribution in
interstitial site-positions is difficult one. Frenkel-type defects consist of either
interstitial atoms or ions and vacancies in a crystal lattice. Small cations and big
anions are favoured for this type of defects. The foremost assumption is that B atoms,
mostly already filled-up, formed vacancies in layers with the highest microstrain

Vol.5, No.2 Structural and Microstructural Characteristics 153
parameters: [h00] and [hh0]. Since Pb and Te atoms are of approximate radii,
Schottky-type defects are expected. This means B atoms sited unattended vacancies.
Considering B atomic radius, which is in comparison to Pb and Te atoms very small
one, a certain amount of B atoms must have sited interstitially into the structure.
Higher values of isotropic displacement parameters of doped samples in comparison
to the pure one can be explained in the manner that B atoms increased overall values
of Pb and Te atoms. So, the crucial conclusion is that B atoms predominantly filled-
up vacancies and, to less extent, degree sited into PbTe structure interstitially.
ACKNOWLEDGMENTS
The authors are gratefully acknowledged to Professor Stevan Đurić and
academician Pantelija Nikolić, who donated the samples and his associates from the
Serbian Academy of Sciences and Arts for their thorough comments and suggestions,
which significantly improved this paper.
REFERENCES
[1] BALZAR, D., LEDBET TER, H., 1997, “Software for comparative analysis of diffraction –
line boadening.” Advances in X – ray analysis, vol. 39, edited by V. Gilfrich et al.,
Plenum Press, New York, pp. 457 – 464.
[2] RODRIGUEZ – CARVAJAL, J., 1995, “User’s guide to program FULLPROF.” 2004-LLB-
JRC (Laboratorie León Brillouin, CEA-CNRS, Centre d’Etudes de Saclay, Gif sur
Yvette, France).
[3] YASUTOSHI, N., SHIGERU, O., SHOISHI, S. & YOSHIHIKO, S., 1983, “Charge
distribution and atomic thermal vibrations in lead chalcogenide crystals.” Acta Cryst.,
B39, pp. 312 – 317.
[4] YASUTOSHI, N., KATASHI, M., SHOISHI, S., YOSHIHIKO, S., KOSHIRO, T & IWAO, I.
1987, “Temperature dependence of atomic thermal parameters of lead chalcogenides,
PbS, PbSe, PbTe.” Acta Cryst., C43, pp. 1443 – 1445.