Atomic defects and physical-chemical properties of PbTe-InTe solid solutions
Crystal-quasichemical equations of probable mechanisms inherent to formation of solid solutions based on lead telluride of the n-type in PbTe-InTe system are offered. Shown is the possibility to satisfactorily explain experimental results by filling with indium atoms In⁺² <--> In⁺¹ In⁺³ (...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2003
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| Cite this: | Atomic defects and physical-chemical properties of PbTe-InTe solid solutions / D.M. Freik, V.I. Boychuk, L.I. Mezhylovsjka // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2003. — Т. 6, № 4. — С. 454-457. — Бібліогр.: 7 назв. — англ. |
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| author | Freik, D.M. Boychuk, V.I. Mezhylovsjka, L.I. |
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| citation_txt | Atomic defects and physical-chemical properties of PbTe-InTe solid solutions / D.M. Freik, V.I. Boychuk, L.I. Mezhylovsjka // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2003. — Т. 6, № 4. — С. 454-457. — Бібліогр.: 7 назв. — англ. |
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| description | Crystal-quasichemical equations of probable mechanisms inherent to formation of solid solutions based on lead telluride of the n-type in PbTe-InTe system are offered. Shown is the possibility to satisfactorily explain experimental results by filling with indium atoms In⁺² <--> In⁺¹ In⁺³ (up to 3 mol. % InTe) octahedral hollows (IH) of close-packed arrangement of tellurium atoms in PbTe crystal lattice. At the greater content of indium telluride, the allocation of both In⁺¹ on OH, and In⁺³ on tetrahedral hollows (TH), accordingly, takes place.
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Semiconductor Physics, Quantum Electronics & Optoelectronics. 2003. V. 6, N 4. P. 454-457.
© 2003, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine454
PACS: 64.90+b
Atomic defects and physical-chemical properties
of PbTe-InTe solid solutions
D.M. Freik, V.Ì. Boychuk, L.I. Mezhylovsjka
Vasyl Stefanyk Precarpathian University, 57, Shevchenko str., 76000 Ivano-Frankivsk, Ukraine,
E-mail: freik@pu.if.ua
Abstract. Crystal-quasichemical equations of probable mechanisms inherent to formation of
solid solutions based on lead telluride of the n-type in PbTe-InTe system are offered. Shown
is the possibility to satisfactorily explain experimental results by filling with indium atoms
312
2
1
2
1 InInIn +++ ↔ (up to 3 mol. % InTe) octahedral hollows (ÎH) of close-packed arrangement
of tellurium atoms in PbTe crystal lattice. At the greater content of indium telluride, the
allocation of both In+1 on ÎH, and In+3 on tetrahedral hollows (ÒH), accordingly, takes
place.
Keywords: lead telluride, indium telluride, solid solution, atomic defects, crystal-quasichemical
reaction.
Paper received 16.07.03; accepted for publication 11.12.03.
1. Introduction
Lead telluride is a basic material for device structures
working in the infrared range of an optical spectrum,
and also in various thermoelectric devices [1�3]. It crys-
tallizes in the structure of NaCl type, the space group
Fm3m-Oh
5 with the lattice parameter α = 6.452 Å and is
melted congruently at 1190 K. The nature of chemical
bonds is rather complicated here and corresponds to the
mixed ionic-covalence-metallic type. The ionicity of lat-
tice determines considerable (by the order of magnitude)
divergebcy between static ε0 and high-frequency dielec-
tric permittivities [2]. For lead telluride the existence of
bilateral field of homogeneity and diversion from a stoi-
chiometrical composition is characteristic, which causes
major values (1018�1020cm�3) of concentration of current
carriers, and various conductances, too. Thus, the sur-
plus of lead determines n-type of conductance, as tellu-
rium � the ð-type [3].
Now nature of atomic defects and their charge states
both in lead telluride and solid solutions based on it has
not been ascertained yet [2]. And there is no common
opinion about the mechanism of forming the solid solu-
tions in Pb-In-Te system [4, 5].
In this paper we offer a crystal-quasichemical ap-
proach suitable for the analysis of a defect subsystem
and mechanisms of solid solution formation in PbTe-InTe
system.
2. Experiment
The state diagram of PbTe-InTe system is related to an
eutectic type (Fig. 1) [4]. The eutectic composition is near
75 mol. % of InTe, temperature of nonvariant equilib-
rium � 913 K [4]. The limiting miscibility InTe in PbTe
has not ascertained ultimately and by the data of various
authors lies within 7 up to 35 mol. % [4, 5].
The alloys were prepared by direct melting of high-
clean components in evacuated at 10�2 Pà quartz am-
poules at 1300 K according to procedure [4]. The melt
was maintained during 10 hours with application of vi-
brating intermixing. The subsequent homogenising an-
nealing carried out at 950 K by 210 h, and quenching �
in ice water.
The phase composition, microhardness and electri-
cal properties of alloys in all the considered range of
existence of these solid solutions we explored.
The experimental data are submitted in Fig. 2. It is
found, that up to 20 mol. % of InTe the alloys are homo-
geneous, thus the lattice parameter decreases (Fig. 2,
curve 1). Both curves of concentration dependences of
the microhardness (Fig. 2, curve 2) and thermo-e.m.f co-
efficient (Fig. 2, curve 1) clearly pronounce two inflec-
tion points: in the vicinity of concentrations ~3 and
20 mol. % of InTe. Stationary values of the lattice pa-
rameter, thermo-e.m.f. coefficient and microhardness
after 20 mol. % of InTe, as well as results of the phase
D.M. Freik et al.: Atomic defects and physical-chemical properties of ...
455SQO, 6(4), 2003
n -P b Te 20 40 60 80
900
1300
500
T,
K
In Te, m o l %
Fig. 1. The state diagram of PbTe-InTe system [4].
Fig. 2. Concentration dependences (à): parameter of a unit cell
(à � 1), microhardness (Í � 2); (b): coefficient of thermo-e.m.f.
(α � 1), specific conductivity (σ�2); (c): concentrations (n�1)
and mobility (µ�2) of current carriers for PbTe-InTe system.
n-PbTe
à
b
100
200
3
3 10 20
O m c m– 1 – 1
s×1 0 – 3,
3 10 20
n,
c
m
–3
10
19
10
18
10
2
10
4
m
, c
m
V
–1
c–1
2
c
analysis confirm existence of biphase field, which is in
accord with the data [4]. Diminution of the thermo-e.m.f.
coefficient in alloys of composition 3�20 mol. % of InTe
(Fig. 2, curve 1) is caused by propagation of the electron
concentration (Fig. 2, curve 1). The observed decrease
in the direct-current conductivity in the field of composi-
tions up to 3 mol. % of InTe (Fig. 2, curve 2) can be ex-
plained by magnification of the contribution of an impu-
rity dispersion, which causes decrease in of the mobility
of current carriers (Fig. 2, curve 2). The stationary value
of the direct-current conductivity for compositions 3 to
20 mol. % of InTe is supplied with the opposite change of
the concentration and mobility of current carriers
(Fig. 2b).
3. Crystal-quasichemical reaction of atomic
defects
Existing models suitable for trying to explain properties
of In impurity are possible to be conditionally separated
into two groups [5]. In one of them indium is considered
as are impurity centre with the basic state In+2, and in
another In is the multiply charged centre with states In+1
and In+3. Therefore, from positions of valence rules, the
chemical formula of indium telluride should be repre-
sented as 23122 TeInInTeIn
2
1
2
1
−++−+ ↔ . It is considered that
the Hubbard energy for electrons of In impurity is nega-
tive, therefore In+2 state is energy unprofitable.
For the analysis of the defect subsystem in PbTe-InTe
solid solution, we have utillized the crystal-quasichemical
approach [6].
This method is based on superposition of crystal-
quasichemical clusters of the basic matrix and doping
element, which is generated on the basis of anti-structure
of the basic matrix. The anti-structure of lead telluride is
456
SQO, 6(4), 2003
D.M. Freik et al.: Atomic defects and physical-chemical properties of ...
halenit ⋅⋅
Te
''
PbVV , where �'� and �.� are the negative and
positive charges, respectively ''
PbV � doubly charged nega-
tive vacancy of lead, and ⋅⋅
TeV � doubly charged positive
vacancy of tellurium.
Crystal-quasichemical reaction of cluster formation
in electronic material n-PbTe (with excess Pb) can be
represented as follows:
⋅⋅⋅⋅ →+ Te
''
Pb
0
Te
''
Pb PbPb VVV ,
(1)
( ) ,'2TePb
)Pb(TePb)1(
Te)1(Pb
Te
''
PbTePb
eV
V
xx
xx
β
ββ
ββ +→
→+−
⋅⋅
−
⋅⋅
where x
PbPb , x
TeTe � lead and tellurium in clusters of the
crystal lattice, accordingly, �õ� � neutral charge, �0� �
zero charge, β � molecular ratio of a doping component,
e' � electron concentration.
Thus, the electronic conduction of lead telluride is
provided by vacancies in anionic ⋅⋅
TeV sublattice of the
crystalline structure of lead telluride.
The doping of lead telluride by telluride of indium
can be carried out by filling with lead vacancies the octa-
hedral hollows of a close-packed arrangement of tellu-
rium atoms in the crystal lattice (mechanism À). For this
case crystal-quasichemical cluster of the doping impu-
rity will be:
xVV Te
Pb
.'23
Te
''
Pb TeInInTeInIn
2
1
2
1
2
1
2
1
→+ −++⋅⋅ . (2)
Besides, the solid solution formation can take place
in such a way that +In ions occupy the lead vacancies of
the basic matrix ( ''
PbIn V→+ ), and triply charged 3In +
ions are implanted in tetrahedral hollows of a close-
packed arrangement of tellurium atoms of lead telluride
crystal lattice ( ...3 InIn i→+ ), which are free (mechanism Â):
i
xVVV )In(TeInTeInIn ...
Te
Pb
'''23
Te
''
Pb
2
1
2
1
2
1
2
1
2
1
→+ −++⋅⋅ . (3)
Let�s consider a superposition of alloying clusters with
the basic matrix of a n-type for various mechanisms of
solid solution formation. The mechanism (À):
( )[ ]
[ ]
[ ] [ ]
.
2
1
')25.0('2
TeInPb
')1(2Te
InInPbTeInIn
'2TePb)1(
Te)1()1)(1(Pb)(1
Te)1()1)(1(
Pb
.'
)(1Te
Pb
.'
Te)1(Pb
2
1
2
1
2
1
2
1
yheye
V
eyV
y
eVy
y
x
yy
x
y
x
y
y
x
yy
yy
x
y
x
xx
+−++
+→
→−+×
×
→
+
++−
⋅⋅
−+−−−
⋅⋅
−+−−
−
⋅⋅
−
ββ
β
β
ββ
ββ
ββ
(4)
Thus, interaction of the doping cluster with the n-type
material, in accord with this mechanism, for the decrease
in vacancy number in the anionic sublattice implies an
increase of majority carriers concentration. Here,
Te)1(Te )()( ⋅⋅
−
⋅⋅ > yVV ββ is valid, and 2βe' < 2βe' + y(0.5 �
2β)e' (y < 1).
The mechanism (Â):
( )[ ]
[ ]
.')25.0('2
InTe
InPbInTeIn
'2TePb)1(
...
Te)1()1)(1(
Pb
''
)(1
...
Te
Pb
'''
Te)1(Pb
2
1
2
1
2
1
2
1
2
1
2
1
eye
V
VVy
eVy
i
yy
x
yy
x
yy
x
y
i
x
xx
ββ
β
ββ
ββ
−++
+
×
×
→
+
++−
⋅⋅
−++−
−
⋅⋅
−
(5)
In this case, the solid solution formation leads to in-
crease of the electron concentration (2βe' + y(0.5 � 2β)e' >
> 2βe� , y < 1), which is determined by redistribution of
vacancies between both sublattices � cationic and ani-
onic. Thus, intercalation of interstitial indium ...
iIn also
takes place tetrahedral hollows in the close-packed ar-
rangement of tellurium atoms of PbTe crystalline struc-
ture.
In the case of embodying the charged In+2 state in
accord with the mechanism of filling the doping cluster,
the reaction will accept the following look:
xxVV TePb
22
Te
''
Pb TeInTeIn →+ −+⋅⋅ . (6)
The solid solution formation will be carried out ac-
cording to:
( )[ ]
[ ] [ ]
[ ] .')1(2Te
InPbTeIn
'2TePb)1(
Te)1()1)(1(
Pb)(1TePb
Te)1(Pb
eyV
y
eVy
y
x
yy
x
y
x
y
xx
xx
−+×
×→+
++−
⋅⋅
−+−−
−
⋅⋅
−
β
β
ββ
ββ
(7)
The decrease of the electron concentration (2βe' >
> 2β(1 � y)e' , y < 1) due to defect redistribution in an
anionic sublattice takes place.
Taking into account the mechanism of In+2 inter-
calaction, the alloy cluster will be:
i
xVVV )In(TeTeIn ..
Te
''
Pb
22
Te
''
Pb →+ −+⋅⋅ . (8)
( )[ ]
[ ] [ ]
[ ] .')1(2)(InTe
Pb)(InTe
'2TePb)1(
..
Te)1()1)(1(
Pb
''
)(1
..
Te
''
Pb
Te)1(Pb
eyV
VVy
eVy
yy
x
yy
y
x
yi
x
xx
−+×
×→+
++−
⋅⋅
−+−−
−
⋅⋅
−
β
β
ββ
ββ
(9)
Similarly to results received in (7), it is seen that the
electron concentration decreases due to defect redistri-
bution between cationic and anionic sublattices of the
basic matrix.
4. Discussion
In accord with the above mentioned crystal-quasichemical
equations (4) and (5) for solid solution formation in PbTe-
InTe system, taking into account both the mechanism of
D.M. Freik et al.: Atomic defects and physical-chemical properties of ...
457SQO, 6(4), 2003
filling (mechanism A (4)), and mechanism of intercala-
tion (mechanism B (5)), doping of indium telluride devel-
ops the donor properties. To determine, which of these
mechanisms plays a preferential role at the given InTe
concentrations, it seemes possible if being based on a
comparison of experimental results (Fig. 2) as well as
crystal-quasichemical parameters of separate atoms
(Tab. 1) and crystal lattice (Tab. 1, 2) [7].
So, apparent from the experiment stationary values
of current carriers concentration (Fig. 2, curve 1) and
thermo-e.m.f. coefficient (Fig. 2, curve 1) in the range up
to 3 mol.% of InTe confirm inappreciable donor activity
of a doping impurity. It can be agree with (4) when em-
bodying the mechanism of filling ÎH by indium in a state
In+1+In+3. For concentration range 3 to 20 mol. % of
InTe, the most probable mechanism of solid solution for-
mation is filling the octahedral (In+1 > ÎH) and tetrahe-
dral hollows (In+3 > ÒH) in close-packed arrangement of
tellurium atoms of PbTe crystalline structure (5). As the
vacancies in cationic and anionic sublattices are formed,
and radius In+3 a little bit differs from radius of the tetra-
hedral hollow in tellurium sublattice (Tab. 1, 2) the dimi-
nution of the lattice parameter, and also increasing the
electron concentration (Fig. 2, curve 1) takes place. The
considerable change of the defect state in the crystal lat-
tice cause a decrease of current carrier mobility (Fig. 2,
curve 2) and increase of microhardness (Fig. 2, curve 2).
Two mechanisms of solid solution formation in ac-
cord with (7) and (9) are improbable, as they cause de-
creasing the majority current carrier concentration, which
contradicts to the experiment (Fig. 2, curve 1).
5. Conclusions
1. The crystal-quasichemical mechanisms of solid
solution formation in the system PbTe-InTe are offered.
2. It is ascertained, that the donor activity of doping
impurity can be caused by two mechanisms, namely: fill-
ing the lead vacancies with indium atoms and simultane-
ous embodying both the mechanism of filling octahedral
hollows with In+1, and tetrahedral hollows with In+3 in
the close-packed arangement of tellurium atoms in PbTe
crystalline structure.
3. Determined are concentration ranges of doping
impurity, for which one of the mechanisms of solid solu-
tion formation prevails.
References
1. Yu.I. Ravich, V.À. Efimova, V.À. Smirnov. The methods of
research of semiconductors in application to lead chalco-
genides PbTe, PbSe, PbS. Science, Moscow (1968).
2. D.Ì. Freik, V.V. Prokopiv, Ì.Î. Galushcjak, Ì.V. Pyts,
G.D. Mateik. Crystal-quasichemical and thermodynamics
of atomic defects at AIVBVI allows. Plai, Ivano-Frankivsk
(1999).
3. V.Ì. Shperun, D.Ì. Freik, R.². Zapukhlyak. Thermal-elec-
trical of lead tellurides and its analogs. Plai, Ivano-Frankivsk
(2000).
4. Å.I. Rogacheva, G.V. Gorne, N.Ì. Panasenko. Phase inter-
action and nature of solid solutions in PbTe-InTe system //
Nonorganic materials, 15(8), pp. 1366-1369 (1979).
5. I.À. Drabkin, Ì.À. Kvantov, V.V. Kogmpaniets, Yu.P. Kos-
tikov, Charging states of In in PbTe // Physics and technique
of semiconductors, 15(7), pp. 1276-1277 (1981).
6. S.S. Lisnyak, D.Ì. Freik, Ì.Î. Galushchak, V.V. Prokopiv,
I.Ì. Ivanyshyn, V.V. Boryk. Crystal-quasichemical of defects
at lead chalcogenides // Physics and chemistry of solids, 1(1),
pp. 131-133 (2000).
7. S.À. Semyletov. Tetrahedral and octahedral covalent radi-
uses // Crystallography, 21(4), pp. 752-758 (1976).
Table 2. Radii of tetrahedral (rÒH) and octahedral (rÎH) hol-
lows for the close-packed arrangement of Pb and Te in various
states of PbTe structure.
Elements rÒH, Å rÎH, Å
Te (at.) 0.73 1.81
Te (cov.) 0.79 1.87
Te (2-) (ionic) 0.04 1.12
Pb (at.) 0.34 1.42
Pb (cov.) 0.68 1.76
Pb (+2) (ionic) 0.89 1.97
Table 1. Electronic structure and elements radii of Pb, Te and In [7].
Element Pb Te In
r, Å
4f145d106s26p2 4d105s25p4 3d104s24p1
atomic 1,81 1,42 2
covalent 1,47 1,36 1,44
ionic 1,26(+2) 2,11(�2) 1,30(+1),
1,27(+2),
0,92(+3)
octahedral 1,62 1,64 1,27
tetrahedral 1,46 1,34 �
|
| id | nasplib_isofts_kiev_ua-123456789-118073 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2025-12-07T16:36:24Z |
| publishDate | 2003 |
| publisher | Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| record_format | dspace |
| spelling | Freik, D.M. Boychuk, V.I. Mezhylovsjka, L.I. 2017-05-28T16:33:02Z 2017-05-28T16:33:02Z 2003 Atomic defects and physical-chemical properties of PbTe-InTe solid solutions / D.M. Freik, V.I. Boychuk, L.I. Mezhylovsjka // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2003. — Т. 6, № 4. — С. 454-457. — Бібліогр.: 7 назв. — англ. 1560-8034 PACS: 64.90+b https://nasplib.isofts.kiev.ua/handle/123456789/118073 Crystal-quasichemical equations of probable mechanisms inherent to formation of solid solutions based on lead telluride of the n-type in PbTe-InTe system are offered. Shown is the possibility to satisfactorily explain experimental results by filling with indium atoms In⁺² <--> In⁺¹ In⁺³ (up to 3 mol. % InTe) octahedral hollows (IH) of close-packed arrangement of tellurium atoms in PbTe crystal lattice. At the greater content of indium telluride, the allocation of both In⁺¹ on OH, and In⁺³ on tetrahedral hollows (TH), accordingly, takes place. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Atomic defects and physical-chemical properties of PbTe-InTe solid solutions Article published earlier |
| spellingShingle | Atomic defects and physical-chemical properties of PbTe-InTe solid solutions Freik, D.M. Boychuk, V.I. Mezhylovsjka, L.I. |
| title | Atomic defects and physical-chemical properties of PbTe-InTe solid solutions |
| title_full | Atomic defects and physical-chemical properties of PbTe-InTe solid solutions |
| title_fullStr | Atomic defects and physical-chemical properties of PbTe-InTe solid solutions |
| title_full_unstemmed | Atomic defects and physical-chemical properties of PbTe-InTe solid solutions |
| title_short | Atomic defects and physical-chemical properties of PbTe-InTe solid solutions |
| title_sort | atomic defects and physical-chemical properties of pbte-inte solid solutions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/118073 |
| work_keys_str_mv | AT freikdm atomicdefectsandphysicalchemicalpropertiesofpbteintesolidsolutions AT boychukvi atomicdefectsandphysicalchemicalpropertiesofpbteintesolidsolutions AT mezhylovsjkali atomicdefectsandphysicalchemicalpropertiesofpbteintesolidsolutions |