CRYSTAL-QUASICHEMICAL ANALYSIS OF DEFECT SUBSYSTEM OF DOPED PbTe: Sb CRYSTALS AND Pb-Sb-Te SOLID SOLUTIONS

: Within crystalquasichemical formalism models of point defects of crystals in the Pb-Sb-Te system were specified. Based on proposed crystalquasichemical formulae of antimony doped crystals PbTe:Sb amphoteric dopant effect was explained. Mechanisms of solid solution formation for РbТе-Sb 2 Те 3 : replacement of antimony ions lead sites 1 P b S b  with the formation of cation vacancies tellurium 0i Te (II) were examined. Dominant point defects in doped crystals PbTe:Sb and РbТе-Sb 2 Те 3 solid solutions based on p-PbTe were defined. Dependences of concentration of dominant point defects, current carriers and Hall concentration on content of dopant compound and the initial deviation from stoichiometry in the basic matrix were calculated.


INTRODUCTION
IV-VI compounds and solid solutions on basis of them are basic materials for making thermoelectric energy converters in high temperature region (500-750) K, as well photodetectors and radiating structures of infrared optical spectrum [1].
Among them, lead telluride has an important place due to its properties: multivalley nature of its energy spectrum (N = 4), low lattice thermal conductivity (χ = 2.09 10 W•К -1 сm -1 ), relatively high current carrier mobility (μ ≈ 10 3 сm -2 V -1 •s -1 ), the largest value of μχ -1 , which causes a significant thermoelectric figure of merit (Zmax) Z = α 2 σ/χ, where α -coefficient of thermo-emf, σ -electrical conductivity , χ -coefficient of thermal conductivity. Clearly, large Z (which determined commercial use of thermoelectric material) depends on α and σ, which are sensitive to the nature of electronic states. Thermal conductivity is defined by phonon spectrum of the crystal (χl) and the concentration of current carriers (χe). Decrease of thermal conductivity components ( le      ) is one of the effective ways of increase of the thermoelectric figure of merit. In this regard, the search for new compounds with complex crystal structures, which have low thermal conductivity is an urgent problem. Among them are quasi-binary systems (A IV -Ge, Sn, Pb; C V -Bi, Sb; B VI -Te) [17].
Lead telluride crystallizes in NaCl structure, which is a characteristic of ionic crystals. Chemical bond is complex and close to the ion-covalent-metallic. PbTe is characterized by significant deviations from the stoichiometric composition and bilateral homogeneity region and can have both n -type (with excess metal) and p-type (with excess chalcogen) conduction, causing significant concentration (10 18 -10 19 сm -3 ) of electrically active intrinsic defects [7].
Performance device structures are largely determined by defect subsystem of used crystals, which depends on the homogeneity region of compounds, the chemical composition of solid solutions based on them, and technological factors of their synthesis and subsequent treatments of the material. Analyzing the current state of the problem, it should be noted that the ambiguity of the experimental data and theoretical interpretation of the nature and type of point defects and their charge states and energy parameters in crystals based on lead telluride greatly complicates the interpretation of their physical and chemical properties. Therefore, further development of theoretical approaches to the study of the defect subsystem and explanation of existing as well as new experimental data obtained from one standpoint remains an urgent problem.

ANALYSIS OF DOPANT BEHAVIOR.
Taking into account that the valence shell of atoms of V group elements has s 2 p 3 configuration, Sb atoms can give (s 2 p 0 configuration, valence +3) or accept (s 2 p 6 configuration, valence -3) 3 electrons from p-state. So dopant in PbTe can be in two charge states Sb 3+ and Sb 3-. In doped crystals PbTe:Sb fraction of electrically active impurity atoms is significantly less than 1, and it evidences that impurity atoms are distributed between the cationic and anionic sublattices [12]. Thus, in doped crystals PbTe:Sb dopant, replacing lead in its sublattice, ionizes from state Sb 0 (s 2 p 3  . The fact that the dopant can occupy lead and tellurium sites in PbTe crystal structure and disproportionation of its charge state can be described by the following reaction: Here

CRYSTALQUASICHEMICAL FORMULAE.
For the analysis of the defect subsystem in investigated crystals crystalquasichemical approach was used, It is based on the concept of antistructure [13], which has the form of // Pb Te VV for lead telluride, where // Pb V and Te V -double-charged lead and tellurium vacancies, respectively; "/" and "•" -negative and positive charges, respectively. Crystalquasichemical formula is written as a superposition of alloying cluster formed on the basis of antistructure of basic matrix and crystal formula of basic compound.
Taking into account the amphoteric effect of Sb dopant in lead telluride crystals (1), alloying cluster can be written as follows: Crystal-Quasichemical Analysis of Defect Subsystem… 57 Crystalquasichemical formula of p-PbTe with the complex range of point defects in the cation sublattice (single and double-charged Pb vacancies) is represented as [4]: Superposition of crystalquasichemical formula of p-PbTe (3) and the alloying cluster (2) presents the crystal-quasichemical formula of p-PbTe:Sb: where x -atomic fraction of dopant (Sb), -the value of the initial deviation from stoichiometry on the side of Te, δ -coefficient of disproportionation of cationic vacancies charge state, γ -fraction of interstitial tellurium, Te  -lead and tellurium atoms in lattice sites.

SOLID SOLUTIONS P-PBTE-SB2TE3
The possible mechanisms of PbTe-Sb2Te3 solid solution formation are substitution of Sb ions Pb sites with the formation of cation vacancies (mechanism I) or the substitution of Sb ions Pb site with the formation of interstitial tellurium (mechanism II).

MECHANISM I.
At calculation per 1 tellurium atom and subject to charge state of Sb 3+ and Те 2-ions chemical formula for alloying component is: 32 Sb Te  . Alloying cluster in this case is: Then crystalquasichemical formula of p-PbTe-Sb2Te3 is: where х -molar fraction of Sb2Те3.

ELECTRIC BALANCE EQUATION
Proposed mechanisms of doping and crystal formulae (4), (6), (8) make it possible to find analytical expressions of the concentration of individual point defects and current carriers on the magnitude of deviation from stoichiometric composition in the base compound (α, ) and dopant content (x).
In particular for p-PbTe:Sb according to crystalquasichemical formula (4), total electroneutrality equation is written as follows: where   , Z -number of structural units per unit cell (Z = 4), a -lattice parameter.
Hall concentration of current carriers nH in this case is defined as: Similar analysis was done for PbTe-Sb2Te3 solid solution. , and Hall concentration in both cases decreases slightly. Above-mentioned specific behavior of Hall concentration depending on the content of dopant and its charge state is well illustrated on 3d-diagram nH-x-z (Fig. 1). Sb  of lead telluride crystal lattice, which concentration increases with dopant content increase (Fig. 2 -curves 2, 3 (Fig. 2 -curves 4, 6). It should be noted that the concentration of 1 Pb V  , 0 i Te vary slightly with antimony content increase (Fig. 2 -curves 5, 7).

Fig. 2. Dependence of Hall concentration (1 -nH) and the concentration of point defects (2-7 -Ni) in p-PbTe:Sb crystals on dopant content. Ni: 2 -
The proposed mechanism of doping satisfactorily explains the experimentally observed behavior of thermoelectric parameters on dopant content. Thus, based on the data of [3,5,11] we can conclude that, in practice, there is realization of condition: z < 0.5, ie the concentration of impurity ions [ 1

Te
Sb  ]. Specifically, comparing the experimental data [5] on the active donor action of antimony ( Fig. 3) with the calculation for p-PbTe:Sb (Fig. 1), it was found the value of disproportionation of dopant charge state: z ≈ 0.45 at the maximum value of the initial deviation from stoichiometry on the side of tellurium. The observed decrease of the concentration of current carriers in PbTe:Sb (Fig. 3 -curve 2) in the content of Sb over 0.3 at. % can be explained by certain predominance of concentrations of impurity ions in tellurium sites ( 11   Pb  Te [Sb ] [Sb ]   ).

SOLID SOLUTIONS P-PBTE-SB2TE3
Thermoelectric parameters of PbTe-Sb2Te3 were studied in several papers [10,13,15,17,18]. In [15] it was found that the increase of Sb2Te3 content in solid solution leads to donor effect with microhardness increase (H) (Fig. 4 -curve 1) and decrease of the coefficient of thermo-emf (α) (Fig. 4curve 3). In alloys containing Sb2Te3 more (1.5-2) mole % Hall concentration nH (Fig. 4 -curve 2) and thermo-emf α (Fig. 4 -curve 3) practically do not change. Issues associated with the decrease of the value of thermal conductivity of PbTe-Sb2Te3 solid solutions with Sb2Te3 content increase were studied in [14,18]. The value of χ for alloy of PbTe with 1.02 mole % Sb2Te3 is 1.25•10 -2 WK -1 cm -1 at 500 K, which confirms the idea of the good thermoelectric efficiency of these solid solutions. The observed phenomenon associated with relation between lattice (χl) and electron (χe) components of thermal conductivity [17].  (2 -n), electrical conductivity (3 -) and thermal conductivity (4 -κ) on antimony content [5] Consider in detail the mechanisms of defect formation in PbTe-Sb2Te3 solid solutions. When realization of mechanism I (stoichiometry for chalcogen) there is slight decrease of concentration of major current carriers with Sb2Te3 fraction increase (Fig. 5, a -curve 1). With realization of mechanism II (stoichiometry for antimony) in р-PbTe-Sb2Te3 (Fig. 5, b -curve 1) with Sb2Te3 fraction increase there is decrease of the concentration of current carriers, change of the conductivity type with low dopant content and further increase of electron concentration. Comparing the results of calculations with experimental data on the active donor effect of Sb2Te3 (Fig. 4 -curve 2), we can conclude that when the dopant content to 2 mole % of Sb2Te3 mechanism II is dominant, and with more of its contents (up to the limit of solubility) mechanism I is dominant.  (Fig. 5, b). Concentrations

CONCLUSIONS
Based on first proposed crystalquasichemical formulae that take into account the amphoteric behavior of Sb in PbTe crystals, it has been found that with prevalence of antimony in cation sites It has been shown that with increasing content of alloying compound in PbTe-Sb2Te3 solid solutions to 2 mole % of Sb2Te3 substitutions of cation sites and the formation of interstitial tellurium predominant. With more dopant content (up to the limit of solubility) there is a replacement of Pb sites and formation of cation vacancies. In the first case there is thermodynamic p-n-conversion in crystals with the initial p-type conductivity. For the second case there is decrease of Hall concentration in р-PbTe-Sb2Te3.
It has been shown that new crystal approaches deepen the possibility of a scientific analysis of the defect subsystem in semiconductor crystals, and determine the technological aspects of the property control.
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