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This paper has presented results of calculations of optical functions for e||c and e^c polarizations in 0 - 12 eV energy interval, band structure and effective masses of electrons and holes of ternary compound InGaTe
_{2}. Genesis of valence band was investigated by using group-theoretical analyses. The main features of spectra of optical functions, the parameters of transition and their theoretical nature were found out. Identified interband transitions are responsible for the main peaks in the optical functions. Calculated results are in good agreement with the known experimental data.

It is known that search of new semiconductor materials is usually conducted in the direction of expansion of crystal structure group of already known materials. In particular interpretation of crystal structure of TlSe, it is revealed that this phase differs from extreme specific features. The lattice of TlSe is made of two independent structural units from eight-vertex polyhedron with ionic nature of binding of Tl^{+}-Se and a tetrahedron with covalent binding between Tl^{3+}-Se and therefore, the chemical formula of TlSe should be written as Tl^{+}Tl^{3}^{+}Se_{2}. Thus, by replacement of trivalent atom of thallium corresponding trivalent atoms, in particular, gallium and indium in a lattice of TlSe are received a new class of semiconductor compounds of type. X-ray diffraction researches [_{2} (Te_{2}), TlGaTe_{2}, InGaSe_{2} (Te_{2}) in domestic and foreign literature there are many data [_{2} having chained crystal structure weren’t carried out.

In this work, results of calculation of optical functions and effective masses of electrons and holes of compound InGaTe_{2} crystallizing in a tetragonal syngony have been presented. In these calculations the pseudo-po- tential method is used.

Semiconductor compound InGaTe_{2} crystallizes in a tetragonal lattice with space group_{2} are investigated in [

The band structure and optical functions of InGaTe_{2} were calculated using pseudopotential method. Calculation of an electronic structure was carried out by DFT, with the help ABINIT software package, using Troiller-Mar- tins pseudopotentials in basis of plane waves. In expansion of wave function plane waves with the maximum kinetic energy of 30 Ry were used. Lattice parameters were defined by total energy minimization and structure parameters were optimized by means of Gelman-Feynman forces.

Minimization process was carried out until

Band structure calculation was carried out in symmetric points Г, T, N, P and on the lines connecting these points. The table of irreducible and double irreducible representations of wave vector groups for space group

In [_{2}. The lowest subband consisting of four states, about ~6 eV are remote from the others with wide energy gap. Group-Theoretical Analysis shows that these bands located about −10 - −11 eV are obliged by the origin to 5 s-states of Te. The following group of four valence bands located at about −5 eV energy region, comes generally from s-states of atoms of In and Ga. The remained big group consisting of ten bands with 5 eV wide occurs from р-states of atoms of In, Ga and Te. The X-ray photoemission structure of a valence band is given in [

Optical functions were calculated by the way described in [

Here

In summation over Brillouin zone in (1) elementary cell of the reciprocal lattice is divided into 64 equal parts on volume, and in them k points were chosen randomly. Calculations were carried out at 3000 k points for smooth histogram. N is defined from a normalization condition

where

The histogram was constructed with 0.2 eV energy step and covered all interband transitions v ® c up to 12 eV. Further ε_{i}(E) dependence was extrapolated by known formula

The real part of dielectric permeability is defined from cramers-kronig relations in Equation (2)

here the symbol P is principal value of integral.

Results of calculations of spectral functions ε_{r}(E) and ε_{i}(E) for e||c and e^c polarizations are given in _{r}(E) in the polarization e||c (_{i}(E) in both polarizations, which we associate with the transitions from the top of the valence band to the bottom of the conduction band are at 3.15 eV. In the spectrum of ε_{i}(E) and in the e^c polarization there are three peaks with the energies of 4.02, 5.9, 6.2 and 7.47 eV.

In e||c the polarization additional peaks located at energies of 3.9, 6.2 and 7.8 eV, but they, especially the last, are weak. The maximum value in e||c polarization is 15.1, and in e^c polarization is 12.8, such difference in value for different polarizations is characteristic for chained crystals with strong anisotropy.

Limiting value of ε_{r}(E = 0) is equal to 7.88 in e||c polarization and 7.21 in e^c polarization.

The main part of refraction index was determined by Equation (3):

The imaginary part of the refractive index is defined as (4),

In _{2} is presented.

For polarization e||c dependence begins with 2.1 eV, then there is an increase in imaginary part of coefficient refraction reaching a maximum at energy of 3.9 eV (2.53), then monotonous reduction and a minimum at energy of 8.3 eV (0.39) and increase to 9.6 eV (0.52) other areas of dependence. In e^c polarization dependence begins with very small energy of equal 0.12 eV, at 3.15 eV (1.93) and 4.02 eV (1.99) two maxima are observed, at energy of 3.65 eV (1.7) and between maxima there is a minimum further dependence monotonously the pronounced maximum decreases and observed at 6.23 eV (4.72) a minimum at 6.88 eV (1.11), a maximum at 7.47 eV (1.19) and further reduction with increase in energy.

For e e||c polarization

The reflection coefficient at normal incidence of light is defined by a Formula (5):

Spectral dependence of Reflectivity of InGaTe_{2} is given in

_{2} for e||c and e^c polarizations. The maximum of the reflection coefficient in the polarization parallel to the optic axis is at an energy »3.9 eV (0.46), and two minima at energies »2.61 eV (0.30), »5.93 eV (0.29). In polarization perpendicular to the optical axis of the crystal main peaks occur at energies »3.15 eV (0.4), »6.23 eV (0.66), and minima at the energies »5.98 eV (0.29), »6.89 eV (0.22). The Characteristic Electron Energy Loss function was shown by (6)

The spectral characteristic of imaginary part of an inverse value of complex dielectric permeability

is presented in

In polarization e^c maxima appear at energy of 6.89 eV (0.41) and 8.2 eV (0.71), and minima at energy of 1.66 eV (0.01) 6.22 eV (0.02).

Real and imaginary parts of optical conductivity were defined by Formula (7):

Dependence

From here two bright minima are visible at energy of 2.61 eV (13.27), 4.57 eV (−8.6) and pronounced maxima at energy of 3.15 eV (21.18), (e||c).And for polarization e^c, the weak minimum here is observed at 3.65 eV (9.79), the bright maximum at 2.66 eV (21.15) and for both polarization occurs further weak reduction

Components of inverse effective mass tensor were determined by the formula

m_{0}-electron rest mass:

operator _{0},

V-volume of elementary cell, E_{n}(k_{0}) and _{0} _{ }

Calculation of band structure shows that maximum of valence and minimum of conduction bands are located at high symmetry point T of k_{0} = 0.5b_{1} − 0.5b_{2} + 0.5b_{3} (b_{1}, b_{2}, b_{3}). Here b_{1}, b_{2}, b_{3} are translation vectors of reciprocal lattice.

In our calculations components of tensor of inverse effective mass of electron were calculated with an accuracy to 0.01 m_{0}._{ }

Components of tensor of inverse effective mass of holes is given by

As can be seen tensors of inverse effective mass of both electrons and holes have diagonal form and therefore isoenergetic surfaces are described by rotational ellipsoids that is corresponds to symmetry of crystal.

So, in this report the spectra of optical fundamental functions of the semiconductor InGaTe_{2} have been calculated for two polarizations e||c and e^c in 0 - 12 eV energy range for the first time. Parameters have been defined, effective masses of electrons and holes of compound InGaTe_{2} were calculated on the basis of the band structure. The results obtained allow a detailed analysis of the optical properties and electronic structure of InGaTe_{2}.