Physics of the Solid State
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Ab initio calculations of electronic properties, frequency dispersion of dielectric coefficients and the edge of the optical absorption of TlInS2<Sn> single crystals
Mustafaeva S. N.1, Asadov M. M.2,3, Huseynova S. S.1, Hasanov N. Z.1, Lukichev V. F.4
1Institute of Physics, National Academy of Sciences of Azerbaijan, Baku, Azerbaijan
2Institute of Catalysis and Inorganic Chemistry named after Academician M. Nagiyev, Azerbaijan National Academy of Sciences, Baku, Azerbaijan
3Scientific Research Institute of Geotechnological Problems of Oil, Gas and Chemistry, Baku, Azerbaijan
4Valiev Institute of Physics and Technology of RAS, Moscow, Russia

Calculations of the band structure and density of states for supercells of TlInS2 and TlInS2<Sn> semiconductor crystals with monoclinic singony within the density functional theory (DFT) are presented. In DFT calculations, the Coulomb repulsion (the Hubbard parameter (U)) was taken into account in order to correctly describe the band gap (Eg) of crystals. It is shown that the maximum of the valence band and the minimum of the conduction band of TlInS2 are located at the center (point ) of the Brillouin zone, which points to the direct energy of the band gap of the TlInS2 and TlInS2<Sn> crystals. Thrue results of calculating the band structure and features of the distribution of the density of electronic states in TlInS2 and TlInS2<Sn> are discussed. TlInS2 single crystals doped with 0.1 mol.% tin (TlInS2<0.1 mol.% Sn>) were synthesized and then grown by the Bridgman-Stockbarger method. The frequency dispersion of the dielectric coefficients and conductivity of a TlInS2 and TlInS2<0.1 mol.% Sn> single crystals in the frequency range f=5·104-3.5·107 Hz is studied. It is shown that relaxation losses occur in TlInS2<Sn>. A hopping mechanism of ac charge transfer in TlInS2<Sn> has been established. In TlInS2<Sn>, the parameters of localized states, such as the density of states near the Fermi level and their energy spread, the average hopping time and distance, and the concentration of deep traps, are estimated. The optical properties of TlInS2 and TlInS2<0.1 mol.% Sn> single crystals have been studied. The values of Eg for direct optical transitions in TlInS2 and TlInS2<0.1 mol.% Sn> crystals were obtained from the optical absorption spectra. It has been shown that the introduction of 0.1 mol.% Sn, which replaces indium atoms, into TlInS2 reduces the value of Eg, for example, at 150 K from 2.539(TlInS2) to 2.486 eV (TlInS2<0.1 mol.% Sn>). From optical measurements, the average temperature coefficient of the band gap d Eg/d T=-7·10-4 eV/K for TlInS2<Sn> was calculated. The decrease in the band gap of the TlInS2Sn> single crystal with respect to TlInS2 is 16 meV at 300 K and 53 meV at 150 K. Keywords: supercell, semiconductor TlInS2, tin doping, monoclinic syngony, density functional theory, electronic structure, single crystals, dielectric properties, optical absorption, charge transfer, parameters of localized states.
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