Ab initio calculation of the structure and frequency dependences of dielectric properties of new semiconductors TlIn$_{1-x}$Tm$_x$S$_2$ ($x$ = 0.001 and 0.005)

The monoclinic structure TlIn$_{1-x}$Tm$_x$S$_2$ was studied based on the density functional theory (DFT). The cases of substitution of indium atoms with thulium are considered. The lattice cell parameters were determined in optimized supercells TlInS$_2$ taking into account the approximation of the local density. Lattice constants for a layered crystal TlIn$_{1-x}$Tm$_x$S$_2$ were theoretically determined based on calculations of a monoclinic structure with a space group $C/2c$ (coordination number $Z$ = 16, No 15) and compared with experimental results. New semiconductor polycrystals of TlIn$_{1-x}$Tm$_x$S$_2$ ($x$ = 0, 0.001 and 0.005) compositions were synthesized in quartz ampoules and corresponding single crystals were grown from them by directional solidification method. Analysis of X-ray diffraction patterns shows that all compositions TlIn$_{1-x}$Tm$_x$S$_2$ have stable monoclinic crystal system with space group $C/2c$. The calculated parameters of the lattice cell of TlIn$_{1-x}$Tm$_x$S$_2$ samples confirm this. Dielectric properties in alternating electric fields with a frequency of $f$ = 5 $\cdot$ 10$^4$–3.5 $\cdot$ 10$^7$ Hz at room temperature were studied in single crystals. The relaxation character of the dielectric constant, the nature of dielectric losses, and the hopping mechanism of charge transfer in TlIn$_{1-x}$Tm$_x$S$_2$ samples were determined. The parameters of localized states in crystals of TlIn$_{1-x}$Tm$_x$S$_2$ samples were calculated using the Mott model. It was shown that, the AC conductivity, the density of localized states near the Fermi level, the average distance and time of charge carrier hops in TlIn$_{1-x}$Tm$_x$S$_2$ increase compared with the undoped TlInS$_2$.