285 ISSN 1063-7826, Semiconductors, 2016, Vol. 50, No. 3, pp. 285–288. © Pleiades Publishing, Ltd., 2016. Original Russian Text © Z.A. Dzhakhangirli, T.G. Kerimova, N.A. Abdullaev, 2016, published in Fizika i Tekhnika Poluprovodnikov, 2016, Vol. 50, No. 3, pp. 289–292. Ab Initio Calculations of Phonon Dispersion in ZnGa 2 Se 4 Z. A. Dzhakhangirli a, b *, T. G. Kerimova a , and N. A. Abdullaev a, b ** a Institute of Physics, Azerbaijan National Academy of Sciences, Baku, Az-1143 Azerbaijan b Azerbaijan Technical University, Baku, Az-1073 Azerbaijan *e-mail: cahanzakir@yahoo.com; **e-mail: abnadir@mail.ru Submitted June 8, 2015; accepted for publication June 10, 2015 Abstract—In the context of density functional theory, the phonon density of states and phonon dispersion are calculated for ZnGa 2 Se 4 . The temperature dependence of the heat capacity of ZnGa 2 Se 4 in the temperature range 5–400 K is obtained. The calculated frequencies and symmetries of phonon modes in the center of the Brillouin zone are in good agreement with experimental data obtained by Raman spectroscopy and infrared spectroscopy. DOI: 10.1134/S1063782616030088 1. INTRODUCTION (II = Zn, Cd; III = In, Ga; VI = S, Se, Te) compounds that crystallize in the space group are attracting attention due to the possibility of the use of these materials in semiconductor device engineering. The characteristic features of these com- pounds are birefringence, large coefficients of nonlin- ear susceptibility, high photosensitivity, and bright photoluminescence. In combination with a wide band gap (2.4–4.5 eV), the above-listed properties puts these compounds into the series of materials that offer promise as a basis for the production of nonlinear optoelectronic converters and devices [1, 2]. There- fore, studying the physical properties of these com- pounds is an important challenge. A significant place is occupied by both theoretical and experimental stud- ies of electron and phonon states. Knowledge of pho- non spectra and their dependences on temperature, pressure, and other external factors is important for interpreting the mechanisms of heat capacity, thermal expansion, thermal conductivity, sound absorption, etc. [3]. Combined theoretical and experimental stud- ies of phonon spectra and lattice dynamics provide a means for obtaining data on phonon frequencies at the center of the Brillouin zone and constants of inter- atomic bonding, on phonon–phonon and phonon– electron interactions, etc. Optical phonons in ZnGa 2 Se 4 were explored by infrared and Raman spectroscopies [4–6]. In [6], the optical phonon frequencies were identified in accor- dance with symmetry types, and with the use of the symmetrized displacements of atoms in the unit cell, it was established which frequencies relate to corre- sponding atomic displacements in the unit cell. In this paper, we report the results of ab initio cal- culations of the phonon density of states (DoS) and phonon dispersion for high-symmetry points and lines of the Brillouin zone of the compound ZnGa 2 Se 4 . In addition, the results for the temperature dependence of the heat capacity of this compound are reported. 2. CRYSTAL STRUCTURE AND METHOD OF CALCULATION Figure 1 schematically shows the crystal lattice of ZnGa 2 Se 4 . This compound is a crystal-chemical ana- log of compounds that crystallize in the zinc blende (T d ) and chalcopyrite ( ) structures. In the crystal lattice, each cation atom is surrounded by four anion atoms. From X-ray diffraction studies, the crystal-lat- tice parameters are determined. The crystal-lattice parameters and the interatomic bond lengths calcu- lated for ZnGa 2 Se 4 in accordance with [7] are given in Table 1. In compounds (the space group), chemical bonding is of the ion–covalent type. In the ZnGa 2 Se 4 compound, as well as in the CdGa 2 S 4 [8] and CdGa 2 Se 4 [9] isostructural compounds, the force constant of II–VI interatomic bonds, f(II–VI), is much larger than the force constant f(III–VI) of II–VI interatomic bonds [10]. In the unit cell of ZnGa 2 Se 4 , there are seven atoms. The atomic coordinates are as follows: Zn (0, 0, 0), Ga 1 (1/2, 1/2, 0)a, Ga 2 (0, 1/2, η/2)a, Se 1 (x, y , zη)a, Se 2 (1 – x, 1 – y , zη)a, Se 3 (1/2 + x, ½ – y , (1/2 – z)η)a, and Se 4 (1/2 – x, ½ + y , (1/2 – z)η)a. Here η = c/a, where c and a are the crystal-lattice parameters. II III VI 2 4 A B C 2 4 S 12 2d D II III VI 2 4 A B C 2 4 S NONELECTRONIC PROPERTIES OF SEMICONDUCTORS (ATOMIC STRUCTURE, DIFFUSION)