Journal of Physical Studies 22(3), Article 3301 [5 pages] (2018) DOI: https://doi.org/10.30970/jps.22.3301 THE BAND ENERGY STRUCTURE OF (N(CH3)4)2ZnCl4 CRYSTALS I. M. Kunyo{1}, A. I. Kashuba{1,2}, I. V. Karpa{1}, V. B. Stakhura{2}, S. A. Sveleba{1}, I. M. Katerynchuk{1}, I. S. Holyns'kyi{1}, T. I. Vozniak{1}, M. V. Kovalenko{2} {1}Electronics and Computer Technology Faculty, Ivan Franko National University of Lviv 107, Tarnavski St., Lviv, UA-79017, Ukraine {2}Physics Faculty, Ivan Franko National University of Lviv 8, Kyrylo and Mefodiy St., Lviv, UA-79005, Ukraine

The $A_{2}BX_{4}$ type crystals (with $A$ = K, Rb, Cs, NH$_{4}$, and N(CH$_{3}$)$_{4}$; $B$ = Se, Zn, Co, Mn, Ni, and Fe; and $X$ = I, Cl, Br, and F) have been interesting because of their incommensurately modulated structures and the successive phase transitions. Most of these materials exhibit many physical properties related to ferroelectric and commensurate or incommensurate phase transitions. $A_{2}BX_{4}$ crystal family shows many physical properties related to structural phase transitions at low temperatures. These fundamental properties make this crystal family suitable for several applications such as temperature and humidity sensors. Significant attention is currently paid to (N(CH$_{3}$)$_{4}$)$_{2}M$Cl$_{4}$ ($M$ = divalent metal) compounds due to the several phase transitions exhibited by such materials below 300 K. The band structure of crystals must be clearly understood in order to study phase transitions using optical spectroscopy and luminescence and to analyze and interpret the spectra. The band-energy structure of (N(CH$_{3}$)$_{4}$)$_{2}$ZnCl$_{4}$ crystals has not been calculated. Extensive experimental investigations of these crystals have not produced a body of data capable of supporting the traditional empirical calculation. Therefore, reliable information about the band-energy spectrum and transition mechanism of (N(CH$_{3}$)$_{4}$)$_{2}$ZnCl$_{4}$ single crystals can only be obtained from calculations based on first principles.

The energy band structure of (N(CH$_{3}$)$_{4}$)$_{2}$ZnCl$_{4}$ is calculated from the first principles within both the local density approximation (LDA) and the generalized gradient approximation (GGA). The band structure and density of states were calculated using a pseudopotential method in the framework of density functional theory. Optical absorption edge in (N(CH$_{3}$)$_{4}$)$_{2}$ZnCl$_{4}$ is found to be formed predominantly by ZnCl$_{4}$ tetrahedra transitions. The highest valence band for the (N(CH$_{3}$)$_{4}$)$_{2}$ZnCl$_{4}$ compound consists of 3$p$ Cl, Zn and 4$d$ Zn orbitals. The lowest conduction bands are filled by $s$ N, H, Zn, Cl òà $p$ Ñ, N, Zn, Cl states. The effective mass of an electron and a hole have been determined using the first-principle calculations of band energy structure. The experimental and theoretical results are in good agreement.

PACS number(s): 31.15.E-

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