First-Principles Study of ZnIn2Te4 and HgIn2Te4 Defect-Chalcopyrite Semiconductors Under Different Pressures: Electronic, Elastic, And Optical Properties

First-principle calculations of electronic, elastic, and optical properties for ZnIn 2 Te 4 and HgIn 2 Te 4 defect-chalcopyrite semiconductors have been performed using local density approximation (LDA). Computed energy bandgaps are 1.398 eV and 1.101 eV, respectively, for ZnIn 2 Te 4 and HgIn 2 Te 4 , which show the indirect bandgaps behavior. Elastic parameters and Debye temperature have also been investigated at 0, 5, 10, 13, and 14 GPa pressures. Calculated results indicate that both semiconductors are covalent in nature at 0 GPa and become ionic afterward. Optical parameters have also been examined under 0, 5, 10, and 13 GPa in the energy span of 0 eV to 15 eV. The calculated values indicate that these semiconductors are mechanically stable up to 13 GPa and become unstable at 14 GPa. The Calculated values of all parameters are compared with the available experimental and reported values at 0 GPa. A reasonable agreement has been obtained between them. The values of these parameters at 5, 10, 13, and 14 GPa pressures are reported for the first time.


Introduction
Defect-chalcopyrites (DCs) are special type of semiconductors of A II B2 III C4 VI family, which have an ordered vacancy compounds (OCV) structure. They have potential applications in the areas of solar cells, optoelectronics, linear and nonlinear optical devices [1][2][3][4][5][6][7][8][9]. As a result, much emphasis has been placed on the experimental synthesis and structural characterization of these materials.

Computational methods
First-principle calculations within DFT have been done using Cambridge Sequential Total Energy Package (CASTEP) [26] code to estimate linear properties such as electronic, optical, and elastic properties of XIn2Te4 (X = Zn, Hg) under different pressures. The calculations are based on local density approximation (LDA) of the Ceperley and Alder scheme parameterized by Perdew and Zunger to define exchange-correlation functions [27,28]. The non-conversing pseudopotentials [29] have been applied with 660 eV cut-off energy for the plane-wave basis set. The reciprocal crystal lattice and Brillouin zone integration have been executed using Monkhorst-pack mesh of 3×3×3 within the Broyden, Fletcher, Goldfarb, and Shanno (BFGS) scheme [30].

Structural properties
Defect-chalcopyrite semiconductors with formula XIn2Te4 (X = Zn, Hg) have a body-centered tetragonal configuration with space group I-4 (#82). Each unit of XIn2Te4 crystal contains two-X, four-In, and eight-Te atoms along with two vacancies per unit cell. Wyckoff atomic coordinates of XIn2Te4 crystal are X (0, 0, 0), In 1 (0, 0, 0.5), In 2 (0, 0.5, 0.5) and Te (Ux, Uy, Uz), where Ux, Uy and Uz are anion displacement parameters in three axes. The value of lattice parameters has been calculated and listed in Table 1, which are in fair agreement with the available data reported experimentally and theoretically [31,32].   Table 1 The density of states provides knowledge about a crystal's angular momentum character. The elements Zn, Hg, In, and Te have the electronic configurations [Ar]3d 10 4s 2 , [Xe]4f 14 5d 10 6s 2 , [Kr]4d 10 5s 2 5p 1 and [Kr]4d 10 5s 2 5p 4 , respectively. In the energy span of -15 eV to 10 eV, the total density of state (TDOS) and partial density of state (PDOS) have been computed and shown in Fig. 2. At 0 GPa pressure, Fig. 2 (a) shows the TDOS and PDOS for the Zn-4s/3p/3d, In-5s/5p, and Te-5s/5p states, which reveals that the valence band is divided into three parts. The first portion is mostly made up of Te-5s, with a small amount of In-5s and In-5p states. The second portion is strongly localized, owing to the presence of Zn-3d in -7.46 eV to -6.44 eV energy region. The valance band, which ranges from -6.09 eV to Fermi energy (EF = 0 eV), is the third and final part.
Mainly In-5s/5p and Te-5s/5p states give rise to make the third part. Figure 2 (a) reveals that the 5 valance band is primarily made up of Zn-4s, Te-5s, and Te-5p states, with In-5s and In-5p making a minor contribution. The major effect of In-5s/5p and Te-5s/5p, with an admixture of Zn-4s/3p/3d, forms the conduction band, which ranges from 1.90 eV to 6.91 eV. The TDOS and PDOS for Hg-6s/5p/5d, In-5s/5p and Te-5s/5p states has been shown in Fig. 2 (b). Figure 2 (b) shows that similar results have also been observed for HgIn2Te4 in the valence and conduction bands.

3.2.Elastic properties
Elastic parameters are essential parameters to convey the mechanical strength of any material. XIn2Te4 crystallizes in the tetragonal structure that comes under the Laue group T11 [4,5]. Tetragonal Laue group T11 does not have an analytical formula to calculate elastic moduli as it contains off-diagonal shear elastic constant 16 C . Due to this, seven elastic constants are obtained in the optimized structure. However, employing 16 C equals zero, seven elastic constants of the Laue group T11 can be transformed into six elastic constants of the Laue group T1. Laue group T1 has a well-known formula to calculate the elastic constant from its six elastic stiffness constants ij C , i.e., 11 C , 12 C , 13 C , 33 C , 44 C and 66 C . Transformation of seven elastic stiffness coefficients of Laue group T11 into six elastic stiffness coefficients of Laue group T1 can be obtained through rotation around the z-axis with the angle given by following relations [4,5]: The estimated values of ij C for   at five different pressures are presented in Table 2 for XIn2Te4.
Plots have also been drawn between ij C and pressure, and presented in Figs. 3 (a) and 3 (b), respectively, for ZnIn2Te4 and HgIn2Te4. Figure 3 shows that the values of ij C increase with the increasing pressure for both the materials. At 14 GPa, the value of ij C defies the stability criteria mentioned above of Eq. (2) and turns into an unstable form, which indicates that XIn2Te4 is stable up to 13 GPa only. It has also been observed that the values of 11 C and 33 C are significantly higher than the values of 12 C 13 C , 44 C and 66 C . This shows that the compounds are anisotropic and have more chances of shear deformation in the direction of a-and c-axes than compression deformation.  2 / ( ) A C C C  [44] and presented in Table   2. For an anisotropic material, the value should be 1 A  otherwise material said to be isotropic material. Our calculated values of A also show the anisotropic character of both compounds.

Debye temperature () D
 is a constant that signifies the temperature of the highest form of a crystal's vibration, which is closely related to the specific heat and melting point of the compounds. Using data of G and B , Debye temperature values () D  have been estimated based on relations given in Ref. [32,45]. The calculated values of D  for ZnIn2Te4 and HgIn2Te4 have been presented in Table 2, together with the reported data [8]. The calculated value of D  for ZnIn2Te4 is found to be in fair agreement with reported values at 0 GPa [8]. However, the known values of D  for CdIn2Te4 and at other pressure are not available for comparison.

Optical properties
The frequency dependence complex dielectric function

Conclusions
The first-principle study is executed effectively to calculate the electronic, elastic, and optical properties for defect-chalcopyrite ZnIn2Te4 and HgIn2Te4 semiconductors at 0, 5, 10, 13, and 14 GPa pressures. The estimated values of electronic parameters such as lattice parameter (a and c), energy bandgap (Eg), anion displacement parameter (Ux, Uy, and Uz), and bond lengths ( X Te d  , 1 In Te d  and 2 In Te d  ) are presented in Table 1, which agree well with available reported and experimental values. The band structure shows that both compounds are indirect semiconductors 9 with an energy gap of 1.398 eV and 1.101 eV, respectively, for ZnIn2Te4 and HgIn2Te4. The TDOS and PDOS plots of ZnIn2Te4/HgIn2Te4 demonstrate that Zn/Hg has a marginal effect around the Fermi level. However, the Te-5s/5p and In-5s/5p states dominate in the forming of valance and conduction bands. The value of 11 C , 12 C , 13 C , 33 C , 44 C , 66 C , G , B , E , A ,  , / BG and D  have been estimated at 0, 5, 10, 13, and 14 GPa pressures and summarized in Table 2 Table 2