Ab-initio investigations of electronic, optical, mechanical and thermal properties of Ca0.875Ba0.125Te

The ground-state properties and optical, mechanical, elastic and thermal properties of the Ca0.875Ba0.125Te alloy have been studied by using the full potential linearized augmented plane wave (FP-LAPW) scheme based on the density functional theory in the frame of generalized gradient approximation (GGA). In order to model Ca1-xBaxTe alloy, 16-atoms supercell of the type 2 × 2 × 2 is employed. The lattice structure of Ca0.875Ba0.125Te alloy is obtained by replacing one Ca atom by one Ba atom in the crystal lattice of CaTe. The charge density plot, electronic structure and density of states plots are made and discussed for the alloy. The lower valence band maxima (VBM) and the upper conduction band minima (CBM) of Ca0.875Ba0.125Te alloy is locaed at Γ point, ensuing in a direct band gap, whereas in case of parent element CaTe the nature of the band gap is indirect. The characteristic properties of Ca0.875Ba0.125Te alloy is dominated by Te 5p electrons (below the Fermi level) and Ba 4d and Ca 3d electrons (above the Fermi level).


Introduction
Recently, the investigation of the II-VI semiconductor compounds has become an area of great activity. A lot of experimental reports and theoretical studies are available for II-VI chalcogenides such as calcium chalcogenides [1], strontium [2] and beryllium chalcogenides [3]. At ambient conditions, the alkaline metal earth chalcogenides crystallizing in the NaCl type structure [4,5]. Technologically, the rare earth chalcogenides are significant materials in the applications namely catalysis, microelectronics, luminescent devices [6,7], infrared sensitive devices [8,9], etc. The II-VI semiconductors and the semiconductor heterostructures are familiar to form ternary alloys with a direct energy band gap and high absorption coefficients [10]. The energy gap values of ternary II-VI semiconductors and its alloys include several light spectra and lattice parameters can be made independently to produce photovoltaic devices on appropriate substrate [11]. They are used as potential resources for making thin film heterojunction photo-voltaic devices. Ca-based chalcogenides are more interesting due to their anion and cation radius ratio ensuing in high phase transition pressures. Many experimental and theoretical investigations have been made to explain the structural, electronic, elastic, optical and thermo dynamical properties. The structural change and pressure volume relationships in CaTe and SrTe at high pressure are investigated by Zimmer et al. [12]. Cohesive property of CaX compounds under pressure reported by Cartona et al. [13]. The elastic properties are studied by using pseudo potential [14] and tight binding theory [15]. Structural and elastic  [16]. By using FP-LAPW scheme, the optical properties of Ca-based chalcogenides have been reported [17]. Ab initio investigations of calcium chalcogenides are made by Slimani et al. [18]. Here, the focus is made on investigation of the ground state properties and elastic, mechanical and optical properties of barium doped CaTe semiconductor. It has been found that the phase transition from NaCl-type structure to CsCl-type structure in ternary Ca0.875Ba0.125Te. The most important characteristics of the absorber material in a solar cell are direct band gap in the range of 1.0 -1.7eV and high absorption coefficient. The parent binary CaTe alloy has indirect band gap and its energy gap value is 1.587 eV, whereas the Ba doped CaTe (ternary Ca0.875Ba0.125Te) alloy has direct band gap and its energy gap value 1.647 eV is close to the optical energy gap of solar cell absorbers. Hence, from this study it has been identified that the ternary Ca0.875Ba0.125Te is suitable for solar cell absorber. Further, the electrical, mechanical and optical properties of Ca0.875Ba0.125Te alloy has been discussed in the present study.

Method of Calculations
FP-LAPW method is employed to calculate the structural properties, electronic, mechanical, elastic and optical properties of CaTe and Ca0.875Ba0.125Te alloys. All the calculations are carried out by the Wien2k code [19] within the frame of DFT. The generalized gradient approximation (GGA) as parameterized by Perdew, Burke and Ernzerhof (PBE) [20] is employed for the exchange-correlation potentials. The value of lmax for the wave function expansions inside sphere is confined to lmax = 10. The RMT x Kmax = 7 and Gmax = 12 is selected for the plane wave expansions in interstitial region and charge density Fourier expansion respectively. The RMT (muffin-tin radius) was assumed to be 2.5 for Ca, 2.5 for Ba and 2.08 for Te atoms. For k-space summation the 10 x 10 x 10 k-points have been used. Self-consistent calculations are repeated up to the total energy converges to less than 0.0001Ry and charge converge to less than 0.001eV. To model the Ca0.875Ba0.125Te alloy, we employ a 16-toms supercell of the type 2 x 2 x 2 and the lattice structure of Ca0.875Ba0.125Te is obtained by replacing one Ca atom with an equal number of Ba atom in the crystal lattice of CaTe.

Structural properties
Structural properties of CaTe and its ternary alloy Ca0.875Ba0.125Te investigated at ambient condition by using GGA scheme. CaTe crystallizes in NaCl-type B1 structure (space group 225) and Ca0.875Ba0.125Te crystallizes in CsCl-type B2 structure (space group 221). The position of Ca and Te atom is situated at (0,0,0) and (0.5,0.5,0.5) respectively. The ternary Ca0.875Ba0.125Te is found to undergo a phase transformation from NaCl-type (Fm3m) to CsCl-type (Pm3m) structure. The lattice constant a0, bulk modulus B and B' (pressure derivative bulk modulus) values are obtained by fitting the energy versus volume according to Birch-Murnaghan's equation [21]. The calculated structural properties of CaTe and Ca0.875Ba0.125Te alloys are presented in Table 1. All the calculated results of the parent compound CaTe are well matched with the reported values. Using cohesive energy calculation, the structural stability of cell is determined. The cohesive energy value for binary CaTe and ternary Ca0.875Ba0.125Te alloy is 3.73eV/atom and 3.68eV/atom respectively.

Electronic properties
Density of states (DOS) calculations and electronic/band structure calculations are done by FP-LAPW scheme associated with GGA is presented in Fig. 1 and 2. The DOS below Fermi level (0 eV) is called as the valence band owing to the fully filled states on the other hand, DOS above the Fermi level (0 eV) is called as the conduction band because of the unoccupied states. In CaTe alloy which is shown in Fig. 1a, below the Fermi level is mostly due to the Te-5s & 5p states and above the Fermi level is mainly due to the Ca-4s & 3d states whereas in ternary Ca0.875Ba0.125Te alloy (Fig. 1b)   The self-consistent relativistic energy band gap (Eg) of the CaTe and Ca0.875Ba0.125Te alloys were calculated and presented in Table 1   To understand the chemical bonding nature between atoms, charge density plots are drawn for parent CaTe and ternary Ca0.875Ba0.125Te alloys as shown in Fig.3 a and b respectively. From Fig. 3a, it is observed that the directional charge density contour that encloses the Ca and Te atoms indicates the hybridization between Ca-d and Te-d states. It reveals the covalent nature of the material. In Fig. 3b, it is clearly seen that the covalent interaction occurs between Ca with Ba atoms, due to charge transfer from Ca atom to Ba atom.

Optical properties
The following optical properties namely complex dielectric function, optical conductivity, absorption coefficient and energy loss function are calculated for CaTe and Ca0.875Ba0.125Te alloys. The optical properties calculations performed with no intra band contributions added. Complex dielectric function [22] is calculated by: ε(ω) = ε1(ω) + i ε2(ω) and is determined by the transition from the valence to conduction band. Real part of the dielectric function corresponds to dispersive behaviour and the imaginary part corresponds to the absorptive behaviour of the material. Static dielectric constant is the most important quantity in real part of the dielectric function, which strongly depends on the energy gap and it is given (from Fig. 4) 6.5 and 6.6 for CaTe and Ca0.875Ba0.125Te alloys respectively. The absorption coefficient determines the ability of material to absorb the incident photon of specific frequency [23]. It can be seen in Fig. 5a, the absorption part of binary CaTe and ternary Ca0.875Ba0.125Te spectra starts with nearly 1.8 eV(CaTe) and 1.75 eV (Ca0.875Ba0.125Te) respectively. The combined graph of optical conductivity (sigma) and energy loss function (Eloss) of the CaTe and Ca0.875Ba0.125Te alloys are shown in Fig. 5b. In binary CaTe, E0 = 1.587 eV, the first peak appears for 4.5 eV and the optical conductivity has the maximum value of 7450 [1/(Ohm cm)], whereas in Ca0.875Ba0.125Te, E0 = 1.633 eV, the first peak appears for 4.7 eV and the optical conductivity(sigma) has the maximum value of 6500 [1/(Ohm cm)] corresponds to visible region of the electromagnetic spectrum. Fast electron energy-loss which is moving in the material is explained by the energy loss spectrum [23]. The main peak which is known as bulk plasma frequency occurs at zero point of ε1(ω) and ε2(ω) and minimum reflectivity. In Fig. 5b, the main peak of energy loss spectrum of CaTe and Ca0.875Ba0.125Te is roughly located at 13 eV and 12.5 eV respectively.    Elastic constants of solids determine the crystal response for external forces and play vital role in strength and stability of the materials. To study the stability of cubic CaTe and Ca0.875Ba0.125Te compounds, the cubic three independent elastic constants namely C11, C12 and C44 are calculated. The calculated elastic constants satisfy the stability criteria [24]. Using elastic constants [25], one can determine the mechanical properties such as shear modulus (G), Young's modulus (E), Cauchy pressure (C12 -C44), G/B ratio, Poisson's ratio (ν), Hardness (HV) and anisotropy factor (A) and these computed values for CaTe and Ca0.875Ba0.125Te alloys are given in Table 2. The higher shear modulus indicates the noticeable directional bonding between atoms [24] and it provides better relation with hardness. Bulk modulus is the ratio of volume stress to volume strain and it measures the resistance to volume by means of applied pressure. Young's modulus is the ratio of longitudinal stress and longitudinal strain in a material and it has an impact on the ductility. From Table 2, the analysis on modulus values and hardness indicates that the stiffness, strength of covalent bond and hardness of the ternary Ca0.875Ba0.125Te is decreased. Anisotropy factor A = 1 indicates an isotropic material, whereas the change of value 1 shows the degree of the material's anisotropy. It can be seen from Table 2, the CaTe and Ca0.875Ba0.125Te are known as anisotropy materials owing to Anisotropy factor A<1.

Mechanical and Elastic properties
The ductile nature and brittle behaviour of the material is investigated by the three main factors such as Cauchy's pressure (C12-C44), degree of brittleness (G/B ratio) and Poisson's ratio (ν) and all the three calculated values are shown in Table 2. When C12-C44 values are negative, G/B ratio is greater than 0.57 and Poisson's ratio is less than 0.3, the material exhibits brittle nature. From the above study, one can confirm that the both materials parent binary CaTe and its ternary Ca0.875Ba0.125Te alloy are brittle in nature, in which ternary Ca0.875Ba0.125Te alloy is less brittle than the parent binary CaTe.

Thermal properties
The following thermal properties namely longitudinal (VL) and shear sound velocities (VS), Debye average velocity (Vm), Debye temperature (θD) [26], melting temperature (Tm) and Gruneisen parameter (ζ) [27] have been calculated for CaTe and Ca0.875Ba0.125Te alloys and presented in Table 3. Debye temperature is correlated to the strength of covalent bonds and it is used to measure the thermal conductivity of materials. The direct relationship between Debye temperature and average sound velocity indicates that the larger the average sound velocity, the larger the Debye temperature. The measure of the anharmonicity of the crystal is known as Gruneisen parameter (ζ). The value of Gruneisen parameter (ζ) varies with respect to the elastic moduli through sound velocities. Therefore, the larger Gruneisen parameter (ζ) and smaller Debye temperature (θD) represent the soft bonding nature of the crystal.

Conclusion
Structural, electronic, mechanical, optical and thermal properties of binary CaTe and ternary Ca0.875Ba0.125Te alloys are investigated by using generalized gradient approximation (GGA). The calculated cohesive energy of CaTe and Ca0.875Ba0.125Te compounds shows that the structures have mechanical stability. From the outcomes of DOS and band calculations, it can be concluded that the ternary Ca0.875Ba0.125Te combination is a direct band gap (1.647 eV) semiconducting material with covalent bonding character. Because of the band matching with the incident light energy, the direct band gap has a technological significance and the existence of sharp band in conduction region and the hybrid band in valence region increases the electron transport. To determine the optical properties of CaTe and Ca0.875Ba0.125Te alloys, the optical parameters such as dielectric constants, absorption coefficient, optical conductivity and Eloss function are calculated for photon radiation up to 13.0 eV. The other important features of Ca0.875Ba0.125Te are the maximum sigma occur at lower photon energy and the maximum Eloss occur at higher energy. Hence, the calculated electronic and optical properties of Ca0.875Ba0.125Te show that it is a suitable material for optical devices and solar cell applications.