Structural, electronic, and optical properties of Ba$_{1-x}$Zn$_{x}$O

We have investigated structural, electronic and optical properties of Ba$_{1-x}$Zn$_{x}$O alloy in the range of (0 $\le $ x $\le $ 1) in the zinc-blende phase. The all-electron full potential linearized augmented plane wave (FP-LAPW) method implemented in WIEN2k code was utilized in these calculations. Structural optimization of Ba$_{1-x}$Zn$_{x}$O alloy for the compositions x $=$ 0, 0.25, 0.50, 0.75, and 1.0 was carried out by minimizing the total energies as functions of the unit cell volume. The calculated equilibrium lattice constant $a$ and bulk modulus B for both binary BaO and ZnO compounds are found to be ($a=$6.04{\AA}, B$=$45.51GPa for BaO) and ($a=$4.689{\AA}, B$=$113.84GPa for ZnO), in good agreement with the values reported by different groups. We have observed a nonlinear behavior of the lattice constant $a$ as varying the composition x. The electronic structure and the band gap of different composition x are calculated using different types of exchange--correlation potentials. Additionally, we will present the electron charge density distribution for different crystallographic planes of the unit cell. Also, we will demonstrate the effects of variation of compositions x on the optical properties such as the complex dielectric function and refractive index of the alloy.