^{1}

^{*}

^{1}

^{1}

^{1}

^{2}

^{1}

^{1}

^{3}

^{1}

We perform self-consistent ab-initio calculations to study the structural and electronic properties of zinc blende ZnS, ZnO and their alloy. The full-potential muffin-tin orbitals (FP-LMTO) method was employed within density functional theory (DFT) based on local density Approximation (LDA), and generalized gradient approximation (GGA). We analyze composition effect on lattice constants, bulk modulus, band gap and effective mass of the electron. Using the approach of Zunger and coworkers, the microscopic origins of band gap bowing have been detailed and explained. Discussions will be given in comparison with results obtained with other available theoretical and experimental results.

The II-VI compound semiconductors have recently received considerable interest a lot of experimental and theoretical work on this alloy’s, they were promoted much interest because of their numerous applications in optoelectronic devices such as visual displays, high-density optical memories, transparent conductors, solid-state laser devices, photodetectors, solar cells, etc. for few studies that have been done on this alloy due the difficulty in the synthesis of this material, due to the large electronegativity differences between O and S [

The organization of this paper is as follows: we explain the FP-LMTO computational method in Section 2. In Section 3, the results and discussion for structural and electronic properties are presented. Finally, a conclusion is given in Section 4.

The calculations reported in this work were carried out by FP-LMTO [4,5] within the density functional theory DFT based on local density Approximation LDA [_{max} = 6. The k integration over the Brillouin zone is performed using the tetrahedron method [

The calculations were firstly carried out to determine the structural properties of ZB binary compounds ZnS and ZnO and alloys. To model the ZB structure alloys, we applied a 8-atom supercell. For the considered structures and at different oxygen concentrations x (x = 0, 0.25, 0.50, 0.75, 1), the structural properties were obtained by a minimization of total energy as a function of the volume for ZnS, ZnO and in the ZB structure. The bulk modulus and their pressure derivatives were obtained by a non-linear fit of the total energy versus volume according to the Birche-Murnaghan’s equation of state [

^{a}Ref. [^{b}Ref. [

_{x}S_{1−x}Zn solid solutions.

^{a}Ref. [^{b}Ref. [^{c}Ref. [^{d}Ref. [^{e}Ref. [^{f}Ref. [^{g}Ref. [^{h}Ref. [^{i}Ref. [^{j}Ref. [^{k}Ref. [^{l}Ref. [^{m}Ref. [^{n}Ref. [

where a_{AC} and a_{BC} are the equilibrium lattice constants of the binary compounds AC and BC Hence, the lattice constant can be written as:

where the quadratic term b is the bowing parameter.

Figures 1 and 2 show the variation of the calculated equilibrium lattice constant and the bulk modulus versus concentration for alloy. A slight large deviation from Vegard’s law [

The calculations of the electronic band structure properties, magnitude of band-gap were carried out for ZnS, ZnO and in ZB structure at the equilibrium calculated lattice constants. The band-gaps calculated using the FP-LMTO method for ZB ZnS, ZnO and are listed in

points Γ and X in the Brillouin zone. All energies are with reference to the top of the valence band at Γ point. The results show that ZnS and ZnO compound is a direct-gap semiconductor with the minimum of conduction band at Γ point.The calculated GGA (LDA) energy gaps of ZnS and ZnO Eg are 1.97(2.12) eV and 0.69(0.79) eV, respectively, which are in good agreement with the theoretical values as listed in

Indeed it is a general trend to describe the bandgap of an alloy A_{x}B_{1−x}C in terms of the pure compound energy gap E_{AC} and E_{BC} by the sem-empirical formula:

where E_{AC} and E_{BC} corresponds to the gap of the ZnO and ZnS for the O_{x}S_{1}_{−}_{x}Zn alloy. The calculated band gap versus concentration was fitted by a polynomial equation. The results are shown in

In order to better understand the physical origins of the large and composition-dependent bowing in alloy alloys, we follow the procedure of Bernard and Zunger [

^{a}Ref. [^{b}Ref. [^{c}Ref. [^{d}Ref. [^{e}Ref. [^{f}Ref. [^{g}Ref. [^{h}Ref. [^{i}Ref. [^{j}Ref. [

coefficient at a given average composition x measures the change in band gap according to the formal reaction.

where a_{AC} and a_{BC} are the equilibrium lattice constants of the binary compounds. which a_{eq} is the equilibrium lattice constant of the alloy with the average composition x.

We decompose reaction into three step:

The first contribution, the volume deformation (b_{VD}) represents the relative response of the band structure of the binary compounds AC and BC to hydrostatic pressure. The second contribution, the charge-exchange (CE) contribution b_{CE}, reflects a charge-transfer effect that is due to the different (averaged) bonding behavior at the lattice constant a. The final step measures by b_{SR}, changes due to the structural relaxation (SR) in passing from the unrelaxed to the relaxed alloy. Consequently, the total gap bowing parameter is defined as

The general representation of the composition-dependent band gap of the alloys in terms of binary compounds gaps of the, and, and the total bowing parameter b is

where, and represents respectively the volume deformation (VD) effect, the charge exchange (CE) contribution and the structural relaxation (SR) of the alloy according to the following expressions:

The addition of the three contributions (11), (12), and (13) leads to the total bowing parameter b. The computed bowing coefficients b together with the three different contributions for the band gaps as a function of the molar fraction (x = 0.25, 0.5 and 0.75) are shown in the _{CE} has been found greater than. This contribution is due to the different electronegativities of the O and S or Zn atoms. Indeed, scales with the electronegativity mismatch. The contribution of the structural relaxation is small, the band gap bowing is due essentially charge exchange effect.

^{a}Ref. [^{b}Ref. [^{c}Ref. [^{d}Ref. [^{e}Ref. [

It is also interesting to discuss at the end of the band structure study the effective masses of electrons and holes, which are important for the excitonic compounds. We have calculated the effective masses of electrons and holes using both LDA and GGA schemes are mentioned in

In summary, we have studied the electronic, structural properties of alloys by using the FP-LMTO method. We found a slight large deviation from Vegard’s law for the lattice constant of. The physical origin of this effect should be mainly due to the significant mismatch between the lattice constants of ZnS and ZnO compounds. Particular attention has been paid to the gap bowing, which exhibits linear behaviour versus the concentration. In addition, we have computed the effective masses of the electron (hole), which increases with the composition x. Our results are compared to other theoretical and experiment values.