Structural and electronic properties of the random alloy ZnSe$_x$S$_{1-x}$

In this article we employ density functional theory in the generalized gradient approximation to investigate the structural and electronic properties of the solid solution alloy $\text{Zn}\text{Se}_x\text{S}_{1-x}$ in the wurtzite structure. We analyzed the character of the bond lengths and angles at the atomic scale, using a supercell approach that does not impose any constraint on the crystal potential. We show that the bond lengths of pristine ZnS and ZnSe compounds are almost preserved between nearest neighbors, which is different from what would be anticipated if Vegard's law were valid at the atomic level. We also show that bond lengths start behaving in accordance to Vegard's law from the third shell of nearest neighbors onward, which in turn determines the average lattice parameters of the alloys determined by diffraction experiments. Fundamental building blocks around the anions are identified and are shown to be non-rigid but still volume preserving. Finally, the geometrical analysis is connected to the trend exhibited by the electronic structure, and in particular by the band gap. The latter is found to exhibit a small deviation from the linearity with respect to the Se concentration, in accordance to available experimental data. By assuming a quadratic dependence, we can extract a bowing parameter and analyze various contributions to it with various calculations under selected constraints. The structural deformation in response to the doping process is shown to be the driving force behind the deviation from linearity. The difference in stiffness between ZnS and ZnSe is showed to play a key role in the asymmetric behavior of the bowing parameter observed in the S-rich and Se-rich regions.