Ab initio study of InxGa1−xN – Performance of the alchemical mixing approximation

• We model from first principles ZB and WZ InxGa1−xN using the alchemical mixing approximation.
• We find the composition dependent structural and elastic constants.
• We find the composition dependent pressure derivatives of elastic constants.
• We find the composition dependent band gap.
• We draw conclusions as for performance of the used approximation.

The alchemical mixing approximation which is the ab initio pseudopotential specific implementation of the virtual crystal approximation (VCA), offered in the ABINIT package, has been employed to study the wurtzite (WZ) and zinc blende (ZB) InxGa1−xN alloy from first principles. The investigations were focused on structural properties (the equilibrium geometries), elastic properties (elastic constants and their pressure derivatives), and on the band-gap. Owing to the ABINIT functionality of calculating the Hellmann–Feynmann stresses, the elastic constants have been evaluated directly from the strain–stress relation. Values of all the quantities calculated for parent InN and GaN have been compared with the literature data and then evaluated as functions of composition x on a dense, 0.05 step, grid. Some results have been obtained which, to authors’ knowledge, have not yet been reported in the literature, like composition dependent elastic constants in ZB structures or composition dependent pressure derivatives of elastic constants. The band-gap has been calculated within the MBJLDA approximation. Additionally, the band-gaps for pure InN and GaN have been calculated with the Wien2k code, for comparison purposes. The evaluated quantities have been compared with the available literature reporting supercell-based ab initio calculations and on that basis conclusions concerning the performance of the alchemical mixing approach have been drawn. An overall agreement of the results with the literature data is satisfactory. A small deviation from linearity of the lattice parameters and some elastic constants has been found to be due to the lack of the local relaxation of the structure in the VCA. The big bowing of the band-gap, characteristic of the clustered structure, is also mainly due to the lack of the local relaxation in the VCA. The method, when applied with caution, may serve as supplementary tool to other approaches in ab initio studies of alloy systems.