Density functional and quasiparticle band-structure calculations forGaxAl1−xNandGaxIn1−xNalloys

Abstract

We investigate the electronic structure of two wide-band-gap semiconductor alloys ${\mathrm{Ga}}_{x}{\mathrm{Al}}_{1\ensuremath{-}x}\mathrm{N}$ and ${\mathrm{Ga}}_{x}{\mathrm{In}}_{1\ensuremath{-}x}\mathrm{N},$ employing three different ab initio band-structure approaches. Local density calculations within density functional theory using conventional as well as self-interaction-corrected pseudopotentials and quasiparticle band-structure calculations are carried out. The stochastical alloy problem is treated within the virtual crystal approximation, as well as within a cluster expansion approximation. One main issue is the evaluation of the bowing of the composition dependence of the fundamental band gap. It turns out that the band-gap bowing for ${\mathrm{Ga}}_{x}{\mathrm{Al}}_{1\ensuremath{-}x}\mathrm{N}$ alloys is described reasonably well within the virtual crystal approximation. For ${\mathrm{Ga}}_{x}{\mathrm{In}}_{1\ensuremath{-}x}\mathrm{N},$ on the contrary, that approximation does not correctly describe the composition dependence of the band gap because it neglects significant local structural relaxations. These are taken into account in the cluster expansion approximation. Our results indicate that in both alloys the band gap exhibits a composition-dependent bowing function rather than a constant bowing parameter.