Spatial Correlations in GaInAsN Alloys and their Effects on Band-Gap Enhancement and Electron Localization

In contrast to pseudobinary alloys, the relative number of bonds in quaternary alloys cannot be determined uniquely from the composition. Indeed, we do not know if the ${\mathrm{Ga}}_{0.5}{\mathrm{In}}_{0.5}{\mathrm{As}}_{0.5}{\mathrm{N}}_{0.5}$ alloy should be thought of as $\mathrm{InAs}+\mathrm{GaN}$ or as $\mathrm{InN}+\mathrm{GaAs}$. We study the distribution of bonds using Monte Carlo simulation and find that the number of In-N and Ga-As bonds increases relative to random alloys. This quaternary-unique short range order affects the band structure: we calculate a blueshift of the band gap and predict the emergence of a broadband tail of localized states around the conduction band minimum.