First-principles determination of band-to-band electronic transition energies in cubic and hexagonal AlGaInN alloys

We provide approximate quasiparticle-corrected band gap energies for quaternary cubic and hexagonal Al_xGa_yIn_1–x–yN semiconductor alloys, employing a cluster expansion method to account for the inherent statistical disorder of the system. Calculated values are compared with photoluminescence measurements and discussed within the currently accepted model of emission in these materials by carrier localization. It is shown that bowing parameters are larger in the cubic phase, while the range of band gap variation is bigger in the hexagonal one. Experimentally determined transition energies are mostly consistent with band-to-band excitations.