Distribution of cations in wurtzitic In _xGa _1-xN and In _xAl _1-xN alloys: Consequences for energetics and quasiparticle electronic structures

The ternary, isostructural, wurtzite-derived group-III mononitride alloys In _xGa _1-xN and In _xAl _1-xN are reexamined within a cluster expansion approach. Using density functional theory together with the AM05 exchange-correlation functional, the total energies and the optimized atomic geometries of all 22 clusters classes of the cluster expansion for each material system are calculated. The computationally demanding calculation of the corresponding quasiparticle electronic structures is achieved for all cluster classes by means of a recently developed scheme to approximately solve the quasiparticle equation based on the HSE06 hybrid functional and the G ₀W ₀ approach. Using two different alloy statistics, the configurational averages for the lattice parameters, the mixing enthalpies, and the bulk moduli are calculated. The composition-dependent electronic structures of the alloys are discussed based on configurationally averaged electronic states, band gaps, and densities of states. Ordered cluster arrangements are found to be energetically rather unfavorable, however, they possess the smallest energy gaps and, hence, contribute to light emission. The influence of the alloy statistics on the composition dependencies and the corresponding bowing parameters of the band gaps is found to be significant and should, hence, lead to different signatures in the optical-absorption or -emission spectra.