A tight-binding-based analysis of the band anti-crossing model in GaN _xAs_1-x

We use an sp³s^* tight-binding (TB) Hamiltonian to investigate the band anti-crossing model for GaN_xAs_1-x alloys. This describes the strong band-gap bowing at low N composition x in terms of an interaction between the conduction band edge (E_-) and a higher-lying band of localized resonant states (E₊). We demonstrate that E_- can be described very accurately by the BAC model, in which we treat the nitrogen levels explicitly using a linear combination of isolated nitrogen resonant states (LCINS). We consider several different random supercell structures and show that there is excellent correlation between the results of our BAC and full TB calculations for both the GaN_xAs _1-x conduction band edge energy and its Γ_1c character. We also show that there is excellent replication of the distribution of Γ_1c character across the higher conduction band states. Finally, we use the LCINS results to identify E₊ in the full TB calculations, showing that at low N composition E₊ forms a sharp resonance in the conduction band Γ-related density of states, which broadens rapidly at higher N composition when the E₊ energy becomes degenerate with the L-related density of states.