Tight-binding and k·p models for the electronic structure of Ga(In)NAs and related alloys

We review how the tight-binding method provides a particularly useful approach to understand the electronic structure of GaInNAs alloys, and use it to derive a modified k·p model for the electronic structure of GaInNAs heterostructures. Using the tight-binding model, we first confirm that N forms a resonant defect level above the conduction band edge in Ga(In)As. We show that the interaction of the resonant N level with the conduction band edge accounts for the strong bandgap bowing observed in GaInN_xAs_1-x, in agreement with experimental analysis but contrary to some theoretical interpretations. We then use a Green function model to derive explicitly the two-level band-anti-crossing model describing the interaction between the resonant states and the conduction band edge in ordered Ga(In)N_xAs_1-x. We extend the Green function model to show that the conventional k·p model must be modified to include two extra spin-degenerate nitrogen states, giving a 10-band k.p model to describe the band structure of GaNAs/GaAs and related heterostructures. We describe how this 10-band model provides excellent quantitative agreement with a wide range of experimental data and finally discuss briefly the effects of disorder on the electronic structure in dilute nitride alloys.