Derivation of 12- and 14-bandk·pHamiltonians for dilute bismide and bismide-nitride semiconductors

Using an sp³s* tight-binding model we demonstrate how the observed strong bowing of the band gap and spin-orbit-splitting with increasing Bi composition in the dilute bismide alloy GaBiₓAs₁₋ₓ can be described in terms of a band-anticrossing interaction between the extended states of the GaAs valence band edge and highly localised Bi-related resonant states lying below the GaAs valence band edge. We derive a 12-band k Hamiltonian to describe the band structure of GaBiₓAs₁₋ₓ and show that this model is in excellent agreement with full tight-binding calculations of the band structure in the vicinity of the band edges, as well as with experimental measurements of the band gap and spin-orbit-splitting across a large composition range. Based on a tight-binding model of GaBiₓNyAs1-x-y we show that to a good approximation N and Bi act independently of one another in disordered GaBiₓNyAs1-x-y alloys, indicating that a simple description of the band structure is possible. We present a 14-band k Hamiltonian for ordered GaBiₓNyAs1-x-y crystals which reproduces accurately the essential features of full tight-binding calculations of the band structure in the vicinity of the band edges. The k models we present here are therefore ideally suited to the simulation of the optoelectronic properties of these novel III-V semiconductor alloys.