Derivation of 12- and 14-band k ? p Hamiltonians for dilute bismide and bismide-nitride semiconductors
Using an sp3s* tight-binding (TB) 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 (VBE) and highly localized Bi-related resonant states lying below the GaAs VBE. We derive a 12-band k ? p Hamiltonian to describe the band structure of GaBixAs1 ? x and show that this model is in excellent agreement with full TB 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 TB 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 ? p Hamiltonian for ordered GaBixNyAs1 ? x ? y crystals which reproduces accurately the essential features of full TB calculations of the band structure in the vicinity of the band edges. The k ? p models we present here are therefore ideally suited to the simulation of the optoelectronic properties of these novel III?V semiconductor alloys.