  We develop an atomistic, nearest-neighbor sp3s* tight-binding Hamiltonian to
investigate the electronic structure of dilute bismide alloys of GaP and GaAs.
Using this model we calculate that the incorporation of dilute concentrations
of Bi in GaP introduces Bi-related defect states in the band gap, which
interact with the host matrix valence band edge via a Bi composition dependent
band anti-crossing (BAC) interaction. By extending this analysis to GaBiAs we
demonstrate that the observed strong variation of the band gap Eg and
spin-orbit-splitting (SO) energy with Bi composition can be well explained in
terms of a BAC interaction between the extended states of the GaAs valence band
edge and highly localized Bi-related defect states lying in the valence band,
with the change in Eg also having a significant contribution from a
conventional alloy reduction in the conduction band edge energy. Our calculated
values of Eg and SO are in good agreement with experiment throughout the
investigated composition range x less than 13%. In particular, our calculations
reproduce the experimentally observed crossover to an Eg < SO regime at
approximately 10.5% Bi composition in bulk GaBiAs. Recent x-ray spectroscopy
measurements have indicated the presence of Bi pairs and clusters even for Bi
compositions as low as 2%. We include a systematic study of different Bi
nearest-neighbor environments in the alloy to achieve a quantitative
understanding of the effect of Bi pairing and clustering on the GaBiAs
electronic structure.
