Full band calculation of doping-induced band-gap narrowing in p-type GaAs

We have calculated the energy shift of the fundamental band gap as a function of dopant concentration in p-type GaAs, using a perturbation theory based on the zero-temperature Green’s function formalism within the random-phase approximation. The electronic structure of the intrinsic crystal was obtained from a relativistic, full-potential band-structure calculation, with the exchange potential of Engel and Vosko [Phys. Rev. B 47, 13 164 (1993)]. We have found that this potential gives accurate band curvatures at the band edges. The nonparabolicity of the uppermost valence bands has a reducing effect on the energy shifts of both the conduction and valence bands for high acceptor concentrations. The resulting narrowing of the band gap is in good agreement with photoluminescence measurements. Thus, it is crucial to take into account the full band structure to calculate the band-gap narrowing accurately for high acceptor concentrations.