Valence band effective-mass Hamiltonians for the group-III nitrides from quasiparticle self-consistentGWband structures

Abstract

We present band gaps, electron effective masses, and valence band effective-mass Hamiltonian parameters as well as strain deformation potentials of the crystal field splittings for AlN, GaN, and InN obtained from quasiparticle self-consistent $GW$ calculations. Excellent agreement is obtained with experimental data for the crystal field and spin-orbit coupling splittings of bulk AlN and GaN. For InN, the discrepancy on the crystal field splitting is likely due to the residual strain in InN thin films from which that experimental value was extracted. We obtain a negative spin-orbit splitting for InN, which is plausible in view of the stronger negative contribution of In-4$d$ in InN than Ga-3$d$ in GaN. The inverse effective-mass parameters ${A}_{i}$ agree well with previous ${G}_{0}{W}_{0}$ calculations except for ${A}_{6}$. We find that the ${A}_{6}$ parameter describing the band dispersion in directions intermediate between parallel and perpendicular to the basal plane is not well described by the quasicubic approximation. Good agreement with the most reliable experimental data is obtained for hole effective-mass parameters in AlN and GaN, extracted from exciton binding energies and their fine structure. For InN and GaN, the spin-splittings of the bands in the plane due to spin-orbit coupling requires the inclusion of linear in k and spin terms.