Consistent set of band parameters for the group-III nitrides AlN, GaN, and InN

We have derived consistent sets of band parameters (band gaps, crystal field splittings, band-gap deformation potentials, effective masses, and Luttinger and ${E}_{P}$ parameters) for AlN, GaN, and InN in the zinc-blende and wurtzite phases employing many-body perturbation theory in the ${G}_{0}{W}_{0}$ approximation. The ${G}_{0}{W}_{0}$ method has been combined with density-functional theory (DFT) calculations in the exact-exchange optimized effective potential approach to overcome the limitations of local-density or gradient-corrected DFT functionals. The band structures in the vicinity of the $\ensuremath{\Gamma}$ point have been used to directly parametrize a $4\ifmmode\times\else\texttimes\fi{}4$ $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ Hamiltonian to capture nonparabolicities in the conduction bands and the more complex valence-band structure of the wurtzite phases. We demonstrate that the band parameters derived in this fashion are in very good agreement with the available experimental data and provide reliable predictions for all parameters, which have not been determined experimentally so far.