Transition energies and direct-indirect band gap crossing in zinc-blende AlxGa1-xN

The electronic and optical properties of zinc-blende (zb) AlxGa1- xN Nover the whole alloy composition range are presented in a joint theoretical and experimental study. Because zb-GaN is a direct (Gamma(upsilon) -> Gamma(c)) semiconductor and zb-AlN shows an indirect (Gamma(upsilon) -> Xc) fundamental band gap, the ternary alloy exhibits a concentration-dependent direct-indirect band gap crossing point the position of which is highly controversial. The dielectric functions of zb-AlxGa1- xN alloys are measured employing synchrotron-based ellipsometry in an energy range between 1 and 20 eV. The experimentally determined fundamental energy transitions originating from the Gamma, X, and L points are identified by comparison to theoretical band-to-band transition energies. In order to determine the direct-indirect band gap crossing point, the measured transition energies at the X point have to be aligned by the calculated position of the highest valence state. Thereby density-functional theory (DFT) based approaches to the electronic structure, ranging from the standard (semi) local generalized gradient approximation (GGA), self-energy corrected local density approximation (LDA-1/2), and meta-GGA DFT (TB-mBJLDA) to hybrid functional DFT and many-body perturbation theory in the GW approximation, are applied to random and special quasirandom structure models of zb-AlxGa1- xN. This study provides interesting insights into the accuracy of the various numerical approaches and contains reliable ab initio data on the electronic structure and fundamental alloy band gaps of zb-AlxGa1- xN. Nonlocal Heyd-Scuseria-Ernzerhof-type hybrid-functional DFT calculations or, alternatively, GW quasiparticle calculations are required to reproduce prominent features of the electronic structure. The direct-indirect band gap crossing point of zb-AlxGa1- xN is found in the Al rich composition range at an Al content between x = 0.64 and 0.69 in hybrid functional DFT, which is in good agreement with x = 0.71 determined from the aligned experimental transition energies. Thus our study solves the long-standing debate on the nature of the fundamental zb-AlxGa1- xN alloy band gap.