Comparison of interband related optical transitions and excitons in ZnGeN2 and GaN

The optical dielectric function of ZnGeN₂ is calculated from the interband transitions using the energy bands calculated in the quasiparticle self-consistent (QS)G ̂ \^W method using two different levels of approximation: the independent particle approximation and the Bethe-Salpeter equation (BSE) approach. The first allows us to relate peaks in ε₂(ω) to specific bands and k points but does not include electron-hole interaction effects. The second includes electron-hole interaction or excitonic effects. The corresponding changes in the shape of ε₂(ω) are found to be similar to those in GaN. The screened Coulomb interaction ̂ \^W is here calculated including electron-hole interactions in the polarization function and gives a band structure already going beyond the random phase approximation. The static dielectric constants including only electronic screening, commonly referred to as ε^∞, were calculated separately by extrapolating the wave-vector-dependent macroscopic εM(q,ω=0) for q→0. Below the quasiparticle gap, we find three bound excitons optically active for different polarization. The convergence of these bound excitons with respect to the density of the k mesh used in the BSE is studied and found to require a fine mesh. It is also found that these bound excitons originate from only the lowest conduction band and the top three valence bands. To incorporate the lattice screening, we include a scaling factor (ε^∞/ε⁰)², which allows us to obtain exciton binding energies of the correct order of magnitude similar to those in GaN. The excitons are related to each of the threefold split valence bands and the splittings of the latter are also studied as a function of strain. Finally, a relation between the anisotropic effective masses and the valence-band splitting is pointed out and explained.