All-electron GW quasiparticle band structures of group 14 nitride compounds

We have investigated the group 14 nitrides (M$_{3}$N$_{4})$ in both the spinel phase (with M$=$C, Si, Ge and Sn) and the beta phase (with M$=$Si, Ge and Sn) using density functional theory (DFT) with the local density approximation (LDA). The Kohn-Sham energies of these systems are first calculated within the framework of full-potential LAPW and then corrected using single-shot G$_{0}$W$_{0}$ calculations, which we have implemented in the Exciting-Plus code. Direct bands gap at the $\Gamma $ point are found for all spinel-type nitrides. The calculated band gaps of Si$_{3}$N$_{4}$, Ge$_{3}$N$_{4}$ and Sn$_{3}$N$_{4}$ agree with experiment. We also find that for all systems studied, our GW calculations with and without the plasmon-pole approximation give very similar results, even when the system contains semi-core 3d electrons. These spinel-type nitrides are novel materials for potential optoelectronic applications.