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We have investigated the group 14 nitrides (M$_3$N$_4$) in the spinel phase($\gamma$-M$_3$N$_4$ with M= C, Si, Ge and Sn) and $\beta$ phase($\beta$-M$_3$N$_4$ with M= Si, Ge and Sn) using density functional theory withthe local density approximation and the GW approximation. The Kohn-Shamenergies of these systems have been first calculated within the framework offull-potential linearized augmented plane waves and then corrected usingsingle-shot G$_0$W$_0$ calculations, which we have implemented in the modifiedversion of the Elk full-potential LAPW code. Direct band gaps at the $\Gamma$point have been found for spinel-type nitrides $\gamma$-M$_3$N$_4$ with M= Si,Ge and Sn. The corresponding GW-corrected band gaps agree with experiment. Wehave also found that the GW calculations with and without the plasmon-poleapproximation give very similar results, even when the system containssemi-core $d$ electrons. These spinel-type nitrides are novel materials forpotential optoelectronic applications because of their direct and tunable bandgaps.

All-Electron GW Quasiparticle Band Structures of Group 14 Nitride Compounds