Electronic band structure ofMg−IV−N2compounds in the quasiparticle-self-consistentGWapproximation

Abstract

We present calculations of the lattice constants, structural parameters, bulk moduli, energies of formation, and band structures of $\mathrm{Mg}\ensuremath{-}\mathrm{IV}\ensuremath{-}{\mathrm{N}}_{2}$ compounds with IV=Si, Ge, Sn by using the full-potential linearized muffin-tin orbital method and the quasiparticle-self-consistent $GW$ approach for the wurtzite-based $Pna{2}_{1}$ crystal structure. The lattice parameters calculated with the generalized gradient approximation (GGA) are found to be in good agreement (within 1%) with experiment for the cases of ${\mathrm{MgSiN}}_{2}$ and ${\mathrm{MgGeN}}_{2}$, where data are available. Similar to the Zn-IV-${\mathrm{N}}_{2}$ compounds, ${\mathrm{MgSiN}}_{2}$ is found to have an indirect gap slightly lower than the lowest direct gap, while the other materials have direct gaps. The direct gaps, calculated at the GGA lattice constant, range from 3.43 eV for ${\mathrm{MgSnN}}_{2}$ to 5.14 eV for ${\mathrm{MgGeN}}_{2}$ and 6.28 eV for ${\mathrm{MgSiN}}_{2}$ in the $0.8\mathrm{\ensuremath{\Sigma}}$ approximation, i.e., reducing the $\mathrm{QS}GW\phantom{\rule{4pt}{0ex}}\mathrm{\ensuremath{\Sigma}}$ by a factor 0.8 and including an estimated zero-point-motion correction. The symmetry character of the valence-band maximum states and their splittings and effective masses are determined. The conduction-band minima are found to have slightly higher Mg $s$- than Si $s$-like character in ${\mathrm{MgSiN}}_{2}$ but in ${\mathrm{MgGeN}}_{2}$ and ${\mathrm{MgSnN}}_{2}$, the group-IV-$s$ character becomes increasingly dominant.