Self-doping behavior and cation disorder in MgSnN2

Investigations on $\mathrm{II}\text{\ensuremath{-}}\mathrm{Sn}\text{\ensuremath{-}}{\mathrm{N}}_{2}$ ($\mathrm{II}=\mathrm{Mg}$, Ca) have been started very recently compared to the intense research of $\mathrm{Zn}\text{\ensuremath{-}}\mathrm{IV}\text{\ensuremath{-}}{\mathrm{N}}_{2}$ ($\mathrm{IV}=\mathrm{Si}$, Ge, Sn). In this work, we study the phase stability of ${\mathrm{MgSnN}}_{2}$ and ${\mathrm{ZnSnN}}_{2}$ in wurtzite and rocksalt phases by first principles calculations. The calculated phase diagram agrees with the experimental observation; i.e., ${\mathrm{MgSnN}}_{2}$ can form in the wurtzite and rocksalt phases while ${\mathrm{ZnSnN}}_{2}$ only crystallizes in the wurtzite phase. Due to the higher ionicity of Mg-N bonds compared to Sn-N bonds and Zn-N bonds, wurtzite-type ${\mathrm{MgSnN}}_{2}$ appears under Mg-rich conditions. The defect properties and doping behavior of ${\mathrm{MgSnN}}_{2}$ in the wurtzite phase are further investigated. We find that ${\mathrm{MgSnN}}_{2}$ exhibits self-doped $n$-type conductivity, and donor-type antisite defect ${\mathrm{Sn}}_{\mathrm{Mg}}$ is the primary source of free electrons. The high possibility of forming the stoichiometry-preserving ${\mathrm{Mg}}_{\mathrm{Sn}}+{\mathrm{Sn}}_{\mathrm{Mg}}$ defect complex leads to our study of cation disorder in ${\mathrm{MgSnN}}_{2}$ by using the cluster expansion method with first principles calculations. It is found that cation disorder in ${\mathrm{MgSnN}}_{2}$ induces a band-gap reduction because of a violation of the octet rule. The local disorder, namely, forming (4,0) or (0,4) tetrahedra, leads to an appreciable band-gap reduction and hinders the enhancement of the optical absorption.