New quaternary semiconductor Cu$_{\mathrm{2}}$MgSnS$_{\mathrm{4}}$ and Cu$_{\mathrm{2}}$MgSnSe$_{\mathrm{4}}$ for photovoltaics

Element substitution of Zn by Mg and Ca is attempted to overcome the problem of potential fluctuation in Cu$_{\mathrm{2}}$ZnSnS$_{\mathrm{4}}$ and Cu$_{\mathrm{2}}$ZnSnSe$_{\mathrm{4}}$ (CZTSSe) due to prevalence of Cu$_{\mathrm{Zn}}+$Zn$_{\mathrm{Cu}}$ defect complex. Through density function theory calculation with hybrid functional, we have shown that Cu$_{\mathrm{2}}$MgSnS$_{\mathrm{4}}$ and Cu$_{\mathrm{2}}$MgSnSe$_{\mathrm{4}}$ (CMTSSe) are stable with respect to secondary phases considered under suitable chemical potential. Stannite CMTSSe is thermodynamically more favorable over the kesterite structure. The alternating Cu and Mg/Sn cation layer of stannite structure may suppress the formation of Mg$_{\mathrm{Cu}}$ antisite due to large stress induced. The electronic and optical properties of CMTSSe are similar to that of CZTSSe with comparable absorption coefficient at the band-edge suggests CMTSSe to be a promising photovoltaic material.