Native point defects and low $p$-doping efficiency in $M{g}_2(Si,Sn)$ solid solutions: A hybrid-density functional study

We perform hybrid-density functional calculations to investigate the charged defect formation energy of native point defects in $M{g}_{2}Si$, $M{g}_{2}Sn$, and their solid solutions. The band gap correction by hybrid-density functional is found to be critical to determine the charged defect density in these materials. For $M{g}_{2}Si$, $Mg$ interstitials are dominant and provide unintentional $n$-type conductivity. Additionally, as the $Mg$ vacancies can dominate in $Mg$-poor $M{g}_{2}Sn$, $p$-type conductivity is possible for $Mg_2 Sn$\mathrm{.}However,theexistenceoflowformationenergydefectssuchas$Mg_{Sn}^{1+}$and$I_{Mg}^{2+}$in$Mg_2 Sn$ and their diffusion can cause severe charge compensation of hole carriers resulting in low $p$-type doping efficiency and thermal degradation. Our results indicate that, in addition to the extrinsic doping strategy, alloying of $M{g}_{2}Si$ with $M{g}_{2}Sn$ under $Mg$-poor conditions would be necessary to enhance the $p$-type conductivity with less charge compensation.