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We perform hybrid-density functional calculations to investigate the chargeddefect formation energy of native point defects in $Mg_2 Si$, $Mg_2 Sn$, andtheir solid solutions. The band gap correction by hybrid-density functional isfound to be critical to determine the charged defect density in thesematerials. For $Mg_2 Si$, $Mg$ interstitials are dominant and provideunintentional $n$-type conductivity. Additionally, as the $Mg$ vacancies candominate in $Mg$-poor $Mg_2 Sn$, $p$-type conductivity is possible for $Mg_2Sn$. However, the existence of low formation energy defects such as$Mg_{Sn}^{1+}$ and $I_{Mg}^{2+}$ in $Mg_2 Sn$ and their diffusion can causesevere charge compensation of hole carriers resulting in low $p$-type dopingefficiency and thermal degradation. Our results indicate that, in addition tothe extrinsic doping strategy, alloying of $Mg_2 Si$ with $Mg_2 Sn$ under$Mg$-poor conditions would be necessary to enhance the $p$-type conductivitywith less charge compensation.

Native point defects and low $p$-doping efficiency in $Mg_2 (Si,Sn)$ solid solutions: A hybrid-density functional study