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We address the role of Sn-substitution and Pb-vacancy (Pb-$\Box$) inregulating stability and carrier concentration ofCH$_3$NH$_3$Pb$_{1-X-Y}$Sn$_X$$\Box_Y$I$_3$ perovskite using density functionaltheory, where the performance of the exchange-correlation functional iscarefully analyzed, and validated w.r.t. available experimental results. Wefind the most stable configuration does not prefer any Pb at 50\% concentrationof Sn. However, the Pb-$\Box$s become unfavourable above 250K due to thereduced linearity of Sn-I bonds. For n-type host the Sn substitution is morepreferable than Pb-$\Box$ formation, while for p-type host the trend is exactlyopposite. The charge states of both Sn and Pb-$\Box$ are found to be dependenton the Sn concentration, which in turn alters the perovskite from n-type top-type with increasing $X$ ($>$0.5).

physical review. b./physical review. b

Elucidating the role of Sn-substitution and Pb-$\Box$ in regulating  stability and carrier concentration in  CH$_3$NH$_3$Pb$_{1-X-Y}$Sn$_X$$\Box_Y$I$_3$