Native point defects in CuIn$_{1-x}$Ga$_x$Se$_{2}$: hybrid density functional calculations predict origin of p- and n-type conductivity

Abstract: We have performed a first-principles study of the p- and n-type conductivity in CuIn${1-x}$Ga$_x$Se${2}$ due to native point defects, based on the HSE06 hybrid functional. Band alignment shows that the band gap becomes larger with $x$ due to the increasing conduction band minimum, rendering it hard to establish n-type conductivity in CuGaSe${2}$. From the defect formation energies, we find that In/Ga${\mathrm{Cu}}$ is a shallow donor, while V${\mathrm{Cu}}$, V${\mathrm{In}/\mathrm{Ga}}$ and Cu${\mathrm{In}/\mathrm{Ga}}$ act as shallow acceptors. Using total charge neutrality of ionized defects and intrinsic charge carriers to determine the Fermi level, we show that under In-rich growth conditions In${\mathrm{Cu}}$ causes strongly n-type conductivity in CuInSe${2}$. Under In-poor growth conditions the conductivity type in CuInSe${2}$ alters to p-type and compensation of the acceptors by In${\mathrm{Cu}}$ reduces, as observed in photoluminescence experiments. In CuGaSe${2}$, the native acceptors pin the Fermi level far away from the conduction band minimum, thus inhibiting n-type conductivity. On the other hand, CuGaSe${2}$ shows strong p-type conductivity under a wide range of Ga-poor growth conditions. Maximal p-type conductivity in CuIn${1-x}$Ga$x$Se${2}$ is reached under In/Ga-poor growth conditions, in agreement with charge concentration measurements on samples with In/Ga-poor stoichiometry, and is primarily due to the dominant acceptor Cu$_{\mathrm{In}/\mathrm{Ga}}$.