Point defects in p -type transparent conductive CuMO2 ( M=Al , Ga, In) from first principles

Abstract

We investigate the native point defects in delafossite $\mathrm{Cu}M{\mathrm{O}}_{2}$ ($M=\mathrm{Al}$, Ga, In) using first-principles calculations based on the Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional approach. The Cu vacancies in all the systems show low formation energies and form relatively shallow acceptor levels, which would contribute mainly to the $p$-type conductivity. The hole compensation by the donor-type native defects does not essentially limit the $p$-type doping in all of $\mathrm{Cu}M{\mathrm{O}}_{2}$ under controlled growth conditions. In contrast, the acceptor-type native defects, especially the Cu vacancies, show low or even negative formation energies at high Fermi level positions in $\mathrm{Cu}\mathrm{Al}{\mathrm{O}}_{2}$ and $\mathrm{Cu}\mathrm{Ga}{\mathrm{O}}_{2}$, thereby compensating carrier electrons to limit the $n$-type doping. The neutral Cu vacancy forms an in-gap state with hole localization to the neighboring Cu atoms in each of $\mathrm{Cu}M{\mathrm{O}}_{2}$, whereas the neutral Cu-on-Al antisite in $\mathrm{Cu}\mathrm{Al}{\mathrm{O}}_{2}$ and the Cu-on-Ga antisite in $\mathrm{Cu}\mathrm{Ga}{\mathrm{O}}_{2}$ form in-gap states with hole localization to themselves. In the framework of the HSE06 hybrid functional, the generalized Koopmans' theorem is almost satisfied for the Cu-on-Al and Cu-on-Ga antisites, but not for the Cu vacancies in all of $\mathrm{Cu}M{\mathrm{O}}_{2}$. However, the absolute positions of the acceptor levels of the Cu vacancies are almost constant regardless of the convex/concave behavior of the hybrid functional controlled by the Fock-exchange parameter, suggesting that the determination of the valence band maximum is mostly relevant to accurate prediction of the acceptor level position. The $n$-type doping limits, namely the upper limits of the Fermi level in thermodynamic equilibrium, determined by the spontaneous formation of the Cu vacancies, are almost common to all of $\mathrm{Cu}M{\mathrm{O}}_{2}$ in the band alignment with respect to the vacuum level. In contrast, the conduction band minimum significantly depends on the system, which suggests, along with the Fermi level restriction by the Cu-vacancy formation, that strong compensation of carrier electrons is avoidable only in $\mathrm{Cu}\mathrm{In}{\mathrm{O}}_{2}$. This finding indicates that the position of the conduction band minimum is an important indicator for discussing and designing $n$-type doping of $\mathrm{Cu}M{\mathrm{O}}_{2}$ as proposed previously.