Approach to achieving a p-type transparent conducting oxide: Doping of bismuth-alloyed Ga2O3 with a strongly correlated band edge state

$P$-type doping in oxides is usually difficult due to their low valence-band energy. In order to make them $p$ type, the electronic structure of the oxides should be fundamentally changed; that is, the occupied valence band should be raised significantly. Here, using first-principles calculations, we propose that by adding a small amount of ${\mathrm{Bi}}_{2}{\mathrm{O}}_{3}$ into ${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ to form dilute ${({\mathrm{Bi}}_{x}{\mathrm{Ga}}_{1--x})}_{2}{\mathrm{O}}_{3}$ alloys and, more importantly, with properly chosen dopants, we can achieve efficient $p$-type doping in a transparent oxide. We show that adding a few percent of Bi to ${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ leads to an intermediate valence band that is sufficiently high in energy to facilitate $p$-type doping; however, the commonly expected shallow acceptors, Mg and Zn substitution on the Ga site (${\mathrm{Mg}}_{\mathrm{Ga}}$ and ${\mathrm{Zn}}_{\mathrm{Ga}}$), are still deep acceptors, whereas the expected deep acceptor, ${\mathrm{Cu}}_{\mathrm{Ga}}$, actually creates a relatively shallow level in ${({\mathrm{Bi}}_{x}{\mathrm{Ga}}_{1--x})}_{2}{\mathrm{O}}_{3}$ alloys. This trend is opposite to what is found in pure ${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$. The puzzling behavior of the acceptor levels in the ${({\mathrm{Bi}}_{x}{\mathrm{Ga}}_{1--x})}_{2}{\mathrm{O}}_{3}$ alloys is attributed to the polaronic character of the holes in the Zn- and Mg-doped cases, and the decoupling of the hole state and the valence-band edge in the Cu-doped case. This understanding provides insights into the realization of $p$-type doping in dilute ${({\mathrm{Bi}}_{x}{\mathrm{Ga}}_{1--x})}_{2}{\mathrm{O}}_{3}$ alloys and paves a way to dope semiconductor materials with a strongly correlated band edge state, i.e., materials with a tendency to form polaronic acceptor or donor states.