Hole conductivity through a defect band in ZnGa2O4

Semiconductors with a wide band gap ($>3.0$ eV), high dielectric constant ($>10$), good thermal dissipation, and capable of $n$- and $p$-type doping are highly desirable for high-energy power electronic devices. Recent studies indicate that ${\mathrm{ZnGa}}_{2}{\mathrm{O}}_{4}$ may be suitable for these applications, standing out as an alternative to ${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$. The simple face-centered-cubic spinel structure of ${\mathrm{ZnGa}}_{2}{\mathrm{O}}_{4}$ results in isotropic electronic and optical properties, in contrast to the large anisotropic properties of the $\ensuremath{\beta}$-monoclinic ${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$. In addition, ${\mathrm{ZnGa}}_{2}{\mathrm{O}}_{4}$ has shown, on average, better thermal dissipation and potential for $n$- and $p$-type conductivity. Here we use density functional theory and hybrid functional calculations to investigate the electronic, optical, and point defect properties of ${\mathrm{ZnGa}}_{2}{\mathrm{O}}_{4}$, focusing on the possibility for $p$- and $n$-type conductivity. We find that the cation antisite ${\mathrm{Ga}}_{\mathrm{Zn}}$ is the lowest-energy donor defect that can lead to unintentional $n$-type conductivity. The stability of self-trapped holes (small hole polarons) and the high formation energy of acceptor defects make it difficult to achieve $p$-type conductivity. However, with an excess of Zn, forming ${\mathrm{Zn}}_{(1+2x)}{\mathrm{Ga}}_{2(1\ensuremath{-}x)}{\mathrm{O}}_{4}$ alloys, this compound can display an intermediate valence band, facilitating $p$-type conductivity. Due to the localized nature of this intermediate valence band, $p$-type conductivity by polaron hopping is expected, explaining the low mobility and low hole density observed in recent experiments.