Deep acceptors in Ga₂O₃

β-Ga₂O₃ is a wide-band-gap semiconductor with promising applications in high-power electronics. While n-type doping is straightforward, p-type doping is elusive, with only deep acceptors available. We use hybrid density functional theory to explore the properties of possible acceptors, and discuss the viability of obtaining semi-insulating material. All dopants we considered lead to deep acceptor levels that are more than 1.3 eV above the valence-band maximum. N and Mg were identified as the most promising deep acceptors. We evaluated incorporation in different configurations, and also considered the effect of native defects as well as complexes. We find that both dopants will lead to Fermi-level positions that are at least 1.3 eV away from the band edges. We also predict diffusion activation energies, finding that Mg is significantly more mobile. The information obtained in this study can be used to analyze and explain ion implantation experiments, and to guide design of semi-insulating Ga₂O₃ layers.