We explore the viability of using transition-metal impurities as $n$-type dopants in $\beta \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$, focusing on W, Mo, Re, and Nb. Our first-principles calculations show that these impurities can incorporate on both crystallographically inequivalent Ga sites, with the octahedrally coordinated sites being preferred. Mo and Re behave as deep donors. Tungsten on a tetrahedral site is a shallow donor, but unfortunately W on an octahedral site is much lower in energy. Niobium emerges as the best candidate for $n$-type doping: It has a low formation energy, is a shallow donor on the tetrahedral site, and has only a modest ionization energy (0.15 eV) on the octahedral site.

• Received 4 August 2016
• Revised 20 October 2016

DOI:https://doi.org/10.1103/PhysRevB.94.195203