This work systematically explores 19 unique configurations of the close-associate Ga–O divacancies $\left(V_{\text{Ga}}{V}_{\text{O}}\right)$ in $\beta \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$, including their complexes with H impurities, using hybrid functional calculations. Interestingly, most configurations are found to retain the negative-$U$ behavior of $V_{\text{O}}$, as they exhibit a thermodynamic ($-/3-$) charge-state transition level energetically located in the upper part of the band gap, where the $3-$ charge state is associated with the formation of a Ga–Ga dimer. The energy positions of the thermodynamic ($-/3-$) charge-state transition levels divide the divacancy configurations into three different groups, which can be understood from the three possible Ga–Ga dimerizations resulting from the tetrahedral and octahedral Ga sites. The relative formation energies of the different divacancy configurations, and hence the electrical activity of the divacancies, is found to depend on the Fermi-level position, and the energy barriers for transformation between different divacancy configurations are explored from nudged elastic band calculations. Hydrogenation of the divacancies is found to either passivate their negative-$U$ charge-state transition levels or shift them down in Fermi level position, depending on whether the H resides at $V_{\text{O}}$ or forms an O–H bond at $V_{\text{Ga}}$, respectively. Finally, the divacancy is discussed as a potential origin of the so-called $E_2^{*}$ center previously observed by deep-level transient spectroscopy.

• Received 3 December 2020
• Accepted 12 January 2021

DOI:https://doi.org/10.1103/PhysRevMaterials.5.025402