We investigate the stability of self-trapped holes (STHs) and the acceptor levels of substitutional Mg and N impurities in $\alpha$-, $\beta$-, $\delta$-, and $\varepsilon \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$ using first-principles calculations based on the hybrid functional approach to assess their $p$-type dopability. When Fock-exchange and screening parameter values in the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional are optimized to satisfy the generalized Koopmans' theorem for a STH level in $\beta \text{−}{\mathrm{Ga}}_2{\mathrm{O}}_3$, the band gap is slightly overestimated, while functionals that well reproduce the band gap show slight convex behavior against the fractional electron number. However, the absolute position of the STH level at a fixed geometry is nearly independent of the parameter value, showing that the results are robust as long as the STH geometry and localized electronic nature are appropriately described and the band edges are well reproduced. In all of the polymorphs, holes localize with high self-trapping energies rather than being delocalized. Furthermore, both Mg and N impurities introduce polaronic acceptor states, and their acceptor levels lie far above the valence band maximum in all the polymorphs. Thus, the $p$-type doping of the four ${\mathrm{Ga}}_2{\mathrm{O}}_3$ polymorphs seems unfeasible in terms of the STH formation and the related deep, polaronic acceptor nature of the Mg and N impurities.

• Received 22 December 2018

DOI:https://doi.org/10.1103/PhysRevMaterials.3.044603

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Published by the American Physical Society