Metal oxides are extremely challenging for defect calculations within density-functional theory because of the underestimation of the band gap and of the polaronic effects due to spurious electron self-interaction in the standard (semi)local implementations. We show here that—similarly to Group-IV semiconductors—the HSE06 screened hybrid functional provides not only a good description of the ground-state properties and an accurate gap of ${\mathrm{TiO}}_2$ modifications, but fulfills the generalized Koopmans’ theorem for host-related defect states—independent of localization. This means that the total energy has the correct dependence on the fractional occupation number, lending credibility to the calculated optical and thermodynamic charge transition levels for acceptors (Al, Ga, In, Sc, and Y on Ti site) and donors (Nb on Ti site, and interstitial H). We find deep, localized hole polarons in anatase and electron polarons in rutile. Therefore, $p$-type doping in anatase and $n$-type doping in rutile are counteracted by carrier self-trapping. Donors in anatase and the acceptors in rutile give rise to effective masslike states, but the latter are deeper. In fact, the polaron bound at In in anatase is about as deep as the effective masslike state induced by In in rutile. The shallow state in anatase and the deep one in rutile for the Nb donor, as well as the deep state for Al in anatase, agree well with experimental observations.

• Received 26 November 2010

DOI:https://doi.org/10.1103/PhysRevB.83.155207