The formation energies of the oxygen vacancy and titanium interstitial in rutile TiO${}_2$ were calculated by the screened-exchange (sX) hybrid density functional method, which gives a band gap of 3.1 eV, close to the experimental value. The oxygen vacancy gives rise to a gap state lying 0.7 eV below the conduction band edge, whose charge density is localized around the two of three Ti atoms next to the vacancy. The Ti interstitial (Ti${}_{\mathrm{int}}$) generates four defect states in the gap, whose unpaired electrons lie on the interstitial and the adjacent Ti 3$d$ orbitals. The formation energy for the neutral oxygen vacancy is 1.9 eV for the O-poor chemical potential. The neutral Ti interstitial has a lower formation energy than the O vacancy under O-poor conditions. This indicates that both the O vacancy and Ti${}_{\mathrm{int}}$ are relevant for oxygen deficiency in rutile TiO${}_2$ but the O vacancy will dominate under O-rich conditions. This resolves questions about defect localization and defect predominance in the literature.

• Received 29 June 2012

DOI:https://doi.org/10.1103/PhysRevB.86.075209