Calculation of TiO 2 Surface and Subsurface Oxygen Vacancy by the Screened Exchange Functional

The formation energies of oxygen vacancies at different surface and subsurface sites of anatase (101), anatase (001), and rutile (110) surfaces are calculated by the screened-exchange (sX) hybrid functional method. Our results show that the oxygen vacancy is more stable on the surface than subsurface for rutile (110), while it is a more stable subsurface than on the surface for anatase surfaces. These results are similar to those found by simple density functional theory, but now the sX hybrid functional gives the correct defect localizations. The defects introduce a gap state near the conduction band edge. For the most stable oxygen vacancy site at each TiO 2 surface, the +2 charge state dominates over a wide range of Fermi energies.