Surface and subsurface oxygen vacancies in anatase TiO2 and differences with rutile

First-principles density-functional theory calculations in the generalized gradient approximation are carried out to study the relative stabilities of oxygen vacancies at surface and subsurface sites of anatase TiO2(101) and TiO2(001), and, for comparison, of the prototypical rutile TiO2(110) surface. Our results indicate that these defects are significantly more stable at subsurface than at surface sites in the case of anatase surfaces, whereas bridging oxygen sites are favored for O vacancies at rutile TiO2(110). Also, calculations of O-vacancy diffusion pathways at anatase TiO2(101) show that the energy barrier to diffuse from surface-to-subsurface sites is sufficiently low to ensure a rapid equilibration of the vacancy distribution at typical surface annealing temperatures. These results could explain why, experimentally, anatase surfaces are found to have a significantly lower defect concentration and/or to be more difficult to reduce than those of rutile.