Intrinsic n-type Defect Formation in TiO2: A Comparison of Rutile and Anatase from GGA+U Calculations

The formations of intrinsic n-type defects, that is, oxygen vacancies and titanium interstitials, in rutile and anatase TiO2 have been compared using GGA+U calculations. In both crystal structures, these defects give rise to states in the band gap, corresponding to electrons localized at Ti3+ centers. O vacancy formation in rutile results in two excess electrons occupying 3d orbitals on Ti atoms neighboring the vacancy. Similarly, for anatase, two Ti 3d orbitals are occupied by the excess electrons, with one of these Ti sites neighboring the vacancy, and the second at a next-nearest Ti position. This localization is accompanied by one oxygen moving toward the vacancy site to give a “split vacancy” geometry. A second fully localized solution is also found for anatase, with both occupied Ti sites neighboring the vacancy site. This minimum is 0.05 eV less stable than the split vacancy and is thus expected to be present in experimental samples. A partially delocalized solution corresponding to the split vacan...