Intrinsic n-type Defect Formation in TiO2: A Comparison of Rutile and Anatase from GGA plus 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. 0 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 vacancy geometry, with one electron occupying the bottom of the conduction band, is also identified as 0.28 eV less stable. Formation of titanium interstitials donates four electrons to the Ti lattice. In anatase, one of these electrons is located at the interstitial Ti site, and three occupied defect states are hybridized between three nearest neighbor Ti sites. In rutile, these excess electrons are mostly localized at four nearest neighbor Ti sites, with only a small amount of excess charge found on the interstitial Ti atom. This difference in the charge on the interstitial atom is a consequence of the differing interstitial geometries in the two polymorphs. Calculated optical absorption spectra for all defects show significant decreases of the optical band gap, with a larger red shift predicted for titanium interstitials in anatase than in rutile. Defect formation energies have been calculated under oxygen-rich and oxygen-poor conditions for both polymorphs. Under all conditions, 0 vacancy formation is slightly more favorable in anatase than in rutile, while Ti interstitials form more easily in rutile than anatase. Under O-rich conditions, 0 vacancies are the favored defect type, but both defect types have high formation energies. Under O-poor conditions, both defect types are stabilized, with Ti interstitials predicted to become the favored defect in rutile samples, particularly at elevated temperatures.