Reduced and n-type doped TiO₂: Nature of Ti³⁺ species

Defect states in reduced and n-type doped titania are of fundamental importance in several technologically important applications. Still, the exact nature of these states, often referred to as "Ti³⁺ centers", is largely unclear and a matter of debate. The problem is complicated by the fact that electronic structure calculations based on density functional theory (DFT) in the local density approximation (LDA) or semilocal generalized gradient approximation (GGA) provide results that do not account for many of the experimentally observed fingerprints of the formation of Ti ³⁺ centers in reduced TiO₂. Here, we investigate the properties of at least four different types of Ti³⁺ centers in bulk anatase, (1) 6-fold-coordinated Ti_6c³⁺ ions introduced by F- or Nb-doping, (2) Ti_6c³⁺-OH species associated with H-doping, (3) undercoordinated Ti_5c³⁺ species associated with oxygen vacancies, and (4) interstitial Ti_5c³⁺ species. The characterization of these different kinds of Ti³⁺ centers is based on DFT+U and/or hybrid functional calculations, which are known to (partially) correct the self-interaction error of local and semilocal DFT functionals. We found that strongly localized solutions where an excess electron is on a single Ti³⁺ ion are very close in energy and sometimes degenerate with partly or highly delocalized solutions where the extra charge is distributed over several Ti ions. The defect states corresponding to these different solutions lie at different energies in the band gap of the material. This has important implications for the conductivity mechanism in reduced or n-type doped titania and suggests a significant role of temperature in determining the degree of localization of the trapped charge.