Quantitative theory of the oxygen vacancy and carrier self-trapping in bulk TiO2

Abstract

Standard approximations of density functional theory often fail for defects in transition metal oxides. Despite its significance in applications and decades of research, the oxygen vacancy in TiO${}_{2}$ is also poorly understood from the theory point of view. The Heyd-Scuseria-Ernzerhof functional (HSE06) provides a total energy that is a linear function of the occupation number (as it should be for the exact functional) also in TiO${}_{2}$. This allows reproduction of the measured infrared absorption, photoluminescence, and thermal ionization data within \ensuremath{\sim}0.1 eV. From our calculations, a consistent and quantitative interpretation of the conflicting experiments emerges. Electron self-trapping in rutile makes the properties of the vacancy concentration dependent. In oxidized samples the vacancies are passivated by native Ti${}^{3+}$/Ti${}^{4+}$ traps. This explains why electrons localized to the vacancy could only be observed after illumination at very low temperature in magnetic resonance experiments. In strongly reduced samples, electrons may stay localized in the vacancy and even the neutral state gives rise to two vertical electronic transitions (at 0.8 and 1.2 eV). The situation is much simpler in anatase, where only holes are self-trapped by O${}^{2\ensuremath{-}}$/O${}^{1\ensuremath{-}}$ transitions. The oxygen vacancy is a shallower donor in anatase than in rutile.