Oxygen deficiency in TiO2: Similarities and differences between the Ti self-interstitial and the O vacancy in bulk rutile and anatase

TiO2 is an oxygen-deficient, intrinsically n-type material, but it is often debated whether the electrons are donated by oxygen vacancies (V-O) or titanium interstitials (Ti-i). Investigating this issue is complicated by the fact that rutile can self-trap electrons in intrinsic small polaron states, while bulk anatase cannot. The screened hybrid functional HSE06 was proven to account for this phenomenon and has provided quantitatively correct results for V-O in our earlier study. Here, we use it for Ti-i in both rutile and anatase, allowing full spin and symmetry freedom, to shed light on the similarities and differences to V-O. We find that these two defects give rise to very similar fingerprints in electron paramagnetic resonance, infrared absorption, or photoelectron spectra. In weakly reduced rutile, the ground state of both defects is (2+), with two electrons in polaronic traps, bound loosely to the defect. Most of the time, only these latter states (crudely resembling a hydrogenic series, with increasing distance from the defect) are likely to be detected. In anatase, both V-O and Ti-i can be expected to be ionized at room temperature (singly and doubly, respectively), and the next vertical ionization energy is similar in the two defects-and very close to the ionization energy of the bound polarons in rutile. Most signals in paramagnetic resonance experiments on rutile must also be related to the polaron states, and, in general, very special conditions have to be fulfilled to detect electrons localized to V-O or Ti-i itself. We show that, in thermal equilibrium, the dominant defect in intrinsic samples is V-O, and Ti-i can be the majority defect only in strongly reduced anatase, or in case of p-type doping.