Doping and compensation in Nb-doped anatase and rutile TiO2

The substitutional Nb donor states in anatase and rutile TiO2 are calculated using the screened exchange hybrid density functional. The calculations find that Nb forms a shallow state in anatase and a deep state in rutile TiO2, as in experiment. Donors in anatase are found to become compensated in O-rich conditions because oxygen interstitial acceptors acquire a negative formation energy for Fermi energies high in the band gap. O-poor conditions permit doping, not by creating O vacancies but by inhibiting the formation of oxygen interstitials which compensate doping.