Doping and compensation in Nb-doped anatase and rutile TiO2

Abstract

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.