Small polarons in Nb- and Ta-doped rutile and anatase TiO₂

Experimental studies of thin-film Nb- and Ta-doped TiO₂ have reported that doped anatase is highly conductive, yet doped rutile is semiconducting. Standard DFT functionals (LDA, GGA) predict that for doped anatase TiO₂ the excess charge occupies the bottom of the conduction band, and is delocalised over all the Ti atoms. This has previously been proposed as the source of the experimentally observed high conductivity. GGA predicts a similar metallic system for Nb-doped rutile, however, in contradiction with experimental data that characterise doped rutile as a semiconductor with a localised gap state. This demonstrates that standard DFT functionals cannot explain the difference in experimental behaviour between polymorphs. Supplementing GGA with a “+U” on-site Coulomb correction recovers an electronic structure for Nb-doped rutile TiO₂ that is in agreement with the experimental data; a localised gap state is seen, corresponding to a small polaron on a single Ti site. GGA + U also predicts a small-polaronic Ti³⁺ gap state within a semiconducting system for {Nb,Ta}-doped anatase. On this basis we suggest the experimental variance between polymorphs in doped thin films is not an inherent property of the bulk crystals, but is due to other factors, e.g. additional defects or sample morphology, dependent on the synthesis history. For both anatase and rutile the defect feature is found to be insensitive to the identity of the dopant, and similar Ti³⁺ polarons are expected generally for doping where electrons are donated to the Ti lattice.