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Density functional theory based first-principle calculation of Nb-doped anatase TiO2 and its interactions with oxygen vacancies and interstitial oxygen.

The structure and electronic properties of Nb-doped anatase (TNO) were studied from first principles using the density functional theory based band structure method. Four independent types of unit cells were studied; i.e., pure anatase, anatase with Nb dopant at Ti sites (Nb(Ti)), and cells with either interstitial oxygen (O(i)) or oxygen vacancies (V(O)). In addition, a unit cell with a Nb(Ti) and O(i), and a cell with Nb(Ti) and V(O) were investigated to clarify the role of nonstoichiometry in TNO. From the calculated results, the importance of the adjacent Nb(Ti)-V(O) and Nb(Ti)-O(i) structures was pointed out, and the experimental observation of the relationship between nonstoichiometry and electronic conductivity was rationalized. The shape of the impurity states found in these structures was used to comprehend the experimental observation of carrier concentration and the charge state of Nb dopant. The changes in lattice constants supported the existence of these structures as well. On the contrary, the cell with a simple Nb(Ti) did not show significant changes in structure and electronic properties, other than the emission of an electron in the conduction band. A stabilization of the impurity state was observed in the adjacent Nb(Ti)-V(O) structure compared to the V(O). The possibility of an essential role of this state in electric conduction was discussed. The formation of the adjacent Nb(Ti)-O(i) structure by O(2) gas annealing was discussed using statistical mechanics. The Gibbs free energies were calculated for O(i) atoms in TNO and compared to that of O(2) molecules in the gas phase. The analysis was qualitatively consistent with experimental behavior under the assumption of the Nb(Ti)-V(O) structures.