Limitation and extrapolation correction of the GGA + U formalism: a case study of Nb-doped anatase TiO2

Abstract

It is rather difficult to model the electronic properties of wide-gap oxides with moderate electronic correlation using first principles methods in the framework of the density functional theory (DFT) together with the Hubbard correction to account for the nonlocal effect in the exchange-correlation (XC) functionals. In this contribution we present a case study of the Nb-doped anatase TiO₂, to demonstrate such limitation in the GGA + U formalism. It is found that overcorrection owing to a big effective Hubbard parameter U′ leads to an erroneous band structure, but an inadequate U′ value results in significantly undervalued prediction of the energy band gap. Fortunately, such limitation in U′ correction can be addressed satisfactorily through a physically justifiable extrapolation scheme, with electronic structures thus corrected being in excellent agreement with the experimentally observed transparent conductivity of Nb-doped anatase. High resolution X-ray photoelectron spectroscopy (XPS) offers solid support to the theoretical work that Nb doping lowers the valence band without introduction of gap states, and the measured valency of Nb in TiO₂ is in excellent agreement with the calculated value. Also, the current method has been successfully applied to other well-known and yet electronically rather different TCO systems, the Al-doped ZnO and F-doped SnO₂.