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 TiO 2 , to demonstrate such limitation in the GGA + U formalism. It is found that overcorrection owing to a big effective Hubbard parameter U 0 leads to an erroneous band structure, but an inadequate U 0 value results in significantly undervalued prediction of the energy band gap. Fortunately, such limitation in U 0 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 TiO 2 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 SnO 2 .

First principles study for band engineering of KNbO3 with 3d transition metal substitution

“…formation energy, lattice parameters, and semiquantitatively, as well as magnetism owing to spin polarization). [37][38][39][40][41] Here we used the PBE functional 42,43 for efficient structure-energy modelling to determine the stable structures of doped/alloyed materials. For dependable band structures, we adopted the well tested HSE06 functionals.…”

“…In summary, being rather different from doping binary oxides such as TiO 2 , [37][38][39][40][41]57,58 the doping effect of 3d transition metals into perovskite oxides is rather complex, owing to the presence of non-transition metals in the A sites. The overall effects on conducting characteristics and potential applications are presented in Table 1, such that early transition metal doping from Ti to V leads to n-type characteristics.…”

Role of materials chemistry on the electrical/electronic properties of CuO thin films

“…It is essential to be able to control the charge carrier concentrations in copper oxides, so that a suitable potential profile around the pn junction(s) can be realized to confine the depletion region in the CuO layer for optimized production of electron-hole pairs [28][29][30]. Fundamentally, these properties of oxide semiconductors depend strongly on the materials chemistry associated with native defect concentration, which in turn depends strongly on the fabrication conditions and particularly the achievable oxygen contents [32][33][34][35][36].…”

Nb‐Dopant‐Induced Tuning of Optical and Electrical Property of Anatase TiO2 Nanocrystals

“…High (> 90%) ionization efficiency due to low ionization energy (4‐30 meV) of niobium (Nb) atom compared to other elements suggests that Nb dopants are very good electron donor to wide band gap semiconductors. Electronic structure calculations indicate that doped Nb atoms generate delocalized states in the conduction band region of TiO 2 anatase phase . The observation of metallic conductivity in Nb doped TiO 2 stimulated many experimental researchers to find a possible application as transparent conducting electrode.…”