Electronic Structure and Defect States of Undoped and (Nb, Ta)-doped Anatase using Density Functional Theory

In this work an overall electronic structure including the position and formation energies of various intrinsic and extrinsic defects are computed for the undoped and (Nb, Ta)-doped anatase using Density Functional Theory aided by Hubbard correction (DFT+U). The intrinsic point defects considered here are, oxygen vacancy ($V_O$), oxygen interstitial ($O_i$), titanium vacancy ($V_{Ti}$) and titanium interstitial ($Ti_i$). Additionally, this study investigated the interaction of the dopant atoms with these native defects. Out of all the intrinsic defects considered here, $V_{Ti}$ and $Ti_i$ are found to be most stable under equilibrium condition. Whereas, conduction band in undoped anatase is consisted of mainly Ti 3d with a minor component of O 2p states, valence band is found to be mainly composed of O 2p with a minor contribution from Ti 3d states. $V_O$ and $Ti_i$ are found to form localized states in the band gap. In Nb- and Ta-doped anatase, hybrid states of Ti 3d and Nb 4d and Ta 5d and Ti 3d are found to form near the conduction band edge along with in the vicinity of conduction band, thereby reducing their band gaps as compared to undoped anatase. Moreover, $O_i$ stabilized near the dopant atom, suggesting higher bond strength between the dopant and the oxygen atoms. Anisotropy in the effective mass is seen, with the extent of anisotropy being higher for doped anatase. Finally, an alignment of band diagrams for all the intrinsic and extrinsic defect states is performed using vacuum potential from slab-supercell calculation as reference.