Electronic properties of disordered anodic TiO₂ (001) surfaces: Application of the equation‐of‐motion method

We report calculations of the electronic properties for rutile TiO₂ (001) surfaces using the equation‐of‐motion (EOM) method. We use a full tight‐binding Hamiltonian developed by Vos to describe the electronic structure. In contrast to the Green's‐function (GF) method which is traditionally used for such a problem, the EOM method gives excellent results with large systems and any number of defects, and puts no restriction on the range of the impurity potential. There is experimental evidence that the observed gap state at 0.7 eV below the conduction‐band edge is due to an oxygen vacancy. For this reason we study the electronic properties of disordered surfaces as a function of oxygen vacancy concentrations (up to 10%). Our results are applied to the interpretation of recent scanning tunneling Microscopy (STM) experiments on anodic rutile TiO₂ (001) films (whose thickness is ∼ 150 Å), and the density of surface defects is estimated. Special care was paid to the study of the nature of gap states. Our results show that these states are localized and play the role of trapping centers which impede the conduction in the films and that no impurity band exists for the studied surfaces. We use both conductivity and local density of states (LDOS) calculations to draw this conclusion. In agreement with experiments, no contribution from gap states in the transport was confirmed in our work. We also report the LDOS calculations on a few sites around the defect at the surface. This in turn gives information about both the spatial decay of the bound‐state wave function (localization) and the existence of the impurity band.