Non-linear electric field response of permittivity of atomically smooth TiO₂(rutile) single crystals studied by an electrochemical approach

Electric field-dependent permittivity of n-TiO₂ (rutile) along different crystallographic axes was investigated by an electrochemical impedance spectroscopy (EIS) measurement. The C^-2 versus U plots were fitted with a quadratic function of U, derived from a model that adds the effects of electric field dependent permittivity to the conventional Mott-Schottky equation. Only when atomically flat n-TiO₂ single crystal electrodes were used, could the intrinsic behavior of the electric field dependent permittivity be observed. The principal components of permittivity in the ab-plane exhibited a weak electric field dependence, while a strong electric field dependence was confirmed along the c-axis direction. By taking the electric field dependent permittivity into account, we were able to evaluate accurately the flat-band potential and the donor density. Different photocurrent behavior between (110), (100), and (001) electrodes is discussed in terms of the electric field strength at the surface and the depletion layer width within TiO₂.