An analytical model for the capacitance between probe tip and dielectric film deduced by high-frequency electromagnetic-field simulations

An analytical model for the capacitance between a probe tip and a dielectric film is presented based on the high-frequency electromagnetic-field simulation of the three-dimensional tip and dielectric film system. We examined the effects of the probe-tip geometry and film properties on the tip-sample capacitance and deduced empirically the analytical model expressed by a simple logarithmic dependence on the tip-film distance, $Z$⁠. Furthermore, the parameters in the analytical model could describe the probe-tip shape, dielectric permittivity, and film thickness. Based on these results, we discuss the capabilities to probe quantitatively the nanoscale dielectric properties of a thin film.