Electrostatic interactions with dielectric samples in scanning probe microscopies

Electrostatic interactions between the conducting tip of a scanning probe microscope and a flat conductor coated with a thin or thick dielectric layer are treated analytically and numerically. Exact and compact approximate expressions for the capacitance, force, force gradient, electric field profiles, and their effective widths are derived for a spherical model tip by generalizing known solutions for the conducting sphere and sample problem. These expressions allow convenient modeling of various measurements involving voltage-biased probes, estimation of lateral resolution, and prediction of trends as a function of relevant parameters.