Evaluation of the capacitive force between an atomic force microscopy tip and a metallic surface

We propose a very simple method to determine the electrical tip-surface force in Atomic Force Microscopes used to study the electrical properties of metallic or insulating materials; the analysis of the measurements as well as determination of the appropriate experimental procedures requiring an analytical model of the tip-surface capacitance. The comparison of force expressions obtained by this method with those obtained by exact derivation in the case of the sphere-infinite plane system shows very good agreement. This method is then applied to determine the tip-surface force, the real shape of the tip being introduced in the derivation. The obtained expression is compared to experimental and numerical data. We emphasize that this method is very general and can be applied to any axially symmetric capacitor.