Quantity measured in frequency-shift-mode atomic-force microscopy: An analysis with a numerical model

Abstract

By using the Lennard-Jones potential and the Morse potential to model the short-range chemical bond interaction and taking the long-range van der Waals potential into account for the tip-surface interaction in atomic force microscopy (AFM), we first investigate the frequency shift as a function of the tip-surface separation for Si surface with a Si tip, by performing a numerical integration. The result is in good agreement with the recent experimental data. Then we examine how the frequency shift depends on the following quantities: the force, the force gradient, and the potential energy. We show that it is not the force gradient but the force itself (for small amplitude) or the geometric mean of potential energy and force (for large amplitude) that is detected in the frequency-shift mode AFM. These observations suggest some possible ways to detect experimentally the tip-surface interaction.