Equivalent point-mass models of continuous atomic force microscope probes

Abstract

The theoretical foundations of dynamic atomic force microscopy (AFM) are based on point-mass models of continuous, micromechanical oscillators with nanoscale tips that probe local tip-sample interaction forces. In this letter, the authors present the conditions necessary for a continuous AFM probe to be faithfully represented as a point-mass model, and derive the equivalent point-mass model for a general eigenmode of arbitrarily shaped AFM probes based on the equivalence of kinetic, strain, and tip-sample interaction energies. They also demonstrate that common formulas in dynamic AFM change significantly when these models are used in place of the traditional ad hoc point-mass models.