Abstract
The periodic impact force induced by tip-sample contact in a tapping mode atomic force microscope (AFM) gives rise to the non-harmonic response of a micro-cantilever. These non-harmonic signals contain the full characteristics of tip-sample interaction. A complete theoretical model describing the dynamical behaviour of tip–sample system was developed in this paper. An analytic formula was introduced to describe the relationship between time-varying tip–sample impact force and tip motion. The theoretical analysis and numerical results both show that the time-varying tip–sample impact force can be reconstructed by recording tip motion. This allows for the reconstruction of the characteristics of the tip–sample force, like contact time and maximum contact force. It can also explain the ability of AFM higher harmonics imaging in mapping stiffness and surface energy variations.