Theory of higher harmonics imaging in tapping-mode atomic force microscopy

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 timevarying 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.