Dynamics of the cantilever in noncontact dynamic force microscopy: The steady-state approximation and beyond

A detailed analysis of models that have been used for describing the dynamics of the cantilever in large-amplitude noncontact dynamic force microscopy is presented. For each model, attention is especially paid to the nonlinear nature of the problem and its implication for experiments. In particular, in the steady-state approximation where the equations of motion for an externally and self-driven oscillator are rigorously identical, the theory predicts the existence of unstable solutions whether the interaction force is dissipative or not. The need to go beyond the steady-state approximation by including the finite-time response of the system to a change of tip-surface separation or interaction during the scanning is also discussed.