Tip motion in amplitude modulation (tapping-mode) atomic-force microscopy: Comparison between continuous and point-mass models

We discuss the influence of high-order frequency components in the operation of an amplitude modulation atomic-force microscope (AFM). A comparative study of point-mass and continuous models is performed to describe the tip motion. The tip–surface interaction force excites high-order frequency components whenever a higher harmonic of the excitation force is close to an eigenmode of the cantilever beam. The strength of those components depends on the set point amplitude and the fundamental resonance frequency of the cantilever. However, for standard operating conditions with quality factors in the $102–103$ range, higher-order components are about three orders of magnitude smaller than the component at the excitation frequency. We conclude that point-mass models are suitable to describe the operation of a tapping-mode AFM in air environments.