Effects of nonlinear forces on dynamic mode atomic force microscopy and spectroscopy

In this paper, we describe the effects of nonlinear tip-sample forces on dynamic mode atomic force microscopy and spectroscopy. The jumps and hysteresis observed in the vibration amplitude (A) versus tip-sample distance (h) curves have been traced to bistability in the resonance curve. A numerical analysis of the basic dynamic equation was used to explain the hysteresis in the experimental curve. It has been found that the location of the hysteresis in the A-h curve depends on the frequency of the forced oscillation relative to the natural frequency of the cantilever