Dynamic analysis of tapping-mode AFM considering capillary force interactions

The Atomic Force Microscope (AFM) scans the topography of a sample surface using a micro-sized flexible cantilever. In tapping-mode AFM, the tip–surface interactions are strongly nonlinear, rapidly changing and hysteretic. This paper explores, numerically, a flexible beam model that includes attractive, adhesive and repulsive contributions, as well as the interaction of the capillary fluid layers that cover both the tip and the sample in ambient conditions common in experiments. Forward-time simulation has been applied with an event handling numerical technique for dynamic analysis, and the Amplitude–Phase–Distance (APD) curves have been extracted. The branches of periodic solutions are found to end precisely where the cantilever comes into grazing contact with event surfaces in state space, corresponding to the onset of capillary interactions and the onset of repulsive forces associated with surface contact. The dissipated power, in the presence of conservative tip–sample interaction forces where the source of hysteresis is the formation and rupture of a liquid bridge between the tip and the sample, has been measured too. This simulation provides a more accurate way to validate the design of a new AFM probe and AFM controller than simulations which use the lumped-mass model.