Dynamics of the cantilever in noncontact atomic force microscopy

The dynamics of a cantilever in noncontact atomic force microscopy (nc-AFM) is theoretically investigated based on an elastic oscillator model of the cantilever interacting with the surface. As for the tip-surface interaction, Lennard-Jones and the hard-wall potentials are assumed. Numerical integration of the equation of motion and the Poincare map method are used for the analyses of the tip motion. As a result of the extremely nonlinear nature of the interaction, various strange features of the tip motion, such as quasiperiodic oscillation and fractional resonance, are found. In particular, the coexistence of the dynamic touching mode and the nontouching mode is revealed. The phase-frequency relationship of the dynamic touching mode is obtained, which could be observed experimentally.