Nonlinear tip-sample interactions affecting frequency responses of microcantilevers in tapping mode atomic force microscopy

Tapping mode atomic force microscopy is receiving a great deal of interest because of its ability to image compliant materials as well as to overcome adhesion forces. In this operation mode, the vibration amplitude of the cantilever is much higher than the equilibrium separation between tip and sample. For our experiments, a silicon microcantilever and a freshly cleaved mica sample were used. Frequency responses were measured for different values of equilibrium separation distance. Experimental results revealed a drastic decrease in vibration amplitude and a large shift of resonant frequency to higher values. This frequency shift and amplitude damping depend drastically on the equilibrium position with respect to the free oscillation amplitude of the cantilever. A model taking into account the attractive Van der Waals force as well as repulsive contact force was used. Parameters such as position of the tip, force acting during intermittent contact and frequency responses have been calculated. Good agreement is obtained and the relevant parameters involved in tapping mode are discussed.