Frequency Response Behavior of Microcantilevers in Tapping-Mode Atomic Force Microscopy

Distributed-parameters vibration model of microcantilevers in tapping-mode Atomic Force Microscopy (AFM) is developed and is shown to be highly nonlinear. The question of why these nonlinearities are important and how they influence the predicted frequency response behavior of the cantilevers is addressed by comparing the results of developed model with a simple lumped-parameters model that has been extensively studied in the literature so far. The interaction forces between the microcantilever tip and the sample is supposed to be the same in both models and consist of attractive and repulsive interaction force regimes. In addition, experimental measurements are provided for a typical microcantilever-sample system to demonstrate the superiority of distributed-parameters formulation over the lumped-parameters model to predict the frequency response behavior of the AFM prob. The results indicate that the nonlinear continuous model is more accurate particularly in the estimation of the saturated amplitude and frequency zone in which the tip-sample contact occurs.