Analytical and Experimental Frequency Response Analysis of Microcantilevers Subject to Tip-Sample Interaction

Abstract

Improvement of microcantilever-based sensors and actuators chiefly depends on how comprehensively they are modeled and precisely formulated. Atomic Force Microscopy (AFM) is the most widespread application of microcantilever beam as a sensor, which is usually influenced by the tip-sample interaction force. For this, vibration of AFM microcantilever probe is analyzed in this paper, along with analytical, numerical and experimental investigation of the influence of the sample interaction force on the microcantilever vibration. Nonlinear integro-partial equation of microcantilever vibration subject to the tip-sample interaction is then derived and numerically simulated. Moreover, multiple time scales method is utilized to estimate the tip amplitude while it is vibrating near the sample. An experimental setup is developed using AFM in order to validate the theoretical and simulation results. Hysteresis, instability and amplitude drop can be identified in the experimental curves inside the particle attraction domain. These are likely related to the interaction force between the tip and sample as well as the presence of the water layer during the experiments. A fair agreement is observed between the theoretical analysis, numerical simulation and experimental findings which obviously demonstrates the effectiveness and applicability of the developed model.