A comprehensive modeling and vibration analysis of AFM microcantilevers subjected to nonlinear tip-sample interaction forces

Abstract

Precise and accurate representation of an Atomic Force Microscopy (AFM) system is essential in studying the effects of boundary interaction forces present between the probe's tip and the sample. In this paper, a comprehensive analytical model for the AFM system utilizing a distributed-parameters based approach is proposed. More specifically, we consider two important attributes of these systems; namely the rotary inertia and shear deformation when compared with the Euler-Bernoulli beam theory. Moreover, a comprehensive nonlinear interaction force is assumed between probe's and sample in order to reveal the response of the system more realistically. This nanoscale interaction force is based on a general form consisting of both attractive and repulsive components as well as a function of the tip-sample distance and the microcantilever's base and sample oscillations. Mechanical properties of the sample could interact with the nanomechanical coupling field between the probe' tip and sample and be implemented in studying the composition information of the sample and the ultra-small features inside it. Therefore, by modulating the dynamics of the AFM system such as the driving amplitude of the microcantilever the procedure for the subsurface imaging is described. The presented approach here could be implemented for designing the AFM probes by examining the tip-sample interaction forces dominant by the van der Waals forces. Several numerical case studies are presented and the force-distance diagram reveals that the proposed nonlinear nanomechanical force along with the distributed-parameters model for the microcantilever is able to fulfill the mechanics of the Lennard-Jones potential.