Vibration response of a piezoelectrically actuated microcantilever subjected to tipsample interaction

Piezoelectric microcantilevers (MCs) are types of MCs which can be used in Atomic Force Microscopy (AFM) as a micro-robot, sensor, and imaging actuator. In this paper, the vibrating motion of piezoelectric MCs in AFM application is analyzed. With respect to the geometrical discontinuities, due to the piezoelectric layer, as well as tip, a non-uniform beam model is chosen for analysis. At first, to determine the accuracy of the non-uniform beam model in simulating the vibrating motion of piezoelectric MC, the simulation results are compared with the experimental ones in the absence of the tip-sample force. Good agreement of these results indicates the ability of this model in modeling this type of MC. A numerical solution and a Multiple Time Scale (MTS) method are used to study the nonlinear response of the MC near the sample surface. Comparison of results, at the non-contact mode, shows good agreement between the two solving methods at normal equilibrium distances (d  2 nm). The effects of the angle of MC, the probe length, and the geometric dimensions of the piezoelectric layer on the nonlinearity of the system are studied and it then becomes clear that they can affect the frequency response curvature of the curve and the nonlinearity of the system.