Modeling the Amplitude Mode of Piezoelectric Microcantilever AFM in Contrast to the Surface of the Sample in a Liquid Medium

Abstract

This paper deals with the modeling and simulation of the vibration behavior of piezoelectric microcantilever based on the Timoshenko theory and using multi-scale method in the liquid environment, considering the interaction forces in the liquid medium. The effect of viscosity and density is investigated on first four bending modes. The results of topographic simulation for rectangular roughness in the liquid medium and the amplitude mode indicate a reduction in the latency of the first mode from 1.54 to 0.48 and in the second mode from 0.49 to 0.18 compared to the air environment. According to the results of simulation in different working environments, with the increase in the radius of the probe tip, the squeeze force of the liquid will also increase; this increase in the force reduces the amplitude of the vibration motion and the natural frequency. According to the results of the simulation, solution based on the theory of string of spheres with 0.1% error has less accuracy than on multi-scale method with 0.031% error. Regarding the multi-scale method, the Rankl model with a percentage error of 13.47 and the string of sphere model with a percentage error of 0.10 have had a higher accuracy than the similar model of FEM with 14.64% error; the accuracy of the Hosaka model with a percentage error of 18.62 is less than the Rankl model; therefore, the Rankl model has the least error for multi-scale method solving in Timoshenko beam theory.