Experimental and theoretical analysis of the DMASP cantilever vibration behavior based on the MCS theory in moist environment

Abstract

A micro cantilever (MC) and a probe are two main components of the atomic force microscope (AFM). The dimensions of these components are in micro scales while their oscillation amplitude is on a nanometer scale. The present study intended to not only increase the accuracy of the simulation with regard to geometric discontinuities based on the Timoshenko beam model using the modified couple stress (MCS) theory but also increase the accuracy of the prediction of a system behavior by considering the hysteresis effect into the system vibration equations based on Bouc–Wen model. Since, the classical theory disregarded the molecular structure of matter and neglected the microstructure size dependency, which raise its physical breakdowns in micro and nanoscale applications. Therefore, some micro continuum theories are developed to account for the microstructure effects by introducing additional material constants to the conventional ones. Due to the lack of the experimental results for this kind of MCs, this paper is focused on the both experimental and simulation results by utilizing the DMASP MC. The roughness of the surfaces affects the MC vibration behavior in the air medium. Therefore, surface roughness affecting van der Waals force has been considered in the air medium. Furthermore, the simulation results are compared with experimental results in the air medium with different moisture content during the surface topography. Due to the results, the best surface topography is achieved in the third vibration mode. Since the piezoelectric MC can tolerate the limited voltage, for this AFM MC type, the best surface topography is achieved in the third mode. Hence, this paper highly recommends using the third vibration mode during the surface topography. Finally, based on the EFAST method the most effective parameters on the AFM MC performance are the piezoelectric layer length, thickness and the probe length.