Regular Article

3D simulation of AFM non-uniform piezoelectric micro-cantilever with various geometries subjected to the tip-sample forces

Robotic Research Laboratory, School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran

^a e-mail: h_korayem@mecheng.iust.ac.ir

Received: 5 November 2016
Revised: 14 January 2017
Accepted: 19 January 2017
Published online: 3 March 2017

Abstract

Atomic force microscope (AFM) is a powerful instrument for investigation of surface topography at different workspaces. It is important to understand the dynamic behavior of AFM to improve its performance. 3D numerical method is suitable in order to simulate experimental conditions. This paper has investigated modeling and dynamic simulation of rectangular, Dagger and V-shaped geometries of AFM piezoelectric micro-cantilever (MC) with two electrode layers in the air environment. For a better understanding of the system dynamic, multi-layer MC dynamic equation has been derived. Euler-Bernoulli beam theory has been used for modeling the AFM cantilever. Hamilton’s principle has been used for the MC modeling and the finite element method (FEM) has been applied for its discretization. In 3D, with respect to the tip-sample forces piezoelectric MC has been simulated via the COMSOL software. The frequency and time responses have been also investigated. The topographies have been performed on different surfaces with various roughness’s types in the tapping and non-contact mode. The results of these two methods have been compared with experimental results. Moreover, the effects of MC geometrical parameters on surfaces topography and frequency responses have been studied and optimal dimensions of topographies have been obtained for each of the beam geometries. Simulations of various tip geometries have been performed in order to examine the effects of tip dimensions on the frequency and time responses. Furthermore, the effect of tip displacement on the frequency response has been investigated for different MC lengths.