Finite element modeling and analysis of an atomic force microscope cantilever beam coupled to a piezoceramic base actuator

Abstract

Characterization and analysis of sample surfaces with nanometer order topologies is essential to study properties such as roughness, resistance, molecular arrangements, failure, among others. Therefore, in recent decades, atomic force microscope (AFM) has become an essential tool, since it has the ability to get 3D nanometer order images of surfaces from some predefined kind of interaction. In order to understand the dynamics and improve the operation of base-cantilever-tip-sample AFM systems, several mathematical models were proposed in the literature. However, it seems that there is still a need of representative and parametric models able to capture material and geometric properties of the cantilever beam and piezoceramic base actuator. Hence, this work focuses on the development and analysis of a parametric model capable of properly representing the dynamics of an AFM cantilever beam when subjected to realistic operation conditions, using a finite element model for the cantilever beam and accounting for translational and rotational inertia of the probe tip and for the piezoceramic actuator that excites and controls the beam motion. All material and geometrical properties for the system (cantilever beam, probe tip and piezoceramic actuator) can be parametrized. Experimental SEM images and frequency responses of a real AFM cantilever beam are used to verify the model and also to define its parameters with very satisfactory results. A dynamic analysis of the cantilever beam when subjected to tip-sample nonlinear interaction forces is performed to develop a proper reduced-order model. The interaction forces were modeled using Lennard Jones potentials. Then, an analysis of the dynamic response of the cantilever beam for varying tip-sample initial distances is performed. Besides the appearance of the expected nonlinear behavior due to the tip-sample interaction forces, it is observed that the closer the sample is to the beam tip, the smaller is the tip displacement amplitude. Based on this observation, an analysis is performed to assess the correlation between the tip displacement and the surface topology of a diamond sample with satisfactory results.