Static and Dynamic Structural Modeling Analysis of Atomic Force Microscope

Abstract

As a cantilever structure, atomic force microscope (AFM) can be either modeled as a beam, plate or a simple one degree-of-freedom (DOF) system depending on its geometry and application scenario. The AFM structure can experience the deformation shapes of vertical bending, lateral bending, torsion, extension and couplings between these four deformations depending on the excitation mode. As a small structure of micron scale, forces like van der Waals (vdW) force, surface stress, electrostatic force and residual stress can have significant influence on the AFM deflection. When the AFM tip is in contact with the sample surface, different contact mechanics models are needed depending on the tip geometry, AFM operating mode and tip, sample surface material properties. In dynamic mode, the AFM tip–sample surface intermittent contact is a complicated nonlinear dynamics problem. As a powerful tool, the AFM application is already beyond the stage of being used to image the sample surface topography. Nowadays, AFM is used more often to extract the sample materials properties such as Young’s modulus, surface energy/adhesion and viscosity. How to properly model the AFM structure with different deformations and their coupling under different forces and the tip–sample surface interaction is vital to linking the experimentally measured data correctly with the sample surface material properties. This chapter reviews the different models concerning the AFM structure (static) deformations, external residual forces modeling, tip–surface contact and the AFM dynamics. This chapter is intended to provide a comprehensive review rather than an in-depth discussion on those models. Because there are too many factors influencing the experimentally measured data during the application of AFM, it is extremely difficult to consider all these factors in one model for AFM if not impossible. Because there are too many factors influencing the AFM deformations/dynamics, it will be extremely difficult if not impossible to link all of the influencing factors to the experimental data. Therefore, in the modeling aspect, certain assumptions must be made to render the problem solvable. One of the major purposes of this chapter is to discuss and analyze the assumptions of those models and by doing so we try to outline the applicability ranges of those models. At the same time by analyzing the assumptions of the models applied to the AFM, the limitations of some models are also presented. Pointing out the limitations of those models which work fine with certain application scenarios is intended to make the applicability ranges of the models clearer and also helps to better interpret the experimental data. Only the dominant factors should be considered in a model and the other factors must be neglected to have a workable model. However, for different AFM applications the dominant factors are varied and thus transferring the model developed for one AFM application to another one can be inappropriate or even wrong. The analysis on the model assumption thus plays an important role of applying one model developed for certain application scenario to other applications.