Effect of size on the dynamic behaviors of atomic force microscopes

Accurate mathematical modeling and simulation of cantilever dynamics are crucial to design and fabrication of the atomic force microscope (AFM). Thickness of AFM cantilevers is in order of few microns or sub-microns and producers trend to make it even smaller because of more resolution and sensitivity. By reducing the cantilever thickness, size effect may be appeared which changes the AFM dynamics. In this paper, effect of size on dynamic behavior of AFM is investigated based on the modified couple stress theory. The AFM is modeled as an Euler-Bernoulli micro-cantilever and the Galerkin projection method is applied to derive the lumped model. Investigation of free vibration amplitude shows the necessity of considering the size effect. Accuracy of solution is verified by comparing the results with two degree-of-freedom model and analogue equations method. Furthermore, stability analysis and frequency response of AFM based on classic and non-classic theories are investigated and the obtained results are compared with each other. Findings of the present study show that considering size effect have significant effect on reliable estimation of the AFM dynamic.