A more comprehensive modeling of atomic force microscope cantilever

This paper focuses on the development of a complete model of an atomic force microscope (AFM) micro-cantilever beam, based on considering the effects of four major factors in modeling the cantilever. They are: rotary inertia and shear deformation of the beam and mass and rotary inertia of the tip. A method based on distributed-parameter modeling approach is proposed to solve the governing equations. The comparisons generally show a very good agreement between the present results and the results of other investigators. As expected, rotary inertia and shear deformation of the beam decrease resonance frequency especially at high ratio of cantilever thickness to its length, and it is relatively more pronounced for higher-order frequencies, than lower ones. Mass and rotary inertia of the tip have similar effects when the mass-ratio of the tip to the cantilever is high. Moreover, the influence of each of these four factors, thickness of the cantilever, density of the tip and inclination of the cantilever on the resonance frequencies has been investigated, separately. It is felt that this work might help the engineers in reducing AFM micro-cantilever design time, by providing insight into the effects of various parameters with the micro-cantilever.