Study of the size-dependant vibration behavior of an AFM microcantilever with a sidewall probe

In this paper, the resonant frequency and sensitivity of an atomic force microscope (AFM) with an assembled cantilever probe (ACP) are analyzed utilizing the modified couple stress theory. The proposed ACP comprises a horizontal microcantilever, an extension and a tip located at the free end of the extension, which make AFM capable of scanning the sample sidewall. First, the governing differential equation and boundary conditions for dynamic analysis are obtained by a combination of the basic equations of the modified couple stress theory and Hamilton principle. Then, a closed form expression for the resonant frequency are derived, and using this expression the sensitivity are also investigated. The results of the proposed model are compared with those of the classic beam theory. The comparison shows that the difference between the results predicted by these two theories becomes significant when the horizontal cantilever thickness comes approximately close to the material length scale parameter, in which for some values of contact stiffness the difference reaches its maximum. It can also be inferred that a decrease in the microcantilever thickness could have a knock on effect on the shifts of first frequency and first sensitivity caused by an increase in the extension length.