Comments on the Dynamic Analysis of V-Shaped Atomic Force Microscopy in Liquid Environment by Considering Timoshenko Beam Theory

Abstract

In this paper, the dynamic of V-shaped atomic force microscopy in liquid environment influenced by the vertical, tangential interactions and hydrodynamic force with Timoshenko beam model has been studied by finite element method. The cantilever composes of three parts, the left part is rectangular in shape and has a fixed width and height, but in the middle and right part of cantilever, width and height are reduced linearly. The effects of geometrical parameters such as the ratio of reduced width, height reduction factor, length of cantilever’s central part, tip position, width of left part, height of the tip and angle between the cantilever and the sample’s surface on the frequency response of the system have been investigated. The results indicate that the resonant frequency, amplitude and phase shift of vertical and rotational displacements are very sensitive to changes in the geometric parameters which mentioned above. Since for biological samples which are made of very soft materials, resonant frequency in tapping mode (AM-AFM) should be in low range to prevent their damage during imaging and scanning and the amplitude of vibration due to the small space specially in liquid environment should be limited to specific range, the effect of geometric parameters on the frequency response of the system should be considered to achieve precise design of micro-cantilever.