Sensitivity of flexural vibration mode of the rectangular atomic force microscope micro cantilevers in liquid to the surface stiffness variations

Abstract

In this paper, the resonance frequencies and modal sensitivity of flexural vibration modes of a rectangular atomic force microscope (AFM) cantilever immersed in a liquid to surface stiffness variations have been analyzed and a closed-form expression is derived. For this purpose, the Euler-Bernoulli beam theory is used to develop the AFM cantilever model in liquid. Then, an expression for the resonance frequencies of AFM cantilever in liquid is derived and the results of the derived expression are compared with the experimental measurements. Based on this expression, the effect of the surface contact stiffness on flexural mode of a rectangular AFM cantilever in a fluid is investigated and compared with the case that AFM cantilever operates in the air. The results show that in the low surface stiffness, the first mode is the most sensitive mode and the best image contrast is obtained by excitation this mode, but by increasing the sample surface stiffness the higher modes have better image contrast. In addition, comparison between modal sensitivities in air and liquid shows that the resonance frequency shifts in the air are greater than the shifts in the fluid, which means that for the similar surface stiffness the image contrast in air, is better than liquid.