Experimental and theoretical studies of frequency response function of dagger‐shaped atomic force microscope cantilever in different immersion environments

Abstract

In this study, the amplitude of frequency response functions of vertical and rotational displacements and resonant frequency of a dagger-shaped atomic force microscope cantilever have been investigated. To increase the accuracy of theoretical model, all necessary details for cantilever and sample surface have been taken into account. In this paper, carbon tetrachloride (CCL4 ), methanol, acetone, water and air have been considered as the environments. In the most cases, presence and absence of tip-sample interaction force have studied. For a sample cantilever immersed in air, both of the Euler-Bernoulli and Timoshenko beam theories have been compared. The results indicate that the tip-sample interaction force raises the resonant frequency. Increasing the liquid viscosity leads to a decrease in the resonant frequency and the amplitude of frequency response functions of vertical and rotational displacements. Increasing the rectangular and tapered parts lengths, decreases the resonant frequency and amplitude of frequency response functions of vertical and rotational displacements. By increasing the cantilever thickness the resonant frequency and amplitude of frequency response functions of vertical and rotational displacements increases. Theoretical model for air and water has been compared with experimental work. Results show good agreement.