Sensitivity Analysis of Atomic Force Microscope Cantilever Made of Functionally Graded Materials

Abstract

The purpose of this paper is the enhancement of the AFM sensitivity through the selection of an optimized FGM micro cantilever beam. In this paper, resonant frequencies and sensitivities of first two modes of micro cantilever which is made of functionally graded materials are investigated and a relationship is developed to evaluate the sensitivity of FGM micro cantilever. Effect of volume fraction of materials and surface contact stiffness on the resonant frequencies and sensitivities are studied. The rectangular FGM beam is modeled by an Euler-Bernoulli beam theory. It is assumed that beam is made of a mixture of metal and ceramic with properties varying through the thickness following a simple power law of n. This variation is a function of the volume fraction of the beam material constituents. The interaction between AFM tip and surface is modeled by a linear spring which expresses the contact stiffness. Results show that, increasing the ceramic volume fraction increases the resonant frequencies of both modes 1 and 2. When contact stiffness is small, for both modes, as ceramic volume fraction increases, sensitivities decreases, while for large contact stiffness, as ceramic volume fraction increases the sensitivities will be increased. Results also show that at each contact stiffness, there is a unique value of n at which the sensitivity is maximized. Using these values for n, the high quality and high contrast images can be obtained.