Effects of anisotropic material property on the spring constant and the resonant frequency of atomic force microscope cantilever

Abstract

Atomic force microscope (AFM) is a powerful tool for force measurement in nanoscale. Many methods have been developed to obtain the precise cantilever's spring constant for improving the accuracy of force measurement. AFM cantilevers are usually made by single crystal silicon of which the anisotropic material property seriously affects the spring constant of cantilevers and has not considered before. In this paper, the density function theory was used to calculate the anisotropic stiffness matrix of crystal silicon, which was used in the finite element analysis to calculate lateral, axial, bending spring constants, and resonant frequencies of rectangular AFM cantilevers. These results were compared with those derived from other theoretical methods and with those provided by the manufacturers. The results showed that the anisotropic material property significantly affected the spring constants and the resonant frequencies of the AFM cantilever. The assumption of equivalent isotropic property of the rectangular AFM cantilever would cause an error up to 29.72%. Furthermore, two equations were proposed to obtain the spring constants and the resonant frequencies of crystal silicon AFM cantilever with the axis located at different cantilever-crystal angles.