FEM-simulations of vibrations and resonances of stiff AFM cantilevers

The quantitative evaluation of atomic force acoustic microscopy images in order to determine local indentation moduli of samples requires the calculation of the vibration behavior and the resonances of the used atomic force microscope cantilevers and of the contact of the sensor tip with the sample surface. Numerical simulations were carried out by finite element methods (FEM) and compared to analytically calculated as well as to measurement results in order to investigate the applicability of the analytical models with effective geometrical data. The numerical simulations take into account the elastic coupling to the chips and the anisotropy of conventional single crystal silicon cantilevers. It was shown that the models of the shape and elasticity of the sensor tip and of its contact to the sample surface are the most critical points rather than the FEM model of the cantilever geometry.