Vibration of the cantilever in Force Modulation Microscopy analysis by a finite element model

The resonance frequency of the cantilever beam of a Force Modulation Microscope is studied in function of the beam shape, the sample stiffness, and the contact model. We used a one dimensional finite element model for the cantilever beam, which permits the exact vibration of the beam to be treated in the contact mode, whatever its shape (rectangular as well as triangular beams) and excitation mode (by the beam holder, by the sample, by a localized, or distributed force). Based on a classic finite element scheme, it is simple to program and as rapid as the usual analytical models. We demonstrate that the mode of excitation of the beam strongly influences the cantilever’s frequency response in the contact mode. Anti-resonance is observed on the amplitude curves, which may perturb the measurements on some samples. We analyzed the true normal and tangential amplitude, for different beams and tip dimensions, in relation with the apparent amplitude of the vibration, as detected by the system. Experimental resul...