Frequency shift of a resonating cantilever in a.c. force microscopy: towards a realistic model

Quantifying the local elastic properties of the material requires realistic modeling of the behavior of the system. In this paper, we present a model in which the cantilever is considered as a continuous medium. The model uses the hertzian contact theory to describe the mechanical contact between the sample and the tip, represented by a spring. Moreover, this model takes into account the experimental aspect of the clamped cantilever base. The associated boundary conditions are physically justified.

Experimental measurements have been performed. They show the evolution of the resonance frequency when contacting different samples. The corresponding fitted theoretical curves give reasonable agreement with experiment and allow measurement of the local elastic properties of the sample with good accuracy (better than 5%).