Theory of multifrequency atomic force microscopy.

We develop a theory that explains the origin of the high force sensitivity observed in multifrequency force microscopy experiments. The ability of the microscope to extract complementary information on the surface properties is increased by the simultaneous excitation of several flexural cantilever modes. The force sensitivity in multifrequency operation is about 0.2 pN. The analytical model identifies the virial and the energy dissipated by the tip-surface forces as the parameters responsible for the material contrast. The agreement obtained among the theory, experiments and numerical simulations validates the model.