Theoretical description of the transfer of vibrations from a sample to the cantilever of an atomic force microscope

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Abstract
The cantilever in an atomic force microscope (AFM) is forced to vibrations if its sensor tip is in contact with an insonified sample. These vibrations and the motion of the sensor tip depend on the forces between the sensor tip and the sample, the mechanical excitation of the sample surface, and the oscillatory behaviour of the cantilever. In this paper, the transfer of vibrations from a sample to an AFM-cantilever is described theoretically supposing a rectangular-beam cantilever with the sensor tip at its very end and taking into account flexural vibrations only. The calculations include nonlinear effects resulting from the nonlinearity of the tip - sample forces. The comparison with experimental results shows a convincing agreement. The presented theory yields the fundamentals to determine elastic properties and adhesive forces of a sample surface with the lateral resolution of an AFM exploiting AFM-cantilever vibrations enforced by a suitable insonification of the sample.