Forces affecting the substrate in resonant tapping force microscopy

We propose a simple model to describe the interaction of a forced cantilever oscillation with a specimen in a tapping-mode scanning force microscope experiment in order to make a rough estimation of the forces affecting the surface with each touch down of the tip. Assuming weak damping of the cantilever (quality factor of the cantilever between 100 and 1000) and of the surface, we can estimate the forces to be in the range of those in the contact mode. These forces can vary by orders of magnitude, e.g. 10-6 to 10-11 N. To reduce the interaction force we suggest scanning on the low-frequency side of the resonance frequency of the non-contact cantilever oscillation. Increasing the difference of phase between the non-contact oscillation of the cantilever in air and the oscillation during contact introduces strong variations of the force. The improvement in resolution which can be achieved for soft samples by using the tapping-mode system results from the elimination of shear forces and the possibility of minimizing the force on the surface by varying the set-point of the scanning amplitude. Forces on the substrate will be enhanced by a large substrate stiffness.

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