Driven nonlinear atomic force microscopy cantilevers: From noncontact to tapping modes of operation

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Abstract
A numerical model of the operation of an atomic force microscope with a driven cantilever is presented. This model takes into account the attractive van der Waals and repulsive indentation forces acting between tip and sample. The time-dependent displacement amplitude and phase of the tip oscillations, and the magnitude, duration, and sign of the short bursts of tip–sample force are derived. It is shown that the stiffness of the tip and sample materials is an important factor in determining the magnitude and duration of the tip–sample repulsive force and the magnitude of sample indentation. The model covers typical operating ranges of vibrating cantilever atomic force microscopes, from the noncontact to the tapping modes.