A dynamic atomic force microscope sensitively probes surface properties with subnanometre lateral resolution. In the amplitude modulation mode, the force-sensing tip oscillates a few nanometres. The force sensor is a harmonic oscillator that interacts with a barrier, which can be described as a non-linear potential consisting of an attractive well and a repulsive wall. Further non-linearities may be introduced by adhesion, electrostatic or magnetic forces. Thus, the character of the non-linearity is intimately related to the material properties. This review highlights the non-linear dynamics in the amplitude modulation mode and how they enable and affect nanoscale material characterisation.

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DOI: 10.1016/S1369-7021(10)70162-0