Coupled molecular and cantilever dynamics model for frequency-modulated atomic force microscopy

A molecular dynamics model is presented, which adds harmonic potentials to the atomic interactions to mimic the elastic properties of an AFM cantilever. It gives new insight into the correlation between the experimentally monitored frequency shift and cantilever damping due to the interaction between tip atoms and scanned surface. Applying the model to ionic crystals with rock salt structure two damping mechanisms are investigated, which occur separately or simultaneously depending on the tip position. These mechanisms are adhesion hysteresis on the one hand and lateral excitations of the cantilever on the other. We find that the short range Lennard-Jones part of the atomic interaction alone is sufficient for changing the predominant mechanism. When the long range ionic interaction is switched off, the two damping mechanisms occur with a completely different pattern, which is explained by the energy landscape for the apex atom of the tip. In this case the adhesion hysteresis is always associated with a distinct lateral displacement of the tip. It is shown how this may lead to a systematic shift between the periodic patterns obtained from the frequency and from the damping signal, respectively.