The faulted and unfaulted halves correspond to the left and right side, respectively. Simulation of cantilever dynamics To obtain atomic resolution in ac-mode AFM, the change in resonance properties of the cantilever must be significantly affected by the short range force acting between the tip apex atom and the individual surface atoms when the tip moves in and out of the interaction region. In order to clarify the interaction mechanism, we have made numerical simulations of cantilever resonance spectra using a model for the tip-surface interaction including a long range van der Waals force, an interatomic force described by a Morse function, and where surface elasticity is treated as a linear spring. The equation describing the cantilever motion is solved for this force field in order to obtain resonance spectra for different interaction conditions. The figure shows the geometry used for modelling the tip-surface interaction and typical force curves.
Positive force corresponds to repulsion.
The top figure shows experimental cantilever resonance curves for different tip to surface separations obtained from a silicon sample. The frequency scales differ as the Q value used in the simulation was lower than for the real cantilever. The simulated resonance spectra show that the general features of the experimental data are well reproduced. The simulations also indicate that binding energy variations on the order of 1 eV in the interatomic interaction should be possible to detect which is also consistent with the experimental data. Smaller tip radius and smaller tip to surface separation enhances the sensitivity to binding energy variations while the influence of surface elasticity is remarkably small.