Numerical simulation of nano scanning in intermittent-contact mode AFM under Q control.

We investigate nano scanning in tapping mode atomic force microscopy (AFM) under quality (Q) control via numerical simulations performed in SIMULINK. We focus on the simulation of the whole scan process rather than the simulation of cantilever dynamics and the force interactions between the probe tip and the surface alone, as in most of the earlier numerical studies. This enables us to quantify the scan performance under Q control for different scan settings. Using the numerical simulations, we first investigate the effect of the elastic modulus of the sample (relative to the substrate surface) and probe stiffness on the scan results. Our numerical simulations show that scanning in an attractive regime using soft cantilevers with high effective Q factor (Q(eff)) results in a better image quality. We then demonstrate the trade-off in setting Q(eff) of the probe in Q control: low values of Q(eff) cause an increase in tapping forces while higher ones limit the maximum achievable scan speed due to the slow response of the cantilever to the rapid changes in surface profile. Finally, we show that it is possible to achieve higher scan speeds without causing an increase in the tapping forces using adaptive Q control (AQC), in which the Q factor of the probe is changed instantaneously depending on the magnitude of the error signal in oscillation amplitude. The scan performance of AQC is quantitatively compared to that of standard Q control using iso-error curves obtained from numerical simulations first and then the results are validated through scan experiments performed using a physical set-up.