  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 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 elastic
modulus of sample (relative to the substrate surface) and probe stiffness on
the scan results. Our numerical simulations show that scanning in attractive
regime using soft cantilevers with high Qeff results in a better image quality.
We, then demonstrate the trade-off in setting the effective Q factor (Qeff) of
the probe in Q control: low values of Qeff 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.
