Numerical simulation of nano scanning in intermittent-contact mode AFM underQ control

Abstract

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 ofthe whole scan process rather than the simulation of cantilever dynamics and theforce interactions between the probe tip and the surface alone, as in most of theearlier numerical studies. This enables us to quantify the scan performance underQ control for different scan settings. Using the numerical simulations, we first investigate theeffect of the elastic modulus of the sample (relative to the substrate surface)and probe stiffness on the scan results. Our numerical simulations show thatscanning in an attractive regime using soft cantilevers with high effectiveQ factor (Qeff) results in a better image quality. We then demonstrate the trade-off in settingQeff of the probein Q control:low values of Qeff cause an increase in tapping forces while higher ones limit the maximumachievable scan speed due to the slow response of the cantilever to the rapidchanges in surface profile. Finally, we show that it is possible to achieve higherscan speeds without causing an increase in the tapping forces using adaptiveQ control (AQC),in which the Q factor of the probe is changed instantaneously depending on the magnitude of the error signal inoscillation amplitude. The scan performance of AQC is quantitatively compared to that of standardQ control using iso-error curves obtained from numerical simulations first and then theresults are validated through scan experiments performed using a physical set-up.