Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2020 / Paper 1 / Section A(i) / 1 / ii

The controlled quantity is the maximum repulsive force in each tapping cycle. In PeakForce quantitative nanomechanical mapping, a vertical modulation below the cantilever resonance produces a force-distance cycle at each pixel. The optical lever measures deflection; the calibrated cantilever stiffness converts this to force. Subtract the measured peak force from the setpoint and use proportional-integral control to adjust the mean vertical scanner position. Excessive peak force makes the controller withdraw the sample or tip; insufficient force makes it approach. The scanner position required to maintain the setpoint supplies the topography signal. This controls the top of the repulsive branch in the preceding curve, rather than the oscillation amplitude used in conventional tapping mode.^[ref]

Two useful properties are adhesion and contact elastic modulus. The pull-off force, the most negative force on retraction relative to the noncontact baseline, maps adhesion. Fit the contact part of the force-indentation relation using a suitable contact mechanics model to obtain a reduced elastic modulus; for example, the DMT contact model useswhere $F_{\mathrm{adh}}<0$, $R$ is the calibrated tip radius and $\delta$ is indentation. Converting $E^{\ast }$ to a sample Young's modulus also requires the tip modulus and the two Poisson's ratios. The approach curve alone does not supply a retraction pull-off measurement. The loop area can additionally map dissipated energy; it is not automatically a purely viscous loss.^[ref]