Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2017 / Paper 1 / Section A(i) / 2 / ii / Solution

An uncorrected amplitude image has a useful vertical range only across the transition between free oscillation and strongly suppressed oscillation. If the free motion is a few tens of nanometres peak-to-peak, its one-sided amplitude is half that excursion. The relevant vertical height range is therefore of the order of the oscillation excursion, only tens of nanometres, rather than micrometres. It is not a sharp universal limit equal to the quoted peak-to-peak value: the chosen mean gap, contact law and usable sensitivity determine the actual range. A sufficiently high feature can quench the motion or produce destructive contact; a sufficiently deep depression leaves the probe oscillating freely with essentially no height sensitivity. This argument limits height tracking, not the lateral width of a feature. Lateral resolution instead depends on AFM tip convolution, sampling and the probe-surface interaction.