Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2020 / Paper 1 / Section B / 8 / i

One image takes $512\mathrm{s}$ if $1\mathrm{Hz}$ means one completed scan line per second. The slow-axis speed is $10/512=0.01953\mu \mathrm{m}{\mathrm{s}}^{-1}$. Recording a wire spanning $1\mu \mathrm{m}$ along that axis therefore takes $51.2\mathrm{s}$. Meanwhile the fast-axis drift is $20/3600=0.005556\mu \mathrm{m}{\mathrm{s}}^{-1}$, giving a transverse displacement of $0.2844\mu \mathrm{m}$. The apparent straight-line length isIts slow-axis projection remains $1\mu \mathrm{m}$; the overestimate refers to length along the slanted trace.

With the wire along the fast axis and drift along the slow axis, its length is acquired within one line, so $L_{\mathrm{app}}\simeq 1.000\mu \mathrm{m}$. Taking a forward sweep of $1\mathrm{s}$ across $10\mu \mathrm{m}$, the wire is crossed in $0.1\mathrm{s}$ and the perpendicular displacement is only $0.556\mathrm{nm}$. The corresponding length change is about $1.5\times 10^{-7}\mu \mathrm{m}$, far below the $19.5\mathrm{nm}$ pixel pitch. For the convention in which one hertz includes a forward and reverse sweep, that already negligible displacement halves. The slow-axis calculation still uses one completed line per second.

Place the wire parallel to the fast scan axis. The endpoints are then recorded in a fraction of a line period, rather than tens of seconds apart, minimizing the differential drift accumulated between them.

This does not remove drift of the wire's transverse position or apparent width between successive lines. A very thin wire parallel to the fast axis may fall between the discrete slow-axis scan lines, so a smaller scan area or denser sampling can be needed. Tip convolution, pixel resolution and feedback lag remain; trace/retrace comparisons and allowing thermal equilibration are still valuable. Increasing the scan speed indefinitely is limited by the scanner and feedback bandwidth.