Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2022 / Paper 4 / 65 / c

One Pt(111) layer has height $d_{111}=a_0/\sqrt{3}=2.269\mathring{\mathrm{A}}$. In constant-height operation the separation above the island is therefore only $5.000-2.269=2.731\mathring{\mathrm{A}}$. With the same decay constant,Thus the ideal predicted current is about $232\mathrm{nA}$. This very large increase can exceed the useful current range or risk tip-surface contact; constant-height imaging is poorly suited to unexpected monolayer steps. Constant-current feedback can follow the height more safely, subject to its response bandwidth.

Potassium is electropositive and transfers electron density toward the metal. The resulting surface dipole generally lowers the metal work function at such submonolayer coverages, reducing the tunnelling barrier and its inverse decay length $q\propto \sqrt{{\Phi }_{\mathrm{effective}}}$.

At the same specified $5\mathring{\mathrm{A}}$ separation, a smaller $q$ gives a larger $\exp (-2qs)$, so the expected tunnelling current is greater than $1\mathrm{nA}$ in the barrier-dominated comparison. No numerical value follows without the modified work function and electronic density of states. A real STM image also depends on the local density of states and adsorbate corrugation; equal geometric separation does not imply equal electronic barrier height.