Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2022 / Paper 2 / Section B / 20 / iii / Solution

For the common $[111]$-axis zinc-blende GaAs wire, a representative cross-section is a faceted hexagon with low-index sidewalls, often described by $\{110\}$-type facets. The threefold crystallographic symmetry of a polar $[111]$ direction can make alternate facets inequivalent, so triangular or truncated-triangular sections are also possible. The zinc-blende label alone does not fix a unique hexagon: growth direction, termination, twins, surface chemistry and kinetic facet selection also matter.

The accompanying sketch shows a representative faceted section rather than a circular cylinder. Facets that advance slowly in their normal direction tend to remain exposed, so a kinetic growth shape need not be an equilibrium Wulff shape.

A simple cause of tapering is continued radial vapor–solid growth on sidewalls while the tip grows axially. A lower wire segment has been exposed to precursors for longer than a segment formed near the end of growth. For a roughly constant radial growth speed $v_r$, its radius gains about $v_r[t_{\mathrm{end}}-t_{\mathrm{formation}}(z)]$, giving a larger base. Substrate-fed species, changing catalyst size and droplet wetting can also contribute. Tapering is not proof that the original VLS droplet was wider at every earlier stage.