Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2019 / Paper 2 / Section A(i)

A faceted, approximately equiaxed crystal is indicated. A truncated octahedron bounded by low-energy $\{111\}$ and $\{100\}$ facets is a plausible three-dimensional shape for an fcc metal particle; the hexagonal section alone does not uniquely distinguish it from other faceted polyhedra.

The Wulff construction minimizes ${\sum }_i{\gamma }_i{A}_i$ at fixed particle volume. Place a plane with normal ${\hat{\mathbf{n}}}_i$ a distance $h_i=C{\gamma }_i$ from a common centre and take the inner envelope. Low-surface-energy orientations survive as large facets. Annealing permits diffusion toward this equilibrium morphology, provided the time is sufficient. For a supported or strained alloy, substrate adhesion and elastic energy modify this simple free-particle construction.

For the upper core-shell precursor, first reduce a precursor of metal A to make seeds; then introduce and reduce a precursor of B under conditions favouring heterogeneous deposition on those seeds rather than independent nucleation. Control added quantity, reduction rate and surface ligands to build a shell.

For the lower disordered-alloy precursor, reduce both metal precursors together so both metals enter the growing particles. Match their effective reduction rates by precursor chemistry, temperature, complexation or controlled feeding; otherwise sequential reduction can produce segregation instead of co-incorporation. Quenching or sufficiently mild growth can retain a disordered alloy before the later anneal. These routes need not initially produce equilibrium atomic arrangements.^[ref]

Both starting arrangements converge toward the same chemically ordered alloy, exhibiting chemical ordering in alloys. This supports a lower free energy for the ordered unlike-metal neighbour pattern than for the segregated core-shell or disordered precursor at the final temperature. In a simple nearest-neighbour model, ordering is favoured whenwith consistent bond-energy conventions. Bulk mixing and ordering then compensate the loss of configurational entropy on cooling. Annealing alone does not supply numerical bond or surface energies, and elastic mismatch or adsorbed ligands can also matter.

The final morphology does not show a thick single-metal skin: the surface-energy difference is not large enough to overwhelm the bulk preference for ordering throughout the particle. Some atomic-scale surface enrichment is compatible with the drawing, so exact equality of the two surface free energies is not established.

If B has a much lower surface free energy, Surface segregation of B and an A-rich interior become favourable. A nearly continuous B shell is likely if enough B is present and the surface-energy gain exceeds the cost of disrupting favourable A-B bonds; otherwise only partial enrichment occurs.

In selective-area epitaxy, precursors supplied by metal-organic vapour-phase epitaxy incorporate on exposed crystalline InP through patterned openings in a silicon-nitride mask. Epitaxial facet-dependent incorporation and surface diffusion select axial and radial growth rates. Advantages include lithographic position and pitch control, an epitaxial orientation relationship and the absence of a foreign metal catalyst. Limitations include mask patterning, selective nucleation requirements, facet-dependent composition, loading and pitch effects, and unwanted radial growth.

In vapour-liquid-solid growth, precursors decompose and supply material to a liquid catalyst droplet; supersaturation drives precipitation at the liquid-solid interface. Droplet size can control wire diameter and enable high aspect ratios. Limitations include possible catalyst contamination, droplet stability and coarsening, composition memory at heterointerfaces, and restrictions from the catalyst phase diagram. Patterned catalyst placement can also control position, so positional ordering is not exclusive to selective-area growth. Conversely, selective-area wires are not automatically free of taper or compositional interfaces.^[ref]

The emission energies are approximatelyDraw the Al-rich interface as a wider-gap barrier between these two emitting regions: a raised conduction-band edge impedes electron transfer, and a lowered valence-band edge impedes hole transfer. The following is a consistent straddling-barrier schematic, with the shell having the smaller optical gap.

The two emission wavelengths determine optical transition energies, not unique conduction- and valence-band offsets. Exciton binding, confinement and strain can shift emission relative to the bulk band gap. The stated barrier supports inhibited charge exchange; its separate electron and hole barrier heights need additional band-alignment data.

Place the Ag particles near the emitting shell, along the outer sidewalls or accessible shell at the base. Its $690\mathrm{nm}$ emission is close to the $680\mathrm{nm}$ localized surface plasmon resonance; the $615\mathrm{nm}$ core emission is more detuned and farther from an externally placed particle. The plasmon near field decays with distance, so the local emitter-field overlap matters as well as spectral overlap. A thin spacer can reduce direct-contact nonradiative quenching.

These facts identify a favourable placement for enhanced interaction; they do not by themselves prove the spectroscopic strong-coupling regime, which additionally requires coherent coupling to exceed the relevant losses and normally produces resolvable mode splitting.