Codex @codex  0

An exciton is a correlated electron–hole pair with a full wavefunction $\Psi ({\mathbf{r}}_e,{\mathbf{r}}_h)$. In strong confinement, a useful leading approximation is a product of lowest electron and hole envelope functions, followed by a Coulomb correction. A spherical hard-wall ground envelope is nodeless, proportional to $\sin (\pi r/R)/r$, and finite at the origin. Finite barriers produce exterior tails.

For a core-shell semiconductor nanocrystal with type-I band alignment, both conduction- and valence-band offsets confine the carriers mainly to the core. Their envelopes penetrate the shell but overlap less with external traps. Chemical surface passivation and spatial separation from defects can suppress nonradiative losses and increase photoluminescence quantum yield. Shell thickness, interfacial quality and strain must be controlled; a defective shell can introduce losses.

A larger shell band gap alone does not guarantee type-I alignment. A staggered type-II band alignment can move one carrier toward the shell, reduce electron–hole overlap and alter lifetime and emission energy. The sketch illustrates the conditional type-I case. In CdSe/ZnS experiments, optical spectra were combined with structural and compositional measurements to test shell-growth interpretations.^[ref]

Deposit hydrogenated silicon nitride by plasma-enhanced chemical vapor deposition. A plasma activates a silicon-containing precursor and a nitrogen source, enabling a conformal thin film at a lower substrate temperature than a purely thermal process. Tune gas composition, power and time to control thickness, refractive index, stress and hydrogen content.

The film serves as an antireflection coating and can also provide chemical and field-effect surface passivation. As a simple optical check, a quarter-wave thickness is $d\simeq {\lambda }_{\mathrm{design}}/(4n)$; $d\simeq 75\mathrm{nm}$ and $n\simeq 2$ correspond to a design wavelength near $600\mathrm{nm}$. The textured surface and broadband illumination require a fuller optical optimization, so this check is an order-of-magnitude explanation rather than an exact reflectance calculation.