= Solution
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 \b[<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.
\b[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.<(CdSe)ZnS Core-Shell Quantum Dots: Synthesis and Characterization of a Size Series of Highly Luminescent Nanocrystallites by B. O. Dabbousi and others>[1997, abstract: spectroscopy, structural/compositional characterization and locally epitaxial shell growth]{ref}
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