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A nanocrystal with one semiconducting composition surrounded by another. band offsets, interface quality and shell thickness govern carrier confinement and coupling to external traps. type-I band alignment favors electron and hole localization together; type-II band alignment can separate them. A larger shell band gap does not by itself determine those offsets.

A double heterostructure laser electrically pumps its central layer for stimulated emission. Band offsets confine charge carriers; refractive index contrast confines the optical normal mode.^[ref]

For an original bookkeeping model, let $R$ be the injected pair rate per unit area, $d$ the active-layer thickness, $N$ its excess pair number density, $\tau$ a recombination lifetime, and ${\tau }_e$ an escape time. Before appreciable stimulated emission, supposeChoose two otherwise identical devices with ${\tau }_e=\tau$ and ${\tau }_e=9\tau$. The resulting steady state populations are $R\tau /(2d)$ and $9R\tau /(10d)$: improved confinement raises the population by a factor $1.8$ at fixed injection. This linear model assumes equal excess electron and electron hole densities, fixed lifetimes, and no laser gain clamping.

Optical confinement enters separately. For a chosen optical normal mode, define $0<\Gamma \le 1$ as its gain-overlap factor with the active layer. With material optical gain $g$, internal loss ${\alpha }_i$, and mirror loss ${\alpha }_m$, a simple laser threshold condition isFor stipulated losses ${\alpha }_i+{\alpha }_m=3$ in inverse-length units, $\Gamma =1/2$ requires $g=6$, whereas $\Gamma =3/4$ requires $g=4$. This calculation varies optical overlap only; the preceding population calculation varies carrier escape only. Their combination explains the usefulness of controlling both the energy band profile and the optical normal mode.

Herbert Kroemer proposed the double heterostructure laser in 1963; he did not participate in its 1970 experimental realization.^[ref] Zhores I. Alferov describes his group's independent 1963 proposal and later experimental program.^[ref]

A double heterostructure laser places a lower-band gap active layer between wider-band gap layers with suitable type-I band alignment. The band offsets confine injected electrons and electron holes in the same small volume, increasing their overlap and reducing escape. Usually the active layer also has larger refractive index, so the same sandwich forms an optical waveguide. Optical confinement increases the gain-overlap factor $\Gamma$, while carrier confinement lowers the injection needed to reach the required quasi-Fermi-level splitting. These two distinct mechanisms reduce threshold current and heating. A band gap difference alone does not establish the sign of both confinement barriers; suitable band offsets are essential.

A double heterostructure laser sandwiches a narrow-band gap active layer between wider-band gap cladding layers. In a type-I band alignment, the conduction band edge is lower and the valence band edge higher in the active layer. Electrons therefore see an energy well, and electron holes also see a well because their excitation energy increases when the valence band edge decreases. Both carrier populations remain concentrated where stimulated emission occurs.

The active layer also normally has the higher refractive index, forming an optical waveguide. The optical normal mode overlaps the injected carriers strongly, and the wider-band gap cladding has less interband absorption at the emitted photon energy. Carrier confinement reduces leakage, while optical confinement reduces the required pump current and hence heating.

Writing $\Gamma$ for the fraction of the optical normal mode overlapping the active layer, the threshold condition is $\Gamma g={\alpha }_i+{\alpha }_m$, with internal and mirror losses ${\alpha }_i,{\alpha }_m$. A larger overlap and a higher carrier number density at a given current both lower the threshold current. The figure shows composition-induced offsets; a working junction also has band bending under bias, which is omitted to make the confinement mechanism visible.

Across a radial section, the narrow-gap indium gallium nitride layer lies between wider-gap n-GaN and p-GaN. A suitable type-I band alignment has a downward conduction-band offset and upward valence-band offset in the indium gallium nitride, confining electrons and holes to the active layer. The original band sketch isolates those offsets; the complete junction also has doping-induced band bending.

At thermal equilibrium the Fermi level is common throughout. Forward bias separates the electron and hole quasi-Fermi levels, injects carriers from the n- and p-regions and permits electron-hole recombination in the thin active layer. A full radial line through the wire crosses two copies of the shell well; a core-to-exterior radial coordinate crosses one.

The 5 nm indium gallium nitride shell is the quantum well active region, not a metallic contact. Finite band offsets, confinement and polarization fields affect its transition energy; the bulk gap alone is insufficient.

A plausible role for the SiN mask is selective-area growth: restrict nucleation to exposed windows and suppress parasitic deposition between wires. Retained insulating material can also help prevent unwanted electrical paths during later processing. Which role dominates depends on the actual fabrication sequence. The cited source concerns core-shell single-wire LEDs and contact engineering, so a qualitative band sketch does not reproduce its complete device model.^[ref]

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]

A type-I band alignment confines electrons and electron holes together: its inner conduction band edge is lower, its valence band edge higher.^[ref]

In the chosen band offset example, the electron barrier is $0.6$, while the electron hole barrier is $0.4$. A hole's excitation energy is measured downward from a valence band maximum: reversing that convention would incorrectly make the two barriers appear to repel opposite carriers. An electrostatic shift $-q\varphi$ moves both electron energy band edges together; changing the band gap also changes their separation. Thus material composition supplies a control beyond the electric potential $\varphi$ alone.

A staggered alignment in which the lowest electron states and most favorable hole states occur in different materials. Unlike type-I band alignment, it can reduce electron–hole spatial overlap. Comparing the two band gaps alone does not determine whether this alignment occurs.