A semiconductor nanocrystal's bandgap is not fixed by its chemistry alone — quantum confinement adds an extra energy term that scales as 1/R², where R is the physical radius. Shrink the crystal and the electron and hole wavefunctions are squeezed into a smaller box, raising their kinetic energy and widening the gap they must cross to recombine and emit a photon. The colour is therefore an engineering dial, not a fixed material property.
E_gap(R) = E_bulk + (ℏ²π²) / (2·μ·R²)
λ_emit = 1240 / E_gap(eV) [nm]
- Green / red mean size — the target radius each population is grown to; QLED TVs use two size-sorted CdSe/InP populations so a single blue LED backlight is down-converted into pure green and red, with the unabsorbed blue serving as the third primary.
- Polydispersity σ — real batches never have perfectly identical dots. A wider size distribution means a wider spread of individual λ values, so the ensemble's summed spectrum broadens and its peak intensity drops — exactly the mechanism a manufacturer fights with careful size-selective precipitation.
- FWHM — full width at half maximum of each emission peak; QDs achieve ~20-30 nm versus ~60-100 nm for phosphors, which is what lets QLED reach a wider, more saturated colour gamut.
- Gamut triangle — narrower peaks sit closer to the spectral locus (maximum possible saturation for that hue), pushing the RGB triangle's corners outward and enlarging the reproducible colour area versus a conventional broad-spectrum phosphor backlight.
This 2D companion draws the identical Brus-equation ensemble as a flat dot array — a schematic cross-section of a QLED down-conversion film — instead of an orbiting 3D scene, so the emission-color-vs-size relationship is what you look at directly.