Quantum Dot Calculator

The calculator explicitly floors the effective bandgap at the bulk value using Math.max(bulkBandgapEv, totalBandgapEv), because real quantum confinement only ever raises the bandgap relative to bulk — the confining energy term is always positive, and while the Coulomb term subtracts from it, physically the net effect for a genuinely confined dot should never push the gap below bulk. If your inputs produce a total below the bulk value, the floor kicks in and the confinement term effectively has no impact on the displayed result.

Shrinking the radius increases the confinement energy term h²/(8m*R²), since it scales with 1/R² — smaller dots confine the electron and hole to a tighter space, raising their kinetic energy and widening the effective bandgap. A wider bandgap means higher-energy, shorter-wavelength photons via E = hc/λ, which is why smaller CdSe dots emit blue-shifted light relative to larger dots of the same material.

It scales the Coulomb correction term, 1.8e/(4πε₀·dielectricConstant·R), which represents the attractive interaction between the confined electron and hole that slightly lowers the effective bandgap. A higher dielectric constant screens that attraction more strongly, shrinking the Coulomb correction and pushing the effective bandgap (and thus the predicted emission wavelength) closer to what confinement energy alone would give.

This uses a simplified single-band effective-mass model (a basic form of the Brus equation) that works reasonably well for weak-to-intermediate confinement in materials like CdSe, but it omits valence-band mixing, dielectric-mismatch (image charge) effects at the dot-solvent interface, and surface-state trapping — all of which shift real emission wavelengths, especially for materials with more complex band structure. Use the defaults for CdSe as a sanity check, and treat results for other materials as a first-order design estimate rather than a lab-grade prediction.