Inside a quantum-dot LED, electrons injected from the ZnO electron-transport layer and holes injected from the hole-transport layer meet inside the quantum-dot emissive layer. Each recombination event follows one of three competing channels, described by the standard ABC rate equation used throughout LED, laser-diode and QLED droop literature:
dn/dt = G − A·n − B·n² − C·n³ = 0 (steady state)
J = q·d·(A·n + B·n² + C·n³)
IQE = B·n²
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A·n + B·n² + C·n³
- A·n — Shockley–Read–Hall trap-assisted capture at a defect/surface state (non-radiative, one carrier).
- B·n² — the wanted radiative bimolecular recombination: an electron and hole form an exciton in a dot and emit one photon.
- C·n³ — three-carrier Auger recombination: a third carrier absorbs the exciton's energy as kinetic energy (heat) instead of light. Because it scales as n³, it is negligible at low carrier density but dominates at high drive current — this is the microscopic origin of efficiency droop, the same rise-then-fall EQE curve reported for InGaN LEDs, QD lasers and high-brightness QLEDs.
The simulator solves the cubic for the steady-state carrier density n at your chosen current density J (via bisection), then derives IQE and the radiative rate directly from n. QD core diameter sets the emission photon energy through quantum confinement (smaller dot → wider bandgap → bluer light) — a separate, purely electronic-structure effect from the ABC competition. Particle counts and event rates on screen are a visual proxy for the real carrier populations (~10¹⁶–10¹⁹ cm⁻³ in an actual device), scaled for legibility; the governing equations and the resulting IQE curve are the real physics. Continuous-wave QLEDs are typically driven well below this Auger-limited regime, where interfacial trapping dominates droop instead — the intrinsic B/C competition modeled here becomes dominant at the high pulsed current densities used in QD-laser and ultra-high-brightness QLED studies (see Bae et al., Nat. Commun. 2013; Shirasaki et al., Nat. Photon. 2013).