Multiexciton Auger Recombination Cascade

Quantum Dot Parameters

Dot radius R 3.0 nm

Auger coefficient γ_A(3nm) 0.50 ns⁻¹

Radiative rate k_r 0.10 ns⁻¹

Simulation speed 5.0 ns/s

Initial Excitation

Excitons injected N₀ 4

Multiexciton State

N = 4 excitons

Elapsed time

0.00 ns

Decay rate Γ(N)

— ns⁻¹

Photons emitted

Auger events

N(t) exciton population

How it works

A short pulse injects N electron-hole pairs (excitons) into one nanocrystal quantum dot. Each exciton can decay by two competing channels. Radiative recombination emits a photon at rate k_r per exciton. Auger recombination is non-radiative: the recombination energy of one pair is transferred to a third carrier (electron or hole), which is kicked to a high-energy state and thermalizes as heat — no photon is emitted.

Radiative rate:  Γ_r(N) = N·k_r
Auger rate:      Γ_A(N) = γ_A          for N = 2
                 Γ_A(N) = γ_A·N(N-1)(N-2)/2   for N ≥ 3
Total decay:     Γ(N) = Γ_r(N) + Γ_A(N)
Event prob./dt:  P = 1 − exp(−Γ(N)·dt)

The N(N-1)(N-2)/2 combinatorial factor counts the ways to pick the recombining pair and the third carrier among N excitons — this is why multiexciton Auger decay accelerates so sharply with N, dominating the earliest, fastest part of the photoluminescence (PL) decay while the surviving single exciton (N=1) decays slowly and purely radiatively.

Auger recombination also obeys a well-established inverse-volume scaling law: confining carriers to a smaller dot increases wavefunction overlap, so γ_A ∝ 1/V ∝ 1/R³. The radius slider rescales γ_A from its 3 nm reference value using exactly this law:

γ_A(R) = γ_A(3nm) · (3nm / R)³

Excite dot — injects N₀ excitons at t = 0 and restarts the stochastic decay cascade.
Each carrier pair removed is marked ● radiative (photon emitted, flash + ring) or ● Auger (hot-carrier flash, no photon).
This stochastic, one-quantum-dot-at-a-time picture is exactly what single-dot PL blinking and time-resolved multiexciton spectroscopy measure — ensembles of dots average this into the classic bi/tri-exponential PL decay curves used to extract Auger lifetimes.

Electron Hole Photon (radiative) Hot carrier (Auger)

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