Quantum Dot Ensemble Auger Decay (2D)

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

Ensemble State

324 dots idle

Elapsed time

0.00 ns

Ensemble mean N̄

—

Photons emitted

Auger events

radiative event Auger event empirical N̄(t)/N₀ analytic (master eqn)

How it works

Instead of watching one quantum dot in 3D, this view runs an ensemble of 324 independent nanocrystals side by side on a 2D lattice — each cell is its own quantum dot, decaying on its own stochastic clock, exactly as single-dot photoluminescence experiments actually work. The per-dot physics is identical to the single-dot picture:

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)
γ_A(R) = γ_A(3nm) · (3nm / R)³   (inverse-volume scaling)

Each cell's brightness encodes its current exciton count N (dark = idle/N=0, bright orange = N=5). A gold flash marks a radiative (photon) event, a grey flash an Auger (non-radiative) event. The bar histogram below the grid shows, live, how many of the 324 dots currently hold each N.

The bottom trace plots the ensemble-averaged population N̄(t)/N₀ (orange, empirical — this is exactly the multi-exponential PL decay curve measured from real ensembles of dots) against the exact analytic solution of the master equation dP_n/dt = −Γ(n)P_n + Γ(n+1)P_n+1 for this finite-state death chain, integrated live with RK4 (white dashed). The two should track closely — any persistent gap flags a coding bug, not sampling noise, since 324 independent dots already average out most of the stochastic jitter.

Excite ensemble — pulses all 324 dots to N₀ at once and restarts every clock.
Because Γ(N) grows combinatorially, high-N cells collapse almost instantly while the last surviving exciton in each dot lingers, decaying slowly and purely radiatively — visible here as the grid quickly darkening from bright orange down to a scatter of faint single-exciton survivors.

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