This is the 2D counterpart of the QLED droop simulator: the identical ABC rate equation as the 3D device model, but instead of animating individual carrier particles drifting through a 3D stack, it solves the equation directly in time and plots the real result.
dn/dt = G − A·n − B·n² − C·n³, G = J/(q·d)
n(t→∞) = n_ss solves G = A·n_ss + B·n_ss² + C·n_ss³
IQE(n) = B·n² / (A·n + B·n² + C·n³)
The top panel is a literal time-domain integration (4th-order Runge–Kutta) of that ODE, rescaled into dimensionless units u = n/n_ss and s = t/τ where τ = n_ss/G is the device's own fill-time constant — so the curve you see climbing to 1 is the actual transient solution, not an animation trick, and it reaches the same n_ss the steady-state bisection solver finds. The stacked bars below it show how the three loss channels split the recombination current at the instantaneous n(t): trap capture (A·n, linear), radiative recombination (B·n², quadratic) and Auger loss (C·n³, cubic) — because Auger scales fastest, it eats a growing share of the split as current density climbs, which is the microscopic origin of droop.
The bottom panel sweeps J on a log axis and re-solves for IQE at every point, tracing the same rise-then-fall efficiency droop curve the 3D version's readouts imply but never actually plots — here you can see the whole curve and where your chosen operating point sits on it at a glance.
- J — drive current density; moves the marker along the droop curve and rescales the fill-time τ.
- Auger coefficient C — governs how sharply the droop curve turns over at high J.
- Trap coefficient A — sets the low-current IQE ceiling; larger A wastes more carriers to non-radiative traps even before Auger matters.
- QD core diameter — sets emission color via quantum confinement (smaller dot → bluer light), independent of the ABC competition.
See Bae et al., Nat. Commun. 2013 and Shirasaki et al., Nat. Photon. 2013 for the real device measurements this rate equation reproduces.