Plot external quantum efficiency against current density for a blue InGaN emitter and the curve peaks early, often below 10 A/cm2, then falls as current climbs. The behavior is called efficiency droop, and it is the reason a single large die driven at 2A does not deliver twice the photon flux of the same die at 1A. The ABC model is the standard way to describe the curve with one equation and three coefficients.
Three Recombination Paths
Electrons and holes in the quantum well recombine through three competing channels, and the ABC model assigns one term to each:
| Path | Term | Rate scales with | Effect |
|---|---|---|---|
| SRH (defect) | A | n | Linear loss, fixed by crystal quality |
| Radiative | B | n squared | The useful path, emits the photon |
| Auger | C | n cubed | Heat instead of light, grows fast at high n |
The internal quantum efficiency then follows EQE proportional to B n^2 divided by A n + B n^2 + C n^3. At low carrier density the defect term dominates and efficiency climbs with current. At moderate density the radiative term wins and the curve plateaus. At high density the cubic Auger term takes over, and efficiency falls because every additional carrier is more likely to produce phonons than photons.
Why the Cubic Term Hurts
Auger recombination is a three-particle event: an electron and a hole recombine and hand the energy to a third carrier. Because its rate scales with the cube of carrier density, doubling the current density roughly doubles the useful rate but multiplies the loss rate by eight. That asymmetry is the shape of the droop curve. The coefficient C is set by the material band structure, not by assembly quality, so a clean wafer droops less but does not stop drooping.
Temperature makes it worse. The SRH coefficient A rises with temperature as carriers find more defects to hop through, so a hot junction sits lower on the same curve. A package that holds the junction cool keeps the emitter on the plateau longer.
What It Means for Drive Current
Droop sets an economic ceiling on how hard a die should be driven. Above the knee, each additional amp buys fewer photons than the amp before it, so the lumen or micromole per watt curve bends down while the junction temperature climbs. Designers respond in three ways:
- Spread the current across more die or more packages instead of driving one die harder.
- Size the thermal path so the junction sits below the range where A grows fast.
- For horticulture fixtures, compare PPE at the real drive current, not the datasheet peak, because the peak is measured at a low current the fixture will never use.
Chip makers attack droop inside the epitaxy: thicker wells, tuned barriers and reduced polarization fields all lower carrier density in the well for the same current. Those changes move the knee to the right but cannot remove the cubic term.
Key Takeaways
- EQE falls at high current because the Auger term scales with the cube of carrier density.
- The ABC model reads EQE as B n^2 over A n + B n^2 + C n^3; each term is one recombination path.
- Heat raises the SRH term, so thermal design holds the curve near its plateau.
- Fixture efficiency must be read at the real drive current, not at the datasheet test point.
Related reading
- how IEC 62471 classifies LED sources for photobiological safety
- more optics and device physics notes in LED Academy
