C-X1c · Where injected carriers go

Blue LED: Recombination and Efficiency

Why can a blue LED become brighter while its efficiency falls? More current can produce more photons in total while each injected carrier has a smaller chance to emit one. In this model, high carrier density strengthens the cubic loss channel faster than radiative recombination, so external efficiency falls even as light output rises.

Inject electrons and holes into a blue-emitting well. Watch radiative recombination compete with defect and high-density losses, then record the external efficiency curve.

Internal efficiency $0$

External efficiency $0$

Power per area

\mathrm W\,\mathrm{cm}^{-2}

$0$

Density in

10^{18}\,\mathrm{cm}^{-3}

$0$

A uniform steady-state ABC model assumes equal electron and hole densities in a three-nanometre active well. Synthetic coefficients define defect, radiative and cubic recombination. The well emits at a fixed wavelength of four hundred and fifty nanometres. Extraction is a prescribed fraction of generated photons. The cubic loss illustrates one possible high-density channel; this model does not establish the cause of droop in an actual LED. Injection leakage, heating, polarization fields, localization, wavelength shifts, optical interference and spatial transport are omitted. The cross-section and particle motion are schematic.

Synthetic model acquisition

Efficiency across injection levels

The stored sweep retains the settings used to generate it.

J/(\mathrm A\,\mathrm{cm}^{-2}),\quad\eta_{\rm EQE}/\%

The current-density axis is logarithmic. The dot marks the operating point stored with this sweep.

Where carrier pairs recombine

Teal: radiative. Amber: defect. Pink: cubic loss. These fractions sum to unity before optical extraction.

Start with the essentials

Focus question: Why can a blue LED become brighter while its efficiency falls?
One-sentence intuition: Brightness counts emitted photons; efficiency counts emitted photons per injected carrier.

Core mathematical model

Steady carrier balance

\frac{J}{qd}=An+Bn^2+Cn^3

The three channels together consume every injected carrier pair in the uniform steady-state model.

External quantum efficiency

\eta_{\rm EQE}=\eta_{\rm ext}\frac{Bn^2}{An+Bn^2+Cn^3}

Only radiative recombination makes photons, and only the extracted fraction escapes.

Common difficulties

A common inference to test

Typical misconceptionThe brightest operating point must also have the best quantum efficiency.

Better mental modelA larger injection can compensate for a smaller radiative fraction. Compare photons per injected carrier as well as total optical power.

Run the experiment

01
Find the bright well
Choose Bright well and change Injection current density.
What to observe: Electrons and holes arrive at the well and blue photons escape.
02
Increase the defect loss
Choose Defect losses and compare the recombination fractions.
What to observe: More injected pairs disappear through the defect channel, reducing useful light.
03
Follow the droop
Choose Efficiency droop, record a sweep, then compare photon output with efficiency.
What to observe: At high injection the cubic channel grows faster than radiative recombination. Light output can rise while efficiency falls.