Glossary entry

Quantum efficiency

The probability that an absorbed or generated photon successfully produces a measurable carrier (or vice versa). The fundamental efficiency parameter for any photonic device.

Quantum efficiency is the ratio of useful quanta out to total quanta in, expressed as a fraction or percentage. The exact definition depends on context:

For photodetectors: the fraction of incident photons that produce a collected electron–hole pair contributing to the photocurrent:

\eta_\text{PD} \;=\; \frac{\text{electrons collected}}{\text{photons incident}} \;=\; \frac{I_\text{ph} / e}{P_\text{opt} / h\nu} \;=\; \frac{\mathcal{R} \cdot h c}{e \, \lambda},

where $\mathcal{R}$ is the responsivity. Unity quantum efficiency gives the maximum responsivity $\mathcal{R}_\text{max} = e\lambda / hc \approx \lambda \, [\mu\text{m}] / 1.24$ A/W.

For light-emitting diodes and lasers (electrical-to-photon):

Internal quantum efficiency $\eta_i$ — fraction of injected carriers (above threshold) producing photons inside the cavity
External quantum efficiency $\eta_\text{EQE}$ — fraction of injected carriers producing photons that exit the device:

\eta_\text{EQE} \;=\; \eta_i \cdot \eta_\text{extraction}, \qquad \eta_\text{extraction} = \frac{\alpha_m}{\alpha_i + \alpha_m},

where $\alpha_m / (\alpha_i + \alpha_m)$ is the fraction of cavity photons exiting through the output facet rather than being absorbed internally.

Differential quantum efficiency $\eta_d$ — slope of light-current curve above threshold, expressed per drive electron

For LEDs, "EQE" usually refers to the unity-current ratio of emitted photons to injected electrons. For lasers above threshold, "EQE" usually means the differential value $\eta_d$ .

Typical values.

Device	Relevant QE	Typical value
InGaAs photodiode at 1550 nm	$\eta_\text{PD}$	0.80 – 0.85
Ge-on-Si waveguide PD at 1550 nm	$\eta_\text{PD}$	0.50 – 0.85
Si photodiode at 850 nm	$\eta_\text{PD}$	0.75 – 0.90
Telecom DFB laser	$\eta_d$	0.20 – 0.40
980 nm pump diode	$\eta_d$	0.50 – 0.70
Industrial Yb-doped fiber laser	$\eta_d$	0.70 – 0.85
LED, blue InGaN	EQE	0.45 – 0.85
LED, white phosphor-converted	EQE (effective)	0.35 – 0.65
Solar cell, monocrystalline Si	EQE peak	0.85 – 0.95
Solar cell, multi-junction (research)	EQE	0.75 – 0.90 per junction

Quantum efficiency vs power efficiency. Quantum efficiency counts photons; power efficiency (e.g., wall-plug efficiency) counts joules. The two differ by the quantum defect for lasers (photon energy / pump energy) and by the voltage-drop term for LEDs.

For an ideal laser at unity internal QE with no loss and no quantum defect: power efficiency = quantum efficiency. For real devices: power efficiency $<$ quantum efficiency due to series resistance (Joule heating), voltage-defect (electron drop in energy through the active region exceeds photon energy), thermal effects, and non-radiative recombination.

Caveat on QE conventions. "Quantum efficiency" appears with various sign conventions and reference points in different sub-fields. Always specify which quantum efficiency is meant in technical communication: detector QE, laser EQE, laser IQE, LED EQE, or differential QE. Confusion between these is one of the most common errors in optoelectronic literature.