Quantum Efficiency (QE) in Photometry, Detectors & Optoelectronics

Quantum efficiency (QE) is a cornerstone metric in photonics, optoelectronics, and imaging science. It describes how efficiently a device converts incident photons into a measurable output—be it an electrical signal or emitted light. QE is essential for evaluating the sensitivity, energy conversion, and overall effectiveness of photodetectors, solar cells, LEDs, lasers, and single-photon counting devices.

Definition and General Equation

Quantum efficiency is defined as the ratio of the number of output events (such as electrons, holes, or emitted photons) to the number of incident photons. It is commonly expressed as a percentage:

[ \text{QE} = \frac{\text{Number of output events}}{\text{Number of incident photons}} \times 100% ]

QE provides a direct measure of a device’s photon-to-signal conversion capability, impacting everything from low-light camera sensitivity to solar panel efficiency.

Quantum Efficiency in Photodetectors

Photodetectors—including photodiodes, CCDs, and CMOS image sensors—rely on high QE to achieve strong, low-noise signals. In these devices, QE is typically measured as a function of wavelength (yielding a spectral QE curve):

[ \text{QE}(\lambda) = \frac{\text{Electrons collected at } \lambda}{\text{Incident photons at } \lambda} \times 100% ]

• Silicon detectors can reach >90% QE in the visible range with optimized anti-reflection coatings and back-illumination.
• CCDs & CMOS sensors: Scientific-grade, back-illuminated CCDs achieve up to 95% QE at peak wavelengths. CMOS sensors utilize micro-lens arrays to increase effective QE.
• Photomultiplier tubes (PMTs) often have lower QE (<30%), depending on photocathode material and wavelength.

Responsivity (output current per optical power, A/W) is closely related to QE, incorporating the energy of photons at each wavelength. Detective Quantum Efficiency (DQE) extends this by factoring in noise, evaluating the overall fidelity of imaging systems.

Typical quantum efficiency curve of a silicon photodiode, showing strong wavelength dependence.

Applications

High-QE photodetectors are vital for:

• Scientific imaging (astronomy, microscopy)
• Low-light surveillance
• Fluorescence detection
• Industrial sensors

Design Considerations

• Back-illumination removes light-blocking frontside structures, boosting QE—especially in UV and blue regions.
• Anti-reflection coatings and micro-lenses minimize photon loss and direct more light to active regions.

Photon Detection Efficiency (PDE) in Single-Photon Counters

For single-photon avalanche diodes (SPADs), silicon photomultipliers (SiPMs), and related detectors, the analogous term is photon detection efficiency (PDE):

[ \text{PDE} = \frac{\text{Number of registered photon events}}{\text{Number of incident photons}} \times 100% ]

PDE incorporates not only QE, but also avalanche triggering probability, fill factor (photosensitive area ratio), and dead time effects. High PDE is critical in applications such as quantum optics, LIDAR, and time-correlated single-photon counting (TCSPC).

Quantum Efficiency in LEDs and Lasers

Internal vs. External Quantum Efficiency

• Internal QE (IQE): Fraction of injected carriers (electrons/holes) that recombine radiatively: [ \text{IQE} = \frac{\text{Photons generated internally}}{\text{Electrons injected}} \times 100% ]
• External QE (EQE): Fraction of electrons resulting in photons emitted from the device: [ \text{EQE} = \text{IQE} \times \text{Extraction Efficiency} ] Extraction efficiency accounts for photon escape from the device (e.g., overcoming total internal reflection).

Example: A blue GaN LED with an IQE of 85% and extraction efficiency of 40% yields an EQE of 34%.

Lasers

In lasers, pump quantum efficiency may exceed 100% in materials with energy transfer (e.g., thulium-doped fibers), where one absorbed photon can yield multiple output photons.

Quantum Efficiency in Solar Cells

Solar cell performance is characterized by external (EQE) and internal quantum efficiency (IQE):

[ \text{EQE}(\lambda) = \frac{\text{Collected charge carriers at } \lambda}{\text{Incident photons at } \lambda} \times 100% ] [ \text{IQE}(\lambda) = \frac{\text{Collected charge carriers at } \lambda}{\text{Absorbed photons at } \lambda} \times 100% ]

EQE spectra diagnose performance losses (reflection, incomplete absorption, recombination) and guide the design of high-efficiency solar cells, including multi-junction and thin-film devices.

External quantum efficiency (EQE) of a silicon solar cell as a function of wavelength.

Factors Affecting Quantum Efficiency

• Wavelength & Bandgap: QE is maximum where photon energy exceeds the material’s bandgap but declines at longer wavelengths as absorption drops.
• Surface Reflection: Anti-reflection coatings (ARCs) are used to minimize photon loss at the surface.
• Device Architecture: Back-illumination and micro-optics (e.g., microlenses) boost QE by enhancing photon collection.
• Temperature: Affects carrier mobility, recombination, and noise—impacting QE and SNR.
• Dead Time & Fill Factor: For photon counters, dead time after each event and the fill factor (photosensitive area fraction) limit effective QE/PDE.
• Optical Windows/Encapsulants: Poorly optimized materials or coatings can absorb or reflect photons, lowering system QE.

Special Case: Quantum Efficiency >100%

In rare cases, such as certain fiber lasers, QE can exceed 100% due to energy transfer processes (e.g., cross-relaxation in thulium-doped fibers). Here, a single high-energy photon can result in the emission of two or more lower-energy photons.

Related Terms

Quantum Efficiency Measurement

• Absolute QE uses calibrated photon flux and device output to determine true conversion efficiency.
• Relative QE compares the device to a reference with known QE.
• Per-pixel QE is important for imaging arrays, as spatial variations can affect image quality.

Measurement involves illuminating the device with monochromatic, calibrated light and recording the output (charge, current, or counts), then calculating QE at each wavelength.

Practical Examples

• Scientific CCD Camera: Back-illuminated CCDs achieve QE up to 95% at visible wavelengths for astronomy or low-light imaging.
• SPAD Array: Single-photon detectors with PDE ~45% at 550 nm are used in fluorescence lifetime imaging and quantum optics.
• Solar Cell: Silicon cells reach peak EQE of 92% at 700 nm, crucial for efficient solar energy conversion.
• LED: Blue GaN LEDs with high IQE and optimized extraction structures achieve high EQE for bright displays and lighting.
• Thulium-Doped Laser: Quantum efficiency approaching 200% via cross-relaxation, enabling highly efficient infrared laser emission.

Advanced Notes

Detective Quantum Efficiency (DQE)

DQE evaluates the overall SNR preservation of an imaging system, factoring in quantum efficiency and noise sources. It is especially important for scientific, medical, and X-ray imaging.

Quantum Defect

Quantum defect quantifies energy loss in lasers between absorbed (pump) and emitted (signal) photons:

[ \text{Quantum Defect} = 1 - \frac{\lambda_{\text{signal}}}{\lambda_{\text{pump}}} ]

Smaller quantum defect means higher energy conversion efficiency and lower thermal losses.

Quantum efficiency underpins performance in nearly all photonic and optoelectronic devices. By understanding and optimizing QE, engineers and scientists can design systems with greater sensitivity, efficiency, and information fidelity—unlocking advances in imaging, sensing, lighting, and energy conversion.