Figure 1: PDE is the fraction of incident photons that produce a detectable signal. For SiPMs it depends on quantum efficiency, geometric fill factor, and avalanche trigger probability.
Table of Contents
- Quantum Efficiency (QE)
- Fill Factor (FF)
- Trigger Probability (Pt)
- Detector Technology Comparison
- Dark Counts and SNR
What Is Photon Detection Efficiency?
Photon detection efficiency (PDE) is the probability that a photon arriving at the detector surface produces a counted output pulse. A perfect detector would have 100% PDE — every incident photon triggers a detection event. In practice, photons are lost at multiple stages: some reflect off the surface, some are absorbed without generating useful carriers, some land on dead regions of the pixel, and some carriers fail to trigger the avalanche process needed for a measurable signal.
PDE determines the performance ceiling of every system built around single-photon or few-photon measurements, from PET scanners and LiDAR to quantum key distribution and particle physics calorimeters. The Noise Figure Calculator handles the electronic noise side of receiver design, while this calculator handles the photon-level detection probability.
The Formulas
PDE = Ndet / NincFrom components:
PDE = QE × FF × PtriggerDetection loss:
dB = 10 log₁₀(PDE)Shot-noise SNR:
SNR = S / √(S + DCR) where S = detected signal counts
The first formula is empirical — count photons in, count detections out, divide. The second is analytical — multiply the three independent probabilities that each represent a physical loss mechanism. Detection loss in dB fits directly into photon link budgets: 50% PDE = −3 dB, 10% PDE = −10 dB. The Decibel Calculator converts these dB values to linear ratios.
Mode 1 — PDE from Photon Counts
Enter detected photon count (Ndet) and incident photon count (Ninc). Optionally enter the dark count rate (DCR) for SNR calculation. The calculator returns PDE percentage, detection loss in dB, linear ratio, photons missed, SNR estimate, and NEP indicator.
Example: SiPM at 80% PDE
PDE = 800 / 1,000 = 80%
Detection loss = 10 log₁₀(0.80) = −0.97 dB
Photons missed: 20%
With DCR = 100 kcps in a 1 ms gate (100 dark counts): SNR = 800 / √(800 + 100) = 26.7. The signal is well above the dark count noise floor.
Example: PMT at 35% PDE
PDE = 35% | Loss = −4.56 dB
With DCR = 500 cps in a 10 ms gate (5 dark counts): SNR = 350 / √(350 + 5) = 18.6. The PMT’s lower PDE yields fewer signal counts, but its extremely low dark count rate partially compensates at low light levels.
Example: SNSPD at 95% PDE
PDE = 95% | Loss = −0.22 dB — nearly lossless detection
With DCR < 1 cps (effectively zero): SNR = 950 / √950 = 30.8. Shot-noise limited on the signal itself. SNSPDs achieve the highest PDE of any current technology, which is why they are the detector of choice for quantum key distribution.
Mode 2 — PDE from Component Factors
This mode breaks PDE into its three physical constituents. Each factor represents an independent probability, and PDE is their product. Understanding which factor limits your detector tells you where improvements have the most impact.
Example: SiPM
PDE = 0.90 × 0.60 × 0.95 = 51.3%
Detection loss = −2.90 dB
The fill factor is the bottleneck. If FF improved from 60% to 80% (modern trench-isolation designs), PDE would rise to 68.4% — a gain of 1.25 dB. The Gain Calculator can express this improvement as an equivalent amplifier gain that would give the same SNR boost.
Example: PMT
PDE = 0.25 × 1.00 × 1.00 = 25%
Detection loss = −6.02 dB
The entire loss is in the photocathode quantum efficiency. FF and Pt are both perfect — PMTs lose photons only at the conversion stage. Ultra-bialkali cathodes push QE above 40%, reducing detection loss to −4 dB.
Quantum Efficiency (QE)
QE is the probability that an absorbed photon generates a usable electron-hole pair. It depends on the semiconductor material, wavelength of incident light, and depth of the absorption region. Silicon achieves QE above 90% near 500 nm but drops sharply below 350 nm (UV) and above 1000 nm (near-IR). InGaAs detectors extend sensitivity to 1550 nm for telecom wavelengths. PMT photocathode materials typically achieve 20–30% QE for bialkali, rising above 40% for ultra-bialkali at higher cost.
Fill Factor (FF)
Fill factor is the ratio of photosensitive area to total pixel area — the dominant loss mechanism unique to SiPMs and SPAD arrays. Each microcell needs a quenching resistor, guard ring, and isolation trench, all of which are optically dead. Early SiPMs had 30–40% fill factor. Modern devices using trench isolation achieve 60–80%. PMTs have effectively 100% fill factor because the photocathode covers the entire entrance window. Increasing microcell size improves fill factor but reduces the total number of cells and therefore the dynamic range.
Trigger Probability (Ptrigger)
The probability that a photogenerated carrier triggers a self-sustaining Geiger-mode avalanche. This depends on the electric field strength, which is set by the over-voltage — the bias voltage above breakdown. At low over-voltage, many carriers fail to trigger an avalanche and are lost. At high over-voltage, trigger probability approaches 95–100%, but dark count rate, crosstalk, and afterpulsing all increase. Optimising over-voltage is a balance between maximising PDE and minimising noise. PMTs effectively have 100% trigger probability because their dynode multiplication chain exceeds 10⁶ gain.
Detector Technology Comparison
| Detector | PDE | Dark Counts | Timing | Key Limitation |
|---|---|---|---|---|
| PMT | 20–40% | 10–100 cps | <1 ns | Photocathode QE |
| SiPM | 30–60% | 100k–1M cps | 100–200 ps | Fill factor, DCR |
| SPAD | 50–70% | 10–1000 cps | <50 ps | Small active area |
| SNSPD | >90% | <1 cps | <30 ps | Cryogenic cooling (2–4 K) |
PMTs remain the workhorse for large-area applications (neutrino detectors, nuclear medicine). SiPMs have largely replaced PMTs in PET scanners and LiDAR due to compact size, low voltage, and magnetic field tolerance. SPADs excel in timing applications (TCSPC, FLIM, depth cameras). SNSPDs are used where maximum PDE is non-negotiable: quantum key distribution, quantum computing readout, and deep-space optical communication. The Signal Attenuation Calculator handles the fibre and free-space losses that determine how many photons reach the detector in the first place.
Dark Counts and SNR
Dark counts are false detections caused by thermally generated carriers triggering avalanches without photons. They set the noise floor for photon counting. The shot-noise-limited SNR is S / √(S + DCR) where S is the detected signal count. At high light levels (S >> DCR), dark counts are irrelevant. At very low levels approaching single-photon detection, dark counts dominate the noise.
PDE has a compounding effect. Higher PDE means more signal counts from the same photon flux. More signal counts improve the SNR by √PDE and increase the margin above the dark count floor. Doubling PDE from 25% to 50% improves the shot-noise-limited SNR by √2 (1.5 dB) and doubles the margin above dark count noise. In photon-starved applications, PDE is the single most important detector parameter. The Bandwidth Calculator relates to this through the Shannon capacity — at the photon level, bandwidth determines how many temporal modes are available for encoding information.
Frequently Asked Questions
What is photon detection efficiency?
What is fill factor and why does it matter?
What is dark count rate?
What PDE values are typical?
How does PDE affect SNR?
How does this calculator relate to the Noise Figure Calculator?
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