The photon detection efficiency calculator above breaks the headline PDE figure of a silicon photomultiplier into the three independent probabilities that produce it. A photon has to arrive on active silicon rather than on dead area, it has to be absorbed and create a carrier pair, and that carrier pair has to trigger a self-sustaining avalanche. Miss any one of those and the photon is simply never counted, which is why PDE = QE × FF × Ptrigger and why the number is always well below the quantum efficiency alone.
Arb Digital publishes free engineering calculators that separate quantities people habitually conflate. The most common conflation on this topic is treating optical crosstalk and afterpulsing as part of the efficiency. They are not. They generate additional counts from photons that were already detected, so they inflate the observed count rate while detecting nothing new, and folding them into a PDE figure makes a detector look better than it is.
What This Photon Detection Efficiency Calculator Does
The three efficiency terms are genuinely independent and genuinely multiplicative. Fill factor is fixed at design time by how much of the surface is microcell rather than trench isolation, quench resistors and metal routing; small microcells give better dynamic range and worse fill factor. Quantum efficiency is set by the silicon's absorption at your wavelength and the anti-reflection coating; it peaks in the blue-green for typical devices and falls away sharply in the near infrared. Trigger probability depends on where in the depletion region the carrier pair appears and on the excess bias above breakdown, and it is the only term you can move from outside the package.
The calculator returns the product as the headline PDE, then reports the detected photon rate, which of the three terms is currently limiting the result, the observed count rate once correlated noise and dark counts are added, and how many photons must arrive on average for one to be counted.
Everything here is a per-photon probability, so it assumes the light level is low enough that microcells are not saturating. At high photon rates a silicon photomultiplier becomes non-linear because a microcell that has just fired is recharging and cannot fire again, and no efficiency figure describes that regime.
How to Use It
- Take quantum efficiency at your actual wavelength. A datasheet peak figure is measured where the device is best, often around 420 nm. If your scintillator or source emits at 600 nm the real figure can be half that.
- Read fill factor from the microcell pitch. Larger cells fill the surface better and count better at low light; smaller cells give more cells per square millimetre and therefore more dynamic range before saturation. The trade is direct.
- Set trigger probability for your overvoltage. It rises steeply as excess bias increases and then flattens. So do dark count rate, crosstalk and afterpulsing, which is why the optimum bias is a compromise rather than a maximum.
- Keep crosstalk and afterpulsing out of the efficiency. Enter them in their own boxes. They belong in the noise budget and in the resolution analysis, never in the PDE.
- Compare the observed count rate to the detected rate. The gap between them is the part of your signal that is not signal, and at high overvoltage it can be a substantial fraction of everything the device reports.
The Formula and a Worked Example
Photon detection efficiency is the product of three probabilities: PDE = QE × FF × Ptrigger. All three are dimensionless fractions between zero and one, entered here as percentages.
Take the defaults: 80 % quantum efficiency, 65 % fill factor and 75 % trigger probability give PDE = 0.80 × 0.65 × 0.75 = 0.39, or 39 %. That figure is typical for a good modern device at a favourable wavelength and moderate overvoltage. With a million photons per second arriving, 390,000 of them are detected. Turned around, an average of 1 ÷ 0.39 = 2.56 photons must arrive for one to be counted, which is the number that matters when you are trying to see single photons against a background.
The observed count rate is a different quantity. Each detected photon has a 15 % chance of firing a neighbouring microcell through optical crosstalk and a 3 % chance of producing a delayed afterpulse, so the 390,000 genuine detections generate 390,000 × 1.18 = 460,200 counts. Adding 50,000 dark counts per second gives 510,200 counts per second observed. Roughly 24 % of what the instrument reports is not a detected photon at all, and any analysis that treats the raw count rate as a photon rate will be wrong by that margin.
Notice which term is limiting. Fill factor at 65 % is the smallest of the three, so pushing quantum efficiency from 80 % to 85 % would add just 2.4 percentage points of PDE, while a device with the same silicon and a 75 % fill factor would add 6. The multiplication makes the weakest link disproportionately important, which is exactly why the calculator names it.
Why Crosstalk Must Not Be Counted as Efficiency
When a microcell avalanches, the several hundred thousand carriers involved emit a small number of secondary photons. Some of those travel sideways through the silicon and trigger a neighbouring cell, producing a two-cell pulse from a single incident photon. That is optical crosstalk, and it is the largest correlated noise source in most silicon photomultipliers.
It is tempting to fold crosstalk into the efficiency because it does increase the count rate. That is a mistake with real consequences. Crosstalk counts are perfectly correlated with real counts, so they do not improve the signal-to-noise ratio at all; they multiply the signal and the fluctuation together. Worse, they degrade photon-number resolution, because a pulse of two cell amplitudes might be two photons or one photon plus crosstalk, and the device cannot tell you which. In a photon-counting experiment that ambiguity is the entire measurement.
Afterpulsing behaves similarly but is displaced in time. A carrier trapped in a lattice defect during an avalanche is released tens to hundreds of nanoseconds later and starts a second avalanche in the same cell. It inflates rates, distorts timing distributions and makes dead-time corrections unreliable. Neither effect is efficiency, and national metrology laboratories characterising these devices treat them as separate parameters for exactly this reason. NIST's work on single-photon detectors for quantum networks describes the full parameter set that characterises a photon-counting detector, of which efficiency is only one entry.
Overvoltage Is One Knob That Moves Everything
A silicon photomultiplier is biased above its breakdown voltage, and the amount above is the overvoltage or excess bias. It is the single control available to the user once a device is chosen, and it moves every parameter at once.
Raising overvoltage increases trigger probability, which raises PDE — steeply at first and then with diminishing returns as trigger probability approaches its ceiling. It increases gain, which improves the separation between the single-photon peak and the electronic noise floor and therefore improves photon-number resolution. It also increases dark count rate roughly linearly or faster, increases crosstalk probability roughly with the square of gain because more carriers emit more secondary photons, and increases afterpulsing because more carriers means more trapping.
There is therefore no universally correct bias. A photon-counting experiment with a low signal rate is usually limited by dark counts and wants a modest overvoltage. A high-rate timing experiment wants gain and speed and can tolerate the noise. A calorimetry application counting many simultaneous photons is limited by crosstalk distorting the amplitude spectrum and wants that suppressed. Every device datasheet plots these curves against overvoltage, and the right operating point comes from your own signal conditions rather than from a maximum on any one curve.
Temperature, Wavelength and the Rest of the Real Device
Breakdown voltage rises with temperature, typically by tens of millivolts per kelvin. If the bias supply is fixed, warming the device reduces the overvoltage and therefore reduces PDE and gain together, which is why serious systems either stabilise temperature or actively compensate the bias. Dark count rate moves the other way and roughly halves for every 8 to 10 °C of cooling, which is the main reason photon-counting systems are cooled at all.
Wavelength dependence is equally severe. Quantum efficiency depends on absorption depth in silicon, which varies by orders of magnitude across the visible band, and the anti-reflection coating is tuned for one region. A device quoted at 40 % PDE at its peak may deliver 15 % at 700 nm and almost nothing beyond 900 nm. Matching the detector's spectral response to the emission spectrum of your source is usually worth more than any bias optimisation. The photon energy calculator and the wavelength calculator connect wavelength to photon energy, and the optical density calculator handles the filters and attenuators that usually sit in front of a detector like this. The NIST reference on fundamental physical constants supplies the exact Planck constant and elementary charge that those photon-level conversions rely on.
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Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Quoting quantum efficiency as detection efficiency — fill factor and trigger probability both sit between them, and the real PDE is typically half the quantum efficiency or less.
- Folding crosstalk into the PDE — crosstalk counts are correlated with real ones, so they raise the count rate without improving signal-to-noise and they destroy photon-number resolution.
- Using the peak-wavelength figure at your own wavelength — quantum efficiency falls steeply away from the peak, and a device rated at 420 nm may be far worse at 650 nm.
- Maximising overvoltage to maximise PDE — dark counts, crosstalk and afterpulsing all rise with it, often faster than the efficiency gain is worth.
- Applying these probabilities at high light levels — once a significant fraction of microcells are recharging, the device is non-linear and no single efficiency figure describes it.
Related Free Tools From Arb Digital
Work out the energy and wavelength of the photons you are counting with the photon energy calculator and the wavelength calculator. Attenuators and filters in front of the detector are handled by the optical density calculator, and absorption in a sample by the Beer–Lambert law calculator or, in the nonlinear regime, the two-photon absorption calculator. For the optics ahead of the detector the Snell's law calculator covers refraction at each surface, while the luminous flux converter moves between radiometric and photometric units. Signal ratios in decibels come from the decibel calculator. Everything is on the free online tools hub.
Frequently Asked Questions
It is the probability that a photon arriving at the device produces a detectable avalanche, and it is the product of three independent terms: the geometric fill factor, the quantum efficiency of the silicon at that wavelength, and the probability that a created carrier pair triggers a self-sustaining avalanche. Because they multiply, the overall figure is always well below the quantum efficiency alone.
Two terms sit between them. A large fraction of the device surface is trench isolation, quench resistors and routing rather than active microcell, which is the fill factor. And a carrier pair created in the silicon can recombine without starting an avalanche, which is the trigger probability. Multiply a 65 per cent fill factor and a 75 per cent trigger probability together and you have already lost half the photons the silicon absorbed.
No. Crosstalk fires a second microcell from a photon that was already detected, so it adds counts without detecting anything new. Those counts are perfectly correlated with the real ones, so they do not improve signal-to-noise, and they make photon-number resolution ambiguous because a two-cell pulse might be two photons or one photon plus crosstalk.
It raises trigger probability and therefore PDE, steeply at first and then with diminishing returns. It also raises gain, dark count rate, crosstalk probability and afterpulsing, the last two roughly with gain. There is no universally best bias point: a low-rate photon-counting measurement usually wants modest overvoltage, while a high-rate timing measurement can trade noise for speed.
Indirectly and strongly. Breakdown voltage rises with temperature by tens of millivolts per kelvin, so a fixed bias supply delivers less overvoltage as the device warms, and PDE and gain both fall with it. Dark count rate moves the opposite way and roughly halves for every 8 to 10 degrees Celsius of cooling.
Because the dead area between microcells does not scale down as fast as the cells do. Larger cells fill the surface more efficiently and give higher PDE, but there are fewer of them per square millimetre, so the device saturates at a lower photon count. Smaller cells give more cells and more dynamic range at the cost of fill factor.
No. Every figure here is a per-photon probability and assumes microcells are essentially always ready to fire. Once a significant fraction of them are recharging after a previous avalanche, the response becomes non-linear and saturates, and the relationship between incident photons and counts has to be modelled with the cell count and recovery time rather than a single efficiency.
This tool is provided for educational and preliminary design use. It multiplies published per-photon probabilities and assumes a low-occupancy regime with no microcell saturation. Manufacturer datasheets and measured characterisation at your own wavelength, temperature and bias are what govern a real detector's performance.
