SiPM Photon Detection Efficiency (PDE) Calculator
Silicon Photomultipliers (SiPMs) detect single photons by triggering Geiger-mode avalanches in an array of micro-cells. Photon Detection Efficiency (PDE) is the probability that an incident photon produces a counted output pulse. Use this calculator to find PDE from its three fundamental components (quantum efficiency, fill factor, triggering probability) and the expected device responsivity, or reverse the calculation to recover PDE from a measured photocurrent responsivity.
What is a SiPM and how does it detect photons?
A Silicon Photomultiplier (SiPM) is a solid-state photodetector made from a dense array of tiny avalanche photodiode micro-cells, each operated above its reverse-breakdown voltage. When a photon enters the active silicon and generates an electron-hole pair, the strong electric field accelerates the carrier through the depletion region. If the carrier has enough energy it triggers a Geiger-mode avalanche: a self-sustaining chain of impact-ionization events that produces a large, fast current pulse (gain of 10^5 to 10^7 electrons per photon). The micro-cell is then quenched by a series resistor so it resets within nanoseconds, ready for the next photon. The SiPM output is the sum of all cells that fire simultaneously, which is proportional to the number of detected photons for low occupancy.
The PDE formula: three independent factors
Photon Detection Efficiency is the probability that one incident photon produces a counted output pulse. It is the product of three independent probabilities: PDE = QE * FF * P_trig. Quantum Efficiency (QE) is the probability that a photon generates an electron-hole pair in the active silicon region; it depends on wavelength, anti-reflective coating design, and how deep the depletion zone reaches into the silicon. Fill Factor (FF) is the fraction of the total SiPM surface that is active - the rest is occupied by quench resistors, metal interconnects and guard rings, so it never sees light. Triggering Probability (P_trig) is the probability that a generated carrier survives long enough without recombination and gains enough energy to trigger the Geiger avalanche; it is strongly controlled by the electric field, i.e. by the overvoltage applied above the breakdown voltage. All three factors must be high simultaneously to achieve a good PDE, and this is why modern SiPMs with large micro-cells, UV-optimised coatings, and high bias voltage achieve PDE values of 50-65% at their peak wavelength.
Responsivity, crosstalk, and afterpulsing
A calibrated way to measure PDE is to illuminate the SiPM with a known optical power P_opt and measure the mean photocurrent I. Responsivity R = I/P_opt (in A/W) combines PDE, gain, photon energy, and the correlated noise terms crosstalk and afterpulsing. The full relation is: R = PDE * e * G * (1 + P_XT) * (1 + P_AP) * lambda / (h*c), where e is the elementary charge, G is the gain per cell, P_XT is the optical crosstalk probability, P_AP is the afterpulsing probability, lambda is the wavelength, h is Planck's constant, and c is the speed of light. Optical crosstalk occurs because a Geiger avalanche in one micro-cell emits secondary photons (at ~3 photons per 10^5 carriers in silicon) that can trigger an adjacent cell, inflating the apparent signal. Afterpulsing is a delayed spurious pulse caused by carriers trapped in crystal defects and released after the primary pulse. Both increase the apparent count rate beyond the true photon arrival rate. This calculator lets you separate the true PDE from these correlated noise contributions.
Overvoltage, temperature, and wavelength dependence
All key SiPM parameters depend on the overvoltage: the excess reverse bias above the breakdown voltage (DeltaV = V_bias - V_bd). Gain rises linearly with DeltaV (G = DeltaV * C_cell / e). Triggering probability increases steeply with DeltaV, so PDE improves with bias - but so does crosstalk and dark count rate. There is always a practical optimum overvoltage that balances sensitivity and noise. Temperature matters because the breakdown voltage increases with temperature (typically +20 to +60 mV/K for silicon); if ambient temperature rises and bias voltage is fixed, DeltaV falls and PDE drops. Temperature-stabilised bias supplies are standard in precision photon-counting systems. Wavelength determines both photon energy and how deep into the silicon the photon is absorbed. Blue and near-UV photons (350-500 nm) are absorbed near the surface where the depletion field is strongest, giving high QE and P_trig. Red and NIR photons (>700 nm) penetrate deeper into field-free regions where carriers recombine rather than trigger avalanches, so PDE falls sharply.
Typical SiPM performance ranges by parameter
| Parameter | Typical range | Best-in-class | Notes |
|---|---|---|---|
| Photon Detection Efficiency | 20-45% | 55-65% | At peak wavelength and optimal overvoltage |
| Quantum Efficiency (QE) | 60-90% | ~95% | With anti-reflective coating in visible band |
| Fill Factor (FF) | 30-80% | ~80% | Larger micro-cells give higher FF |
| Triggering Probability (P_trig) | 50-90% | ~95% | Increases strongly with overvoltage |
| Gain (G) | 1e5-1e6 | ~1e7 | Linear in overvoltage above breakdown |
| Optical Crosstalk (P_XT) | 2-20% | <2% | Lower at smaller micro-cell pitch |
| Afterpulsing (P_AP) | 1-10% | <1% | Decreases with improved silicon purity |
| Peak wavelength | 380-500 nm | 420 nm typical | Blue/near-UV for standard SiPMs |
| Breakdown voltage (V_bd) | 25-70 V | Device-specific | Temperature-sensitive, dV_bd/dT ~ 20-60 mV/K |
| Typical overvoltage (DeltaV) | 1-5 V | Up to 10 V | Excess bias above V_bd |
Representative values for commercial SiPMs from Hamamatsu (MPPC), SensL/onsemi, and AdvanSiD. Exact values are device- and bias-dependent.
Frequently asked questions
What is a typical PDE for a commercial SiPM?
Modern high-end SiPMs (for example, Hamamatsu S13360 series, onsemi MicroFJ, AdvanSiD ASD-NUV) achieve PDE of 40-55% at their peak wavelength (420-450 nm) and standard overvoltage. Older designs or devices with small micro-cells (lower fill factor) typically show 20-35%. UV-sensitive back-illuminated or through-silicon-via SiPMs can reach 65%+ but at extra cost and complexity.
How does overvoltage affect PDE?
PDE increases with overvoltage because triggering probability (P_trig) is the overvoltage-dependent term in PDE = QE * FF * P_trig. A higher electric field accelerates carriers faster, raising their probability of triggering an avalanche before recombination. However, gain, crosstalk and dark count rate also rise with overvoltage, so the usable range is limited - most SiPMs are rated for 2-5 V overvoltage, and going beyond degrades signal-to-noise despite higher raw PDE.
What is the difference between PDE and quantum efficiency?
Quantum efficiency (QE) is only one of three factors in PDE. QE measures how efficiently a photon creates an electron-hole pair in silicon (photon-to-carrier conversion). PDE additionally accounts for whether the carrier lands in the active area at all (fill factor) and whether it successfully triggers a Geiger avalanche (triggering probability). A bare photodiode has R = QE * e * lambda / (hc) with no gain; a SiPM multiplies this by gain G and the two noise factors, giving responsivity 10^5 to 10^6 times higher than a photodiode.
How is PDE measured in practice?
The most common approach is photocurrent measurement: illuminate the SiPM with a calibrated source of known optical power and measure the resulting mean anode current. PDE is extracted from the measured responsivity after correcting for gain, crosstalk and afterpulsing. An alternative is single-photon pulse counting: use a pulsed attenuated laser (mean photons per pulse much less than 1) and compare the detected pulse rate to the expected photon rate. Both methods require a calibrated reference detector and careful suppression of stray light.
What wavelength should I use with a SiPM?
Standard SiPMs built on p-on-n silicon peak around 420-500 nm (blue to green). Using them for red (>650 nm) or NIR (>800 nm) light causes significantly lower PDE - often less than 10% at 850 nm. For red/NIR applications, choose a device with a deep p-well or an n-on-p structure that shifts the peak toward longer wavelengths, and note that triggering probability for long-wavelength (deeper) absorption also tends to be lower. For UV below 350 nm, look for SiPMs with UV-transparent windows and UV-enhanced coatings.
What is optical crosstalk and how can it be reduced?
Optical crosstalk (P_XT) occurs because an avalanche in one micro-cell emits secondary photons (via intraband transitions in silicon) that travel to neighbouring cells and trigger additional avalanches. This makes a single-photon event look like a two- or three-photon event. Manufacturers reduce crosstalk by etching optical trenches filled with absorbing material between cells, which intercepts secondary photons before they reach neighbours. Modern devices with deep-trench isolation show P_XT below 3%, whereas older designs without trenches can have 10-20% crosstalk.
Why does this calculator have two modes?
Component mode (PDE = QE * FF * P_trig) is for design and simulation: you know or estimate the device sub-parameters and want to predict overall PDE and expected responsivity. Responsivity mode is for measurement and characterisation: you have made a calibrated photocurrent measurement and want to extract the actual PDE of your device, accounting for gain, wavelength, crosstalk and afterpulsing. Both modes use the same underlying physics - they are the forward and inverse of the same formula.