Photon Detection Efficiency Calculator (SiPM)
Calculate the photon detection efficiency (PDE) of a SiPM or SPAD detector and estimate the signal-to-noise ratio for photon counting and time-of-flight measurements.
🔬 What is Photon Detection Efficiency in a SiPM?
Photon detection efficiency (PDE) is the probability that a single photon incident on a Silicon Photomultiplier (SiPM) actually registers as a detected count. PDE is the product of three independent probabilities: the quantum efficiency (QE, the chance that the photon creates a free electron-hole pair), the geometric fill factor (FF, the fraction of the chip surface that is active detector area), and the avalanche trigger probability (P_trig, the chance that the freed carrier triggers a self-sustaining avalanche). A typical SiPM achieves PDE of 15 to 55 percent at its peak wavelength.
SiPMs are used across a wide range of photon-counting and light-sensing applications. In Positron Emission Tomography (PET) scanners, arrays of SiPMs convert scintillation light from LYSO or BGO crystals into electrical pulses that locate the annihilation photon pairs. In LiDAR systems for autonomous vehicles, SiPMs detect single photons reflected from distant targets with sub-nanosecond timing precision. In high-energy physics experiments, SiPM arrays read out scintillator fibres in calorimeters and muon detectors. In quantum optics, SPADs (individual microcells of a SiPM) serve as single-photon counters for photon correlation measurements.
A common misconception is that quantum efficiency alone determines sensitivity. In practice, fill factor is equally important. A SiPM with QE = 60 percent but fill factor = 30 percent achieves a QE times FF product of only 18 percent, worse than a PMT with QE = 25 percent but 100 percent active photocathode coverage. Modern SiPMs address this by increasing microcell size to improve fill factor, at the cost of higher capacitance and slower recharge time.
The dark count rate (DCR) is the other key figure of merit. Every thermal generation event in the depletion region that triggers an avalanche creates a false count indistinguishable from a real photon event. DCR increases with temperature and overvoltage, and limits the minimum detectable signal level. The signal estimation mode of this calculator quantifies the trade-off between PDE (which benefits from higher overvoltage) and DCR (which worsens with higher overvoltage) by computing the signal-to-noise ratio for a specific measurement scenario.
📐 Formulas
PDE = QE × FF × Ptrig
QE = quantum efficiency - probability that an incident photon generates a carrier pair (0 to 1)
FF = geometric fill factor - fraction of chip area that is active SPAD region (0 to 1)
Ptrig = avalanche trigger probability at operating overvoltage (0 to 1)
SNR = Nsig ÷ √(Nsig + Ndark)
Nsig = PDE × Φ × twin = signal counts in integration window
Ndark = DCR × twin = dark counts in integration window
Example: QE=30%, FF=50%, Ptrig=70% → PDE = 0.30 × 0.50 × 0.70 = 10.5%
📖 How to Use This Calculator
Steps
1
Choose the calculation mode - select Find PDE to compute photon detection efficiency from device parameters, or Signal Estimation to compute the expected SNR and count statistics for a specific measurement scenario with a known photon flux.
2
Enter QE, fill factor, and trigger probability (Find PDE mode) - read QE from the datasheet spectral response curve at your operating wavelength. Fill factor and trigger probability are listed in the datasheet technical specification table. Trigger probability is sometimes given as a function of overvoltage in the PDE breakdown table.
3
Enter photon flux, DCR, and window (Signal Estimation mode) - enter the incident photon rate in kHz, the dark count rate at your operating temperature and overvoltage, and the duration of your measurement or gating window in nanoseconds.
4
Read and apply the results - PDE mode shows overall efficiency and photons detected per 1000 incident. Signal mode shows SNR and contrast ratio (signal rate divided by DCR), which helps determine whether the detector can distinguish the signal from background at the chosen operating conditions.
💡 Example Calculations
Example 1 - Typical SiPM at 450 nm (Blue Light)
QE = 55%, Fill Factor = 60%, Ptrig = 75%
1
PDE = QE × FF × P_trig = 0.55 × 0.60 × 0.75 = 0.2475 = 24.75%
2
Detected per 1000 incident: 1000 × 0.2475 = 247.5 photons detected on average
3
Photon loss fraction: 100 - 24.75 = 75.25% of incident photons are not counted
Result: PDE = 24.75%, 248 per 1000 detected, Loss = 75.25%
Try this example →Example 2 - Low Fill Factor SiPM (High-Speed Small Microcell)
QE = 60%, Fill Factor = 30%, Ptrig = 80%
1
PDE = 0.60 × 0.30 × 0.80 = 0.144 = 14.4%
2
Despite high QE (60%), the low fill factor (30%) limits overall PDE to only 14.4%. A device with QE=40%, FF=60%, Ptrig=70% would give PDE=16.8%, higher than this despite lower QE.
3
This illustrates that fill factor is often the most important design lever for improving SiPM sensitivity.
Result: PDE = 14.40%, Fill factor limits sensitivity
Try this example →Example 3 - High-PDE SiPM at Peak Sensitivity
QE = 70%, Fill Factor = 75%, Ptrig = 85%
1
PDE = 0.70 × 0.75 × 0.85 = 0.4463 = 44.63%
2
Detected per 1000 incident: 446 photons. This represents a premium SiPM design at its optimal operating wavelength and overvoltage.
3
QE × FF product = 0.70 × 0.75 = 52.5%. Even without the trigger probability reduction, this product shows the underlying photon-to-carrier conversion efficiency.
Result: PDE = 44.63%, Best-in-class detection
Try this example →Example 4 - PET Scanner Signal Estimation (Signal Estimation Mode)
PDE = 30%, Incident = 10000 kHz, DCR = 100 kHz, Window = 1000 ns
1
Signal counts = PDE × incident rate × window = 0.30 × 10000e3 Hz × 1000e-9 s = 3.00 counts
2
Dark counts = DCR × window = 100e3 Hz × 1000e-9 s = 0.10 counts
3
SNR = 3.00 / sqrt(3.00 + 0.10) = 3.00 / 1.761 = 1.703. Contrast = 3000 kHz / 100 kHz = 30 : 1.
Result: SNR = 1.703, Signal = 3 counts, Dark = 0.10 counts, Contrast 30 : 1
Try this example →❓ Frequently Asked Questions
What is photon detection efficiency (PDE) in a SiPM?
PDE is the probability that an incident photon actually registers as a count. PDE = QE times FF times Ptrig, where QE is quantum efficiency (photon-to-carrier conversion), FF is the geometric fill factor (active area divided by total chip area), and Ptrig is the avalanche trigger probability at the operating overvoltage. Typical commercial SiPMs achieve PDE of 15 to 55 percent at their peak wavelength. PDE is always less than QE alone because fill factor and trigger probability both reduce sensitivity further.
What is a Silicon Photomultiplier (SiPM)?
A SiPM is an array of single-photon avalanche diodes (SPADs) connected in parallel on a silicon chip, all biased above breakdown voltage. Each SPAD cell fires a fixed charge pulse (gain of roughly 10 to the sixth) when a photon or dark carrier triggers an avalanche. The total SiPM output is the sum of all firing cells, giving a semi-analog output proportional to the number of detected photons. SiPMs are used in PET scanners, LiDAR, high-energy physics, and quantum optics.
What is the geometric fill factor and why is it important?
Fill factor is the ratio of active SPAD area to total chip area. Regions between cells (guard rings, quenching resistors, metal interconnects) are insensitive to photons. A fill factor of 50 percent means half the light is wasted. Modern SiPMs achieve 60 to 80 percent fill factor by using larger microcells. However, larger cells have higher capacitance, slower recharge time, and lower maximum count rate before saturation. Fill factor is typically the most impactful parameter for improving PDE.
What is dark count rate (DCR) and how does it limit SiPM sensitivity?
DCR is the rate of avalanche events triggered by thermally generated carriers rather than photons. It appears as background counts and sets the noise floor. DCR is typically 50 to 500 kHz per mm squared at 25 C, and doubles roughly every 8 to 10 degrees Celsius. In low-light measurements, DCR limits the minimum detectable photon flux. For SNR greater than 1, the signal count rate must exceed sqrt(DCR times window) counts per measurement period. Cooling the SiPM dramatically reduces DCR.
How is SNR calculated for a SiPM measurement?
For Poisson statistics: SNR = N_sig divided by sqrt(N_sig plus N_dark), where N_sig = PDE times incident_rate times t_window and N_dark = DCR times t_window. A longer window improves SNR because signal scales linearly with time but noise scales with square root. However, a longer window also smears timing information. The optimal window matches the signal pulse duration in time-correlated applications such as LiDAR or FLIM.
What is overvoltage and how does it affect PDE?
Overvoltage (Vov = Vbias - Vbr) is the excess bias above the breakdown voltage. Higher Vov increases the electric field, raising both the avalanche trigger probability (improving PDE) and the gain per cell (C times Vov per discharge). However, DCR, optical cross-talk, and after-pulsing also increase with Vov. The optimal operating point is usually 1 to 5 V above breakdown, where PDE improvement from additional overvoltage levels off but noise penalties continue to increase.
What wavelengths give the highest PDE in silicon SiPMs?
Silicon QE peaks at 400 to 550 nm (blue to green), where the photon absorption depth matches the depletion region depth. Most SiPMs achieve peak PDE at 400 to 500 nm. At 800 nm, photons penetrate too deeply, reducing QE to 10 to 20 percent. UV-optimised SiPMs use special anti-reflection coatings and shallow junction designs for wavelengths below 350 nm. Near-infrared applications at 905 nm or 1550 nm typically use InGaAs-based SPADs rather than silicon.
What is optical cross-talk in a SiPM?
When a microcell avalanche fires, the hot carriers emit secondary photons via hot-carrier luminescence. If a nearby cell absorbs one of these photons, it fires in the same clock cycle, creating a correlated false count. Cross-talk probability is typically 1 to 15 percent and increases with fill factor and overvoltage. It inflates the apparent photon count. Trenched-isolation structures between cells reduce cross-talk to below 1 to 3 percent in premium SiPMs. Cross-talk is a systematic error that cannot be reduced by signal averaging.
What is the difference between a SiPM and a photomultiplier tube (PMT)?
A SiPM is a solid-state device operating at 25 to 70 V, immune to magnetic fields, compact, and rugged. A PMT uses vacuum tube dynode multiplication, requires 1 to 2 kV bias, is sensitive to magnetic fields, and is fragile. SiPMs now match or exceed PMT PDE at visible wavelengths and are the standard choice in most new medical imaging and physics detector designs. PMTs retain advantages in large-area low-noise formats (20 to 50 cm diameter) and in ultraviolet applications where silicon is not sensitive.
How does temperature affect SiPM performance?
Breakdown voltage increases by 20 to 50 mV per degree Celsius, so a fixed supply reduces effective overvoltage as temperature rises, lowering PDE and gain. DCR doubles roughly every 8 to 10 C. After-pulsing probability decreases with temperature because carriers are released faster from traps at higher temperature. Most SiPM systems include thermal compensation to maintain a constant overvoltage across temperature, either by tracking Vbr with a lookup table or by using a temperature-compensated bias circuit.
What is after-pulsing in a SiPM and how does it affect measurements?
After-pulsing occurs when a carrier trapped in a crystal defect during an avalanche is released after the cell has recharged, triggering a second avalanche. The second pulse appears 10 to 100 ns after the original event and is falsely counted as a second photon. After-pulsing probability is 0.5 to 5 percent and increases with overvoltage and radiation damage. In photon counting applications, after-pulsing inflates the measured count rate by a factor of (1 plus after-pulsing probability), which must be subtracted in precision measurements.
How do I select the right SiPM for a specific application?
Match peak PDE wavelength to the emission peak of your scintillator or light source. Choose microcell density so that the expected photon burst occupies less than 5 percent of total cells to avoid saturation non-linearity. Verify DCR is low enough at your operating temperature to achieve the required SNR. For timing-critical applications (TCSPC, LiDAR, PET), choose SiPMs with single-photon time resolution below 200 to 300 ps FWHM. Use this calculator with your actual QE, FF, and Ptrig values at your operating wavelength and overvoltage to predict PDE accurately.
What is microcell saturation in a SiPM?
A SiPM microcell can fire only once per recharge cycle (typically 10 to 100 ns). If the incident photon rate is so high that many photons arrive before cells recharge, the response becomes non-linear. The expected fired cells is N_cells times (1 - exp(-N_photons times PDE / N_cells)), which saturates asymptotically to N_cells. For linear operation, keep the expected number of simultaneously detected photons below 5 percent of the total cell count. A 1 mm squared SiPM with 1000 cells should handle no more than 50 simultaneous photons per recharge cycle for linear operation.