Photon Detection Efficiency Calculator (SiPM)

Background.

A silicon photomultiplier, or SiPM, is a grid of hundreds to tens of thousands of microscopic avalanche photodiodes wired in parallel and biased just above their breakdown voltage. In that state a single absorbed photon can set off a self-sustaining avalanche in one cell, which a series resistor then quenches, so the device can count individual photons. How many of the photons that reach it it actually counts is its photon detection efficiency, and that one figure decides how much light a PET scanner crystal, a LiDAR receiver or a scintillator in a physics experiment needs before a signal stands out.

Three probabilities multiply to give it. Quantum efficiency is the chance a photon creates an electron-hole pair in the sensitive silicon. Fill factor is the share of the surface that is actually sensitive, rather than given over to trenches, quench resistors and wiring between cells. Triggering probability is the chance that the freed carrier starts an avalanche, and it rises with the overvoltage, the bias above breakdown. So PDE is never a single number for a device: it changes with wavelength, with bias and, through the breakdown voltage, with temperature.

The figure here is the plain measured ratio: detected events divided by incident photons, times 100. Typically the incident number comes from a calibrated reference photodiode and the detected number from the SiPM's own pulse count.

That ratio is only as clean as the counts. Dark counts, optical crosstalk between cells and afterpulsing all add events that were not new photons, pushing the result up; dead time and saturation of the cells at high light levels push it down. None of these is corrected, so unless you remove them first the answer is an apparent PDE. A result above 100% is a sure sign that extra counts have crept in.

What is photon detection efficiency calculator (sipm)?

Photon detection efficiency (PDE) is the probability that a photon arriving at a silicon photomultiplier's surface produces a counted signal, expressed as a percentage. It is the product of quantum efficiency, geometric fill factor and avalanche triggering probability, so it varies with wavelength and with the overvoltage applied above breakdown. Measured directly, it is the number of detected photon events divided by the number of incident photons over the same exposure.

How to use this calculator.

1. 01Enter the detected photon events: the SiPM counts recorded during the exposure, after subtracting the dark counts from a run of equal length with the light blocked.
2. 02Enter the incident photons for the same exposure and the same area, usually taken from a calibrated reference photodiode: optical power divided by the energy per photon, hc/λ, multiplied by the exposure time.
3. 03Use totals or rates for both inputs, as long as they share the same basis: both per second, both per light pulse, or both over the whole run.
4. 04Read the PDE in percent, and record the wavelength, overvoltage and temperature with it, since each of them changes the result.

The formula.

PDE = N_detected ÷ N_incident × 100%. N_detected is the number of photon events the SiPM registered and N_incident the number of photons that reached its surface in the same interval; their ratio is a probability, and multiplying by 100 turns it into a percentage. Physically, the ratio estimates the product QE × FF × P_trigger of quantum efficiency, fill factor and triggering probability. The division is exact, but the inputs rarely are. The incident count normally comes from a reference detector, so its calibration error passes straight into the answer: an incident count 3% too high makes the PDE roughly 3% too low. Correlated noise inflates N_detected, while cell saturation at high light levels deflates it.

A worked example.

Frequently asked questions.

References& sources.

1. [1]IEC 60747-19-1:2019, Semiconductor devices — Smart sensors — Photodetectors (BIBLIOGRAPHIC/PAYWALL).
2. [2]Hamamatsu Photonics, MPPC technical information.
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.