PDE SiPM Calculator - SiPM Responsivity to PDE

The PDE SiPM calculator turns the responsivity of a silicon photomultiplier into photon detection efficiency, the fraction of incident photons the SiPM actually counts. It accepts gain, wavelength, crosstalk probability, and afterpulsing probability, so the result reflects the same corrections that lab datasheets apply when they publish a PDE curve. A second readout, photon energy, supports the wavelength input with a direct electron-volt value.

• • Reading a SiPM datasheet: Convert a published responsivity at a known wavelength into the PDE percentage a PET, SPECT, or LiDAR designer is shopping for.
• • Comparing devices at a fixed wavelength: Hold wavelength constant and swap gain, crosstalk, and afterpulsing to see which combination keeps PDE highest for a single-photon timing application.
• • Plotting a PDE curve by hand: Sweep wavelength in 50 nm steps while leaving the noise terms fixed, and use the PDE percentages to sketch a wavelength response curve before measuring it.
• • Lecture and lab problem sets: Work through the PDE expression during a detector-physics class to show how the Planck constant, the speed of light, and the elementary charge combine into a sensor-level percentage.

Photon detection efficiency is the probability that an incoming photon starts a measurable avalanche in one of the microcells, and it is the headline number for a SiPM. The Omni PDE SiPM reference expresses that probability in terms of the sensor's responsivity, so the same formula works whether the data sheet lists the device at 420 nm or at 905 nm. The calculator uses a single closed-form expression that keeps the relationship between responsivity, gain, wavelength, and the noise terms visible.

The same Planck-constant and speed-of-light terms that the PDE SiPM calculator uses for photon energy also appear in Compton Wavelength Calculator, where they describe the photon-electron rest-length scale.

The calculator solves the standard PDE expression from the Omni SiPM reference. It combines responsivity with three SI constants and divides by wavelength, gain, and two correction factors for crosstalk and afterpulsing.

• R: Responsivity in amperes per watt (A/W).
• h: Planck constant, 6.62607015e-34 J*s (NIST CODATA 2018).
• c: Speed of light in vacuum, 299,792,458 m/s (NIST CODATA 2018).
• e: Elementary charge, 1.602176634e-19 C (NIST CODATA 2018).
• lambda_m: Incident wavelength in meters, converted from nanometers.
• G: SiPM gain, the number of charge carriers per detected photon.
• P_XT: Crosstalk probability as a fraction, the share of avalanches that trigger a neighboring microcell.
• P_AP: Afterpulsing probability as a fraction, the share of avalanches followed by a trapped-carrier release.

The calculator first converts the wavelength from nanometers to meters because the SI form of the PDE expression uses meters in the denominator. It also turns the crosstalk and afterpulsing percentages into fractions before applying the (1 + P_XT)(1 + P_AP) correction. When the wavelength or gain is zero, or the responsivity is empty, the calculator returns zero PDE and zero photon energy.

According to Omni Calculator PDE SiPM reference, photon detection efficiency is given by PDE = (R h c) / (e lambda G (1 + P_XT) (1 + P_AP)), with a worked example of 35.48% for G=1e6, P_XT=20%, P_AP=4%, lambda=420 nm, and R=150,000 A/W.

For photon-energy and wavelength work that the PDE SiPM calculator depends on, Bragg's Law Calculator handles the diffraction side of the same optical detector course.

Five ideas keep the PDE expression on solid ground. They separate the sensor from the photon, the gain from the crosstalk, and the optical power from the avalanche charge.

The three SI constants in the formula are fixed in the 2019 SI, so the calculator can keep the same high-precision values for any SiPM. Photon energy in electron volts is a useful sanity check: at 420 nm it is roughly 2.95 eV, which matches the silicon bandgap behavior that determines where SiPM PDE starts to roll off.

When the same photon energy is needed for a discrete atomic transition instead of a SiPM avalanche, Bohr Model Calculator uses the same Planck constant and elementary charge.

Enter the five SiPM parameters in any order. The PDE percentage, photon energy, and numerator/denominator update on every keystroke.

1. 1 Enter the responsivity: Start with the responsivity from the device datasheet or your own current-versus-power measurement, in amperes per watt. The default of 150,000 A/W matches the Omni reference example.
2. 2 Set the wavelength: Type the incident wavelength in nanometers. Values between 400 nm and 900 nm are typical, and the photon-energy readout in electron volts confirms the choice.
3. 3 Set the SiPM gain: Use the gain listed in the datasheet, usually 1e5 to 1e7. A higher gain inflates the denominator and tends to lower PDE for the same responsivity.
4. 4 Add crosstalk and afterpulsing: Enter the two noise probabilities as percentages. The calculator converts them to fractions and multiplies the denominator by (1 + P_XT)(1 + P_AP).
5. 5 Read the PDE percentage: The primary result shows PDE as a percentage rounded to two decimal places. The supporting rows show photon energy, the numerator R*h*c, and the denominator e*lambda*G*(1 + P_XT)*(1 + P_AP).

A teaching lab wants to check whether a SiPM still detects more than 30% of photons at 550 nm. With G=2.5e6, P_XT=10%, P_AP=2%, and R=300,000 A/W, the calculator reports 24.11% PDE, the number to compare with the published curve.

When the same responsivity and gain values need to be turned into an output power or energy budget for a downstream amplifier, Work-Energy-Power Calculator handles the energy and power side of the same calculation.

The calculator keeps the standard SiPM PDE expression visible and reproducible, and pairs the result with photon energy so the same form supports detector-physics work.

• • Reproducible PDE percentage: Every input is a datasheet number and the result is closed-form, so two students with the same five parameters always land on the same PDE percentage.
• • Visible noise correction: Crosstalk and afterpulsing are entered as percentages and applied as (1 + P_XT)(1 + P_AP). The supporting numerator and denominator rows make the effect of each noise term visible.
• • Direct photon-energy readout: Photon energy in electron volts is printed alongside PDE so the same wavelength is interpreted as a quantum energy that tells a user whether the wavelength is plausible for the SiPM.
• • SI constants locked to NIST: Planck's constant, the speed of light, and the elementary charge use the 2019 SI values, so the calculation matches current datasheets and reference textbooks.
• • Supports wavelength sweeps: The form is fast enough to re-enter a wavelength on every line of a quick table. The PDE percentage can be recorded at 400, 450, 500, 550 nm to sketch the response curve by hand.

The PDE SiPM calculator is meant for a single SiPM at a time. It is not a replacement for a SPICE model or a vendor PDE curve, but it is a quick check between a published value and the numbers on a lab datasheet.

When the same SiPM is illuminated by a thermal source rather than a laser or scintillator, Blackbody Radiation Calculator returns the spectral photon flux at the chosen wavelength and temperature.

Five measurement choices change the PDE percentage. They sit on the input side of the formula, and the calculator is transparent about how each one enters the result.

• • The PDE expression is a closed-form model. It does not include dark counts, afterpulsing timing, or correlated noise from temperature changes, all of which matter in a full SiPM system design.
• • The constants are fixed in the 2019 SI. Older textbooks may use slightly different values for the elementary charge or Planck's constant, and a calculation that mixes conventions should be checked against the same SI definition.

The calculator is designed for a single SiPM at a single wavelength. Comparing two devices means entering each one's parameters separately, and the PDE expression assumes the SiPM is in the linear regime, so heavy pile-up is outside the formula.

According to NIST CODATA 2018 fundamental constants, Planck's constant is 6.62607015e-34 J*s, the speed of light is 299,792,458 m/s, and the elementary charge is 1.602176634e-19 C, all exact in the 2019 SI.

When the photon energy for the chosen wavelength is set against a Compton recoil problem instead of a SiPM avalanche, Compton Scattering Calculator keeps the same Planck constant and elementary charge in the expression.