# Photon Detection Efficiency Calculator (SiPM)

Created by Dominik Czernia, PhD
Reviewed by Bogna Szyk and Jack Bowater
Last updated: Dec 21, 2022

The photon detection efficiency calculator is designed to minimize the time spent on laborious calculations concerning Silicon Photomultipliers (SiPM). SiPMs are novel silicon detectors that are capable of detecting faint and fast light signals, even at a single photon level. Because of their high gain and quick response, they may find future applications in medical imaging, e.g., Positron Emission Tomography (PET) or Single-Photon Emission Computed Tomography (SPECT). SiPMs are also compact and compatible with magnetic resonance devices.

We have prepared a tool to quickly switch between a photon's energy, frequency, and wavelength. Check the photon energy calculator if you need to analyze this quantum of the electromagnetic field!

## Photon detection efficiency formula

The photon detection efficiency PDE is a quantity that measures the sensitivity of SiPMs. You can easily calculate it from the responsivity, R, of the sensor - with responsivity being the average photocurrent produced per unit of optical power. To make the conversion from R to PDE, you can use the following :

PDE = R * h * c / [e * λ * G * (1 + P_XT) * (1 + P_AP)],

where:

• PDE is the photon detection efficiency;
• R is the responsivity, expressed in amps per Watt A/W;
• h = 6.626 * 10⁻³⁴ m²*kg/s is Planck's constant;
• c = 2.998 * 10⁸ m/s is the speed of light;
• e = 1.602 * 10⁻¹⁹ C is elementary charge;
• λ is the wavelength of the incident light;
• G is the gain, i.e., the amount of charge created for each detected photon;
• P_XT is the crosstalk probability; and
• P_AP is the afterpulsing probability.

To accurately determine PDE, you should always take into account contributions due to optical crosstalk and afterpulsing. The former occurs when a single incident photon generates signals equivalent to two or more photons. The latter happens when some carriers become trapped in defects in the silicon. After some time, up to several nanoseconds, they are released, creating an additional signal. You can determine the probability of both phenomena separately by taking the appropriate measurements.

The intrinsic carrier concentration calculator might be a helpful tool if you need to investigate this physical quantity. Intrinsic carrier concentration is a crucial parameter to consider for photoactive materials.

## Photon detection efficiency calculator - an example

This photon detection efficiency calculator is straightforward to use and will calculate any missing variable if all of the others are provided. Simply enter any five quantities, and the sixth will be automatically estimated. For example, let's find out what the PDE of a SiPM with the following parameters will be:

• gain G = 1,000,000
• crosstalk probability P_XT = 20 %
• afterpulsing probability P_AP = 4 %

Let the incident light's wavelength be λ = 420 nm, and the responsivity R = 150,000. What is the photon detection efficiency? Fill in the appropriate fields, and you'll find that PDE = 35.48 %. Isn't that simple with the photon detection efficiency calculator?

Are you interested in electronics? Check out our other exciting calculators! Visit the Shockley diode calculator to analyze the electrical properties of a real diode or the drift velocity calculator to find out how fast electricity travels.

Dominik Czernia, PhD
Gain (G)
Afterpulsing probability
%
Crosstalk probability
%
Wavelength (λ)
Å
Responsivity (R)
A/W
Photon Detection Efficiency (PDE)
%
People also viewed…

### Chilled drink

With the chilled drink calculator you can quickly check how long you need to keep your drink in the fridge or another cold place to have it at its optimal temperature. You can follow how the temperature changes with time with our interactive graph.

### Gay-Lussacs's law

With Gay-Lussac's law calculator, you can quickly work out the pressure and temperature values in an isochoric process.

### Mass to density

The mass to density calculator will help you calculate the density of an object from its weight if you know its volume.

### Snowman

The perfect snowman calculator uses math & science rules to help you design the snowman of your dreams! 