# Photon Detection Efficiency Calculator (SiPM)

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 application 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.

## 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 photon detection efficiency formula:

`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`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.

## 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 appropriate fields, and you'll find that `PDE = 35.48 %`

. Isn't that simple with the photon detection efficiency calculator?

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