# Photon Detection Efficiency Calculator (SiPM)

Photon Detection Efficiency Calculator (SiPM) is a handy tool that finds the photon detection efficiency (PDE) easily. This easy to use calculator takes gain, afterpulsing probability, crosstalk probability, wavelength, and responsivity values as inputs and generates PDE as output in a fraction of seconds.

### How to Find Photon Detection Efficiency (PDE)?

Have a look at the detailed step by step process to calculate the photon detection efficiency of SiPM in the following sections. Obtain the steps and follow them carefully to get the result.

- Make a note of the SiPM gain, crosstalk probability, afterpulsing probability, wavelength and responsivity.
- Get the PDE formula and substitute the given values in the formula.
- Perform the required math operations to check the output.

### Photon Detection Efficiency Formula

The photon detection efficiency is a quantity that measures the sensitivity of SiPMs.

The PDE formula is as follows:

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

Where,

PDE is the photon detection efficiency

h is the planck's constant and its value is 6.626 x 10-34 m²kg/s

c is the speed of light, its value is 2.998 x 108 m/s

e is the elementary charge and e = 1.602 x 10-19 C

R is the responsivity

λ is the wavelength of the incident light

G is the gain which is the amount of charge created for each detected photon

P_XT is the crosstalk probability

P_AP is the afterpulsing probability.

This PDE formula can also be used to find the responsivity of the sensor.

**Example**

**Question: Calculate the PDE of a SiPM if gain of SiPM is 100000, crosstalk probability is 10%, afterpulsing probability is 1%, wavelength of incident light is 210 nm and responsivity is 12000?**

**Solution:**

Given that

Gain G = 100000

crosstalk probability P_XT = 10%

Afterpulsing probability P_AP = 1%

Wavelength λ = 210 nm

Responsivity R = 12000

The formula to compute the photon detection efficiency is PDE = (R x h x c)/[e x λ x G(1 + P_XT) (1 + P_AP)]

PDE = (12000 x 6.626 x 10-34 x 2.998 x 108)/[1.602 x 10-19 x 210 x 100000(1 + 10) (1 + 1)]

= 63.77%

Therefore, the photon detection efficiency of SiPM is 63.77%

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### FAQs on Photon Detection Efficiency Calculator (SiPM)

**1. What is photon detection efficiency definition?**

The photon detection efficiency is defined as the ratio of the number of photons discharged microcells to the number of incident photons.

**2. What is meant by SIPM?**

SIPM means Silicon Photomultiplier. It is a solid state photodetector that in response to absorption of photon and generate current pulse having 105 to 106 electrons.

**3. What is the photon detection efficiency formula?**

The formula used to calculate photon detection efficiency is PDE = (R x h x c)/[e x λ x g(1 + P_XT) x (1 + P_AP)].

**4. How is responsivity calculated?**

The simple formula to calculate the responsivity of photon detection efficiency is R = [PDE x λ x G x e(1 + P_AP)(1 + P_XT)]/(h x c x 100%). Substitute the values in the formula to get the responsivity value easily.