# Photon Detection Efficiency Calculator (SipM), Formula, Calculation

### Photon Detection Efficiency Calculator (SipM):

The Photon Detection Efficiency Calculator is designed to reduce time spent on difficult calculations related to silicon photomultipliers (SiPM).

SiPMs are innovative silicon detectors, They are capable of detecting faint and fast light signals even at the single photon level. Due to their high gain and fast response, they may find future application in medical imaging, eg, positron emission tomography (PET) or single-photon emission computed tomography (SPECT). SiPMs are compact and compatible with magnetic resonance devices.

This free calculator is developed to quickly calculate the value of Silicon Photomultipliers (SiPM) without difficulty.

### Photon Detection Efficiency Formula:

Photon Detection Efficiency formula PDE (p) in percent is equal to the  responsivity R(A/W) in Ampere per watts and multiply the plank’s constant h(m2 kg/s) in meter2 per kilogram per second and multiply the speed of light c(m/s) in meter per second and divided by the elementary charge e(C) in coulomb’s and multiply the wavelength of the incident light λ(m) in meter and multiply the the gain which is the amount of charge created for each detected photon G and multiply the one addition the crosstalk probability P_XT(p) in percent and multiply the one addition the afterpulsing probability p_AP(p) in percent.Hence Photon Detection Efficiency formula can be written as

PDE (p)= (R(A/W)*h(m2 kg/s)*c(m/s) ) / [(e(C) * λ(m) *G ) (1+P_XT(p)) (1+p_AP(p))]

Where

PDE=is the photon detection efficiency

H=is the plank’s constant and its value is 6.626*10-34 m2 kg/s

C=is the speed of light, its value is 2.998 *108 m/s

E=is the elementary charge and e=1.602 *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

### Example:1

Calculate the PDE of a SipM if gain of SipM is 1000000, crosstalk probability is 20%, afterpulsing probability is 4%, wavelength  of  incident light is 0.00000042m m and responsivity  is 15000?

Given that

Gain G =1000000

Crosstalk probability P_XT =20%

Afterpulsing probability P_AP =4%

Wavelength λ =0.00000042m

Responsivity R=150000 A/W

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

PDE = 150000 *6.626 *10-34 *108 / [1.602 *10-19 *0.00000042 *1000000 * (1+20 /100 ) * (1+4 /100)]

PDE =35.48525509550%

### Example:2

Calculate the PDE of a SipM if gain of SipM is 26000, crosstalk probability is 18%, afterpulsing probability is 12%, wavelength  of  incident light is 250 nm and responsivity  is 25000?

Given that

Gain G =25000

Crosstalk probability P_XT =18 %

Afterpulsing probability P_AP = 12%

Wavelength λ =250nm

Responsivity R=26000A/W

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

PDE = 26000 *6.626 *10-34 *2.998 *108 / [ 1.602 *10-19 *250 / (1+e+9 )*25000 * (1+18/100 )* (1+12 /100)]

Photon Detection Efficiency (PDE ) =390.31374%