Free Photon Detection Efficiency Calculator (SiPM)

Understanding Photon Detection Efficiency (PDE) for SiPMs

Silicon Photomultipliers (SiPMs) are solid-state detectors prized for their ability to sense extremely weak and fast optical signals, down to the single-photon level. Their high gain and rapid response make them promising for medical imaging technologies such as Positron Emission Tomography (PET) and Single-Photon Emission Computed Tomography (SPECT), where they also offer synergy with magnetic resonance imaging (MRI) systems. To evaluate the performance of a SiPM, the photon detection efficiency (PDE)—the probability that an incident photon triggers a measurable output—serves as the fundamental metric. This Photon Detection Efficiency Calculator (often called a SiPM PDE Calculator) converts the sensor’s responsivity into PDE while incorporating essential corrections for secondary effects.

PDE Formula from Responsivity

The transformation from responsivity ($R$, in A/W) to PDE depends on the energy of the incident photon, the internal avalanche gain, and the likelihood of spurious events. The SiPM Responsivity PDE Converter inside this tool applies the following relation:

$$\text{PDE} = \frac{R \cdot \dfrac{h c}{\lambda}}{e \cdot G} \cdot \frac{1}{(1+P_{\text{XT}})(1+P_{\text{AP}})}$$

where:

Symbol	Meaning	Typical value / unit
$h$	Planck’s constant	$6.626 \times 10^{-34}\ \text{m}^2\!\cdot\!\text{kg/s}$
$c$	Speed of light in vacuum	$2.998 \times 10^{8}\ \text{m/s}$
$e$	Elementary charge	$1.602 \times 10^{-19}\ \text{C}$
$\lambda$	Wavelength of the incident light	meters (nm often used)
$G$	Gain (number of charge carriers generated per detected photon)	dimensionless (e.g., $10^6$)
$P_{\text{XT}}$	Optical crosstalk probability	fraction (e.g., 0.20)
$P_{\text{AP}}$	Afterpulsing probability	fraction (e.g., 0.04)

Hence, the photon detection efficiency formula above shows that uncorrected responsivity tends to overestimate PDE because crosstalk and afterpulsing add extra signal.

Optical Crosstalk and Afterpulsing Explained

Optical crosstalk happens when a primary photon excites an avalanche whose secondary photons escape the cell and trigger neighboring pixels, mimicking the arrival of additional photons. Afterpulsing originates from charge carriers trapped in silicon lattice defects; when released nanoseconds later, they generate a delayed fake pulse. Both phenomena artificially raise the measured photocurrent, leading to a biased PDE if not accounted for. The factors $(1+P_{\text{XT}})$ and $(1+P_{\text{AP}})$ in the denominator compensate for this overcount, giving a more realistic silicon photomultiplier calculator result.

Worked Example

Imagine a SiPM that possesses the following characteristics:

• Gain $G = 1{,}000{,}000$
• Crosstalk probability $P_{\text{XT}} = 20\%$ (0.20)
• Afterpulsing probability $P_{\text{AP}} = 4\%$ (0.04)
• Incident light wavelength $\lambda = 420\ \text{nm}$
• Responsivity $R = 150{,}000\ \text{A/W}$

Enter these five numbers into the Photon Detection Efficiency Calculator, and the tool instantly computes a PDE of 35.48%. This example demonstrates how the Responsivity to PDE conversion works seamlessly, saving time and avoiding manual error.

Versatility of the Tool

The calculator acts as a two‑way SiPM PDE Calculator: you can provide any five of the six input fields (R, G, λ, $P_{\text{XT}}$, $P_{\text{AP}}$, and the target PDE) to obtain the missing value. Whether you are optimizing a PET detector, comparing SiPM data sheets, or performing laboratory characterization, this silicon photomultiplier calculator streamlines the evaluation of PDE directly from responsivity measurements.