Analytical models of probability distribution and excess noise factor of Solid State Photomultiplier signals with crosstalk

TL;DR

This paper develops analytical models for the probability distribution and excess noise factor of SSPM signals considering crosstalk as a branching Poisson process, improving understanding of noise characteristics in solid state photomultipliers.

Contribution

It introduces analytical models based on the Borel distribution for SSPM crosstalk and excess noise, advancing beyond Monte Carlo and numerical methods.

Findings

Models agree well with experimental data on dark counts and photon spectra.

The models capture super-linear behavior of crosstalk ENF.

Analytical approach provides insights into SSPM noise processes.

Abstract

Silicon Photomultipliers (SiPM), also so-called Solid State Photomultipliers (SSPM), are based on Geiger mode avalanche breakdown limited by strong negative feedback. SSPM can detect and resolve single photons due to high gain and ultra-low excess noise of avalanche multiplication in this mode. Crosstalk and afterpulsing processes associated with the high gain introduce specific excess noise and deteriorate photon number resolution of the SSPM. Probabilistic features of these processes are widely studied because of its high importance for the SSPM design, characterization, optimization and application, but the process modeling is mostly based on Monte Carlo simulations and numerical methods. In this study, crosstalk is considered to be a branching Poisson process, and analytical models of probability distribution and excess noise factor (ENF) of SSPM signals based on the Borel distribution as an advance on the geometric distribution models are presented and discussed. The models are found to be in a good agreement with the experimental probability distributions for dark counts and a few photon spectrums in a wide range of fired pixels number as well as with observed super-linear behavior of crosstalk ENF.