Analytical models of probability distribution and excess noise factor of solid state photomultiplier signals with crosstalk

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.

Perfomance of Silicon Photomultipliers in photon number and time resolution

“…Branching Poisson model initially was focused on a long-distance crosstalk process when all generations of secondaries have not been affected by a limited number of available (ready-to-be-fired) pixels. As verified in several experiments [10], [13], [14], the probability distribution of the crosstalk process agrees fairly well with the branching Poisson process model. However, there is also an observation of depressed high-order crosstalk probabilities with respect to the Borel prediction [15], probably, because of a short-distance crosstalk effect.…”

“…adjacent to the primary one (4 side-by-side or 8 with extra corner-by-corner ones) [9] -Binomial distribution; 3) Random single chain or sequence of binary counts -Geometric distribution [2], [10]; 4) Branching Poisson process when a primary event, as well as every secondary one, creates the next generation of Poissonian-distributed secondary events [10]- [12]; as shown in [10], this process results in Borel distribution of a total number of events. In case if SIPM detects a light pulse with a Poissonian number of photons when a total number of detected events obeys a compound Poisson distribution combined by the Poisson distribution of primaries and the specific distribution of secondaries pointed above 1)-4).…”

“…Recently, an afterpulsing is simulated as a branching Poisson process assuming a single avalanche creating a Poisson-distributed number of afterpulses, and when iteratively applied to each of the generated afterpulses [12]. ENF of the correlated processes was initially derived in [2] and discussed [3], and then advanced results were presented in [10].…”

Modeling crosstalk and afterpulsing in silicon photomultipliers

“…The error bars of the remaining ratios were determined propagating the uncertainties of the experimental probabilities. The comparison includes two previous analytical models described in [3], where P(k) is assumed to follow a geometric or a Borel distribution. As explained in [1], these two models can be regarded as limit situations of ours.…”

“…4) and were determined from the time-amplitude information of afterpulses with short delay. 3 A Monte Carlo simulation was carried out to describe the timing and relative contributions of the AP-diff and CT-diff effects (bottom plot of Fig. 1).…”