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First order statistic of afterpulsing and crosstalk events in SiPMs

Sergey Vinogradov

TL;DR

This work addresses the timing distribution of the first detected event after a primary avalanche in SiPMs, where delayed crosstalk and afterpulsing compete with dark counts. It introduces an order-statistic framework in which a random number of Poisson-distributed seeds drive correlated events, yielding closed-form expressions for the first-arrival distribution, such as $F_{\min}(t) = 1 - \exp(- \mu F_C(t))$ and $f_{\min}(t) = \mu f_C(t) \exp(- \mu F_C(t))$, and a total-intensity formulation $I_{\rm sum}(t)$ with $N_{\rm sum}(t) = \int_0^t I_{\rm sum}(t') dt'$. The approach unifies prompt and delayed crosstalk with afterpulsing and dark counts, enabling extraction of timing information for delayed correlated events. It clarifies how the distribution sharpens as the seed count grows and provides a consistent Poisson-based framework, which is particularly relevant for radiation-damaged SiPMs where multiple seeds are plausible.

Abstract

This paper briefly presents an order statistic approach to the time distribution of the first detected event after a primary avalanche breakdown from a mixture of correlated and dark counting processes. The well-known order statistic method, commonly used to describe the time resolution of scintillation detectors, is applied to the arrival times of correlated events. The established model of crosstalk as a branching Poisson process is extended to afterpulsing, and correlated events are considered starting from their seeds -- free (de-trapped or diffused) charge carriers capable of triggering secondary avalanche breakdowns. The proposed approach enables the extraction of timing information for delayed crosstalk and afterpulsing events mixed with dark counts and predicts that the distribution of the first arrival time narrows as the number of seeds increases, corresponding to a higher probability of correlated events.

First order statistic of afterpulsing and crosstalk events in SiPMs

TL;DR

This work addresses the timing distribution of the first detected event after a primary avalanche in SiPMs, where delayed crosstalk and afterpulsing compete with dark counts. It introduces an order-statistic framework in which a random number of Poisson-distributed seeds drive correlated events, yielding closed-form expressions for the first-arrival distribution, such as and , and a total-intensity formulation with . The approach unifies prompt and delayed crosstalk with afterpulsing and dark counts, enabling extraction of timing information for delayed correlated events. It clarifies how the distribution sharpens as the seed count grows and provides a consistent Poisson-based framework, which is particularly relevant for radiation-damaged SiPMs where multiple seeds are plausible.

Abstract

This paper briefly presents an order statistic approach to the time distribution of the first detected event after a primary avalanche breakdown from a mixture of correlated and dark counting processes. The well-known order statistic method, commonly used to describe the time resolution of scintillation detectors, is applied to the arrival times of correlated events. The established model of crosstalk as a branching Poisson process is extended to afterpulsing, and correlated events are considered starting from their seeds -- free (de-trapped or diffused) charge carriers capable of triggering secondary avalanche breakdowns. The proposed approach enables the extraction of timing information for delayed crosstalk and afterpulsing events mixed with dark counts and predicts that the distribution of the first arrival time narrows as the number of seeds increases, corresponding to a higher probability of correlated events.

Paper Structure

This paper contains 4 sections, 12 equations, 2 figures.

Table of Contents

  1. Introduction
  2. First order statistic of correlated and dark events
  3. Discussion
  4. Conclusion

Figures (2)

  • Figure 1: Cumulative distribution function (CDF) of the arrival times of the first correlated event from the Poisson branching process (Eq. (\ref{['C6']})) and a single correlated event from a geometric chain process (Eq. (\ref{['C4']})). The Poissonian means $\mu$ are set to equalize the probabilities $p$ via Eq. (\ref{['InfP']}), with an exponential time constant $\tau = 10$ ns.
  • Figure 2: Probability density function (PDF) of the arrival times of the first correlated event from the Poisson branching process (Eq. (\ref{['C5']})) and a single correlated event from a geometric chain process (Eq. (\ref{['C3']})). The Poissonian means $\mu$ are set to equalize the probabilities $p$ via Eq. (\ref{['InfP']}), with an exponential time constant $\tau = 10$ ns.