First-Order Statistic of Afterpulsing and Crosstalk Events in Silicon Photomultipliers

This paper presents an order statistic approach to the time distribution of the first detected event following a primary avalanche pulse, considering a mixture of correlated and primary dark counts. 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 analyzed starting from their initial seeds-free (detrapped or diffused) charge carriers capable of triggering secondary avalanche breakdowns. The proposed approach enables the extraction of true timing information for delayed crosstalk and afterpulsing and predicts a narrowing of the first arrival time distribution as the number of seeds and the probability of correlated events increase.