The statistical behavior of silicon-based single-photon-avalanche-diodes (SPADs) is investigated by using self-consistent 3-D Monte Carlo simulations. The coupling of Poisson and Boltzmann transport equations allows us to go beyond the analysis of avalanche breakdown and its timing and to extend the investigation to the quenching of the photodetector circuit. We find out that the quenching of SPADs is probabilistic and strongly depends on the surrounding circuit, in particular on the so-called quenching resistance. Independently of the SPAD deadtime, it appears that the extinction time needed to suppress any avalanche event may vary over a very large range.
