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A new method to reliably simulate the PDE and jitter tail for realistic three-dimensional SPAD devices is presented. The simulation method is based on the use of electric field lines to mimic the carriers’ trajectories, and on one-dimensional models for avalanche breakdown probability and charges transport. This approach allows treating a three-dimensional problem as several one-dimensional problems along each field line. The original approach is applied to the McIntyre model for avalanche breakdown probability to calculate PDE, but also for jitter prediction using a dedicated advection-diffusion model. The results obtained numerically are compared with an extensive series of measurements and show a good agreement on a wide variety of device designs.

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.