Avalanche buildup and propagation effects on photon-timing jitter in Si-SPAD with non-uniform electric field

Improving SPAD performances, such as dark count rate and quantum efficiency, without degrading the photontiming jitter is a challenging task that requires a clear understanding of the physical mechanisms involved. In this paper we investigate the contribution of the avalanche buildup statistics and the lateral avalanche propagation to the photon-timing jitter in silicon SPAD devices. Recent works on the buildup statistics focused on the uniform electric field case, however these results can not be applied to Si SPAD devices in which field profile is far from constant. We developed a 1-D Monte Carlo (MC) simulator using the real non-uniform field profiles derived from Secondary Ion Mass Spectroscopy (SIMS) measurements. Local and non-local models for impact ionization phenomena were considered. The obtained results, in particular the mean multiplication rate and jitter of the buildup filament, allowed us to simulate the statistical spread of the avalanche current on the device active area. We included space charge effects and a detailed lumped model for the external electronics and parasitics. We found that, in agreement with some experimental evidences, the avalanche buildup contribution to the total timing jitter is non-negligible in our devices. Moreover the lateral propagation gives an additional contribution that can explain the increasing trend of the photon-timing jitter with the comparator threshold.