Statistics of self-quenching time in single photon avalanche diodes

Single-photon avalanche diodes (SPADs) convert a single photo-excitation event, resulting from the absorption of a photon, into a measurable self-sustaining current in the external circuit consisting of a DC-bias source and a series load resistor. This avalanche current is produced with a certain probability that depends upon the bias voltage and the SPADpsilas structure. The mechanism for generating the self-sustaining avalanche current is the cascade of impact ionizations in the multiplication region of the SPAD, which occurs at or beyond the condition of avalanche breakdown. The breakdown condition corresponds to the smallest electric field (or bias) at which the multiplication factor of an avalanche photodiode becomes infinite, on average; equivalently, it is the smallest electric field at which the breakdown probability is nonzero. In practice, a SPAD is biased slightly above the breakdown voltage to maximize the probability that avalanche breakdown occurs without introducing too many dark carriers (that may result from band-to-band tunneling, for example) that can result in false counts.