Model for passive quenching of SPADs

Infrared single-photon avalanche photodiodes (SPADs) are used in a number of sensing applications such as satellite laser ranging, deep-space laser communication, time-resolved photon counting, quantum key distribution and quantum cryptography. A passively quenched SPAD circuit consists of a DC source connected to the SPAD, to provide the reverse bias, and a series load resistor. Upon a photon-generated electron-hole pair triggering an avalanche breakdown, current through the diode and the load resistor rises quickly reaching a steady state value, after which it can collapse (quench) at a stochastic time. In this paper we review three recent analytical and Monte-Carlo based models for the quenching time. In the first model, the applied bias after the trigger of an avalanche is assumed to be constant at the breakdown bias while the avalanche current is allowed to be stochastic. In the second model, the dynamic negative feedback, which is due to the dynamic voltage drop across the load resistor, is taken into account, albeit without considering the stochastic fluctuations in the avalanche pulse. In the third model, Monte-Carlo simulation is used to generate impact ionizations with the inclusion of the effects of negative feedback. The latter model is based on simulating the impact ionizations inside the multiplication region according to a dynamic bias voltage that is a function of the avalanche current it indices. In particular, it uses the time evolution of the bias across the diode to set the coefficients for impact ionization. As such, this latter model includes both the negative feedback and the stochastic nature of the avalanche current.