Modeling Negative Feedback in Single Photon Avalanche Diodes

Recently, considerable attention has been placed upon exploiting the negative-feedback effect in accelerating the quenching time of the avalanche current in passively quenched single-photon avalanche-diode (SPAD) circuits. Reducing the quenching time results in a reduction in the total charge generated in the SPAD, thereby reducing the number of trapped carries; this, in turn, can lead to improved after-pulsing characteristics. 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 recent analytical and Monte-Carlo based models for the quenching time. In addition, results on the statistics of the quenching time and the avalanche pulse duration of SPADs with arbitrary time-variant field across the multiplication region are presented. The calculations of the statistics of the avalanche pulse duration use the dead-space multiplication theory (DSMT) to determine the probability of the avalanche pulse to quench by time t after the instant s at which the electron-hole pair that triggers the avalanche was created. In the analytical and Monte-Carlo based models for the quenching time, the dynamic negative feedback, which is due to the dynamic voltage drop across the load resistor, is taken into account. In addition, in the Monte-Carlo simulations the stochastic nature of the avalanche current is also considered.