Characterization-Based Modeling of Retriggering and Afterpulsing for Passively Quenched CMOS SPADs

The current trend in the design of systems based on CMOS SPADs is to adopt smaller technological nodes, allowing the co-integration of additional electronics for the implementation of complex digital systems on chip. Due to their simplicity, a way to reduce the area occupied by the integrated electronics is the use of passive quenching circuits (PQCs) instead of active (AQCs) or mixed (MQCs) ones. However, the recharge phase in PQCs is slower, so the device can be retriggered before this phase ends. This paper studies the phenomena of afterpulsing and retriggering, depending on the characteristics of the SPADs and the working conditions. In order to do that, a test chip containing SPADs of different size has been characterized in several operating environments. A mathematical model has been proposed for fitting afterpulsing phenomenon. It is shown that retriggering can be also described in terms of this model, suggesting that it is linked to carriers trapped in the shallow levels of the semiconductor and that should be taken into account when considering the total amount of afterpulsing events.