SPICE Electrical Models and Simulations of Silicon Photomultipliers

We present and discuss a comprehensive electrical model for Silicon Photomultipliers (SiPMs) based on a microcell able to accurately simulate the avalanche current build-up and the self-quenching of its Single-Photon Avalanche Diode (SPAD) "pixel" with series-connected quenching resistor. The entire SiPM is modeled either as an array of microcells, each one individually triggered by independent incoming photons, or as two macrocells, one with microcells all firing concurrently while the other one with all quiescent microcells; the most suitable approach depends on the light excitation conditions and on the dimension (i.e. number of microcells) of the overall SiPM. We validated both models by studying the behavior of SiPMs in different operating conditions, in order to study the effect of photons pile-up, the deterministic and statistical mismatches between microcells, the impact of the number of firing microcells vs. the total one, and the role of different microcell parameters on the overall SiPM performance. The electrical models were developed in SPICE and can simulate both custom-process and CMOS-compatible SiPMs, with either vertical or horizontal current-flow. The proposed simulation tools can benefit both SiPM users, e.g. for designing the best readout electronics, and SiPM designers, for assessing the impact of each parameter on the overall detection performance and electrical behavior.