Behavioral model of silicon photo-multipliers suitable for transistor-level circuit simulation

Silicon Photomultipliers (SiPMs) are photo-electronic devices able to detect single photons and permit the measurement of weak optical signals. Single-photon detection is accomplished through high-performance read-out front-end electronics whose design needs accurate modeling of the photomultiplier device. In the past, a useful model was developed, but it is limited to the device electrical characteristic and its parameter extraction procedure requires several measurement steps. A new silicon photomultiplier model is proposed in this paper. It exploits the Verilog-a behavioral language and is appropriate to transistor-level circuit simulations. The photon detection of a single cell is modeled using the traditional electrical model. A statistical model is included to describe the silicon photomultiplier noise caused by dark-count or after-pulsing effects. The paper also includes a procedure for the extraction of the model parameters through measurements. The Verilog-a model and the extraction procedure are validated by comparing simulations to experimental results.