A Comprehensive and Accurate Analytical SPAD Model for Circuit Simulation

The single-photon avalanche diode (SPAD) is an attractive photosensor due to its high sensitivity and low dead time. In this paper, a comprehensive, accurate analytical SPAD circuit simulation model is proposed and implemented in Verilog-A hardware description language. It shows great application universality and is fully compatible with mainstream commercial circuit simulators. This model incorporates all important operating features of the SPAD. Most importantly, to the best of our knowledge, it is the first time that the band-to-band tunneling mechanism and the temporal dependence of after-pulsing probability are included in an SPAD circuit simulation model. The parameter extraction processes from interavalanche time measurement of a free-running SPAD device are discussed. The simulation results indicate that the proposed model works well. In addition, the primary dark counts from the model are validated against the measurement results. A maximum relative error of 8.7% is observed at 20 °C with an excess voltage of 0.5 V. The accuracy of this paper can be greatly improved by using more accurate physical parameters available from the SPAD fabrication vendor.