Improved Stochastic SPAD Quenching Model Including Build-Up Field Effect

We present an improved stochastic model for simulating avalanche quenching in Single-Photon Avalanche Diodes (SPADs), incorporating the build-up field effect caused by space-charge accumulation during avalanche events. Built upon a one-dimensional Monte Carlo framework, our model introduces a correction term that accounts for the transient electric field induced by the charge dipole, derived from self-consistent Advection-Diffusion Monte Carlo (ADMC) simulations. This hybrid approach preserves the computational efficiency of fast stochastic methods while capturing key physical effects often neglected in simplified models. The inclusion of the build-up field is shown to impact significantly the simulated voltage and current transients, enabling more accurate prediction of quenching behavior, especially in cases of delayed or failed quenching. Comparison with full ADMC simulations shows strong agreement, validating the accuracy and relevance of the correction scheme. The proposed model provides a practical and scalable solution for SPAD simulation and design, particularly in applications requiring precise timing and high-frequency operation.