An accurate circuit model of Ge/Si single photon avalanche diode

Ge/Si single-photon avalanche diodes (SPADs) have benefits of low after-pulsing probability, low-cost and compatibility with CMOS electronics compared to InGaAs/InP counterpart, thus presenting great potentials for imaging and optical quantum applications in short-wave infrared (SWIR). In this work, an equivalent circuit model mimicking the behavior of pseudo-planar Ge/Si SPAD is constructed to provide accurate electronic information for the co-design of front-end circuit. The DC properties are modelled by nonlinear resistors, voltagecontrolled switches and voltage sources, and the AC characteristics are emulated by junction and stray capacitances. To accurately evaluate the statistical behavior, thermal excitation and trap-assisted tunneling are incorporated in the built SPAD circuit models, where three-level traps are adopted to effectively fit the afterpulsing probability. The key model parameters such as electric field profile, breakdown voltage and avalanche triggering probability, are extracted from 2D device simulation. The developed Ge/Si SPAD circuit model implemented in Verilog-A hardware description language (HDL) with a gated passive quenching/reset architecture is validated by circuit simulation platform. The simulation results are in good agreement with the previously reported measurement data, demonstrating the effectiveness and accuracy of our Ge/Si SPAD circuit model.