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

Abstract

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, voltage-controlled 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 after-pulsing 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.