An analytical solution for McIntyre’s model of avalanche triggering probability for SPAD compact modeling and performance exploration

Single photon avalanche diodes (SPADs) are widely used to monitor fast and weak optical signals. The modeling of two main figures of merit of SPAD, namely the dark count rate (DCR) and the photon detection probability, requires one to calculate the avalanche triggering probability (ATP), usually obtained by numerically solving two transcendental equations (the McIntyre model) as post processing of technology computer-aided design simulations. This paper proposes an analytical alternative to this approach, exploiting an approximation of the impact ionization rates, in principle valid only under high field conditions, but extended to all fields by a simple fitting procedure. The proposed approximated/analytical ATP calculation can be efficient and relevant for SPAD compact modeling that is compatible with a spice-like simulator. As an illustration, a full analytical calculation for DCR based on both ATP and generation terms for a P + N abrupt diode junction is presented.