Afterpulsing model based on the quasi-continuous distribution of deep levels in single-photon avalanche diodes

TL;DR

This paper models afterpulsing in silicon single-photon avalanche diodes using a continuous distribution of deep levels, providing a better fit to experimental data than discrete exponential models.

Contribution

It introduces a novel continuous distribution model for afterpulsing, replacing traditional sum-of-exponentials approaches with a physically meaningful band of deep levels.

Findings

Continuous distribution model fits data well across the entire response range.

Discrete exponential models have dubious physical interpretation.

Deep levels in the detector's active area cause afterpulsing.

Abstract

We have performed a statistical characterization of the effect of afterpulsing in a free-running silicon single-photon detector by measuring the distribution of afterpulse waiting times in response to pulsed illumination and fitting it by a sum of exponentials. We show that a high degree of goodness of fit can be obtained for 5 exponentials, but the physical meaning of estimated characteristic times is dubious. We show that a continuous limit of the sum of exponentials with a uniform density between the limiting times gives excellent fitting results in the full range of the detector response function. This means that in certain detectors the afterpulsing is caused by a continuous band of deep levels in the active area of the photodetector.