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

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.

Comparative study of afterpulsing behavior and models in single photon counting avalanche photo diode detectors

“…Ref. 19 showed that the hyperbolic sinc model was better than the power law model using id100-MMF50 SPAD module from idQuantique, we were able to duplicate those results only with 6 of the 16 detectors we tested.…”

“…We define the total afterpulse probability to be the sum total of the afterpulse probability in each bin of the corrected g (2) histogram for a duration of 900 ns (We chose a value of 900 ns such that we include a significant amount of the afterpulse tail while avoiding any potential effects due to the earliest possible subsequent pulse 1 μ s later. In silicon based SPADs the afterpulse tail dies off some hundred nanoseconds, whereas in InGaAs detectors it can last for several μ s) 18 , 19 . Regardless of the model, in order to obtain a good fit we had to ignore the first two points of the afterpulse tail.…”

“…In an another attempt to create a more physically meaningful model ref. 19 derived the “hyperbolic Sinc model” from the Arrhenius law (once more assuming a continuum of levels), where the afterpulse probability ( P sinc ( t )) is given by: where Δ and γ are both functions of the minimum and maximum energies of the deep levels in which charges may be trapped.…”

Parity-based, bias-free optical quantum random number generation with min-entropy estimation

“…In the photonic scenario just described, bias may arise from sources such as imperfect state preparation with nonequalized amplitudes, a polarizing beam splitter that does not reliably separate H and V polarizations, and imbalanced detectors. Correlations may be caused, for example, by dead-time and afterpulsing effects in the detectors [29,31,32]. In practical implementations, these imperfections often have a significant influence and can be difficult to avoid [6].…”

Advanced Statistical Testing of Quantum Random Number Generators

“…The two main effects in the behavior of our APDs which can introduce undesired correlations in the resulting sequences of bits are called after-pulsing and dead time [22,23]. The first effect, roughly speaking, corresponds to a false detection event due to the residual effects of an avalanche triggered by a previous event, while the dead time is the time period after each event during which the system is not able to record a subsequent incoming optical signal.…”