Power law temporal dependence of InGaAs/InP SPAD afterpulsing

Abstract

The characterization and analysis of afterpulsing behavior in InGaAs/InP single photon avalanche diodes (SPADs) is reported for gating frequencies between 10 and 50 MHz. Gating in this frequency range was accomplished using a matched delay line technique to achieve parasitic transient cancellation, and FPGA-based data acquisition firmware was implemented to provide an efficient, flexible multiple-gate sequencing methodology for obtaining the dependence of afterpulse probability P ap on hold-off time T ho . We show that the detrapping times extracted from the canonical exponential fitting of P ap (T ho ) have no physical significance, and we propose an alternative description of the measured data, which is accurately fit with the simple power law behavior P ap / T À ho with $ 1.2 AE 0.2. We discuss the physical implications of this functional form, including what it may indicate about trap defect distributions and other possible origins of this power law behavior.

Single-Photon Detectors for Infrared Wavelengths in the Range 1–1.7 μm

“…There has been a significant quantity of work focused on the study of the afterpulsing phenomenon, and there have been many advances in understanding and reducing the effect [32]. It has been reported that there is evidence that the traps responsible for afterpulsing can be found in the InP layers [24] and focused research into the elimination of these traps will lead to a reduction in dark count rates and a [24].…”

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

“…(1) having 5 independent parameters. This excellent fitting result is shown in Fig.3, where it is compared to another simple afterpulsing model: the power law, suggested recently for the description of afterpulse distribution in InGaAs/InP SPADs [9] p…”

“…It should be noted that the relation Eq. (4) was explored by Itzler and co-workers [9] among other test densities for fitting the afterpulse distribution in InGaAs/InP SPADs [9] and showed the results almost as good as the power law. In contrast, we came to Eq.…”

“…We have supplemented the power law of Ref. [9] by the dark count rate v, important for the description of long waiting times. For the power law the values of the statistics are χ 2 /χ 2 crit = 11.5 and 1 − R 2 = 0.006, which is much worse than that for the 'hyperbolic sinc' distribution.…”

“…Though these imperfections cannot nowadays be overcome completely, in many applications, especially in ones related to security, like quantum cryptography and quantum random number generators, it is sufficient to provide a precise quantitative characterisation of the imperfections, thus enabling the users to distinguish the regular non-ideal detector operation from an intrusion of a malevolent adversary. And though at present the quantum efficiency, deadtime and dark count rate of SPADs can be measured with acceptable precision and are typically included into the detector specifications by the manufacturer, the situation with afterpulses is far less optimistic, notwithstanding considerable efforts in this area [4,5,6,7,8,9,10,11,12]. In particular the exact shape of the distribution function for the apterpulse waiting time is not generally known and the methods for its precise characterisation are still in the process of development.…”