Characteristics of InGaAs/InP Single-Photon Avalanche Detectors by WOORIRO (Korea)
Single-photon detectors (SPD) are increasingly used in such areas as quantum key distribution (QKD) [1, 2], positron emission tomography , optical reflectometry , and biomedical research . Currently, various devices and methods for detecting single photons are known, for example, photomultipliers, single photon avalanche photodiodes (SPAD) , detectors based on the sum-frequency generation (up-conversion) , superconducting thin-film nanostructures (SSPD)  and SPD based on quantum dots and semiconductor defects . The given classes of devices differ in design features, in the spectral range of sensitivity, in quantum efficiency and in the ability to distinguish single photons.
Recently, extensive and high-speed QKD systems have stimulated the development of high-speed single-photon detectors of the near IR range. For use in the field of quantum cryptography, SPD must have high detection efficiency, high signal-to-noise ratio, low dead time, low jitter and the ability to distinguish the number of photons is desirable as well . Suitable candidates are superconducting single-photon detectors SSPD, detectors based on up-conversion and single-photon APDs. However, the use of SSPD requires cryogenic temperatures (4K), and detectors based on up-conversion have spurious non-linear noise.
Main characteristics for two models of single-photon APDs: WPACBGMACNN, produced by Wooriro (Korea) and PGA‑016u‑1550TFZ by Princeton Lightwave (USA) were measured in this work. First, their quantum efficiencies were obtained for different bias voltages, and then the dark count rate and the afterpulsing probability dependence on the quantum efficiency at different temperatures were recorded.
More exactly, the following characteristics were measured at temperatures: t = –40 °C; t = –50 °C; t = –60 °C:
1. Dependences of quantum efficiency on bias voltage;
2. Dependences of the dark count rate on the quantum efficiency;
3. Dependences of the afterpulsing probability on the quantum efficiency for different pulse repetition frequencies.
According to the research results, named SPAD models were compared. The data obtained can be used when choosing the optimal parameters of the SPAD for specific applications.
The traditional approach to measuring the characteristics of single-photon APDs is the substitution method, based on a comparison of the readings of the reference device with the test device. In the case of the study and calibration of single-photon detectors, laser radiation power is measured by a calibrated photo detector and then attenuated by a calibrated attenuator to the level of single photons, which are recorded by the avalanche photodiode under test.
The measurement scheme is presented in Fig. 1. Its main elements are: a continuous-wave DFB laser at a wavelength of 1550 nm (Thorlabs S1FC1550PM), a precise attenuator with 0.07–60 dB attenuation range (Exfo FVA‑3100) and the self-made SPAD registration module. A detailed description and the principle of operation of the single-photon registration module is presented in article .
The laser radiation power was chosen in such a way that over the time interval equal to the duration of the time gate τg, an average number of photons µ = 0.1 would fall on the SPAD.
The duration of the time gate during all measurements was τg = 1 ns, therefore, the required power at sensitive area of the SPAD should be:
where µ is the average number of photons entering the time gate; hν is the energy of a single photon. The attenuator was adjusted to the maximum attenuation of radiation, i. e., 60 dB, therefore, the laser output power should be:
Thus, the APD sensitive area is illuminated with a continuous laser radiation of 0.1 photons / ns.
The single-photon registration module allows one to control the following parameters (in brackets the values set for the experiment):
• SPAD bias voltage Ubias, V;
• time gate duration (τg = 1 ns);
• SPAD temperature (–40 °C, –50 °C, –60 °C);
• dead time duration (10 ns);
• gating pulses frequency;
• discriminator response threshold (70.2 mV).
The SPAD operates in a gating mode as described in  with adjustable gate repetition frequency. The only photons that have arrived at the time gate could be registered. The gating pulses are not fed to the SPAD for 10 ns (dead time) after photon or dark count registration (SPAD click).
MEASUREMENT OF DETECTION EFFICIENCY AND QUANTUM EFFICIENCY
Detection efficiency is the ratio of the number of recorded events to the number of incident photons. Detection efficiency can be measured by sending single photons with a known repetition rate and measuring the number of responses of the recording module. In this work, we study the SPAD modules that are not able to distinguish the number of photons in a pulse, i. e., they react in the same way by one click on any number of incident photons other than zero. Since the registration process of detector clicks refers to Bernoulli’s tests, and the statistics of the distribution of photons in a pulse is described by the Poisson distribution, according to , the random photon detection process is also described by the Poisson distribution. In this case, the probability of detecting a photon by SPAD is related to quantum efficiency by the following formula:
where µ is the average number of photons per pulse, η is the quantum efficiency of the SPAD.
Thus, measuring the detector response (click) frequency pi, which, with a large number of pulses sent, tends to the probability of detection, it is possible to calculate quantum efficiency using formula (3).
When measuring the probability of detection, it is necessary to consider the contribution of dark noise and the afterpulsing effect. It is convenient to characterize these undesired signals by the probability of the dark count pdark and the probability of the occurrence of the afterpulsing pap, respectively. All three values are related by the expression:
where pi is the current count of the photodetector (the ratio of the number of operations to the number of gate pulses).
Assuming that at low frequencies the probability of afterpulsing tends to zero  (pap|10kHz≈ 0), and quantum efficiency does not depend on the frequency of gating pulses, the probability of detection can be determined by knowing the SPAD counting and the probability of dark count at certain low frequency. For this reason, to measure the quantum efficiency depending on the bias voltage, the frequency of the gating pulses was set to 10 kHz and the detection probability was calculated using the formula:
pdet= pi|10kHz − pdark |10кГц , (5)
where is the photodetector click frequency at a gate pulse frequency f, count / pulse. The results of quantum efficiency calculations are presented in Fig. 2 and Fig. 3.
THE DARK COUNT RATE MEASURING
The dark count rate (DCR) is measured by recording the number of detector clicks, in the absence of a photon flux. Therefore, for these measurements, the optical input of the single-photon registration module was closed from the incident radiation with a black plug.
While DCR measuring the frequency of gating pulses was set to 1 MHz in order to improve the statistics and increase the measurement accuracy. As will be shown later, the afterpulsing influence on DCR value is negligible.
As could be seen from the graphs presented in Fig. 4, SPAD dark count rates produced by Wooriro and Princeton Lightwave SPADs at t = –50 °C are comparable and do not exceed 3.2 · 10–6 count / pulse.
MEASUREMENT OF AFTERPULSING PROBABILITY
As noted earlier, the afterpulsing effect is characterized by the probability pap. This value is related to the current SPAD counting at the frequency f, , the detection probability pdet (see formula 3) and the dark count probability pdark (see formula 4) and can be expressed therefrom as follows:
The DCR probability was measured earlier, therefore, in order to measure the afterpulsing probability depending on the duration of the time interval after the APD click, it is necessary to measure the counting of single-photon APD at different gate pulses repetition frequencies. We measured the counting at the following frequencies: 0.1, 1.0, 2.5, 5.0, 6.25, 7.5 and 10 MHz. The results for WPACBGMACNN SPAD by Wooriro at different temperatures are shown in Fig. 5.
On the basis of the characteristics shown in Fig. 5, it is possible to determine the optimal operating parameters of single-photon APDs for specific applications. When a single-photon photodetector is used in QKD systems, the DCR value is the most important because it determines the error in the quantum key and eventually the communication fiber line length.
Examples of optimal parameters of a single-photon APD for use in quantum key distribution systems are: dark noise level 2 · 10–6 with quantum efficiency 20%. These parameters correspond to the following conditions for WPACBGMACNN SPAD: temperature is –50 °C, bias voltage is 68.8 V. In this case, the probability of afterpulsing is 8% at a gate frequency of 10 MHz and less than 1% at a frequency of 1 MHz.
It is also worth noting that the SPAD by Wooriro, tested in this paper, is not inferior to the widely used single-photon detectors by Princeton Lightwave in terms of the dark count probability.
In this work, the characteristics of single-photon avalanche photodiode by Wooriro were studied. The results allow us to conclude about the applicability of these detectors in various areas, in particular, in the systems of quantum key distribution. According to the characteristics given in the article, it is possible to choose the working parameters of the SPAD to meet various conditions. The dark count rate and quantum efficiency comparison of SPAD WPACBGMACNN by Wooriro (Korea) and SPAD PGA‑016u‑1550TFZ by Princeton Lightwave (USA) showed that the tested single-photon detector by Wooriro is not inferior to the commonly known Princeton Lightwave detectors.
The authors are grateful for financial support of the studies in the framework of the project of the Ministry of Education and Science of the Russian Federation (project 03.G25.31.0254), within which a scheme was developed for measuring the SPAD characteristics.
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