1. Introduction

The Micius Quantum Science Experimental Satellite is equipped with twelve silicon avalanche photodiode (APD) single-photon detectors [1]. Among them, eight are used for performance monitoring and polarization control of quantum entanglement sources [2], while four are used for ground-to-satellite quantum teleportation experiments [3,4]. These detectors have been subjected to long-term in-orbit monitoring of their dark count performance while supporting quantum science experiments. Additionally, we conducted in-orbit detector high-temperature annealing experiments to explore the in-orbit repair effects of detector radiation damage. Compared to photomultiplier tubes [5,6] and superconducting single-photon detectors, low-cost and compact silicon APD single-photon detectors are particularly suitable for single-photon detection on space platforms [7]. However, due to radiation-induced damage, the dark count rate (DCR) of silicon APD single-photon detectors operating in space increases linearly over time. For example, in NASA's ICESat, APD single-photon detectors are used for single-photon laser radar signal detection, and their dark count performance is affected by irradiation, increasing by approximately 55.5 cps per day [8]. This requires that space silicon APD single-photon detectors not only have high performance features such as detection efficiency, dark count rate, and after-pulsing but also possess radiation hardness.

The Micius quantum science experimental satellite selected Excelitas SLiK APD components, which include a SLiK silicon APD, a dual-stage TEC, and a thermistor, integrated into a TO-56 package. The APD is manufactured by Canada Excelitas and is the same type as the APD inside the single photon counting modules (SPCM) [9]. We have reinforced the temperature control circuit and quenching circuit to adapt to the in-orbit environment. Additionally, to mitigate radiation damage, the operating temperature of the APD is lower than that of the SPCM, while the excess voltage is essentially consistent.In order to suppress the increased rate of the silicon APD single-photon detectors’ dark count caused by space radiation, additional radiation-hardening measures were implemented for the detector, including radiation shielding and lower operating temperature.

Since the detectors were deployed in space, we conducted long-term on-orbit dark count performance monitoring. The in-orbit dark count growth rate over seven years is approximately 6.79 cps/day operating at -24 °C, and 0.37 cps/day operating at -55°C. Currently, the dark count of these detectors is approximately 15,000 cps at -24 °C and 1,000 cps at -55 °C. In May 2022, we performed a cumulative 5.7-hour high-temperature annealing operation on four of these detectors. The results showed that high-temperature annealing had no significant effect on the long-term accumulated dark count caused by radiation exposure, and there was no noticeable change in the annealed dark count rate.

2. In-orbit performance

To perform in-orbit monitoring of the dark count performance of a single-photon detector operating at -24 °C, SPD#5-12, dark count tests were conducted on the detector after each entanglement distribution experiment [2]. For the single-photon detectors operating at -55 °C, SPD#1-2, we conducted regularly tests on its dark count performance. Figure 1(a) shows the dark count of two single-photon detectors, SPD #1-2, operating at -55 °C over the past 2507 days. The dark count rates of eight single-photon detectors (SPD#5-12) operating at -24 °C over the past 2156 days are shown in Fig. 1(b). the dark count rate of the detector increases linearly with the in-orbit time. Additionally, there may be random nonlinear increases in the dark count, as shown in Fig. 1(a) and Fig. 1(b). It is preliminarily suspected that these irregular increments may be caused by extensive damage from heavy particles interacting with the detector. There is a significant variability in the in-orbit dark count rate changes for different detectors, which is determined by the differences in the detectors themselves. Similar differences are observed during ground radiation simulation tests, where detectors exhibit significant variations in dark count rate increments under the same radiation dose [1].

 

Fig. 1. In-orbit dark count rate performance of ten single-photon detectors. a, The dark count rates of eight single-photon detectors (SPD#1-2) operating at -55 °C over the past 2507 days. b, The dark count of two single-photon detectors, SPD #5-12, operating at -24 °C over the past 2156 days. c, The average dark count rate increment for the single-photon detector used for quantum teleportation and polarization control over the past 2507 days, 2156 days.

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Due to space radiation damage, the dark count of both the single-photon detector used for ground-satellite quantum teleportation experiments and the single-photon detector used for polarization control increases linearly over time. When the detectors are not in operation, they are stored at a temperature of approximately -5 °C and 15 °C, respectively. During operation, the single-photon detectors for quantum teleportation and polarization control are cooled to -24 °C and -55 °C, respectively. The average dark count rate increments for the single-photon detector used for quantum teleportation and polarization control are 0.37 cps/day and 6.79 cps/day, respectively, as shown in Fig. 1(c). For every 8 °C decrease in APD temperature, the dark count rate decreases by a factor of 2 [10]. The two groups of detectors operate at temperatures of -24 °C and -55 °C respectively. According to the exponential relationship between dark count and temperature, the dark counts of the two detector groups differ by approximately 17.4 times. The dark count growth rates of the two detector groups in orbit are 6.79 cps/day and 0.37 cps/day respectively, differing by approximately 18.4 times. If we do not consider the temperature difference, the dark count growth rates of the two detector groups in orbit are consistent. Additionally, detectors operating at -55 °C have thicker shielding, but their storage temperature is lower, which may offset the advantage against radiation. In Fig. 1(c), we primarily focus on the long-term dark count variations of the two groups detectors. The lack of an obvious nonlinear trend in the early dark counts of SPD#1-2 is mainly due to both datasets being plotted on the same axis, with the axis scale being too large relative to the dark counts of SPD#1-2. In the subsequent study of the annealing model, when plotting the dark count rates of SPD#1-2 on an independent axis, the nonlinear trend in early dark count rates becomes much more apparent.

The silicon APD single-photon detector dark count rate performance is mainly affected by displacement damage caused by space radiation [11–16]. The space radiation environment is primarily composed of protons, neutrons, and heavy particles. Using the AP8-min and AE8-min models from SPENVIS (space environment information system) [17], calculations for a circular Sun-synchronous orbit of approximately 500 km and an inclination of 97.4° indicate that, considering a 3 mm aluminum protection, the annual cumulative displacement radiation dose is approximately $\textrm{4}\textrm{.30} \times {10^\textrm{8}}\textrm{ protons/}c{m^2}@10MeV$. The shield thicknesses of single-photon detectors used in quantum teleportation experiments and polarization control experiments are 22 mm and 3 mm equivalent aluminum, respectively [18,19]. The annual cumulative displacement radiation dose for single-photon detectors used in quantum teleportation experiments is approximately 2.5 times lower than that for single-photon detectors used in polarization control experiments. Furthermore, both the polarization control and quantum teleportation single-photon detectors have an excess voltage of 15 V and operate at -24 °C and -55 °C, respectively. Based on previous ground test data [20], the dark count growth rates in orbit for polarization control and quantum teleportation single-photon detectors are estimated to be approximately 67.41 cps/day and 1.24 cps/day, respectively. The expected results are approximately one order of magnitude higher than the actual in-orbit data. One possible reasons is the differences between ground radiation simulation conditions and space irradiation environment, the accumulation of radiation during ground radiation tests at a high dose rate for a short period, testing the dark count rate without a comparably long annealing time, fast-recoverable radiation defects contributed to some of the dark counts [21]; while in orbit, the radiation dose rate is very low, and annealing at room temperature occurs concurrently with radiation, fast-recoverable radiation defects basically do not contribute to dark counts, and we will provide further explanation in the following section. Another possible reason is that other structural components of the satellite provide additional shielding, resulting in a lower received radiation dose rate than expected.

In addition, in the 289^th day, the DCR of SPD #2 jumped from ∼300 cps to ∼1600 cps, deviating from linearity, the preliminary judgment is the disparity in energy levels of radiation-induced carrier generation centers [1]. When the energy level of new radiation-induced carrier generation center is very close the intrinsic Fermi energy level, then the carrier generation rate of the new radiation-induced carrier generation center would be very high, subsequently lead to the DCR increment rate jump. Note that the DCR jump was observed in the ground tests when the radiation dose is low [1]. In order to mitigate the radiation-induced DCR sharp increment of SPD #2, make a trade-off between the DCR and detecting efficiency, optimizing the receiving end SNR (signal-to-noise rate), we further lower the SPD #2 excess voltage.

3. Storage and annealing

The literature [21–24] reported on the effects of radiation damage on silicon APD single- photon counters and found that high-temperature or laser annealing can effectively reduce the dark count caused by radiation. Based on the previous study [21], the annealing effect on the radiation-induced dark counts of silicon APD single-photon counters diminishes gradually with time and temperature after radiation damage, and the dark count at time t can be represented as follows,

Here ${K_B}$ is the Boltzmann constant and $T$ is the single-photon detector storage temperature in Kelvin. Besides the first fast component and higher-order components with subscripts greater than three, which were not detectable, the second and third components have been observed [25], with parameters ${E_2}\textrm{ = (0}\textrm{.95} \pm \textrm{0}\textrm{.01)eV}$, ${\theta _2}\textrm{ = (7}\textrm{.9} \pm \textrm{1}\textrm{.5)} \cdot \textrm{1}{\textrm{0}^{\textrm{ - 16}}}\textrm{days}$, ${E_3}\textrm{ = (0}\textrm{.45} \pm \textrm{0}\textrm{.01)eV}$, ${\theta _3}\textrm{ = (2}\textrm{.2} \pm \textrm{1}\textrm{.0)} \cdot \textrm{1}{\textrm{0}^{\textrm{ - 6}}}\textrm{days}$.

According to ground radiation tests and orbit parameters [1], without radiation protection shield and lower operating temperature, the Micius satellite single-photon detectors’ in-orbit dark count increment rate is estimated to be around 219 cps. At the same time, due to the annealing effect, some of the material damage caused by radiation is repaired [22–24]. The ultimate dark count is the balanced result of radiation damage and annealing effects. S. Baccaro et al. used neutron radiation to study the annealing model of dark current in avalanche photodiodes (APDs) after displacement damage [21]. According to literatures [11,26], different particles’ displacement damage to silicon materials is generally measured using non-ionizing energy losses (NIEL). Different types of particles and different energy levels result in varying NIEL, but their displacement damage effects are the same. That is, the displacement damage to silicon materials by protons and neutrons can be considered equivalent. Heidi N. Becker et al. investigated the effects of radiation on silicon APD with different structures [13]. The sensitivity of the current noise of different structured silicon APDs to radiation is mainly correlated with their depleted region volume. Since the depleted region material of different structured silicon APDs is the same, the same radiation annealing model can be used to describe the noise current variation after radiation. In our work, the radiation dark count rate annealing model proportional parameters of components of BC-24 was used [21], its annealing temperature was around 20°C, close to our experimental condition. Due to the short recovery time constant of the 1^st-class defects, which is only 1.27 days, we only utilize the combination of 2^nd-class and 3^rd-class defects, ${\textrm{g}_2} = 0.26,{g_3} = 0.17,{g_{ \ge 4}} = 0.22$.

For the Micius single-photon detectors, SPD#1-2, and SPD#5-12, in-orbit parameters as shown in Table 1. Shield thickness of 22 mm and 5 mm, the corresponding reduction in radiation dose by approximately 2.5 times and 1.6 times, respectively. The operating temperature decreased from -12 °C to -55 °C and -24 °C, corresponding to a reduction in dark counts by approximately 41 times and 2.8 times, respectively. Additionally, reducing the excess voltage from 15 V to 10 V can decrease dark counts by approximately 1.5 times. During the experimental phase, detectors SPD#1-2 and SPD#5-12 operate for approximately 15 minutes per day, with operating temperatures of -55 °C and -24 °C respectively. The remaining time is spent in storage mode, with storage temperatures of -5 °C and 15 °C respectively. The working time accounts for approximately 1% of the total time.

Table 1. The in-orbit parameters of the Micius single-photon detectors, SPD#1-2, SPD#5-12

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With radiation protection shield and lower operating temperature, the Micius satellite single-photon detectors, SPD#1-2, SPD#5-12, in-orbit dark count increment rate is estimated to be around 1.4 cps, 32.6 cps, respectively. Considering the annealing effect from different storage temperatures, according to formula (1), the expected dark count rates and in-orbit test results as shown in Fig. 2, are consistent with in-orbit test data. Additionally, according to the fitting results, the detector experienced a rapid increase in dark counts during its initial time in orbit, then reached a steady increase state. The lower the storage temperature of the detector, the more noticeable this phenomenon becomes.

 

Fig. 2. The expected dark count rates and in-orbit test results.a. SPD#1-2 in-orbit tests results and expected dark count rates. b. SPD#5-12 in-orbit tests results and expected dark count rates.

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In fact, in May 2022, from the 2084^th day of the Micus satellite in-orbit, we also conducted 16 high-temperature annealing tests on four of SPD#5-12, with a duration of 21.45 minutes each, limited by the satellite power system, totaling approximately 5.7 hours. The annealing process for a single test is that, from 0 to 86 seconds, dark counts of SPD#5-12 were tested under -24 °C conditions; from 87 to 1374 seconds (21.45 minutes), SPD#5-6 were controlled at 76 °C for high annealing, while SPD#7-8 were controlled at 64 °C, with SPD# 9-12 serving as a reference, being controlled at -24 °C. From 1375 to 1638 seconds, dark counts of SPD#1-8 were tested after annealing at -24 °C. During and after the annealing process, the SPD#5-12 dark counts are shown in Fig. 3(b). After total 5.7 hours of high-temperature annealing, the reduction of the dark count rates of SPD#5-12 is not noticeable. According to the simulation in Fig. 3(a), the expected dark count rate reduction after continuous 5.7 hours of high-temperature annealing is around 87 cps, this would be submerged in the measurement fluctuations of the current dark counts. High-temperature annealing tests on the in-orbit detectors show no measurable change on dark count rate, consistent with the in-orbit test results of ICESat [27].

 

Fig. 3. (a) In-orbit SPD#5-12 dark counts simulation when raising the storage temperature from 15 °C to 76 °C. (b) The dark counts of SPD#5-12, end of each annealing test.

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According to our radiation annealing simulation model and in-orbit data, raising the storage temperature of the detector can partially reduce the dark counts caused by space radiation damage, but the effect is very limited. Conversely, lowering the storage temperature of the detector will result in an increase in the dark count growth rate during the radiation-annealing transition phase. Additionally, short-term high-temperature annealing has little improvement on the dark count degradation caused by in-orbit radiation damage. Similar conclusions were also reported in the ICESat project [27–29], which conducted a thorough 7-year test of the in-orbit performance of silicon APD single-photon detectors, particularly on the impact of radiation on detector dark counts, accumulating an amount of valuable data, as showed in Fig. 4(a).

 

Fig. 4. (a) Single-photon counting modules(SPCM) dark rate and the case temperature over the ICESat mission duration to July 2006 [28]. (b) Simulation results of the in-orbit dark counts of ICESat.

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At the beginning of the in-orbit mission of ICESat, the detectors storage temperature was set to 20 °C. Approximately 253 days after launch, the detector underwent a power-on test that lasted for 57 days. Subsequently, the storage temperature of the detector was adjusted to 5 °C, and around the 97^th day after this adjustment, the detector underwent another power-on test [28]. Before and after the storage temperature adjustment, the growth rates of dark counts were 46.8 cps/day and 55.5 cps/day, respectively. Here, we employed our model to simulate the in-orbit dark counts of ICESat. The simulation parameters included no additional radiation shielding, an operating temperature of -12 °C, an avalanche voltage of 15 V, and other parameters identical to those of the Micius satellite detector. The simulation results are illustrated in Fig. 4(b). Before and after the storage temperature adjustment, from 20°C to 5°C, the expected average growth rates of dark counts were 51.8 cps/day and 57.8 cps/day, consistent with the in-orbit test results of ICESat. Thus, when the storage temperature is not very low and remains constant, a linear fit to the growth of on-orbit dark count rates can be a good choice. However, it is more appropriate to use our model for fitting during the transitional phase right after the detector is launched or when there is a change in its storage temperature.

4. Conclusion

We conducted in-orbit testing of the single-photon detectors on the Micius satellite for approximately seven years. Since the satellite launched on August 16, 2016, we have continuously monitored the performance of the detectors. Due to radiation effects, the dark count growth rate is approximately 6.79 cps/day at -24 °C and 0.37 cps/day at -55 °C. Lowering the operating temperature has a significant suppression effect on the growth of radiation-induced dark counts. High-temperature annealing tests on the in-orbit detectors show no measurable change on dark count rate, and we proposed a 2e + c radiation annealing model to explain that the radiation dose on the in-orbit detectors gradually accumulates over time, storage temperature annealing is sufficient to recover no-permanent displacement damage, and increasing the storage temperature appropriately can reduce the detector's dark count rate. The simulation results based on the proposed 2e + c radiation annealing model are consistent with the Micus satellite and ICESat in-orbit results.

Our work has accumulated experience in the long-term in-orbit operation of silicon single-photon detectors. Simultaneously, we have explored the short-term high-temperature annealing and different storage temperature effects on the in-orbit detectors’ dark count rate; according to the results, it is meaningful to increase in-orbit detectors storage temperature. This provides new references for the long-term operation and improvement of silicon APD single-photon detectors in orbit.