Laser annealing heals radiation damage in avalanche photodiodes

2.1 Test samples

For every detector, the dark count rate after irradiation (and any thermal annealing) is so high that the devices are saturated when operating at room temperature. For this reason, all samples are characterized at \({-}80^{\circ}\mathrm{C}\) in our cold-temperature characterization apparatus. However, unlike the other devices, each Excelitas SLiK comes with a built-in thermistor and thermoelectric cooler (TEC), allowing additional testing to be performed in-situ in our laser annealing apparatus at an operating temperature of \({-}30^{\circ}\mathrm{C}\).

The samples are held in detector modules, which are moved between the annealing and characterization apparatuses as necessary and provide avalanche detection and quenching. We employ a passive quenching circuit [25, 38] (see Figure 1) for processing output avalanche pulses. In this circuit, the APD is reverse-biased in Geiger-mode [25], where the bias voltage (\(V_{\text{bias}}\)) is set above the detector’s breakdown voltage (\(V_{\text{br}}\)) and the APD becomes sensitive to single photons [38]. \(V_{\text{excess}}~(= V_{\text{bias}} - V_{\text{br}})\), typically \({\sim}20~\mathrm{V}\), generates a high electric field in the detector’s depletion and avalanche regions. When a detection takes place (ideally, by a photon incident on the APD active area), an electron-hole pair is generated. The high electric field in the p-n junction causes impact ionization and produces an avalanche current flow. The current flow is detected as a voltage drop across R2 in parallel with a \(50~\Omega\) impedance coaxial cable. If this voltage drop is greater than a discriminator’s fixed threshold voltage, a detection event is recorded. R1 quenches the current flow by lowering the voltage across the APD close to \(V_{\text{br}}\) [38]. Once the diode voltage reaches near \(V_{\text{br}}\) and the steady-state current flow (\(V_{\text{excess}}/\text{R}1\)) is below a latch current of \({\sim }100~\mu\mathrm{A}\), the avalanche current flow stops [38]. Our detector module has the steady-state current of \({\approx}50~\mu \mathrm{A}\) for \(V_{\text{excess}} = 20~\mathrm{V}\).

We measure the dark count rate, relative changes in photon detection efficiency (\(P_{\text{de}}\)) (and absolute \(P_{\text{de}}\) for SLiKs characterized at \({-}30^{\circ}\mathrm{C}\)), and afterpulsing time distribution through the analysis of detection event times produced by a time-tagging unit with 156.25 ps resolution (UQDevices 16-channel model). Timing jitter (\(\Delta t_{\text{jitter}}\)) is measured using an oscilloscope (LeCroy 640Zi).

2.2 Laser annealing apparatus

Figure 2(a) shows the laser annealing apparatus, which improves upon the laser annealing experimental setup of Ref. [36]. Our apparatus allows us to laser-anneal APDs, take pictures of their active areas, measure their dark count rates and \(P_{\text{de}}\), and scan \(P_{\text{de}}\) across the entire active area to check whether laser annealing has produced any local damage.

Our setup consists of a single-mode (SM) continuous-wave 808 nm signal laser (QPhotonics QFLD-808-100S), and one multi-mode (MM) 0-30 W continuous-wave 808 nm annealing laser LD2 (Jenoptik JOLD-30-FC-12). The 808 nm wavelength is selected for the annealing laser to ensure that APDs fully absorb photons in the depletion region and generate heat energy. Typical depletion region thickness of thick-junction silicon APDs is \(20\mbox{-}150~\mu\mathrm{m}\) [38]. At 300 K, if the wavelength is too long (\({>}1\text{,}100~\mathrm{nm}\)), the APDs transmit most photons. If the wavelength is too short (\({<} 500~\mathrm{nm}\)), most photons are absorbed only at the surface of the APDs [39]. Absorption depth of 808 nm photons, at which the light intensity has fallen to \(1/e\) of the initial value, is \({\sim}10~\mu\mathrm{m}\) [39]. The pigtail of the signal laser LD1 is connected to a 90:10 fiber beamsplitter (Thorlabs FC780-90B FC). One output port is connected to a power meter (PM1; OZ Optics POM-300-VIS), while the other output port is connected to two attenuators in series: a screw attenuator reduces laser power to the nW range, and a digital variable attenuator (OZ Optics DA-100-35-770/830/850-5/125-5-40-LL) then brings laser illumination down to the single-photon level. The degree of attenuation and the output power from the weak coherent continuous-wave light source are calibrated to apply the mean photon count rate of 48.8 kHz at the sample. The attenuated continuous-wave laser beam is sent to a collimation setup in SM fiber, then collimated by an aspheric lens (Thorlabs C280TME-B) and reflected off two dielectric mirrors (Thorlabs BB1-E03-10) to provide four degrees of freedom for alignment. It then goes through 90:10 (reflection:transmission) non-polarizing beamsplitter (Thorlabs BS029 90:10), a mechanical shutter (Thorlabs SH05 with Thorlabs SC10 controller), a focusing lens (Thorlabs C220TME-B), and reaches the APD.

The continuous-wave annealing laser LD2 is coupled to a \(200~\mu\mathrm {m}\) diameter core MM fiber (RPMC Lasers OAL-200/220/245). The annealing laser beam is collimated by an aspheric lens (Thorlabs C220TME-B) and reflected at the 90:10 non-polarizing beamsplitter. The beams of the annealing and signal lasers overlap so that both can be focused on the same spot. A power meter (PM2; Thorlabs S142C) located in the transmission arm of the annealing laser allows us to accurately control the annealing power at the APD.

A camera (Canon 7D with macro lens MP-E 65 mm f/2.8 \(1\mbox{-}5{\times}\)) and a light-emitting-diode photography illuminator are mounted beside the laser setup. The XYZ translation stage, on which the detector module is mounted, enables us to move the samples between the laser setup and the camera.

2.3 Cold-temperature characterization apparatus

A separate apparatus, shown in Figure 2(b), is built to measure the dark count rate, relative changes in \(P_{\text{de}}\), \(\Delta t_{\text{jitter}}\), and afterpulsing probability at \({-}80^{\circ}\mathrm{C}\). The low temperature significantly suppresses thermally excited dark counts [35]. The detector module is extracted from the laser annealing apparatus and placed inside a cooling chamber (Delta Design 9023) at \({-}80^{\circ}\mathrm{C}\).

The apparatus necessary to measure the absolute \(P_{\text{de}}\) cannot fit in the cooling chamber; consequently, we measure \(P_{\text{de}}\) relative to a reference by sending diverging weak coherent pulses (WCPs) from the end of a fiber onto the APDs. Each APD’s active area is sufficiently small that it receives approximately uniformly distributed light intensity, despite the overall Gaussian profile of the incident optical mode. We use a 780 nm laser LD3 (PicoQuant LDH 8-1) as the WCP source, pulsed at 40 MHz with full width at half maximum (FWHM) of 188 ps. The laser pulses are split by a 50:50 fiber beamsplitter (Thorlabs FC780-50B-FC). One output port is connected to a digital variable attenuator (OZ Optics DA-100-35-770/830/850-5/125-5-40-LL) and sends the laser pulses through a fiber to the APDs placed inside the cooling chamber. The other output port is connected to an optical-to-electrical converter (LeCroy OE455, DC-3.5 GHz) and the oscilloscope. Having oscilloscope access to both input laser pulses and output avalanche pulses allows us to measure \(\Delta t_{\text{jitter}}\) (which requires using a pulsed laser, as opposed to continuous-wave such as LD1).

3.1 Laser annealing

To perform laser annealing, the detector module is positioned to ensure that the high-power annealing laser beam is focused on the active area of an APD. (The FWHM beam diameter is \(92~\mu\mathrm{m}\).) Next, the desired annealing power is set by monitoring the power meter PM2 with the shutter closed. We then open the shutter and laser-anneal the APD for 60 s, immediately afterwards closing the shutter and letting the device cool down to the room temperature for another 60 s. We then perform characterization.

For most samples, we perform multiple stages of laser annealing and characterization, with laser power increased between each stage. To determine whether this stepwise laser annealing process has any additional effects, we apply only a single-shot power of 1 W to SLiK-4 and SLiK-5 for comparison (1 W is chosen based on observed results of the first three SLiKs to ensure a dark count rate reduction). Similarly, C30902SH-2 is laser-annealed at two specific powers, chosen based on C30902SH-1’s observed results.

The temperatures reached by the APDs during laser annealing are of interest because, for some temperature ranges, alternative heating methods may be more practical to implement on a satellite (e.g., using an electric heater). We can measure the temperature of SLiK samples using their integrated thermistor (mounted on the cold plate of TEC, close to the APD). The temperature of SLiK-1’s thermistor is recorded at the end of the 60 s exposure, for most annealing powers. According to our measurements (see Appendix), the thermal resistance between the photodiode chip and thermistor is negligible; thus, the temperature reading by the thermistor provides an accurate reading of the temperature reached by the APD during laser annealing.

3.2 Characterization

All nine samples’ parameters are measured at \({-}80^{\circ}\mathrm{C}\) in the cold-temperature characterization apparatus, while SLiKs are also characterized at \({-}30^{\circ}\mathrm{C}\) (reached using their built-in TECs) in the laser annealing apparatus.

Breakdown voltage. We measure \(V_{\text{br}}\) by observing avalanche pulses on an oscilloscope. As \(V_{\text{bias}}\) is gradually increased from 0 V, avalanche pulses begin to appear when \(V_{\text{br}}\) is reached. We estimate the accuracy of this \(V_{\text{br}}\) measurement to be better than \({\pm}0.3~\mathrm{V}\). This measurement is performed at the start of every full characterization. Both C30902SH samples and SLiK-1, SLiK-2, and SLiK-3 are subsequently biased \({+}14~\mathrm{V}\) above \(V_{\text{br}}\), whereas SLiK-4, SLiK-5, and both SAP500S2 samples are biased \({+}20~\mathrm{V}\) above \(V_{\text{br}}\). The choice of \(V_{\text{excess}}\) is arbitrary; however, we change \(V_{\text{excess}}\) values to explore its effects on laser-annealed APDs.

Dark count rate. We record dark counts with the time-tagging unit for 500 s. The mean dark count rate is calculated from the collected time-stamped data. We define the dark count rate reduction factor as the ratio between the reference mean dark count rate before any laser annealing and the mean dark count rate after laser annealing. Some of the samples were already thermally annealed in another experiment [35]; thus, having further dark count rate reduction in those samples imply that laser annealing mitigates proton radiation damage better than thermal annealing.

Photon detection efficiency. To measure relative \(P_{\text{de}}\) at \({-}80^{\circ}\mathrm{C}\) in the cold-temperature characterization apparatus using diverging WCPs, we take the mean count rate over 500 s. Following the completion of laser annealing and measurements of the two C30902SH samples, it was discovered that the output power of LD3 varies over time. As the C30902SH samples have undergone laser annealing, measurements unfortunately cannot be retaken. Consequently, for all other samples, we normalize the count rate by the average laser power (measured at the oscilloscope immediately before and after a measurement). We then calculate the relative change in \(P_{\text{de}}\) by subtracting the mean dark count rate and then normalizing against the initial photon count rate.

For SLiKs we determine the absolute \(P_{\text{de}}\) while operating at \({-}30^{\circ}\mathrm{C}\) in the laser annealing apparatus. The continuous-wave signal laser LD1 is applied, with its photon rate calibrated via loss and laser power measurements in our optical setup. Then, we measure a mean count rate over 500 s using the time-tagging unit. Subtracting the mean dark count rate from the mean count rate and dividing the difference by the calibrated input photon rate gives \(P_{\text{de}}\).

Testing within the laser annealing apparatus also allows us to scan \(P_{\text{de}}\) at various points over the active area of the SLiK devices. We measure the signal laser’s illumination spot size using a beam profiler - the beam waist is \({\sim}20~\mu\mathrm{m}\) (FWHM). We thus step the translation stages in \(10~\mu\mathrm{m}\) increments, such that \(P_{\text{de}}\) of the active area is fully and tightly covered. We scan a square region that covers the active area, with appropriate pauses at each step for vibration dissipation.

Timing jitter. To measure \(\Delta t_{\text{jitter}}\), both the laser output pulses and the APD’s avalanche pulses are connected to the oscilloscope. We then plot a histogram of the relative time difference between these two signals over at least 10⁵ avalanche pulses (see example in Figure 3), and measure the FWHM.

Afterpulsing probability. Afterpulsing probability is calculated from time-stamped counts. We typically use dark counts, but if the dark count rate for an APD is too low, we use a dim light pulsed at 100 Hz to facilitate a measurement. The extra light increases the background count rate by a few Hz (otherwise, the background count rate tracks the APD’s dark count rate), and does not influence the afterpulsing distribution.

For every detection event, our software adds all subsequent detection events occurring up to \(10^{-2}~\mathrm{s}\) later to a histogram, with exponentially growing time bins [37], as shown in Figure 4. Unlike the standard autocorrelation method, this improved analysis produces a plot that converges to the background count rate, instead of following an exponential decay. Using exponentially increasing bin sizes filters out statistical fluctuations in the tail and also resolves the fast changing avalanche peak.

The shape of this histogram (Figure 4) presents four features: an APD’s dead time, its recharge time, its trapped-electron time constants, and the background count rate. In Figure 4, the dead time begins immediately after a photon detection (time 0) and ends when counts begin to reappear at roughly \(0.8~\mu\mathrm{s}\). The recharge time is the time it takes for the count rate to reach the peak value after the dead time. Trapping time constants can be found by fitting the exponentially decaying slope of the peak. The plot levels off to the background count rate and the black shaded area is the afterpulsing probability.

For a quantum communications protocol such as QKD, the afterpulsing peak contributes to the quantum bit error rate (QBER), and it is thus desirable to remove the peak by extending the dead time out to the flattened region [28, 29, 38]. In practice, this can be performed by discarding all counts before the end of a user-selected dead time in post-processing [40, 41] or by using an active quenching circuit [42]. Such additional dead time, however, limits the maximum detection rate [27, 28]. Because long distance transmissions reduce the expected detection rate [43], the amount of additional dead time could be optimized to balance the QBER with the detection rate to maximize the final key rate [37, 40, 41].