Single photon detector (SPD) is a device, that is sensitive to single photons with a specific wavelength. SPD‘s have many applications, such as quantum key distribution (QKD) [1], 3D imaging systems (LIDAR) [2], optical time domain reflectometry (OTDR) [3], fluorescence microscopy [4], biomarker tomography [5], astronomical telescopy [6] etc. SPD’s structure is not universal, it’s designed for a specific application and operating parameters and is based on various physical principals. There are several kinds of devices that can be used as a single photon sensor, for example, avalanche photodiode (APD) [7], single photon avalanche diode (SPAD) [8], negative feedback avalanche diode (NFAD) [9], semiconductor matrices [10], superconducting nanowires [11].
Sometimes there is confusion about the use of the terms APD and SPAD because their structures are quite similar. But there is a significant difference between them. APD is designed for work in linear mode when it’s biased less than breakdown voltage, and to be sensitive for many-photon optical signals. SPAD is designed for work in Geiger mode, when its bias periodically rises higher than breakdown voltage, and to be sensitive for single photons. However, at the very beginning of the development of single-photon detectors, APD was used to detect single photons [12]. But such devices have low detection efficiency and high noise. Nowadays, such use of avalanche photodiodes is rare
Negative feedback avalanche diode (NFAD) has a series integrated resistor with InGaAs/InP SPAD, allowing faster avalanche quenching, using only the circuit resistor, and consequently lower afterpulsing. In terms of device operation, afterpulse is a detection event that follows a previous detection event, is correlated to a prior detection event, and is not due to photon incident at detectors input. But these diodes have high noise characteristics due to many problems while producing [13]. Superconducting nanowire single-photon detectors (SNSPD) have high detection efficiency and low noise. Still, nanowires need to be cooled up to 3 K (depends on the material), which requires bulky and expensive cryostat. This issue doesn’t allow the creation of a compact QKD device. In this case, InGaAs/InP SPAD is the optimal device for creating a miniature SPD and compact QKD device as a whole.
In this paper, we investigated a set of ten (10) custom single-photon detectors based on InGaAs/InP SPAD’s from various manufacturers and batches (more about it in Section IV). These SPD’s are sine-gated and designed for use in compact (standard server rack compatible) QKD devices [14]. This device works on a 1550 nm optical wavelength.
InGaAs/InP SPAD control electronics [15], [16] for performing sine-gating has a set of important for effective diode’s work parameters, such as DC bias voltage, AC bias voltage (gating signal), the shape of gating signal, and dead time. It’s quite an important but a laborious task to find the optimal parameters list to make photon detection efficiency (PDE) high enough (10–20%), dark count rate (DCR) low enough (< 200 Hz) and afterpulse probability (AP) low enough too (< 1\%). In this paper, we explore the influence of gating parameters on PDE, DCR, and AP to make some recommendations about tuning the InGaAs/InP SPAD biasing scheme to increase the efficiency of a whole QKD device.
There are a lot of similar works, where investigated sine-wave [17], [18] or square-pulse [19] gated InGaAs/InP SPAD, with figures for functional parametrers depend on each other [20], or on the temperature [21], or on the excess [22] or bias voltage [23], [24]. From this, we can highlight some works that directly present parameters optimization.
In the paper [25], a detailed study of InGaAs/InP SPAD optimization for QKD device was performed with commercially available SPD (WT-SPD-300, Qasky). But this SPD has a square-pulsed gating scheme, and authors variate only DC bias voltage and temperature parameters and investigate its influence on the PDE, DCR, and AP parameters. We test our devices with fixed temperature and variate AC bias voltage.
Section II presents the used InGaAs/InP SPAD biasing scheme and the influence analysis of the gating parameters on PDE, DCR, and AP. SPD’s measuring stand scheme and methodology for characterizing SPD’s parameters are described in Section III. Section IV presents experimental data analysis and general recommendations for improving SPD’s performance. In Section V, we make a summary of a work.
SECTION II.
Influence of the Gating Parameters
The development of electrical control circuitry of InGaAs/InP SPAD to provide certain operations with diode is an important task when designing SPD. Our SPD device has sine-gated InGaAs/InP SPAD with passive quenching and active reset, which provides a dead time [26]. We consider the dead time (\tau) as the time when the detector cannot detect photons after the previous detection event.
We show the functional circuit of the developed SPD in Fig. 1. InGaAs/InP SPAD is reverse biased with the DC bias voltage V_{b1} (or V_{b2} if we set InGaAs/InP SPAD to off-state) and AC bias voltage V_g from the cathode side. We can set gate amplitude to V_g \in [1, 7] V (right bound depends on the circuit realization features and can vary from 5 - 9 V). The AC bias voltage (gates) is a 312.5 MHz frequency sine electrical wave. This frequency is due to the QKD device with a frequency of laser pulses generation 312.5 MHz [27]. One can scale up such a system to 1.25 GHz by multiplying the frequency of internal generators to 4 times. We can set arbitrary laser pulse frequency in our experiment because the experimental stand uses its laser pulse generator block (see Section III).
Gating voltage has to exceed InGaAs/InP SPAD’s breakdown voltage V_{br} on a value V_{ex}, to make single-photon detection possible – this regime is called Geiger mode. Time, during which InGaAs/InP SPAD is in on-state, we call Geiger mode time (t_g). DC bias voltage V_{b1} falls to V_{b2} after detection to exclude the probability of following avalanche breakdown. The dead time pulse shape is made as shown in Fig. 2 to reduce the effect of transient processes on single-photon detection. The time during that bias voltage does not exceed the breakdown voltage of the InGaAs/InP SPAD is a dead time \tau. In our SPD devices, we set up dead time in the range \tau \in [4 - 6] \ \mu s to suppress the afterpulse probability. We accept this range as optimal because increasing dead time lowers the maximum SPD count rate. However, reducing dead time leads to the growth of afterpulse probability. If dead time is in this range, our QKD device’s maximum count rate and afterpulse probability are optimal.
Quenching resistor R_{q} and terminating resistor R_L are used to quench the avalanche and reset the InGaAs/InP SPAD after a registration event. There are amplifiers and suppression filters to eliminate the gating signal influence on the avalanche signal processing on the anode side of the InGaAs/InP SPAD. The comparator converts analog avalanche signals to certain logic-level digital ones. This signal arrives at the output logic block and the reset driver simultaneously. Output logic block makes a signal with a certain amplitude and duration to the receiver. Reset driver makes a dead time pulse. It decreases the DC bias voltage by a fixed amount V_q within a \tau time.
We should highlight that our scheme has passive quenching by sine-gating and by quenching resistor. Reset driver does not perform directly quench. It only decreases the voltage after about 100 ns after passively quenched the avalanche. Also, this driver resets voltage to a previous value.
The most important InGaAs/InP SPAD’s operating parameters in our circuit are: DC bias voltage V_{b1}, AC gate amplitude V_g, dead time \tau. The maintaining temperature of the InGaAs/InP SPAD also has particular importance. One must select these parameters for each specific used InGaAs/InP SPAD since its performance can vary significantly from diode to diode even in the same batch [28]. This approach allows us to achieve the best performance of SPD. However, in this article, we will concentrate only on two parameters – DC bias voltage V_{b1} and AC gate amplitude V_g.
It is Geiger mode when bias voltage on the InGaAs/InP SPAD V_a is more than breakdown voltage V_{br}: V_a> V_{br}. Caught in InGaAs/InP SPAD’s multiplication region-free carriers generate a positive feedback avalanche process. Free carriers in InGaAs/InP SPAD’s heterostructure can appear due to different effects. I.e., photogeneration, direct and indirect tunneling, relaxation of traps, and other less probable effects, like Poole-Frenkel effect and photon-assisted generation through defects [29]. Photogeneration and thermal generation prevail in the absorption region because of the low energy gap of the InGaAs material, as is shown in [29], [30]. The tunneling generation effect is determined by the energy gap and the value of an electric field in the material. It takes place in absorption and multiplication regions.
Traps for charge carriers (mainly for holes) prevail in InGaAs/InP SPAD heterointerface and have less concentration at the bulk material. Relaxation of these traps can trigger avalanches without external influence, which is the nature of the afterpulsing effect. It imposes some severe restrictions on the key distribution rate in QKD systems.
Such parameters like DC bias voltage V_{b1}, gate signal shape V(t) (1), and amplitude V_g define maximum InGaAs/InP SPAD’s excess voltage V_{ex} and diode’s time in Geiger mode. This time interval strongly influences the DCR and afterpulsing probability and less on the PDE. These values can be estimated from 2 and 3.
\begin{align*}
V(t) &= V_{b1} + V_g \cos (2 \pi \nu t), \tag{1}
\\
V_{ex} &= V_{b1} + V_g - V_{br}, \tag{2}
\\
t_g &= \frac{1}{2 \pi \nu } \left(\pi - 2 \arcsin \left(\frac{V_{br} - V_{b1}}{V_g}\right)\right), \tag{3}
\end{align*}
View Source
\begin{align*}
V(t) &= V_{b1} + V_g \cos (2 \pi \nu t), \tag{1}
\\
V_{ex} &= V_{b1} + V_g - V_{br}, \tag{2}
\\
t_g &= \frac{1}{2 \pi \nu } \left(\pi - 2 \arcsin \left(\frac{V_{br} - V_{b1}}{V_g}\right)\right), \tag{3}
\end{align*}
where \nu is a frequency of sinusoidal gating signal, t is a moment of time.
Analytical graphs for the shape of InGaAs/InP SPAD’s excess voltage V_{ex} under a different gate amplitude presented at Fig. 3(a). Laser pulse waveform from the measuring stand (see Fig. 4) presented at Fig. 3(b). Dependencies t_g versus V_g and t_g versus V_{b1} under different V_{ex} diagrams presented at Fig. 3(c) and (d).
The rise of excess voltage increases the probability of an avalanche excitation with free charge carriers in the multiplication region, that if unchanged, t_g increases PDE, DCR, and AP.
An increase of Geiger mode time t_g with fixed V_{ex} leads to a rise of DCR [31] and PDE due to increasing of time interval, during which avalanche growing can occur, that increase the probability of SPD triggering. Also, passive quenching due to the gate with high gate amplitude (low t_g) is faster than low amplitude (high t_g). In this case, lowering of t_g leads to lowering of afterpulsing AP due to lower generated charge in the heterostructure and consequently lower traps filling [32].
In sine-gated SPD, we can not explicitly change the V_{ex} and t_g parameters because we can change only two operational parameters: gate amplitude V_g and DC bias voltage V_{b1}. And we have two non-linear transitions between parameters: V_g and V_{b1}, that cause the V_{ex} and t_g. Simultaneously, V_{ex} and t_g cause PDE, DCR and AP. It is non-trivial to obtain optimal operational parameters because all transitions are non-linear. Due to this fact, searching optimal operational parameters of InGaAs/InP SPAD is not a trivial task that we solve in this article.
SECTION III.
SPAD Parameters Measurement
We have used the setup shown in Fig. 4 to measure the SPD’s parameters. This setup includes a synchronization system, laser source (HF laser driver), beam splitters system, a system of controlled optical attenuators with output power control, measured SPD, a frequency meter, and oscilloscope. All elements of this system are controlled with the LabVIEW program.
Laser source emits optical pulses at 1550 nm wavelength. These pulses are generated in the same frequency grid as the gating signal – 312.5 MHz. In the experimental data, we present below, the repetition rate of laser pulses is 100 kHz. The phase between gating signal and optical pulses is controlled with the synchronization system. Our synchronization system is a programmable logic device (PLD) used as a reference frequency generator for the high-frequency laser driver and our SPD. We can change the relative phase between laser pulses and sine gates of SPD to set the count rate to the maximum possible with other fixed parameters.
Optical pulses arrive at the input of a 90/10 beam splitter, and then they are split into two beams with different intensities. We use this element to have a possibility to control our laser pulses shape, duration, and repetition rate (see Fig. 3(b)).
A beam with a lower intensity arrives at the two series-connected controlled attenuators system input. Due to the possibility of measuring the power of light radiation after the first attenuator and a fixed attenuation coefficient of the second attenuator, it is possible to adjust and maintain the power of laser pulses at the output of about 0.1 photons per pulse, which arrives at the input of SPD.
The number of one-photon states twenty (20) times exceeds the number of two-photon states at given energy of light radiation [33], which ensures the maximum approximation of the results of stand measurements of the SPD performance to the actual SPD performance in the QKD setup. Using lower laser pulse energy is impractical because we will increase the time of experiments without noticeable changes in results errors.
The output signal from the detector incidents simultaneously to a frequency counter and an oscilloscope using an electric power divider. Indications of the frequency counter determine PDE and DCR. The oscilloscope displays a time histogram of triggers that determines the dead time and the afterpulsing probability AP.
This work determines the effective operation mode of sine-gated InGaAs/InP SPAD as ensuring the minimum DCR value at a given PDE. The afterpulse probability AP is also essential, but it’s a secondary parameter in our optimization criteria. If we have a similar DCR with constant PDE with different operational parameters, we will choose the optimal point according to AP. Such optimization criteria are suitable for long-distance QKD, where the count rate is not so much higher than DCR. Also, we offer one more optimization criteria – the minimum of SNR = PDE / DCR \ [\%/Hz], but the main disadvantage of such approach is that the optimal point usually has low PDE (< 5 \ \%). This point will not be optimal for QKD as a whole.
We investigate nine commercially available InGaAs/InP SPADs with similar back-illuminated structures with a diameter of the active region D \approx 25 \ \mu m.
Investigated InGaAs/InP SPADs were from different manufacturers and bathes. We summarize details in the Table I. We show breakdown voltage V_{br} for tested temperature, and not the device passport value.
We use InGaAs/InP SPADs from RMY Electronics and Wooriro manufacturers. InGaAs/InP SPADs from RMY we can group by same batches with SPD id: {#1, #2, #3}, {#4}, {#5}, {#6}. InGaAs/InP SPADs from Wooriro was from two batches: {#7, #8}, {#9, #10}.
Our results present measurements only for a single temperature because, in our article, we aim to show the dependence between functional and gated parameters. One can expand obtained dependencies on different temperatures.
A. SNR Dependencies
Now we consequently introduce our measurements. Firstly, we will clearly show the impractical use of the SNR parameter. The heatmap of SNR dependence on DC bias and AC gate voltage for a set of measured SPD’s is presented in the Fig. 5.
We can see optimal points on these heatmaps, obtained with maximum SNR criteria – it has dark red color. We can split our SPDs into two groups based on the position of the red area on the SNR heatmap. If this area is near the bottom bound, it will be group 1. If, near the upper bound, it will be group 2. The y axis is responsible for DC bias voltage V_{b1}, and with increasing this value, PDE and DCR increase too. But with different speeds that we can observe on SNR heatmaps. In group 1, DCR grows faster than PDE, but in the second group, vise versa. But even in the second group, this statement is relative. Due to some value of bias voltage, DCR always grows faster. We can evaluate the optimal point for SPDs from the second group with SNR criteria, and it will have high enough PDE. But for SPD growth of the first group, we should not do this.
As we can see, many measured SPDs belong to group 1.
Approach with SNR based optimization is also not so good because, in practice, we need to set up two SPDs with similar PDE parameters for effective QKD device work. We desire that DCR and AP parameters have coincided too, but this is not a critical requirement.
Now we have more practical tasks – we need to obtain optimal point for fixed desired PDE.
B. DCR Dependencies
This task is not so trivial due to experiment methodology. We can change DC bias voltage on our stand, and we obtain changes in frequency meter count rate. We convert this count rate to PDE only at the postprocessing step. We perform measurements on some grids to obtain information about a wide range of device parameters. It’s unlikely that our measurement point will have PDE equal to 10 \ \% or 20 \ \%. We use linear interpolation based on two nearest grid points to obtain desired PDE.
We used the described approximation approach for PDE and AP. On the Fig. 6 we present DCR dependencies on gate amplitude for different PDE slices for different SPDs.
Based on these graphics, we can again split our SPD into two groups based on the behavior of DCR curves. If the DCR curve lowers with increasing V_g, then it will be group 1. It also can grow after some critical V^{crit}_g, but it starts only with lowering. If the DCR curve only grows, it will be group 2. We marked V^{crit}_g as the vertical dashed lines. We placed the critical value at the rightest measured point for some detectors. We assume that increasing of DCR will happen at a higher gate amplitude.
The nature of this lowering is based on the dependence between gate amplitude V_g and Geiger mode time t_g, as was shown in Section II. For fixed PDE observe, that our excess voltage V_{ex} changes for some of the SPDs in range V_{ex} = [V_{ex0}, \ V_{ex0} + 0.3] V, with increasing of gate amplitude V_g. For all the detectors, excess voltage for PDE = 10 \ \% is in range V_{ex} \approx [1, 1.5] V, and for PDE = 20 \ \% is in range V_{ex} \approx [2, 2.5] V.
It turns out that with fixed V_{ex} if we lower Geiger mode time t_g, PDE will lower too. To avoid the PDE lowering, we need to increase V_{ex} by increasing bias voltage. But at the same time, all the same, t_g will be lower than at the start of manipulations. Now, there are two possible scenarios. The first scenario is when V_{ex} increases not sufficiently, and lowering of t_g leads to DCR lowering – this is group 1. Another scenario is when V_{ex} grows sufficiently, and even with decreasing of t_g, we observe the growth of DCR – this is group 2.
But DCR can’t permanently decrease because to keep PDE, we will need to increase V_{ex}, which leads to the appearance of some undesirable effects. These effects are manifested in the fast-growing DCR when it reaches some critical V^{crit}_g.
This effect is not due to the fast-growing probability of direct and indirect tunneling of electrons through band gap, because excess voltage V_{ex} doesn’t increase sufficiently in our experiment, as an electric field [19]. There is no field-enhancement of traps relaxation effects because dependencies are not so sharp [34]. There is no thermal-assisted generation because we perform measurements with fixed temperatures. We think that this effect is due to a charge-persistence effect, described at works [35]–[37].
The charge-persistence effect was observed in these works on square-pulses gated InGaAs/InP SPAD. Authors obtain that with increasing of “undervoltage” V_{uv} – the difference between breakdown voltage V_{br} and voltage at the InGaAs/InP SPAD off-state, DCR can fastly grow when reaching some critical V^{crit}_{uv}. Undervoltage parameter for square and sinusoidal gating presented on Fig. 7(a)).
Authors conclude that charge persists at the heterobarrier on the multiplication/absorption regions at the low-field depleted and neutral regions. If undervoltage is low (absolute voltage is high), then charges in the low field region have high diffusion speed and can quickly dissolve before the next InGaAs/InP SPAD switching to on-state. But if undervoltage is high (absolute voltage is low), then charges do not have time to dissolve during InGaAs/InP SPAD off-state. It accelerates after switching on and leads to avalanche generation, i.e., dark click. This processes we schematically demonstrate on the Fig. 7(b)), that presents front-illuminated InGaAs/InP SPAD from work [36]. We mention that our investigated InGaAs/InP SPADs have a back-illuminated structure. Still, the heterobarrier is similar in these two structure types because the sequence of semiconductors layers and their properties are the same.
With the sinusoidal gating charge, the persistence effect can be observed, too, because with increasing the gate amplitude, we increase the undervoltage if we keep V_{ex} fixed.
We can conclude that we can increase the gate voltage for a lot of SPDs to decrease the DCR with fixed PDE, up to fast DCR growing, due to the charge-persistence effect.
C. AP Dependencies
We have one more functional parameter that we need to consider when optimizing gating parameters – afterpulsing. Afterpulsing should be made dominant if in QKD we have low line losses, for example, in low distance QKD. In this case, there is high photon count rate on the SPD, up to maximum count rate, that can be determined by dead time: \nu _{max} = 1 / \tau. In our case, \tau \in [4, \ 5] \ \mu s, and \nu _{max} \in [200, 250] kHz. For example, we have afterpulsing probability 1\%, which means the primary dark count rate would be at least 2 kHz. That is much higher than the observed dark count rate on our SPDs: DCR \in [50, 500] Hz.
There are few widely used afterpulsing measurement approach, as example: Bethune 2004 [38], double-pulse method [39], Yuan 2007 [12]. The main disadvantage of these methods is that it is necessary to carry out long measurements to obtain the afterpulse probability for specific DC and AC bias voltage values. Since we have a large number of grid points for measurements, the main criterion for us was the speed of determining the afterpulse. We used the following method.
We set up laser pulse repetition rate to 10 kHz with an average energy of 1 photon per pulse in our installation 4. It means, that photon arriving time has a period of 100 \ \mu s. We set the oscilloscope sweep to 25 \ \mu s, and on the histogram, we can see only a single tall bin, which is mainly due to light triggering (see Fig. 8). After a triggering bin, there is dead time with empty bins. After a dead time, we see the periodic bins count distribution. It is an exponential distribution that has a period of dead time. This bins distribution is due to the afterpulsing effect. At the right-hand side of the histogram (at time interval [15 - 25] \ \mu s), the afterpulsing effect is quite small, and we can assume, that its triggers are essentially the dark counts. This histogram is all we need to obtain afterpulse probability. This method is faster, than previously mentioned, because we need to obtain only one histogram, instead of two and more, and we don’t need to change dead time. We can obtain afterpulse probability AP with the next equation:
\begin{equation*}
AP = \sum _{i \in [\tau, 25] \ \mu s} (C_i - C_{dcr}) / C_0, \tag{4}
\end{equation*}
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\begin{equation*}
AP = \sum _{i \in [\tau, 25] \ \mu s} (C_i - C_{dcr}) / C_0, \tag{4}
\end{equation*}
where
i is a bin number, that is in time interval
[\tau, 25] \ \mu s,
C_i is i’th bin’s count,
C_{dcr} is the average dark count per bin, that we obtain in time interval
t \in [15, 25] \ \mu s,
C_0 is a count in trigger bin.
We measure afterpulse probability in a way similar to measuring the DCR and photon-induced clicks. For each gate amplitude V_g, we measure afterpulse histogram in three different V_{b1} voltages. After that, we approximate function AP(V_{b1}) with an exponential curve. We observe this exponential dependence for a lot of SPDs when performing precision measurements with 20 different V_{b1} voltages. The need to use only three points is due to the necessity of reducing the time of general measurements of the SPD because AP measurements in a single grid point take a lot of time.
On the Fig. 9 we present AP dependencies on gate amplitude for diferent PDE slices for different SPDs.
Some of the presented AP graphics have artifacts due to exponential approximation. We observed, that half of the measured SPDs have high AP > 15 \ \% at PDE \in [20, 25] \ \%, while at PDE < 20 \ \% AP has adequate values AP < 5 \ \%. With high excess voltage V_{ex} avalanches generate sufficiently faster, and the charge flowing through the structure during the avalanche existence is sufficiently higher, which leads to more trap filling. Moreover, the probability of avalanche generation due to charge relaxed from traps increases too.
For many SPDs, we observe, afterpulse probability AP decreases with an increase of gate amplitude V_g, which is due to Geiger mode time t_g lowering. As for DCR(V_g) dependencies, on this graphics, we see the manifestation of charge-persistence effect – the afterpulse probability became equal to 0 for a lot of measured SPDs. It happens because dark counts sufficiently exceed the light-induced counts, and we can’t correctly determine the afterpulse probability by postprocessing histogram. We shouldn’t consider this point optimal with the afterpulse criteria because this is an artifact.
We can conclude that increasing gate amplitude V_g with fixed PDE helps decrease afterpulse probability AP, and the charge-persistence effect leads to incorrectly determining its actual value.
In this work, we have studied the influence of the gating signal parameters on the main operational parameters of the SPD: PDE, DCR, and AP.
We proposed universal recommendations for increasing the performance of the SPD with sinusoidal gating. Recommendations are based on the established relationship of DCR and AP decrease with increasing gate amplitude. The presented method for reducing the noise characteristics is based on reducing the Geiger mode time t_g. We observed this effect on most of the studied sample, and we have only two SPDs, where such optimization has no effect. However, when reaching a critical gate amplitude V^{crit}_g, a sharp increase in the DCR value begins due to the charge-persistence effect. We observe the manifestation of the charge-persistence effect on AP dependencies. It incorrectly determines this value and represents as point AP = 0 \ \% for many measurement SPDs. Using the described dependence has made it possible to reduce the DCR up to three times and AP up to 7 times for one of the measured SPDs. Other SPDs have lower optimization impacts but are still very significant. The proposed simple optimization algorithm has shown practical use at the QKD device.
The charge persistence effect has been previously obtained on the square-pulses gating. We demonstrate the existence of this effect at the sine-gated SPDs. We show that we can’t sufficiently increase gate amplitude – in our measurements, the critical amplitude was around V^{crit}_g \approx 4 - 6 V. We do not observe this effect on some SPDs. Perhaps, its critical amplitude is higher than the maximum possible amplitude for set up. It is due to the circuitry features of creating and amplifying a sinusoidal signal.
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![Fig. 7. - a) Square and sinusoidal gate pulses for visualize difference between undervoltage (based on work [35]). b) Schematic description of charge persistence effect in front-illuminated InGaAs/InP SPAD (based on work [36]).](/mediastore/IEEE/content/media/4563994/9714037/9705167/koziy7-3148204-large.gif)
