Abstract
Singlephoton detectors (SPDs) are the most sensitive instruments for light detection. In the nearinfrared range, SPDs based on III–V compound semiconductor avalanche photodiodes have been extensively used during the past two decades for diverse applications due to their advantages in practicality including small size, low cost and easy operation. In the past decade, the rapid developments and increasing demands in quantum information science have served as key drivers to improve the device performance of singlephoton avalanche diodes and to invent new avalanche quenching techniques. This Review aims to introduce the technology advances of InGaAs/InP singlephoton detector systems in the telecom wavelengths and the relevant quantum communication applications, and particularly to highlight recent emerging techniques such as highfrequency gating at GHz rates and freerunning operation using negativefeedback avalanche diodes. Future perspectives of both the devices and quenching techniques are summarized.
Introduction
A single photon is the indivisible minimum energy unit of light, and therefore, detectors with the capability of singlephoton detection are ultimate tools for weak light detection.^{1,2} So far, singlephoton detectors (SPDs) have been widely used in numerous applications such as quantum communication, quantum information processing, Lidar and photoluminescence. Most nearinfrared SPDs can be sorted into three principal categories of devices: photomultiplier tubes, superconducting devices and semiconductor singlephoton avalanche diodes (SPADs). Apart from these devices, there are also some new technologies for singlephoton detection such as quantumdot optically gated fieldeffect transistor^{3} and quantum dot resonant tunneling diodes.^{4} Upconversion detectors^{5,6,7} combining the nonlinear optical process of sum frequency generation and Si SPADs are still considered to belong to semiconductor devices.
Photomultiplier tubes are operated in highvacuum tubes with high voltages between anodes and photocathodes.^{8} A primary electron is produced in the photocathode material as a consequence of the photoelectric effect, and high gain results from a multiplication mechanism that creates secondary electrons. Photomultiplier tubes can have large active areas, but they suffer from low efficiency and high dark count rate.
Superconducting SPDs include superconducting nanowire singlephoton detectors (SNSPD),^{9} transition edge sensors^{10} and superconducting tunnel junctions.^{11} In the SNSPD, a hotspot is created after the absorption of a single photon in superconducting nanowires, and subsequently, the superconducting current density increases due to the size expansion of the hotspot. Once the superconducting current density in the nanowires reaches the critical value, the nanowires are changed from the superconducting state to the normal resistance state. This transition generates a voltage signal of singlephoton detection. The primary advantages of SNSPDs are low dark count rate, high photon count rate and very accurate time resolution. The detection efficiency was low (at the level of a few percent) for early generation devices, but recently, this parameter has been significantly improved through the efforts of the SNSPD community.^{12} However, the cryogenic operating conditions required for SNSPDs limit their use for practical applications.
Currently the mainstream solution for singlephoton detection in practical applications is the use of SPADs. In the literature covering photodetectors, one finds the terminologies of avalanche photodiode (APD) and SPAD. Normally, a device is referred to as an APD when it operates below the breakdown voltage in the linearmode, for which the output photocurrent is linearly proportional to the input optical power. The term SPAD refers to a device operated in Geiger mode, for which biasing above the breakdown voltage can result in a selfsustaining avalanche in response to the absorption of just a single photon. For a SPAD based detector system, there are two crucial parts: the SPAD device^{13,14,15} and the quenching electronics.^{16,17,18} Therefore, the performance of SPD system depends both on the SPAD device itself and the quenching electronics as well.
In the following sections, we will first introduce the basic semiconductor structure, device performance improvement, and Geiger mode operations for InGaAs/InP SPADs. The characteristics and the characterization methods relevant to InGaAs/InP SPADs are subsequently presented, and then we will focus on recent advances of quenching techniques, particularly in the regimes of lowfrequency gating, highfrequency gating and freerunning operation. The applications for diverse quantum communication protocols such as quantum key distribution (QKD),^{19,20} quantum teleportation,^{21} quantum secret sharing (QSS),^{22,23,24} quantum secure direct communication^{25,26,27,28} and counterfactual quantum cryptography^{29} using InGaAs/InP SPADs will also be described briefly and representatively, and finally we conclude with a discussion of future perspectives on both SPAD devices and quenching techniques.
Relevant reviews concerning quantum cryptography,^{30,31} quantum communication,^{32,33} SPDs for quantum information applications,^{1} singlephoton sources and detectors,^{2} solidstate SPDs^{34} and avalanche photodiodes^{35,36} could also be of significance to the reader as references.
InGaAs/InP SPAD
For the singlephoton detection in the nearinfrared, group III–V heterostructure devices such as InGaAs/InP and InGaAs/InAlAs with separate absorption, grading, charge and multiplication structures^{35,36} as shown in Figure 1 are the primary candidates. In these devices, an InGaAs (In_{0.53}Ga_{0.47}As) layer with a roomtemperature band gap E_{g} of 0.75 eV and a cutoff wavelength of around 1670 nm is used as the absorption material, while the latticematched InP layer or InAlAs layer is used as the multiplication material (Figure 1). The electric field in the multiplication layer is sufficiently high to provide the desired avalanche probability, while the electric field in the absorption layer is adequately low to minimize fieldinduced leakage currents.^{13} The charge layer is designed to provide high electric field in the multiplication layer and low electric field in the absorption layer, while the grading layer avoids carrier accumulation in the heterojunction interface.^{13} To improve SPAD performance, both the device structure design and device fabrication should be optimized specifically for singlephoton detection.^{37,38,39}
In Geiger mode, the reverse bias voltage of the SPAD (V_{b}) is larger than the breakdown voltage (V_{br}). When a photon is absorbed, an electron–hole pair of electrical carriers is created. One carrier is subsequently injected into the depletion zone of multiplication layer and may initiate a selfsustaining avalanche due to the impact ionization mechanism at high electric field (on the order of 10^{5} V cm^{−1}). The avalanche current reaches a macroscopic steady state within a buildup time on the order of a few hundred picoseconds.
The device structure of the InGaAs/InP SPAD illustrated in Figure 1 bears similarities to that of more mature ‘linearmode’ APDs used at modest gains below their breakdown voltage. However, despite these structural similarities, the optimization of SPAD performance is significantly different from that of linearmode APDs because these two device types are employed in dramatically different contexts.^{13} Linearmode APDs can provide sensitivity improvements in optical receivers (relative to more conventional receivers based on p–i–n photodiodes, which lack gain) as long as the noise of the APD is less than the noise of the amplifier which follows the APD in the receiver circuit. In general, linearmode APDs only provide a sensitivity advantage for highbandwidth (e.g., >1 GHz) receivers in which the necessarily broad frequency response leads to high amplifier noise. Therefore, linearmode APD design emphasizes low excess noise and high bandwidth.^{35,36}
In contrast, the role of SPADs is to provide an avalanche response that is sufficiently large to reliably detect the injection of a single photoexcited carrier into the multiplication region (Figure 1). This behavior is achieved by operating in Geiger mode (i.e., above V_{br}), and in this capacity, the SPAD is more appropriately described as a photonactivated switch with an essentially digital response that is noisefree, at least in the sense that the threshold for detecting avalanches can be set far beyond the level of any background circuit noise. The only noise in a SPAD originates in ‘dark counts’ induced by thermal or fieldmediated mechanisms in the absence of input signal photons. While the average dark count level can be subtracted from the overall device output, the shot noise of these dark counts is unavoidable.
The different operating modes for linearmode APDs and SPADs require optimization of distinct performance attributes. For instance, linearmode operation benefits from a high gainbandwidth product, and since gainbandwidth product is nominally inversely proportional to the width of the multiplication region (W_{m}), linearmode APD design tends to emphasize narrow W_{m} of well under 1 µm. Conversely, gainbandwidth product bears no direct impact on SPAD performance. Instead, wider multiplication regions can provide lower breakdown fields with a consequently smaller tunneling contribution to the dark counts, and so SPAD design tends to emphasize wider W_{m} of well beyond 1 µm.^{37,40} In a similar vein, linearmode APDs benefit from lower excess noise, which can be provided by narrower multipliers, particularly when deadspace effects are prevalent.^{41} However, excess noise is not directly relevant to SPAD performance, and design considerations related to excess noise are absent during SPAD design.
From the perspective of underlying materials properties and fabrication technology in the InGaAsP material system, the sources of noise in linearmode APDs and SPADs are also considerably different. One key consideration is that the dark current in stateoftheart InGaAs/InP avalanche diode structures (including both linearmode APDs and SPADs) is dominated by perimeter leakage mechanisms.^{42} Although this perimeter leakage does not pass through the multiplication region and remains unmultiplied, for InGaAs/InP avalanche diodes at typical operating temperatures, it is still dramatically larger than the multiplied bulk leakage current. Therefore, the dark current performance of linearmode APDs is dominated by perimeter leakage, and improvements in this device type will require wafer fabrication improvements such as better surface passivation techniques. For SPADs, however, because the perimeter leakage is not multiplied, it does not induce detection events, and only the multiplication of bulk dark carriers influences the dark counts. Therefore, the most profitable strategy for improvement beyond the stateoftheart dark count in SPADs will include a focus on the bulk material properties of the base epitaxial wafers.
Beyond these considerations of underlying SPAD device design, overall device performance is critically dependent on the detection circuitry that follows the SPAD. An appropriate circuit, referred to as quenching electronics,^{16} is necessary to rapidly suppress the avalanche by lowering the reverse bias down to V_{br}, to output the detection signal of the incident photon by discriminating the leading edge of the avalanche current and to restore the SPAD to its armed state to detect the next incoming photon. Note that rapid quenching also reduces afterpulsing as we will discuss below, therefore the quenching electronics plays a key role in a SPAD system. Quenching technologies include passive quenching, active quenching, gated quenching and hybrid quenching.^{16}
In a passive quenching circuit,^{43} a SPAD is connected with a reverse bias through a highvalue ballast resistor (on the order of 100 kΩ). When avalanches occur, the voltage difference between the anode and the cathode of the SPAD decreases swiftly due to the voltage drop across the resistor. Once the voltage difference is lowered sufficiently close to V_{br}, avalanches will spontaneously quench. For a welldesigned SPAD and associated quenching circuit, the quenching time, defined as the time duration from avalanche occurrence to avalanche termination, is on the order of 1 ns. Passive quenching is well suited for asynchronous singlephoton detection (freerunning mode). However, this technique suffers from long recovery times on the order of 100 ns due to the large time constant of resistance capacitance (RC).
To solve the problem of slow recovery in passive quenching, active quenching is implemented^{44,45} by using fast discrimination electronics to sense the leading edges of avalanches. The output signals of the discrimination electronics are used to switch the SPAD bias below V_{br}, and the device is maintained in this disarmed state for a certain time period called the holdoff time or deadtime. Following the holdoff time, the bias is actively switched back to the initial armed state. In this scheme, both the quenching time and the recovery time can be a few nanoseconds or less using commercially available electronics components.
Gated quenching^{46} is widely used for applications requiring synchronous singlephoton detection such as QKD.^{30} In such a scheme, gate pulses with a repetition frequency of f_{g}, voltage amplitude of V_{g} and time duration of τ_{g} (with a resulting duty cycle of τ_{g}f_{g}) are coupled to a SPAD. The SPAD is working in Geiger mode only when the pulses are gated on. However, avalanche signals generated during the gate pulses are superposed with parasitic derivative signals that result from capacitive responses of the SPAD to the gate pulses. The key technical challenge in gated quenching is to extract avalanche signals from the background capacitive responses.
Each quenching technique has its own advantages and disadvantages. Therefore, hybrid quenching schemes combining the above techniques are sometimes applied. For instance, the scheme of passive quenching and active reset, which will be introduced in the later section, can efficiently shorten the recovery time. In the gated quenching scheme, for long gate width, the use of active quenching instead of gated quenching can significantly reduce the quenching time.
Characteristics and characterization of SPAD
For a SPADbased SPD system, there are quite a few parameters that are important for performance evaluation, and optimization of one parameter often involves performance tradeoffs with other parameters. In this section, we first introduce the definitions and the mechanisms of these parameters, and then describe the experimental characterization.
The first important parameter is (single) photon detection efficiency (PDE),^{40} defined as the probability that the detector system produces a desired output signal in response to the arrival of an incident photon. From the view of SPAD structure, PDE is determined by PDE=η_{coup}×η_{abs}×η_{inj}×η_{ava}, where η_{coup} is the coupling efficiency of SPAD, η_{abs} is the absorption efficiency or (internal) quantum efficiency in the absorption layer of SPAD, η_{inj} is the collection efficiency of the photoexcited carriers injected from the absorption layer to the multiplication layer and η_{ava} is the probability of a detectable avalanche given the successful injection of a carrier into the multiplication layer. η_{coup} depends on multiple factors such as insertion loss, surface reflectance and active area of device. η_{abs} is calculated by η_{abs}=1e^{αd}, where α is the absorption coefficient and d is the absorption depth. For InGaAs, α is around 7500 cm^{−1} at 1550 nm illumination. Given d=1.5 µm, η_{abs} is 0.68. η_{inj} and η_{ava} have a sensitive dependence on the electric field, which is determined by the excess bias (V_{ex}) defined as V_{ex} = V_{b} − V_{br}.
Dark count rate (DCR)^{47} is used to characterize the noise performance of the detector system. DCR is defined as the normalized count rate in the absence of illumination. DCR depends on the conditions of temperature (T) and V_{ex}. Dark counts originate from the mechanisms of thermal excitation, tunneling excitation or trapassisted tunneling excitation. At sufficiently high operation temperatures, thermal excitation will be the dominant contribution to DCR, while at low temperatures or high electric fields (large V_{ex}), tunneling excitation will dominate the contributions to DCR.^{13} Although DCR is analogous to APD dark current in the linearmode—e.g., the shot noise of both of these phenomenon plays a comparable role in their overall noise performance—DCR is generally not correlated with the device dark current measured in the linearmode. This is due to the fact that dark current in the linearmode is usually dominated by perimeter leakage currents that do not flow through the multiplication region and therefore do not result in Geiger mode avalanches.
Afterpulse probability (P_{ap}) is another important parameter of SPAD. During an avalanche, some carriers are trapped by defects and impurities in the multiplication layer. Subsequently these carriers are released and can initiate new undesired avalanches called afterpulses.^{48,49} P_{ap} is defined as the probability of producing afterpulsing counts due to the previous photon detection during a time period. Reducing P_{ap} to an appropriately low level is crucial for most applications. Improving the crystal quality of multiplication material can effectively suppress the afterpulsing effect, but advances in fundamental material quality such as significant reduction in defect density are likely to take many years given the current relative maturity of the InGaAsP materials system. Alternatively, reducing the quantity of charge carriers during the avalanche process or shortening the lifetime of trapped carriers can also decrease P_{ap}. For a detector system, P_{ap} is related to multiple conditions, which can be roughly modeled as , where C_{d} is the diode capacitance, C_{p} is the parasitic capacitance of circuit including the lead capacitance of device, δ is the avalanche duration time, τ_{d} is the holdoff time and τ is the lifetime of detrapping carriers. From the above equation, the approaches to reduce P_{ap} include: (1) minimizing C_{p}; (2) limiting δ; (3) lowering V_{ex}; (4) increasing τ_{d}; and (5) decreasing τ by increasing the operation temperature. However, these approaches also have consequent disadvantages. For instance, approach (1) and approach (2) can effectively reduce avalanche charge quantity, but the technical challenge is to extract weak avalanches from background noise. Approach (3) decreases PDE. Approach (4) limits the maximum count rate. Approach (5) increases DCR. Therefore, obtaining the desired afterpulsing performance can often force compromises with other SPAD performance parameters.
Timing jitter (time resolution) is usually defined as the total time uncertainty between incident photons and corresponding electrical signal outputs, which includes the contributions of the SPAD itself and the quenching electronics as well. The intrinsic timing jitter of the SPAD device strongly depends on V_{ex}. With large V_{ex}, high electric field greatly shortens avalanche buildup time and also its time uncertainty.
Maximum count rate is determined by the capability of the SPAD in the limit of saturated photon detections, which can be approximated by the reciprocal of τ_{d}. The ratio of the maximum count rate and the DCR determines the dynamic range of the SPAD.
Photon number resolution (PNR) is important for specific applications such as quantum computation and quantum optics. With conventional techniques of gating mode and freerunning mode, the SPAD is believed not to have the capability of PNR since avalanches always reach the saturation stage due to relatively long quenching time. Operated in such a fashion, the SPAD can only resolve between zero photons and nonzero photons. Using a SPAD array (multipixels) or timemultiplexing scheme^{50} can implement PNR with conventional quenching techniques. Recently, experiments have shown that with ultrashort quenching time as described in later section, for instance, using the technique of highspeed gating, SPAD can also exhibit PNR capability.
The methods to characterize these parameters include the singlephoton scheme^{51,52} and photon pair scheme.^{53} In the singlephoton scheme,^{51,52} a calibrated optical power meter with high accuracy and low uncertainty is used to measure the power of a pulsed laser, and a calibrated attenuator is used to highly attenuate the laser power down to the singlephoton level. Therefore, the calibration for these optical instruments themselves is crucial in such a method. In the photon pair scheme,^{53} correlated photon pairs are generated via a nonlinear optical technique such as spontaneous parametric downconversion, in which signal and idler photons are sent to two detectors for calibrating and triggering, respectively. The output signals of detectors are further processed by a coincidence counter. In this method, the SPAD parameters, particularly PDE, can be precisely measured without requiring a calibrated power meter. Nevertheless, coupling efficiency in each channel is an important factor to be carefully considered.
A typical experimental setup of the singlephoton calibration method is shown in Figure 2. The SPAD is working in the gated mode with low repetition frequency (f_{g}), e.g., 10 kHz. A signal generator outputs original gates and synchronized signals with the same frequency to drive a laser diode. Short optical pulses emitted from the laser diode are divided by a beam splitter. One port of the beam splitter is monitored by a power meter and the other one is connected with a variable attenuator. The power of pulses after the attenuation reaches quasisinglephoton level. The detection signals produced in the quenching electronics are finally connected with a counter. To well illustrate the calibration and the tradeoffs of the SPAD parameters, we construct an experimental singlephoton test bench according to Figure 2 and characterize an InGaAs/InP SPAD as an example. The typical experimental results are plot in Figure 3.
Given that measured count rates are C_{on} and C_{off} with and without laser illumination, respectively, the normalized DCR can be calculated as , where t_{w} is the effective gating width (in ns). Considering the Poisson distribution of incident photons, PDE can be calculated as , where μ is the mean photon number per optical pulse.
The characterization of PDE and DCR as V_{ex} linearly increases is shown in Figure 3a. Apparently, PDE is a linearly function and DCR is an exponential function of V_{ex}. Therefore, the relationship between DCR and PDE is exponential.
To precisely characterize P_{ap}, doublegate method^{51} is widely used. The first gate is for photon detection while the second gate with tunable delay relative to the first gate is for measuring afterpulse counts. In such a way, by varying the delay between the two gates the afterpulsing distribution can be clearly plotted after the subtraction of DCR contribution.
The experimental results of the afterpulsing distribution at different temperatures are plot in Figure 3b, in which the normalized afterpulse probabilities (P_{ap}/t_{w}) exponentially decay in time. The gap between the two lines in Figure 3b clearly shows that increasing temperature can effectively suppress the afterpulsing effect.
Timing jitter is usually measured using an instrument capable of timecorrelated singlephoton counting or a common timetodigital converter. The detection signal in the quenching electronics and the synchronized output from the signal generator can be used as ‘Start’ and ‘Stop’ of the timing measurement instrument, respectively. After eliminating the intrinsic jitter due to the signal generator, the laser, and the timing measurement system, the timing jitter of the whole detector system can be obtained.
Lowfrequency gating
Gated mode is a simple and effective approach to suppress DCR and afterpulses for synchronous singlephoton detection.^{46} When the electronic signals of the gates are coupled to a SPAD, derivative signals are created due to the capacitive response of the SPAD, and avalanche signals are superimposed on the derivative signals. Suppressing the derivative signals to effectively extract avalanche signals is the key task in the gated quenching electronics. The amplitudes of derivative signals depend on the rise (and fall) time of gates, gate amplitudes and quenching circuits. The amplitudes of avalanche signals depend on V_{ex} and t_{w}. t_{w} is the most important parameter in the gated quenching scheme. If t_{w} cannot be too short, e.g. 1 ns or less, the afterpulsing contribution is still considerably high. To suppress the afterpulsing effect, a long holdoff time at the level of microseconds is necessary, which substantially limits the gating frequency. Using conventional gating techniques, the maximum frequency is limited to a few tens of MHz.
The evolution of gating frequency is shown in Figure 4. Dramatic increases in gating frequency occurred during the dozen years between 1998 and 2010. In this Review, we define 100 MHz as a critical point, which means that gating techniques with frequency below (above) 100 MHz are categorized as lowfrequency (highfrequency) gating. In this section, we describe the development and evolution of lowfrequency gating, and introduce some representative gating techniques among numerous works^{46,51,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75} in the past, which could be good references to invent new quenching techniques.
The coincidence method^{64} is a standard technique for avalanche extraction in lowfrequency gating. Electronic gate signals, as shown in Figure 5b(1), are alternating current (AC) coupled to the cathode of SPAD. Output signals with the superposition of avalanches and derivative signals at the anode of SPAD (Figure 5b(2)) are discriminated by a comparator. The comparator outputs (Figure 5b(3)) and the auxiliary signals synchronized to the gates (Figure 5b(4)) are inputs to an AND logic gate, whose outputs (Figure 5b(5)) are effective avalanche events. The timing of the auxiliary signals is precisely controlled to avoid the coincidence with the discrimination outputs of the derivative signals. The coincidence method can be easily implemented using analog and digital circuits. However, there are still some drawbacks in such a scheme. For instance, to avoid false detections due to electronic noise, the threshold of the comparator is necessarily increased. This may result in small avalanches not being detected, e.g., avalanches that have less time to build up because they occur near the end of gates. If the derivative signals are well suppressed, the amplitude ratio of avalanches to background signals can be effectively improved and hence, the comparator threshold can be further lowered.
Commonmode cancellation is the basic idea behind suppressing capacitive responses, and there are diverse approaches to cancelling the derivative signals. In 2000, Bethune and Risk^{57} reported a transient cancellation technique using radio frequency (RF) delay lines, and based on this detector, they implemented an autocompensating quantum cryptography system.^{57,59} Details about the detector can be found in Ref. 63.
The RF delay line scheme and its timing diagram are shown in Figure 6. Electronic pulses (Figure 6b(1)) are AC coupled to the cathode of the SPAD via a directional coupler and are also connected with an opencircuit cable whose length is L. The noninverted reflection at the end of the opencircuit cable forms an additional gate pulse (Figure 6b(2)) delayed by a time interval of 2L/v relative to the original pulse, where v is the propagation speed of electromagnetic waves in the cable. The anode of the SPAD is connected to another cable whose length is the same as the upper cable, but a shortcircuit termination of this second delay cable results in an inverted reflection. The transient signal at the anode is the superposition of the SPAD response signal due to the initial gate pulse and its noninverted reflection from the upper cable along with its inverted reflection that is delayed by 2L/v. As a result of this superposition, the parasitic derivative signals from the two reflections cancel each other, and with appropriate timing of photon arrivals the avalanche signal clearly stands out (Figure 6b(3)). After passing the controlling gate (Figure 6b(4)) and amplifier, the amplified avalanche signals (Figure 4b(5)) then can be easily discriminated. With effective cancellation, the discrimination threshold is substantially lowered, which allows for further reduction of the gating width. As a consequence of shorter gate, the afterpulsing performance of the SPAD is improved. The primary drawback of this approach is that the intrinsic delay due to the cable reflections severely limits the maximum gating frequency.
In 2002, Tomita et al.^{60} implemented a twochannel detector system using the doubleSPAD technique. Two SPADs are operated as shown in Figure 7. These two SPADs have very similar semiconductor parameters such as diode capacitance and excess biasefficiency relationship. Electronic pulses (Figure 7b(1)) are AC coupled to the cathodes of both the SPADs in parallel. The anodes of SPADs are connected with a 180° hybrid coupler (HC). Due to the similar capacitive responses, the derivative signal shapes at the anode of the upper SPAD (Figure 7b(2)) and that at the anode of the lower SPAD (Figure 7b(3)) are almost the same, given that avalanches of the two SPADs are created at different gates. After passing the HC, the derivative signals cancel each other. The avalanche of the upper SPAD is reversed and the avalanche of the lower SPAD remains the same polarity, as shown in Figure 7b(4). The avalanches are then discriminated by two comparators with negative (Figure 7b(5)) and positive (Figure 7b(6)) thresholds, whose outputs indicate detection clicks at the upper and the lower SPADs, respectively.
This doubleSPAD technique also has some drawbacks. The primary drawback is avalanche cancellation. When avalanches of the two SPADs are created at the same gate, the two avalanche signals will cancel each other due to the HC. Therefore, the two detectors cannot output detection clicks at the same time. For some specific applications, this drawback is still acceptable. When a single photon arrives at twoport devices such as beam splitter and polarizing beam splitter, the photon can only be detected by one of the SPADs. In a QKD system, this technique is well suited for the receiver integration. In addition, to maximize the suppression ratio for this scheme, selecting two SPADs with very similar parameters is necessary, which may be achieved with efforts of device screening in practice.
There are also some variant techniques to avoid the above drawbacks. For instance, using a common diode to replace one of the SPADs is a practical solution to avoid both the problems of avalanche cancellation and device screening at the cost of a potential decrease in the suppression ratio. The HC as shown in Figure 7 is the key component to eliminate the derivative signals. Besides the HC, there are some common devices that can implement the function of signal suppression such as commonmode choke coils, radiofrequency transformers and differential amplifiers. In lowfrequency gating, these common devices may be used for practical implementations.
Highfrequency gating
Increasing the gating frequency for SPADs is critical for applications requiring high count rate. Actually, the invention of highfrequency gating techniques was originally driven by highrate QKD applications. For a pointtopoint QKD system, the raw key rate (R_{raw}) is roughly calculated as^{30} , where f is the system clock frequency that is usually the same as f_{g}, t is the channel transmission, and η is detection efficiency. Given a QKD system operating at a certain distance, t and η are fixed. Also, for security consideration, μ cannot be simply increased. Therefore, increasing f is the only way to achieve higher bit rate.^{30}
As explained in the above sections, the primary obstacle of highfrequency gating is the afterpulsing effect. One of the most effective approaches for afterpulsing suppression is reducing t_{w}. Hence the key technology challenge of highfrequency gating is weak avalanche extraction among strong stray signal when t_{w} is ultrashort. In 2006, Namekata et al.^{76} first reported a highfrequency gating detector with a clock rate of 800 MHz. The technique is called sine wave gating (SWG), as shown in Figure 8.
In this scheme, sine waves (Figure 8b(1)) with peakpeak amplitude of V_{pp} are used as gates. Since the frequency spectrum of an ideal sine wave is pure, the response signals are only composed of sine waves with the fundamental frequency and higher order harmonics. Avalanches are superimposed over the response signals (Figure 8b(2)). These response signals can be easily eliminated by cascaded bandstop filters at center frequencies of f_{g}, 2f_{g}, 3f_{g}, etc. After the process of filteringamplificationfiltering, weak avalanches can be finally extracted (Figure 8b(3)) and discriminated (Figure 8b(4)). Lowpass filters are normally used before the comparator in order to smooth the analog signals of amplified avalanches.^{76}
When f_{g} is at the level of GHz, t_{w} is generally very short and this parameter may be further reduced by tuning V_{pp}. Ideally, t_{w} can be calculated as . Empirically, in a GHz SWG detector system, t_{w} can be as short as around 200 ps, which drastically suppresses the afterpulsing effect and hence greatly improves the count rate. The maximum count rate of the SWG scheme can in principle reach the same value as f_{g}. However, due to remaining afterpulsing contributions, a small holdoff time of tens of ns may still be necessary, which limits the maximum count rate to the range of tens of MHz. This is higher than lowfrequency gating detectors, often by several orders of magnitude. Since the conventional holdoff time method cannot be directly applied to the SWG scheme, ‘countoff time’ is normally utilized instead.^{77}
In 2007, Yuan et al.^{78} implemented a new highfrequency gating technique called selfdifferencing. As shown in Figure 9, square waves with a clock rate of GHz (Figure 9b(1)) are coupled to the cathode of the SPAD. The response signals at the anode are first split by a power divider, and signals at one of output ports are delayed by one period. The two signals (Figure 9b(2) and Figure 9b(3)) are then subtracted from each other. As a result, the derivative signals can be effectively eliminated. After amplification, avalanches (Figure 9b(4)) with positive and negative parts can be easily discriminated. The selfdifferencing method is similar to the doubleSPAD technique introduced in the previous section. For practical implementation, the subtraction circuit can be achieved using devices such as RF transformers. Similarly, the drawback of avalanche cancellation also exists when avalanches occur in adjacent gates. Therefore, the maximum ideal count rate is only f_{g}/2.
Presently sine wave gating and selfdifferencing are the two fundamental techniques used for highfrequency singlephoton detection. Each technique has its own advantages and disadvantages in practice. So far, many groups have already implemented highfrequency detector systems using these two techniques or improved schemes,^{76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94} and the clock rate has been increased to over 2 GHz.
In 2009, the Geneva group reported a practical solution for highfrequency gating by combining sine wave gating and selfdifferencing together.^{77} Sine waves were applied as gates, and filters were used to partly reduce response signals while a selfdifferencing circuit was used to finally eliminate response signals. In such a way, the suppression requirement for the filtering circuit and the selfdifferencing circuit was moderate compared to that of using each technique individually.^{77} Wu et al.^{95} demonstrated an optical selfdifferencing method. The response signals of the SPAD were used to drive a laser diode after amplification, and then the optical pulses emitted from the laser diode with the same shapes as the response signals were divided by an optical beam splitter. One output port of the beam splitter was delayed by one period, and two channels of optical pulses were coupled to two balanced photodiodes for cancellation, respectively.
In 2010, the Geneva group presented a SWG detector with a clock rate of 2.23 GHz.^{82} This frequency is the fastest reported so far and approaches the bandwidth limit of current commercial InGaAs/InP SPADs. Applying such detectors to QKD applications, simulations show that the detector performance is already comparable to a common SNSPD, and the maximum communication distance can reach around 200 km.^{82} Chen et al.^{84} invented an improved gating technique called double selfdifferencing. This cascaded selfdifferencing circuit could more effectively reduce response signals and thus further improve the SNR of avalanches.
In 2012, Liang and coworkers^{88} first developed a standalone instrument consisting of a fully integrated SPD system with 1.25 GHz sine wave gating. The 2U rack instrument included diverse functionalities such as precise controls for temperature, bias, amplitude, comparator threshold, delay, and friendly userinterface and relevant auxiliary hardware interfaces. Walenta et al.^{89} also implemented a 1.25 GHz SWG detector module using only lowpass filters, which was well suited for QKD system integration. Similar work has also been done by Liang et al.^{87} and based on the 1 GHz gating detector, they demonstrated a laser ranging experiment.^{85}
Apart from sine waves and square waves, in 2013, Zhang et al.^{93} demonstrated a highfrequency gating detector using Gaussian pulses. Given timedependent Gaussian pulses , where σ is related to pulse width, its derivative signals can be written as . The exponential term in the derivative is the same as that in G(t). The falling edge shape of the bipolar response signals is similar to that of the original Gaussian pulses. If this falling edge is combined with the rising edge of a referencing attenuated and phasematched Gaussian pulses which are synchronized to the original one, the falling edge can be cancelled and a steady plateau is formed. Avalanches are superimposed onto the plateau and hence, can be easily discriminated.
Recently, Restelli et al.^{94} used harmonics subtraction instead of bandstop filters for SWG, which could bring better afterpulsing performance compared with the standard filtering method. The harmonics subtraction method is shown in Figure 10. A sine wave (Figure 10b(1)) and its second harmonic (Figure 10b(2)) are combined and then amplified up to 20 V peaktopeak (Figure 10b(3)). Although the amplified gates are distorted, the rising and falling edges are steeper than those of the fundamental sine wave. High amplitude and steep slope can further shorten the gating width compared with the standard SWG scheme. The first, second and third harmonics are synthesized with phase and amplitude control and then combined with the response signals (Figure 10b(4)) at a power divider. As a result, frequency components due to the harmonics are removed so that remaining avalanches are easily extracted after passing through a lowpass filter and a lownoise amplifier (Figure 10b(5)).
SPADs are traditionally believed to output only click or nonclick for incident photons, but not to resolve photon numbers. However, with the highfrequency gating techniques SPADs may have the capability of PNR. Owing to ultrashort avalanche duration, weak avalanches are always in the subsaturation stage so that different numbers of photongenerated carriers can result in different avalanche amplitudes. Experiments of PNR using highfrequency gating SPADs have been demonstrated.^{95,96,97} However, the incident photon numbers, cannot be effectively resolved, due to the low detection efficiency.
In all the above highfrequency gating schemes, InGaAs/InP SPADs have been used. However, these techniques can be widely applied for other SPADs of different materials. For instance, photon number resolving^{97} and high efficiency^{98} Silicon SPADs using highfrequency gating techniques have been reported.
Freerunning operations
Passive quenching^{16} is the fundamental approach for freerunning singlephoton detection,^{43} and this scheme was initially demonstrated about two decades ago. However, there are still two technical problems to be solved. One is long recovery time and the associated baseline shift due to avalanche pileups during recovery. The other is large afterpulse probability. The recovery problem could be overcome using a resetting circuit in practice. Thus, the afterpulsing problem remains the key challenge in implementing freerunning detectors. Simply increasing the holdoff time severely limits the count rate. Some groups reported different feasible methods to reduce the afterpulsing contribution. Warburton et al.^{99} implemented a freerunning InGaAs/InP SPAD through carefully optimizing the operation conditions such as lowering excess bias and increasing temperature. The Virginia group implemented a sophisticated method for the afterpulsing reduction,^{100,101,102} i.e., removing the package of device and connecting the contacts of the SPAD and the quenching circuit by chiptochip wire bonding. In such a way, the stray capacitance was minimized.
Apart from passive quenching, freerunning SPADs using active quenching have also been reported. In such cases, reducing the quenching time was crucial for the afterpulsing suppression. The Geneva group implemented a freerunning detector based on an active quenching ASIC to minimize the parasitic capacitance of the electronics.^{103}
Highfrequency gating can also be used to mimic freerunning operation, and relevant experiments for applications have been demonstrated.^{85,104} The advantages of this method are low afterpulsing probability and high count rate, while the disadvantage is photon loss due to the duty cycle. For instance, given a gating frequency of 1 GHz and a gating width of 200 ps, the equivalent detection efficiency in the freerunning mode is only 1/5 of that in the gating mode.
In this section, we will focus on the recent progress of freerunning detectors including passive quenching and active reset (PQAR) and negative feedback avalanche diodes (NFADs).
Figure 11 shows a typical PQAR scheme implemented by the Virginia group.^{101} The large resistor in the standard passive quenching schemes is replaced by a highfrequency GaAs FET. The FET is appropriately biased to hold the offstate. In the offstate, the FET has high impedance so that avalanches can be quenched passively. The avalanche signals are direct current coupled to a lownoise amplifier at the cathode of the SPAD. The discrimination outputs of the amplified avalanches are used to drive a pulse generator, which creates reset signals after the period of the holdoff time. The reset signals are AC coupled to the gate terminal of the FET to activate the FET into the onstate. In the onstate, the FET has low impedance so that the voltage at the anode of the SPAD can be rapidly recharged to the initial value (V_{b}). This PQAR scheme offers good dynamic range performance.
Recently a new kind of SPAD device, i.e., NFAD, was invented.^{105,106,107,108,109,110} The NFAD monolithically integrates a highresistance thin film resistor with the semiconductor structure, as shown in Figure 12a. With this design, the NFAD exploits passive quenching. Due to the integration, the parasitic capacitance of the quenching circuit is minimized so that the afterpulsing performance of the NFAD is significantly improved compared with the common SPAD. In the equivalent circuit of the NFAD (Figure 12b), integrated resistor (R_{L}) is larger than diode equivalent impedance (R_{d}) by several orders of magnitude. Therefore, avalanches can be quenched swiftly due to the voltage drop on R_{L}. When the NFAD is recharging, the recovery time is determined by R_{L}C_{d}. The quenching electronics of the NFAD can be similar to that of PQAR circuits, as shown in Figure 12c. Avalanches are AC coupled out. After amplification and discrimination, the outputs are driven by a holdoff time circuit. The amplified holdoff time signals are DC coupled to the anode of the NFAD. When holdoff time signals are at a high level, the bias of the NFAD is below V_{b} due to the voltage lift at the anode of the NFAD. Using such quenching electronics, Lunghi et al.^{111} demonstrated an NFADbased detector system with a detection efficiency of 10% and a DCR of 600 Hz at −50 °C.
In 2012, Yan et al.^{112} implemented a similar freerunning detector using the NFAD in which a transformer was used as an avalanche readout circuit. At −80 °C, a detection efficiency of 10% and a DCR of 100 Hz was achieved. Using a Stirling cooler, the Geneva group significantly improved the noise performance of the freerunning detector.^{113} At −110 °C, with a detection efficiency of 10%, DCR was reduced down to a record level of only 1 Hz, and P_{ap} was 2.2% for 20 µs holdoff time. Such impressive performance implies that NFADs could be comparable to SNSPDs except for the limited count rates. In particular, these detectors are the ideal choice for longdistance QKD, where the limitation in count rate is not an issue.
Quantum communication applications
InGaAs/InP SPADs have been widely used for optical fiber quantum communication, what we would like to illustrate in this section. Particularly in QKD, progress in transmission distance has been since ever closely linked to the progress in the development of lownoise SPDs. InGaAs/InP SPADs, in the lowfrequency gating mode, were used first for QKD at the end of the 1990s using autocompensating plugandplay systems.^{114} In 1999, Bourennane et al.^{115} performed a plugandplay experiment with a fiber transmission distance of 40 km. Hughes et al.^{116} realized oneway phaseencoding QKD implementing both the BB84 and B92 protocols over 48 km of optical fiber. In 2002, Stucki et al.^{117} reported a field QKD experiment over 67 km installed fiber between Geneva and Lausanne. Then Kosaka et al.^{118} increased the QKD distance up to 100 km with InGaAs/InP singlephoton detectors using a doubleSPAD scheme as introduced previously. In 2004, the Toshiba group further increased the QKD distance up to 122 km using low DCR SPADs.^{119} All the above QKD experiments used weak laser pulses (coherent states) to mimic a singlephoton source. However, due to the photonnumbersplitting attack, the secure distance was significantly limited. Thanks to the decoystate scheme subsequently proposed, this primary obstacle was completely eliminated so that practical applications of QKD could be possible. In 2007, Peng et al.^{120} first demonstrated a decoystate QKD experiment over 100 km using InGaAs/InP SPADs.
Longer distances and higher rates were achieved using highfrequency gating featuring less afterpulsing. In 2007, Namekata et al.^{121} first implemented a differential phase shift QKD experiment using SWG SPADs. At a clock rate of 500 MHz, the final secure key rate reached 0.33 Mbps over a distance of 15 km. The same group then implemented 24kbps secure key rate over 100 km fiber distance^{122} by increasing the clock rate up to 2 GHz and optimizing the SPAD performance with an ultralow dark count probability per gate of 2.8×10^{−8} at a detection efficiency of 6%. In 2008, Yuan et al.^{123} demonstrated a GHz QKD experiment using selfdifferencing SPADs and achieved 27.9 kpbs secure key rate at 65.5 km. Then the Toshiba group further improved both the bit rate and the system stability to push forward GHz QKD system for practical uses.^{124} In 2010, they demonstrated 1 Mbps bit rate at 50 km over a continuous operation of 36 h.^{125} In 2014, they performed the coexistence experiment of GHz QKD with classical optical communication,^{126} in which quantum data and bidirectional 10 Gbps classical data were combined in a single fiber using dense wavelength division multiplexing. The secure key rate reached 2.38 Mbps over 35 km and the fiber distance could be extended up to 70 km.
Due to the very short gates and holdoff times, dark count probabilities per gate are becoming pretty low and the afterpulsing may become the main noise contribution for QKD. For this reason the optimal operation temperature of SPADs can be close to room temperature, which is very convenient for commercial systems.^{89,127}
For even longer distances, unpractical SNSPDs are generally employed. However, very recently secure QKD over more than 300 km of fiber have been realized, using ultralow noise freerunning NFADs.^{128}
Apart from weak coherent states, entanglement distribution is another approach to implement QKD. In 2004, the Geneva group implemented the distribution of timebin entangled photon pairs over 50 km fiber.^{129} Takesue demonstrated experimental distribution of timebin entanglement generated using spontaneous fourwave mixing over 60 km.^{130} In 2007, the distribution of polarization entanglement over 100 km was achieved by the Vienna group.^{131} Finally, Dynes et al.^{132} demonstrated distribution of timebin entangled photons over a record distance of 200 km using selfdifferencing InGaAs/InP SPADs.
Except QKD, other quantum communication protocols have also been implemented in optical fiber. The Geneva group demonstrated quantum teleportation over 2 km of telecom fiber^{133,134} and also in an installed fiber network.^{135} In 2008, Bogdanski et al.^{136} reported a QSS experiment for five parties based on a singlequbit protocol. In 2013, Ma et al.^{137} increased the fiber distance up to 50 km for singlequbit QSS, and circular QSS was also demonstrated in fiber.^{138} Counterfactual quantum cryptography was proposed in 2009^{29} and experimentally demonstrated by Ren et al.^{139} and Liu et al.^{140}
Conclusions and outlooks
III–V SPADs are the most practical tools for ultraweak light detection in the nearinfrared. In the past decades, both the academic and industrial communities have made great efforts to achieve performance improvements of SPADs. In the field of semiconductor devices, dedicated devices for singlephoton detection are designed and fabricated, while APDs designed for classical optical communication are no longer widely used in photon counting applications. The device performance of the SPAD itself has been gradually improved. Also, new devices like NFADs and selfquenching SPADs^{141,142} have appeared, which may particularly improve the performance of certain parameters and alleviate the requirements of quenching electronics. In the field of quenching electronics, diverse techniques have been invented for both gating and freerunning operations. The gating frequency has been increased up to 2 GHz and relevant techniques have been quickly applied to QKD. In this review, we have surveyed the technical advances in lowfrequency gating, highfrequency gating and freerunning operation, and we have described some representative quenching schemes.
In the future, the development and evolution of SPADbased nearinfrared detectors will be continuously pushed forward in the same way. On the one hand, the SPADs themselves should have better devicelevel performance. This requires research and focused efforts addressing various device attributes such as structure design and optimization, highquality material growth and fabrication technology. The key parameters to be considered in device design include PDE, DCR and P_{ap}. PDE and DCR are the intrinsic parameters and are generally independent from quenching electronics, which means that the parameter performance cannot be improved using different electronics at the same operating conditions. Thus, high PDE and low DCR are the two core objectives in future device design. Shrinking the size of the SPAD could be an effective approach for the reduction of DCR and P_{ap}, and relevant investigations have started. However, fiber coupling could be a crucial technology challenge for smallsize SPADs. Another benefit of improvements in the DCR versus PDE tradeoff is operation at higher PDE given the same DCR performance. Apart from III–V SPADs, siliconbased devices could also be potential candidates for singlephoton detection in the future—e.g., Ge/Si and InGaAs/Si—although currently, the DCR of these devices are still high compared with III–V SPADs.
On the other hand, quenching electronics is also important for practical detector systems. Therefore, inventing new quenching techniques and continuously optimizing the present quenching techniques are the fundamental tasks for the singlephoton community. For these mature techniques, developing integrated circuits for quenching electronics is the future trend due to various advantages including costeffectiveness, detector miniaturization, parasitic capacitance minimization and power reduction. For Si SPADs, such integrated circuits were achieved over a decade ago.^{143,144,145,146} Also, integrated quenching electronics is favorable for SPAD arrays. Due to both the improvement of device performance and the integration of readout circuits, in the future, developing practical III–V SPAD arrays is possible and significant for applications requiring multipixel nearinfrared singlephoton detection.
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Acknowledgements
We acknowledge WenHao Jiang for technical assistance. This work has been financially supported by the National Basic Research Program of China (Grant No. 2013CB336800), the National HighTech R&D Program (Grant No. 2011AA010802), the National Natural Science Foundation of China (Grant No. 61275121) and the Innovative Crossdisciplinary Team Program of CAS. HZ acknowledges the financial support from the Swiss NCCR QSIT.
Note: accepted article preview online 5 February 2015
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Zhang, J., Itzler, M., Zbinden, H. et al. Advances in InGaAs/InP singlephoton detector systems for quantum communication. Light Sci Appl 4, e286 (2015). https://doi.org/10.1038/lsa.2015.59
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Keywords
 avalanche photodiode
 detector
 InGaAs/InP
 quantum communication
 singlephoton avalanche diode
 singlephoton detection
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