Avalanche photodiodes and quenching circuits for single-photon … · 2017-10-27 · Avalanche photodiodes and quenching circuits for single-photon detection S. Cova, M. Ghioni,A

Avalanche photodiodes andquenching circuits for single-photon detection

S. Cova, M. Ghioni, A. Lacaita, C. Samori, and F. Zappa

1956 APPLIED OPTICS @

Avalanche photodiodes, which operate above the breakdown voltage in Geiger mode connected withavalanche-quenching circuits, can be used to detect single photons and are therefore called single-photon avalanche diodes SPAD’s. Circuit configurations suitable for this operation mode are criticallyanalyzed and their relative merits in photon counting and timing applications are assessed. Simplepassive-quenching circuits 1PQC’s2, which are useful for SPAD device testing and selection, have fairlylimited application. Suitably designed active-quenching circuits 1AQC’s2make it possible to exploit thebest performance of SPAD’s. Thick silicon SPAD’s that operate at high voltages 1250–450 V2 havephoton detection efficiency higher than 50% from 540- to 850-nm wavelength and still ,3% at 1064nm. Thin silicon SPAD’s that operate at low voltages 110–50 V2 have 45% efficiency at 500 nm, decliningto 10% at 830 nm and to as little as 0.1% at 1064 nm. The time resolution achieved in photon timing is20 ps FWHM with thin SPAD’s; it ranges from 350 to 150 ps FWHM with thick SPAD’s. The achievedminimum counting dead time and maximum counting rate are 40 ns and 10 Mcps with thick siliconSPAD’s, 10 ns and 40 Mcps with thin SPAD’s. Germanium and III–V compound semiconductor SPAD’sextend the range of photon-counting techniques in the near-infrared region to at least 1600-nmwavelength.Key words: Photon counting, photon timing, avalanche photodiodes, quenching circuits. r 1996

Optical Society of America

1. Introduction: Photon Counting, Single-PhotonAvalanche Diodes, and Quenching Circuits

Photon counting and time-correlated photon-count-ing techniques have been developed over many yearsby exploiting the remarkable performance of photo-multiplier tubes 1PMT’s2.1–3 In recent years, specialsemiconductor detectors, called single-photon ava-lanche diodes 1SPAD’s2, have been developed to de-tect single optical photons.4–6 In the literature theyhave also been referred to as Geiger-mode avalanchephotodiodes or triggered avalanche detectors. Sig-nificant experimental results have been obtainedwith these techniques in various fields: basic quan-tum mechanics7,8; cryptography9; astronomy10,11;single molecule detection12,13; luminescence micros-copy14–16; fluorescent decays and luminescence inphysics, chemistry, biology, andmaterial science17–21;

The authors are with the Dipartimento di Elettronica e Informa-zione and Centro di Elettronica Quantistica e StrumentazioneElettronica, Consiglio Nazionale delle Ricerche, Piazza LeonardoDa Vinci 32, Milano 20133, Italy.Received 20 December 1994; revised manuscript received 26

July 1995.0003-6935@96@121956-21$06.00@0r 1996 Optical Society of America

Vol. 35, No. 12 @ 20 April 1996

diode laser characterization22; optical fiber testing incommunications23–26 and in sensor applications27,28;laser ranging in space applications and in telem-etry29,30; and photon correlation techniques in laservelocimetry and dynamic light scattering.4,31,32Among other advantages with respect to PMT’s,remarkable progress has been made for photondetection efficiency, particularly in the red and near-infrared range.Silicon SPAD’s have been extensively investigated

and are nowadays well developed; considerableprogress has been achieved in design and fabricationtechniques, and devices with good characteristicsare commercially available.4,33 The devices so farreported can be divided into two groups, based on thedepletion layer of the p-n junction, which can be thin,typically 1 µm,5,6,34,35 or thick, from 20 to 150 µm.4,31,33Their main features can be summarized as follows.For thin-junction SPAD’s 1i2 the breakdown voltageVB is from 10 to 50 V; 1ii2 the active area is small witha diameter from 5 to 150 µm; 1iii2 photon detectionefficiency is fairly good in the visible range, ,45% at500 nm, declines to 32% at 630 nm and to 15% at 730nm and is still useful in the near IR, being ,10% at830 nm and as little as 0.1% at 1064 nm; 1iv2resolution is very high in photon timing, remarkably

better than 100 ps FWHM. In particular, deviceswith a small active area 1,10-µm diameter2 attainbetter than 30 ps FWHM at room temperature andbetter than 20 ps when cooled to 265 °C.5,6,34–37 Forthick-junction silicon SPAD’s 1i2 the breakdown volt-age, VB is from 200 to 500 V; 1ii2 the active area isfairly wide, with a diameter from 100 to 500 µm; 1iii2photon detection efficiency is very high in the visibleregion, remarkably better than 50% over all the540–850-nm wavelength range and declines in thenear IR but is still ,3% at 1064 nm; 1iv2 resolution inphoton timing is fairly good, better than 350 psFWHM for reach-through types33 and around 150 psFWHM for devices having a smoother field profile.4,12In recent years deeper insight has been gained in thephysical phenomena that underlies detector opera-tion, and ultimate limits of the performance inphoton timing have been understood for both thinand thick detectors.6,36–39With germanium SPAD’s, photon detection effi-

ciency greater than 15% at the 1300-nm wavelengthand photon timing with 85-ps FWHM resolutionhave been experimentally verified.9,26,40–43 With re-gard to III–V devices, photon detection efficiencyabove 10% at the 1550-nm wavelength and photontiming with 250-ps FWHM resolution have beenverified for InGaAsP SPAD’s.44,45 In both cases,devices specifically designed to work in the Geigermode have not yet been reported, and the behavior ofcommercially available photodiodes is plagued bystrong afterpulsing effects because of carrier trap-ping 1see Section 22. The situation bears some simi-larity to that of silicon devices 25 years ago,46meaning that there is much room for improvementin the material technology.Essentially, SPAD’s are p–n junctions that operate

biased at voltage VA above breakdown voltage VB.At this bias, the electric field is so high that a singlecharge carrier injected into the depletion layer cantrigger a self-sustaining avalanche.46–49 The cur-rent rises swiftly 1nanoseconds or subnanosecondrise time2 to amacroscopic steady level in themilliam-pere range. If the primary carrier is photogener-ated, the leading edge of the avalanche pulse marksthe arrival time of the detected photon. The cur-rent continues to flow until the avalanche can bequenched by lowering the bias voltage to VB or below.The bias voltage is then restored, in order to be ableto detect another photon. This operation requires asuitable circuit that must 1i2 sense the leading edge ofthe avalanche current, 1ii2 generate a standard out-put pulse that is well synchronized to the avalancherise, 1iii2 quench the avalanche by lowering the biasto the breakdown voltage, 1iv2 restore the photodiodevoltage to the operating level. This circuit is usu-ally referred to as the quenching circuit. As dis-cussed below, the features of the quenching circuitdramatically affect the operating conditions of thedetector and, therefore, its actual performance.Our aim in this paper is to discuss different quench-ing strategies, comparing simple passive-quenching

arrangements and more elaborate active-quenchingcircuits. We also discuss the suitability of the vari-ous quenching circuits for operation with a remoteSPAD connected by a coaxial cable, with reference todetectors mounted in receptacles within an appara-tus or a cryostat, where the circuit cannot bemountedunless it is integrated with the detector.A brief review of the main features of SPAD’s,

which must be taken into account in the design orselection of the quenching circuit, is given in Section2. The operation of SPAD’s in passive-quenchingcircuits is analyzed in Section 3. The operatingprinciple and the essential features of the active-quenching circuits are dealt with in Section 4.Gated detector operation is analyzed in Section 5 forboth passive and active circuits. Circuits withmixedpassive–active features are discussed in Section 6.In conclusion, the main advantages offered by SPADdetectors and the role of active and passive circuitsin their application and development are highlightedin Section 7. All the experimental data reportedhave been obtained in our laboratory unless other-wise specifically quoted.

2. Single-Photon Avalanche Diode OperatingConditions and Performance

Bias supply voltage VA exceeds breakdown voltageVB of the junction by an amount called excess biasvoltage VE 5 1VA 2 VB2, which has a determininginfluence on detector performance. It is worthstressing that the value of ratio VE@VB matters, notthe VE value alone, because the performance isrelated to the excess electric field above the break-down level.4,6,36–39 Since VB ranges from 10 to 500 Vin the different available SPAD’s, the VE values to beconsidered are from ,1 to 50 V and more.

A. Photon Detection Efficiency

For a photon to be detected, not only must it beabsorbed in the detector active volume and generatea primary carrier 1more precisely, an electron–holepair2, it is also necessary that the primary carriersucceeds in triggering an avalanche. The efficiencyof photon detection thus increases with excess biasvoltage VE, since a higher electric field enhances thetriggering probability.4,6 Typical data obtainedwiththin-junction and thick-junction SPAD’s are shownin Fig. 1.

B. Time-Resolution

The resolution in single photon timing also improvesat a higher electric field and hence at higher VE,6,36–39as illustrated in Fig. 2.

C. Dark-Count Rate

As it happens in PMT’s, thermal generation effectsproduce current pulses even in the absence of illumi-nation, and the Poissonian fluctuation of these darkcounts represents the internal noise source of thedetector. As illustrated in Fig. 3, the SPAD dark-count rate increases with excess bias voltage.

20 April 1996 @ Vol. 35, No. 12 @ APPLIED OPTICS 1957

The dark-count rate includes primary and second-ary pulses.46 Primary dark pulses are due to carri-ers thermally generated in the SPAD junction, sothat the count rate increases with the temperatureas does the dark current in ordinary photodiodes.The rate also increases with VE because of twoeffects, namely, field-assisted enhancement of theemission rate from generation centers and an in-crease of the avalanche triggering probability.Secondary dark pulses are due to afterpulsing

effects that may strongly enhance the total dark-count rate. During the avalanche some carriers arecaptured by deep levels in the junction depletionlayer and subsequently released with a statisticallyfluctuating delay, whose mean value depends on thedeep levels actually involved.46,47 Released carrierscan retrigger the avalanche, generating afterpulsescorrelated with a previous avalanche pulse. Thenumber of carriers captured during an avalanchepulse increases with the total number of carrierscrossing the junction, that is, with the total charge of

Fig. 1. Dependence of the photon detection efficiency of SPAD’son excess bias voltage VE: 1a2 detection efficiency for photons at830-nm wavelength versus VE for a thin SPAD developed in ourlaboratory6,34 11-µm junction width, breakdown voltage VB 5 16 V,10-µm active area diameter2; 1b2 detection efficiency versus wave-length with parameter VE for a thick SPAD, the EG&G Slik4

125-µm junction width, breakdown voltage VB 5 420 V, 250-µmactive area diameter2. Experimental data are from our labora-tory.

1958 APPLIED OPTICS @ Vol. 35, No. 12 @ 20 April 1996

the avalanche pulse. Therefore afterpulsing in-creases with the delay of avalanche quenching andwith the current intensity, which is proportional toexcess bias voltage VE. The value of VE is usuallydictated by photon detection efficiency or time resolu-tion requirements, or both, so that the trappedcharge per pulse first has to beminimized byminimiz-ing the quenching delay. If the trapped chargecannot be reduced to a sufficiently low level, afeature of the quenching circuit can be exploited forreduction of the afterpulsing rate to a negligible or atleast an acceptable level. By deliberatelymaintain-ing the voltage at the quenching level 1see Section 32,during a hold-off time after quenching, the carriersreleased are prevented from retriggering the ava-lanche.47 As shown in Fig. 31a2, for silicon SPAD’s atroom temperature a few hundred nanoseconds holdoff can reduce by orders of magnitude the totaldark-count rate at higher excess bias voltage, since itcovers most of the release transient and practicallyeliminates afterpulsing. For SPAD’s that work atcryogenic temperatures the method is less effective,since the release transient becomesmuch slower andthe hold-off time required to cover it may be much

Fig. 2. Dependence of the FWHM resolution in photon timing onexcess bias voltage VE: 1a2 thin-junction SPAD of Fig. 11a2 at roomtemperature 1filled circles2 and cooled to 265 °C 1filled squares2,1b2 thick-junction SPAD of Fig. 11b2 at room temperature.Experimental data are from our laboratory.

longer and hence seriously limit the dynamic rangein photon-counting measurements.43The key factor for attaining a low dark-count rate

is detector fabrication technology. In silicon technol-ogy, efficient gettering processes minimize both theconcentration of generation centers that are respon-sible for the primary dark-current pulses and of deeplevels that act as traps of avalanche carriers. Asillustrated in Fig. 31b2, silicon SPAD’s have beenrecently produced with a very low dark-count rate,that is, with an extremely low generation rate andalmost negligible trapping 1extremely weak trappingwith very short release, ,10 ns at room tempera-ture4,482.

D. Thermal Effects

Breakdown voltage VB strongly depends on junctiontemperature. The thermal coefficient value de-pends on the SPAD device structure and is fairlyhigh, typically around 0.3%@K.4,46,49 At constantsupply voltage VA, the increase of VB causes adecrease of excess bias voltage VE, which in percent-age terms is greater than that of VB by the factorVB@VE. The resulting percent variation ofVE is very

Fig. 3. Dependence of the dark-count rate on excess bias voltageVE: 1a2 thin SPAD of Fig. 11a2 at room temperature; the parameterquoted is the hold-off time after each avalanche pulse 1see text2;1b2 thick SPAD of Fig. 11b2 operated at room temperature with40-ns hold-off time; substantially equal results are obtained withlonger hold off, indicating that trapping effects are almost negli-gible in this device. Experimental data are from our laboratory.

strong at a low VE level, ,30%@K, and fairly highalso at a high VE level, ,3%@K. The effects ondevice performance are significant. The avalanchecurrent itself dissipates considerable energy in thedevice: the instantaneous pulse can attain watts ofpower. The thermal resistance from the diode junc-tion to the heat sink strongly depends on the type ofmounting 1packaged device, chip on carrier, etc.2 andcan range from less than 0.1 to 1 °C@mW. At a highcounting rate, the mean power dissipation causes asignificant temperature increase, particularly inSPAD’s with highVB 1see Sections 3 and 42. Remark-able effects are observed in detector performance,particularly in cases in which the photodiode chip isnot mounted on an efficient heat sink and the meancount rate of the avalanche pulses varies.4 It istherefore important to stabilize accurately the junc-tion temperature in working conditions. It is alsopossible to stabilize VE directly by increasing thesupply voltage VA as the junction temperature rises.However, this introduces a positive feedback withmoderate loop gain, since it slightly increases thepower dissipation 1see Sections 3 and 42. For SPAD’shaving high VB, an upper limit or a coarse stabiliza-tion of the temperature must be associated with thebias voltage feedback.

3. Passive-Quenching Circuits

In the experimental setups employed in the earlystudies on avalanche breakdown in junctions,46,49 theavalanche current quenched itself simply by develop-ing a voltage drop on a high impedance load. Thesesimple circuits, illustrated in Fig. 4, are still cur-rently employed and have been called50,51 passive-quenching circuits 1PQC’s2. The SPAD is reversebiased through a high ballast resistorRL of 100 kV ormore, Cd is the junction capacitance 1typically ,1pF2, and Cs is the stray capacitance 1capacitance toground of the diode terminal connected to RL, typi-cally a few picofarads2. The diode resistance Rd isgiven by the series of space–charge resistance of theavalanche junction and of the ohmic resistance of theneutral semiconductor crossed by the current. TheRd value depends on the semiconductor device struc-ture: it is lower than 500 V for types with a widearea and thick depletion layer 3Figs. 11b2, 21b2, and31b24 and froma fewhundred ohms to various kiloohmsfor devices with a small area and a thin junction3Figs. 11a2, 21a2, and 31a24.Avalanche triggering corresponds to closing the

switch in the diode equivalent circuit. Figure 5shows the typicaly waveforms of diode current Id anddiode voltage Vd, or of the transient excess voltageVex 5 Vd 2 VB:

Id1t2 5Vd1t2 2 VB

Rd5Vex1t2

Rd

. 112

A. Quenching Transition

The avalanche current discharges the capacitancesso that Vd and Id exponentially fall toward the


asymptotic steady-state values of Vf and If:

If 5VA 2 VB

Rd 1 RL>VE

RL

, 122

Vf 5 VB 1 RdIf. 132

The approximation is justified since it must be RL :Rd, as shown in the following. The quenching timeconstant Tq is set by the total capacitance Cd 1 Csand by Rd and RL in parallel, i.e., in practice simplyby Rd,

Tq 5 1Cd 1 Cs2RdRL

Rd 1 RL> 1Cd 1 Cs2Rd. 142

Fig. 5. Pulse waveforms of a SPAD of the type in Fig. 1 thatoperates in the PQC of Fig. 41b2, displayed on a digital oscilloscope:a, avalanche current Id; b, diode voltage Vd.


If If is very small, Vf is very near to VB. When thedeclining voltageVd1t2 approachesVB, the intensity ofId1t2 becomes low and the number of carriers thattraverse the avalanche region is then small. Sincethe avalanche process is statistical, it can happenthat none of the carriers that cross the high fieldregion may impact ionize. The probability of such afluctuation to zeromultiplied carriers becomes signifi-cant when the diode current Id falls below <100 µA,and rapidly increases as Id further decreases.49 Theavalanche is self-sustaining above a latching currentlevel Iq , 100 µA and is self-quenching below it.The Iq value is not sharply defined, as is evidenced bya jitter of the quenching time with respect to theavalanche onset and by a corresponding jitter ofdiode voltage Vq at which quenching occurs. Inmost computations Vq can be assumed practicallyequal to VB although it is slightly higher:

Vq 5 VB 1 IqRd. 152

The total charge Qpc in the avalanche pulse, animportant parameter for evaluating the trappingeffects 1see Section 12, can thus be evaluated, settingin evidence its relation to asymptotic current If andcharacteristic time constant Tr of the voltage recov-ery

Qpc 5 1VA 2 Vq21Cd 1 Cs2 > VE1Cd 1 Cs2 > IfTr, 162

Tr 5 RL1Cd 1 Cs2. 172

Fig. 4. Basic PQC’s: 1a2 configuration with voltage-mode out-put, 1b2 configuration with current-mode output, 1c2 equivalentcircuit of the current-mode output configuration. The avalanchesignal is sensed by the comparator that produces a standardsignal for pulse counting and timing.

B. Minimum Value of the Load Resistor

If the asymptotic current If is set to a value muchlower than the latching current level Iq, the behaviorof the PQC is the correct one: the declining ava-lanche current crosses the Iq level with good slope, sothat the avalanche is neatly quenched after a well-defined time, with fairly small jitter. However, ifthe If value is raised toward Iq, quenching occurswith a progressively longer delay and wider timejitter.49 With If very close to Iq, quenching stilloccurs, but with very long and wildly jittering delay.Finally, when If is made higher than Iq, the ava-lanche is no longer quenched and a steady currentflows, in a situation just like that of diodes currentlyused as voltage references in electronic circuits.In this case, if the power dissipation IfVf > IfVB is toohigh for the actual device mounting, excessive heat-ing may even cause permanent damage to the diode.The experimentermust always check that the asymp-totic If value is sufficiently lower than the quenchinglevel Iq; that is, that the load resistance RL issufficiently high. As a rule of thumb, If should notexceed 20 µA, that is, the RL value should be at least50 kV@V of applied excess bias voltage VE. There-fore, the minimum values of RL to be employed inPQC’s range from 50 to 500 kV for thin-junctionSPAD devices 3see Figs. 11a2 and 31a2 and Refs. 5, 6,34, 35, and 374 that work with VE from 1 to 10 V, from200 kV to 2.5 MV for thick-junction SPAD’s 3such asthe EG&G C30902S and Slik; see Figs. 11b2 and 31b2and Refs. 4 and 31–334, that work with VE from 4 to50 V. Lower values of RLmay be used with caution.

C. Recovery Transition and Small-Amplitude Pulses

Avalanche quenching corresponds to opening theswitch in the diode equivalent circuit 3Fig. 41c24 sothat the capacitances are slowly recharged by thesmall current in ballast resistor RL. The diodevoltage exponentially recovers toward the bias volt-age 1curve b of Fig. 62with time constant Tr, so that ittakes ,5Tr to recover the correct excess voltagewithin 1%. Given the typical values of load RL andof the total capacitance Cd 1 Cs, Tr is typically in themicrosecond range. As recovery starts, the diode

Fig. 6. Retriggering of a SPAD in a PQC 1same as in Fig. 52during the recovery transient after an avalanche pulse, which isthe first one displayed on the left-hand side. The a, diode currentand b, voltage waveforms are displayed on a fast oscilloscope in asingle-sweep mode. Experimental data are from our laboratory.

voltage Vd rises above VB. A photon that arrivesduring the first part of the recovery is almost cer-tainly lost, since the avalanche triggering probabil-ity is very low. Subsequently, the arriving photonshave a progressively higher probability of triggeringan avalanche. However, as illustrated in Fig. 6, thediode fires at a voltage lower than VA. It thenoperates with lower photon detection efficiency andimpaired photon-timing resolution and produces volt-age and current pulses having smaller amplitude asshown in Fig. 7.

D. Output Pulse

One can obtain an output pulse from a PQC byinserting a low-value resistor Rs in series on theground lead of the circuit. A convenient value isRs 5 50 V, since it provides matched termination fora coaxial cable. The sign of the output pulse can bechanged by interchanging the diode terminal connec-tions and by changing the polarity of the bias supplyvoltage.With Rs on the ground lead of the ballast resistor,

as shown in Fig. 41a2, the pulse is an attenuatedreplica of the diode voltage waveform 1see curve b ofFig. 52 and is therefore called voltage-mode output,with peak amplitude Vu of

Vu 5 1VA 2 VB 2 IqRd2Rs

RL 1 Rs> VE

Rs

RL> If Rs. 182

A drawback of the voltage-mode output is that thedetector timing performance is not fully exploited,because of the intrinsic low-pass filter with timeconstant Tq that acts on the fast current pulse toproduce the voltage waveform. It has been seen intheoretical analysis and verified by experiments39,52that such filtering has a detrimental influence on thephoton-timing accuracy, which can be only partlycompensated by employing a very low thresholdlevel in the timing circuit. Furthermore, the limita-tion to If 1see Subsection 3.B.2 causesVu to be necessar-ily small. When Rs 5 50 V, Vu 5 1 mV, so that theconnection to an external comparator by way of a

Fig. 7. Avalanche current pulses of a SPAD in a PQC 1same as inFig. 52 that occur at different times during the recovery from aprevious pulse, which triggers the oscilloscope scan and is the firstone displayed on the left-hand side. Note that the pulse ampli-tude tracks the recovery diode voltage 3compare with Fig. 61b24.The waveforms are displayed on a fast oscilloscope in a repeated-sweep mode. Experimental data are from our laboratory.


coaxial cable is not advisable. It is better to employa higher Rs value, typically 1 kV, and mount thecomparator 1or a voltage buffer2 close to the detector.With Rs on the ground lead of the photodiode as

shown in Fig. 41b2, the waveform of the pulse isdirectly that of the diode current 1see curve a of Fig.52 and is therefore called current-mode output. It isimportant to realize that, in order to have a signifi-cant voltage pulse on Rs, the stray capacitance Csmust be comparable to or greater than the diodecapacitance Cd. Otherwise, only a small fraction ofthe avalanche current will flow through Rs: onlythe current that discharges Cs flows in the loopincluding Rs 3see Fig. 41c24, whereas the currentdischarging Cd flows in the internal loop within thediode. The steplike voltage transition observed onRs has amplitude Vs:

Vs > VE

Rs

Rd11 1Cd

Cs2

> If Rs

RL

Rd11 1Cd

Cs2

> Vu

RL

Rd11 1Cd

Cs2. 192

The waveform has the same fast rise time of theavalanche current 1,1 ns or less2 and amplitude Vsfrom tens to hundreds of millivolts with Rs 5 50 V.The timing performance of the detector is bestexploited, and a coaxial cable can be directly con-nected to the SPAD terminal. Vs is inherentlymuchhigher than Vu because it is generated by the highcurrent VE@Rd of the avalanche 1or most of it, seeabove2 flowing in Rs, whereas Vu is due to the smallcurrent VE@RL 5 If drawn by load RL.The current-mode output 3Fig. 41b24 offers the best

performance in high-rate counting and in precisionpulse timing and is usually preferred. The voltage-mode output 3Fig. 41a24 is fairly simple and has usefulfeatures. For example, since it produces pulseswith longer duration, it is easier to monitor anavalanche pulse sequence on a long time scale of theoscilloscope.

E. Small-Pulse Effects in Photon Counting

Pulses having amplitude lower than the threshold ofthe comparator are not sensed. Figure 7 illustratesthe situation: since the comparator threshold levelcannot be very low because of electronic noise andtemperature drift, each pulse is followed by a quitelong dead time Tpd. Since the pulse repetition ratent 5 np 1 nb 1sum of the detected photon rate np andof dark pulse rate nb2 is random, significant countlosses ensue at higher counting rates.One might consider correcting these count losses

by applying the well-known methods developed forcounting pulses from nuclear radiation detectors.However, the available correction equations1,2,53,54apply to detection systems having behavior eitherstrictly paralyzable 1a radiation quantum that ar-


rives during a dead time does not generate an outputpulse, but it restarts the dead time2 or strictlynonparalyzable 1during the dead time the system iscompletely insensitive: no output pulses are gener-ated, and there is no restarting of the dead time2.Furthermore, these equations can be reliably em-ployed only if the value of the dead time is constantand accurately known. None of these conditions isfulfilled in the case of SPAD’s in PQC’s. After eachavalanche pulse, the triggering probability has acontinuous evolution, starting from practically niland finally reaching a steady value. The behaviorof the detector is thus quite peculiar: it is paralyz-able, but with time-dependent sensitivity to trigger-ing events. The result is a loss of linearity at highcounting rates, which may be measured empiricallybut for which equations for accurate correction of thecount losses have yet to be worked out. Moreimportant, the precise value of Tpd depends on therelative height of the threshold level and of thenormal output pulse and is neither well known norvery stable, so that even an empirically measuredcorrection may not be fully reliable. The pulseamplitude may vary 3see Eq. 1824 because of variationsof excess bias VE, that is, of the supply voltage VA or,more likely, of the breakdown voltage VB. A typicalexample may better clarify the question. Let usassume thatVE 5 2V,Rd 5 1 kV,Cd 5Cs 5 1 pF,RL 5

1 MV, Rs 5 50 V, so that Vs 5 50 mV and Tr 5 2 µs.With the discriminator threshold set at 25 mV, thedead timeTpd is,Tr@25 1 µs. Ashift of 1 mV in thethreshold level causes a variation of 20 ns in Tpd.The same occurs for a variation of 2 mV in Vs, whichmay be due to a variation of 80 mV in excess bias VE.The latter may arise from a variation in the junctiontemperature of 0.1 K for a thick-junction SPAD withVB 5 250 V 1e.g., the EG&G C30902S42 or 1.7 K for athin-junction SPADwithVB 5 16 V 3e.g., the device ofFigs. 11a2 and 31a24.6,34,35,37In summary, with a counting dead time depending

on the SPAD voltage recovery, photon-counting mea-surements can be obtained with an accuracy betterthan 1% only if the total counting rate nt is lowenough to make count losses negligible and correc-tion unnecessary. This corresponds to keeping alower than 1% probability PL of having one or morepulses within the time interval Tpd following acounted pulse. From Poisson statistics, we havePL 5 31 2 exp12ntTpd24 or approximately PL 5 ntTpdfor low values of the average number ntTpd of eventsin Tpd. Accurate counting can therefore be obtainedwith total pulse counting rate nt , 1@100Tpd. In theexample considered above, this means nt , 1@50Tr,that is, counting rates lower than 10 kcps. Thesituation can be improved by inserting a circuithaving constant dead time Ted after the comparatorwith Ted . Tpd, typically Ted $ 2Tr. This electronicdead time will have a dominant effect on the countlosses and, therefore, equations valid for constantdead time will yield fairly accurate corrections to a

moderate count rate, i.e., to nt # 1@10Ted 5 1@20Tr,that is, to 25 kc@s in the example considered.

F. Small-Pulse Effects in Photon Timing

The time resolution is severely degraded by variouseffects connected to small-pulse events. First, theintrinsic time resolution of the SPAD is impairedwhen the diode voltage is reduced.5,6,33–39,42–44 Sec-ond, the reduction of the pulse amplitude causes thetriggering time of the comparator to walk along therising edge of the avalanche pulse. With a pulserise time of ,1 ns, a 10% reduction in the pulseamplitude causes a delay of ,100 ps in the thresholdcrossing time. One might try to avoid this walk byemploying a constant-fraction-trigger circuit55 in-stead of a simple threshold trigger, but this solutionturns out to be only partially effective. In fact, aconstant-fraction-trigger circuit can only eliminateor strongly reduce the walk time in the case of pulseshaving varying amplitudes but constant shape,whereas the avalanche pulses have a rise time thatbecomes progressively slower as the diode voltage islowered.6,33,36–39,43,44As shown in Fig. 8, a degradation of the resolution

is experimentally observed at a higher counting ratent because a higher percentage of photons corre-spond to small-pulse events and, therefore, are timedwith intrinsically lower resolution and with addi-tional random delay. The probability of such eventsis the Poisson probability of having one or morephotons over the entire recovery transient, whichlasts ,5Tr. This recovery is much longer than thedead time Tpd, so that a more stringent limitation tothe counting rate is set for photon timing than forphoton counting, notwithstanding that the allowedpercentage of events that occur during the guardinterval is somewhat higher in photon timing than inphoton counting. In fact, setting the limit to 5%,the corresponding limitation is nt , 1@100Tr, whichin the example considered above means nt , 5 kcps.With regard to the experimental results in Fig. 8, a

question may arise about the effect of the conversiontime of the time-to-amplitude converters 1TAC’s2 thatwere used to record the timing resolution. TheSPAD pulses are sent to the stop input, whereas apulse synchronous with the light pulse is sent to thestart input. TAC’s typically have a conversion timeof several microseconds, during which time they donot respond to subsequent start and stop pulses.It might be concluded that, if a photon is detectedduring a SPAD recovery period, it is usually notrecorded because the TAC is usually busy processingthe prior photon, which is detected with full biasvoltage. However, in a typical high counting ratesituation, SPAD pulses time correlated to the lightpulse are mixed with a steady rate of uncorrelatedpulses because of dark counts and stray light.Uncorrelated SPAD pulses that occur before thestart pulse are not accepted, since the TAC does notrespond to stop pulses that occur before the start.The TAC then accepts a subsequent time-correlatedpulse that may occur during a SPAD voltage recov-

ery caused by one of the uncorrelated events. Thesituation is also similar in the so-called reverse TACconfiguration 1in which SPAD pulses are sent to thestart input of the TAC and the pulse synchronouswith the light signal to the stop input by way of adelay greater than the measured time range2, sincethe fast input gating facility of TAC’s is usuallyexploited to reject pulses that occur before the timeinterval of interest.

G. Working at Higher Counting Rates

To extend the working range toward higher countingrates, the recovery time of SPAD’s in PQC’s must beminimized by minimizing the values of ballast resis-tor RL and stray capacitance Cs. However, exces-sive reduction of RL will bring the steady current Ifclose to the latching current level Iq 1see Subsection3.B.2. The turn-off probability is then so low that theduration of the avalanche current 1or turn-off time492will contribute significantly to the counting deadtime Tpd and eventually will dominate it. Further-

Fig. 8. Effect of the counting rate on the FWHM resolution inphoton timing with SPAD’s in PQC’s. The total counting rate isprogressively increased by increasing the steady background lightthat falls on the detector. For comparison, the performanceobtained with the same SPAD operating with an AQC is alsoreported: 1a2 thin SPAD device of Fig. 11a2 that operates at roomtemperature with excess bias VE 5 2.5 V in a PQC with recoverytime constant Tr 5 500 ns; 1b2 thick SPAD of Fig. 11b2 that operateswith excess biasVE 5 20 V in a PQCwithTr 5 500 ns and cooled to0 °C to reduce the dark-count rate.


more, this duration fluctuates, so that Tpd becomesnot well defined. For example, with If 5 50 µA, theturn-off probability is ,104 s21,49 so that the dura-tion of the avalanche current has a 100-µs averagevalue and is affected by fluctuations with 100-µs rmsdeviation. Even in the most favorable cases, thatis, for SPAD’s with low capacitance 1Cs and Cd # 1pF2 that operate at low excess bias VE 1between 1 and2 V2withminimum ballast resistorRL 1from 50 to 100kV2, the recovery time constant Trwill be around 200ns and the entire recovery will take ,1 µs. There-fore, the counting rate limitations for accurate pho-ton counting and photon timing can be improved, butnot much beyond 200 and 50 kc@s, respectively.

H. Power Dissipation

The energy Epd dissipated in the SPAD during anavalanche pulse corresponds to the decrease of theenergy stored in the capacitance Cd 1 Cs:

Epd 51

21Cd 1 Cs21VB 1 VE2

2 21

21Cd 1 Cs2VB

2

5 1Cd 1 Cs2VE1VB 1VE

2 2 > 1Cd 1 Cs2VEVB,

i.e., to the pulse charge Qpc 3see Eq. 1624 falling by avoltage slightly higher than VB:

Epd 5 Qpc1VB1VE

2 2 > QpcVB.

The dissipation therefore depends not only on excessbias voltage VE and total capacitance Cd 1 Cs, butalso on breakdown voltage VB. At moderate totalcounting rate nt, the mean power dissipation is givenby ntEpd and may cause significant heating, particu-larly in SPAD’s with high VB. For example, withVB 5 400 V,VE 5 20 V, andCd 1Cs 5 5 pF, at nt 5 100kcps the mean power dissipation is 4 mW. With athe thermal resistance of 1 °C@mW, this may in-crease the junction temperature by 4 °C and VB by,5 V. It is worth stressing, however, that PQC’s arefairly safe for SPAD’s, since they inherently avoidexcessive power dissipation. At higher nt values,the dissipation rise is limited by the increasedpercentage of small-pulse events; at very high nt, thelimit dissipation corresponds to the product of latch-ing current Iq and breakdown voltage VB.

I. Operation with a Single-Photon Avalanche DiodeRemote from the Circuit

Working with a SPAD mounted in a position remotefrom the quenching circuit implies long electricalconnections between the detector and circuitry. Forthe ballast resistorRL, a long connection is unaccept-able because it strongly increases the stray capaci-tance Cs, the avalanche pulse charge 3Eq. 1624 and thetransition times 3Eqs. 142 and 1724, enhancing theassociated drawbacks. Luckily, mounting RL closeto the SPAD is not a problem: the physical size of


RL can be very small, since the power dissipation in itis much smaller than in the SPAD. For the signaloutput, a coaxial cable connected to the remotecircuit is perfectly suitable, provided it is terminatedin its characteristic resistance: it then represents apurely resistive load and guarantees good transmis-sion of a fast signal. In the configuration withcurrent-mode output 3Fig. 41b24, Rs 5 50 V can benormally employed, so that a PQC, in which only theSPAD and load resistor RL are remote from thecircuit board, can be readily assembled. The PQCconfiguration with voltage-mode output is not aswell suited: a higher Rs must be employed so thatat least a voltage buffer must be mounted near theSPAD.

4. Active Quenching

A. Active-Quenching Principle

To avoid drawbacks that are due to the slow recoveryfrom avalanche pulses and exploit fully the inherentperformance of SPAD’s, a new approach was devisedand implemented experimentally in our laboratory.56The basic idea was simply to sense the rise of theavalanche pulse and react back on the SPAD,forcing, with a controlled bias-voltage source, thequenching and reset transitions in short times. Aterminology that focuses on the essential features ofthe circuits was also introduced in our laboratory50,51and has been universally adopted: active-quench-ing circuits 1AQC’s2 are based on the new principleand PQC’s are those without a feedback loop. Thestudies carried out in various laboratories on activeor partially active 1see Section 62 quenching circuitscan be outlined as a sort of family tree. The firstAQC configuration 1opposite terminal type, see be-low2 dates back to 1975,56 but it was 1981 before itsapplication to photon timing was attempted,50 fastgating of the detector was demonstrated,51 a secondbasic AQC configuration 1opposite terminal type, seebelow2 was introduced,51 and an AQC based oncomplementary metal oxide semiconducting inte-grated circuit blocks was reported.57 In 1983 theapplication of SPAD’s and AQC’s to time-resolvedfluorescence measurements was demonstrated.17In 1987 a fast AQC was specifically developed forphoton correlation and laser Doppler velocimetry.32In 1988 an AQC configuration suitable for remoteSPAD operation was introduced, patented, and li-censed for industrial production.58 In 1990 the ap-plication of AQC’s to satellite laser ranging withcentimeter resolution was reported.29 In 1991 acompact AQC module was specifically developed forastronomy.10 In 1993 application of SPAD’s withAQC’s to fiber-optic sensors was reported.27 Variousquenching circuits based on fast semiconductorswitches 3double-diffused metal oxide semiconductor1DMOS2 field-effect transistors 1FET’s24 have alsobeen developed and reported: in 1988 an active-reset circuit48; in 1993 twoAQC’s, one to be employedas a component of detectors for elementary particlephysics experiments,59 the other as the basic ele-

ment of a high-performance general-purpose photon-counting module to be produced industrially4; in1994 a compact AQC for detectors in adaptive-opticstelescopes.11Figure 91a2 illustrates the principle of the active-

quenching method. The rise of the avalanche pulseis sensed by a fast comparator whose output switchesthe bias voltage source to breakdown voltage VB orbelow. After an accurately controlled hold-off time,the bias voltage is switched back to operating levelVA. A standard pulse synchronous to the avalancherise is derived from the comparator output to beemployed for photon counting and timing. Thebasic advantages offered by the AQC approach arethe fast transitions 1from quenched state to operat-ing level and vice versa2 and the short and well-defined durations of the avalanche current and of thedead time. The approach is fairly simple and bearssome similarity to an approach employed in anoriginal study with true Geiger–Mueller gas detec-tors for ionizing radiation, but completely new prob-lems arise in its development and application withSPAD’s, as discussed below.

B. Basic Active-Quenching Circuit Configurations andDesign Problems

AnAQC inherently has two connections to the SPADfor sensing the avalanche current and for applyingthe quenching pulse. Therefore, two basic AQCconfigurations can be considered, one with a quench-ing terminal opposite the sensing terminal 1Fig. 102,

Fig. 9. 1a2 Principle of active quenching: current–voltage I–Vcharacteristic curve of the SPAD and switching load line 1dashedlines2 of theAQC controlled voltage source. The Q arrow denotesthe quenching transition, theR arrow the reset transition. 1b2Out-put pulses from an AQC designed for minimum dead time thatoperates with a SPAD of the type in Fig. 1, biased 0.9 V above thebreakdown voltage, displayed on a fast oscilloscope at 5 [email protected] data are from our laboratory.

the other with a coincident quenching and sensingterminal 1Fig. 112. In any case, the sensing terminalhas a quiescent voltage level at ground potential ornot far from it, since it is directly connected to theAQC input.The quenching and reset driver, labeled D in Figs.

10 and 11, represents circuit means that, whendriven from a low-level logic pulse, generate a high-voltage pulse. It can be implemented with either apulse-booster circuit stage10,17,27,29,32,50,51,56,57 or withelectronic switches4,11,48,59 connected to two differentdc voltage sources that correspond to the operatingand quenching voltage levels. For example, suchswitches can be DMOS FET’s capable of withstand-ing the required voltage and of switching in nanosec-ond time from a low-series-resistance on state to ahigh-series-resistance off state and conversely.Both solutions have their relative merits and havebeen employed in practice. With fast switches theAQC can be simpler, more compact, and have lowerpower dissipation, since the driver dissipates poweronly during the transitions. With a pulse-boostercircuit the AQC output can better approximate aconstant impedance source, as required for remoteSPAD operation 1see below2, and better control andfine adjustment of the pulse waveform is usuallyobtained.The amplitude of the quenching pulse should be

larger than excess bias VE. The amplitude marginshould be sufficient to overcome possible reignition

Fig. 10. Simplified diagram of the basic AQC configuration withopposite quenching and sensing terminals of the SPAD. Thenetwork in the dotted box compensates the current pulses injectedby the quenching pulse through the SPAD capacitance, thusavoiding circuit oscillation. The voltage waveforms drawn corre-spond to the circuit nodes marked with the same letter.


effects that are due to nonuniformities of the break-down voltage over the detector area. For SPAD’swith high VB, deviations from uniformity can attainseveral volts4 and make more severe the require-ment of producing large voltage swings with shorttransition times. Determining suitable electroniccomponents and devising circuit schemes for work-ing with excess bias voltage higher than 20 V arenontrivial tasks for the circuit designer.

1. Opposite Terminal ConfigurationIn the opposite terminal configuration10,50,51,56 thequenching pulse must be superimposed on the detec-tor dc bias voltage. An ac coupling could be em-ployed for the quenching pulse, but dc coupling ispreferred. With ac coupling, if it happens even oncethat the avalanche is not quenched, for example,because of an interfering electromagnetic distur-bance from a spark, the SPAD is locked in a station-ary avalanche-on condition, insensitive to subse-quent photons and possibly subject to catastrophicend, caused by excessive heating. Even in theabsence of such anomalous events, with ac couplingthe baseline of the voltage applied to the SPADsuffers a count-rate-dependent mean shift toward alower value 1see Section 52; furthermore, it is affectedby random fluctuations because of the random-timedistribution of the pulses. On the other hand, theproblems met in the design of a dc coupled circuit

Fig. 11. Simplified diagram of the basic AQC configuration withcoincident quenching and sensing terminals of the SPAD. Thenetwork in the dotted box is employed to avoid 1i2 locking of thecircuit in the triggered state by the quenching pulse, and 1ii2 circuitoscillation that is due to small overshoots and ringing of thequenching pulse. The voltage waveforms drawn correspond tothe circuit nodes marked with the same letter.


become increasingly difficult as the bias voltage isincreased. In practice, the configuration is not suit-able for SPAD’s having breakdown voltage higherthan 30 V. A further problem has to be faced withany SPAD, which arises from the current pulse thatis injected into the AQC input through the detectorjunction capacitance by the fast quenching pulsetransition. The reset transition injects a pulse withpolarity that is equal to the avalanche pulse andcomparable amplitude and that retriggers the circuitforcing it into steady oscillation. For example, inthe case of Cd 5 1 pF, VE 5 2 V, with a 2-ns transitiontime, the current injected is 1 mA. Specific provi-sions to avoid such spurious retriggering should betaken. Fast integrated circuit comparators usuallyhave a latch input60: by applying to it a pulsecovering with sufficient margin the SPAD voltagereset transition, spurious retriggering is inhibited.While the comparator is still latched, however, thevoltage on the SPAD recovers and the device can betriggered by incoming photons that are sensed asevents that occur at the end of the latch command.In order to discard such incorrectly timed events, thecircuit must be further elaborated. An alternativesolution, adopted in the first AQC design,50,56 is tocompensate the capacitive pulse by deliberately in-jecting another pulse through an auxiliary capacitorthat has been trimmed to match the detector capaci-tance. If the compensating pulse is returned to thesame input terminal connected to the detector, aninverted quenching pulse has to be applied to thecapacitor, as shown in Refs. 50, and 56. If the AQCcomparator has a differential input, the compensat-ing capacitor can be connected to the other inputterminal and the quenching pulse itself can beemployed,10 as shown in Fig. 10.

2. Coincident Terminal ConfigurationCoincident terminal configuration4,11,17,27,29,32,48,51,57,59has the basic advantage of being suitable for allSPAD’s with any breakdown voltage because one ofthe device terminals is free, not connected to anyAQC point, and is available for applying any re-quired dc bias voltage. The quenching pulse isapplied to the same terminal and with the samepolarity of the avalanche pulse; thus it locks thecomparator in the triggered state unless suitablecircuit means are provided to avoid it. A mono-stable circuit that limits the duration of the quench-ing pulse is a simple solution. If carefully designed,such a circuit produces clean rectangular pulseswith fast transitions affected by minimal overshootsand ringings, typically limited from 1 to 3% of thepulse amplitude. However, the pulse amplituderanges from a few volts to tens of volts: in absoluteterms, this means overshoots from tens to hundredsof millivolts applied to the AQC input. Since thecircuit must be sensitive to pulses smaller than 50mV 1avalanche pulse of 1 mA or less on inputresistance of 50 V2, the overshoots on the resettransition can retrigger the comparator and drivethe circuit into oscillation. The overshoots could be

minimized by slowing down the transition, but at thecost of giving up some of the basic advantages of theAQC. As in the opposite terminal configurationand with the same remarks, the latch input may beemployed for inhibiting spurious retriggering. Abetter solution, illustrated in Fig. 11, was devised forthe second generationAQC’s.17,51 Acomparator withdifferential input is employed and the quenchingpulse is applied to both terminals 1common-modesignal2, whereas the avalanche pulse is applied toone side only 1differential signal2. If the waveformson the two input sides are identical, the action of thequenching pulse on the comparator is canceled. Toequalize the shape of the pulse transitions, one canimprove the input symmetry by adding a capacitor inparallel to the second terminal, emulating the detec-tor capacitance. There is some analogy with thecompensating capacitor of the previous configura-tion, but in practice the capacitance matching turnsout to be not at all critical in this configuration.

C. Hold-Off Time

The hold-off feature can be introduced in any AQCconfiguration with simple circuit means. A mono-stable circuit, triggered by the leading edge of thecomparator output and combined with the latter inOR configuration, can be employed to extend thequenching pulse for a controlled time. The hold-offtime is effective in reducing the effects of trappedcarriers in the dark-count rate 1see Section 22.However, it adds to the AQC dead time and is not aconvenient solution for cases with a long trap releasetransient.43

D. Remote Detector Operation

In AQC’s the ports connected to the detector termi-nals inherently have a low resistive impedance, sothat it is possible to select a 50-V value, providing amatched termination to a coaxial cable. In prin-ciple, AQC’s appear inherently suitable to work withremote SPAD’s connected by coaxial cables; in prac-tice, nontrivial problems are met in the design ofsuch circuits. The coaxial cable enhances the prob-lem of avoiding spurious retriggering of the AQC atthe end of the reset transition, particularly in caseswith high amplitude of the quenching pulse or longcables, or both. Since the cable cannot be termi-nated at the detector end, the inductive and capaci-tive mismatches generate there and reflect back tothe AQC input overshoots and ringing, correspond-ing to the transitions of the quenching pulse. Thequenching driver is therefore subject to more severerequirements. It must provide a good terminationto the cable at the circuit end; therefore, it mustprovide a constant impedance output, which is usu-ally better obtained with a pulse generator circuitrather than with DMOS FET switches. It mustcharge not only the stray and detector capacitance,but also the capacitance of the coaxial cable 1,100pF@m of cable2; therefore, it has to supply a highercurrent surge.In summary, circuits based on the AQC principle

and suitable for remote detector operation appearattractive but present severe problems for the circuitdesigner. In recent years, the practical value andthe high-performance level obtainable with suchcircuits has been demonstrated in many experi-ments carried out in our laboratory; a reliable circuitof this kind has been developed and patented.27,58

E. Active-Quenching Circuit Essential Features

From the previous discussion, the essential featuresand basic characteristics ofAQC’s can be highlightedas follows.

1a2 Duration Tac of the avalanche pulse is con-stant and can be very short. It is set by thequenching delay, given by the sum of circulation timeTL in the quenching loop 1from detector to sensingcircuit and back from quenching circuit to detector2,plus rise time Taq of the quenching pulse:

Tac 5 TL 1 Taq. 1102

The least obtainable Tac value depends on the re-quired excess bias voltage VE, since the value of Taqincreases with the amplitude of the quenching pulse.The minimum Tac values verified range from lessthan 5 ns with VE below 1 V 3see Fig. 91b24 to ,10 nsfor VE around 20 V.4,11 In cases for which one mustset the duration of the current at longer values, forexample, for studying carrier trapping phenom-ena,43,47 this can be simply and accurately obtainedby inserting a known additional delay in the loop.1b2 Dead time Tad of an AQC is constant, well

defined, and can be accurately controlled. Its mini-mum value 1Tad2min is given by twice the circulationtime TL in the quenching loop plus the sum of risetime Taq and fall time Tar of the quenching pulse:

1Tad2min5 2TL 1 Taq1 Tar. 1112

As for Tac, the shortest attainable 1Tad2min valueincreases with excess bias voltage VE. The mini-mum value experimentally obtained is 10 ns work-ing at low VE 3below 1 V, see Fig. 91b24 and 40 ns athigh VE 1approximately 20 V, see Refs. 4 and 112.1c2 A hold-off time after avalanche quenching can

be easily introduced, with simple circuit means thatmaintain low voltage for a longer and accuratelycontrolled time.1d2 Since duration Tar of the reset transition is

very short, the probability of small-pulse eventsduring recovery is minimized. Avalanche trigger-ing almost always occurs at a well-defined, constantbias voltage condition. Furthermore, the few small-pulse events occur only in correspondence with thewell-defined and short reset transition, so that theycan be easily recognized and inhibited or discardedby suitable auxiliary circuits.1e2 Thanks to the low resistance of the bias source,

practically all the avalanche current contributes tothe detector output pulse by flowing in the externalcircuit 1that is, through resistor Rs1 in Figs. 10 and112.


1f2 The total charge Qac in the avalanche pulse isconstant and well defined. It can be evaluated byassuming that it has a trapezoidal pulse shape withnegligible rise time, a constant current at the maxi-mum value Idmax 5 VE@Rd during circulation time TL,and a linearly declining current during quenchingtransition Taq. We can make reference to pulsewidth Tw of a square pulse with equal area and equalamplitude,

Tw 5 TL 1Taq

2, 1122

and write

Qac 5VETw

Rd5 IdmaxTw. 1132

For a given SPAD device, it is interesting to compareAQC’s and PQC’s from the standpoint of avalanchecharge, which is the source of trapped charge andrelated afterpulsing effects. From Eqs. 162 and 1132,one can see that

Qac . Qpc for Tw . Tq, 114a2

that is,

Qac . Qpc for 1TL 1Taq

2 2 . Rd1Cd 1 Cs2. 114b2

The comparison depends on excess bias voltage VEapplied, because at higher VE rise time Taq of theactive-quenching pulse becomes longer, increasingpulse width Tw. It is interesting to note that, tominimize the trapped charge, depending on the case,the active- or passive-quenching approach may beadvantageous. For SPAD devices having small Rdand Cd and small stray capacitance Cs, passivequenching provides the least pulse charge, becauseTq is shorter than the characteristic times in anyAQC loop, that is, shorter than any possible Tw.On the other hand, for detectors with higher resis-tance Rd and larger stray capacitance Cs, activequenching minimizes the charge. As discussed inSection 6 a mixed passive–active-quenching ap-proach may be the most suitable for minimizing theavalanche charge. In any case, it is necessary tobear in mind that it is not the trapped charge alone,but the resulting afterpulsing effect in actual work-ing conditions that doesmatter. Therefore, an accu-rate comparison between different circuits shouldalso take into account the presence or absence of thehold-off feature in the quenching circuit.1g2 The energy Ead dissipated in the SPAD during

an avalanche pulse depends on breakdown voltageVB, on excess bias voltage VE, on SPAD resistanceRd,and on pulse duration Tw, since it is due to pulsechargeQac 3see Eq. 11324 falling by voltage VB 1 VE:

Ead 5 Qac1VB 1 VE2 > QacVB 5 VEVBTw@Rd.


Qac 1and therefore pulse width Tw2 must also beminimized for reducing the dissipation, not only thetrapping effects. Therefore, also from the stand-point of power dissipation mixed passive–active-quenching circuits 1see Section 62 may be most suit-able. The mean power dissipation is given by pulseenergy Ead multiplied by the pulse-counting rate.In the operation of SPAD’s having high VB in anAQCwith a minimum dead time, the high counting ratecapability is essentially limited by thermal effects inthe SPAD. Caution is necessary, since at very highcounting rates the mean power can be fairly high,not much lower than the instantaneous pulse power1VB 1 VE2VE@Rd.

5. Gated Detector Operation

In various applications, it is necessary or at leastadvantageous to operate a highly sensitive photode-tector under the control of a gate command. Typicalcases are laser ranging,29,30 testing of fibers withoptical time-domain reflectometry,23–28 and measure-ments of weak fluorescent emissions immediatelyfollowing an intense light pulse that is due toscattering from an excitation laser.12–21 With PMT’sfor gated operation it is necessary to apply voltagepulses of hundreds of volts to a PMT dynode. WithSPAD’s, the task is much easier: a pulse withamplitude Vg slightly larger than excess bias voltageVE is sufficient to switch the detector from gated off1at bias voltage VA , VB2 to gated on 1at the operatingbias voltage VA 1 Vg 5 VB 1 VE2. Furthermore,gated operation can also be effective in avoiding thedark-count rate enhancement that is due to trappingeffects in SPAD’s. If the SPAD has been gated offfor a sufficiently long time interval 1much longerthan the trap release time2 before bringing it intooperation, trap levels are almost all empty and donot interfere with the following measurement.40–44,47The operation and performance of circuits suitable

for gated detector operation are analyzed and dis-cussed. The gate command is a rectangular voltagepulse from a low impedance source, with duration Tgand fast rise and fall times. The time intervalbetween a gate pulse and the following is Ta, therepetition rate is fa 5 1@Ta, the duty cycle is w 5Tg@Ta 5 faTg. In cases for which the repetition rateis not periodic but random, Ta and fa represent themean interval and repetition rate.

A. Passive Gated Circuits: Basic Features

As outlined in Fig. 12, the passive gated circuitconfigurations can have gate input with either dc orac coupling. In both cases, the pulse actually ap-plied to the SPAD is modified by the filtering actionof the circuit.

1. Direct Current Coupled GateThe gating pulse is added directly in series to dc biasVA. It can be added at the same terminal where dcbias VA is applied 3Fig. 121a24, leaving the other SPADterminal at ground potential free to take the output

signal. For SPAD’s with high VB, however, thisapproach implies nontrivial problems in the gate-driver circuit. Alternatively, the gate pulse can beadded at the other terminal, but it is then necessaryto employ an elaborate electronic output stage thatseparates the avalanche signal at this terminal fromthe gate pulse. In any case, the voltage signalactually applied to the detector is modified by thelow-pass integrator filter made by resistance RL inseries with capacitance Cd 1 Cs 3see the SPADequivalent circuit in Fig. 41c24. The actual rise andfall times of the gating voltage are thus slowed downto,2.2Tr. Of course, during these transitions small-pulse events may occur 1see Section 32.

2. Alternating Current Coupled GateThe voltage pulse actually applied to the detector3Fig. 121b24 is modified by the differentiator filtermade by Cg in series with resistance RL paralleled bycapacitance Cd 1 Cs. Two effects have to be consid-ered. First, the actual amplitude Vg8 is attenuatedwith respect to Vg by the capacitive voltage divider:

Vg8 5 Vg

Cg

1Cg 1 Cd 1 Cs2. 1152

If Cg were comparable with Cd 1 Cs, the attenuationwould be significant and not well controlled, becausethe value of Cd 1 Cs is usually not accurately known.It is advisable to minimize the relative loss in pulseamplitude 1Vg 2 Vg82 # 0.01Vg by employing a suffi-ciently high Cg:

Cg $ 1001Cd 1 Cs2. 1162

Second, the shape of the gating pulse applied tothe detector is modified by the differentiator withtime constant

Tgr 5 RL1Cg 1 Cd 1 Cs2 > RLCg. 1172

The top of the gate pulse is no longer flat; it decaysalmost linearly from the initial Vg to Vg11 2 [email protected] order to keep the decrease within 1%, it is

Fig. 12. PQC configurations for gated detector operation: 1a2 dccoupled gate input, 1b2 ac coupled gate input. The equivalentcircuit of the SPAD 3see Fig. 41c24must be taken into account in thecircuit analysis.

required that

g 5Tgr

Tg$ 100. 1182

The gate pulse is followed by a long negative tail,starting with amplitude VgTg@Tgr 5 Vg@g and decay-ing exponentially with the slow time constant Tgr,which corresponds to the slow release of the chargeaccumulated by Cg in the gate-on interval Tg. Witha periodic sequence of gate pulses with duty cycle w,the linear superposition of exponential tails build upa negative baseline offset Vn:

Vn 5 Vgbw, 1192

wherre b is a numeric factor that can be easilycomputed as b > 1 forw . 1@g and b , 1 forw # [email protected] Vn has an effect equivalent to a loss inamplitude Vg and is subject to the same limitationVn # 0.01 Vg. Therefore, ac coupling is suitable foroperation only with low duty cyclew:

w #0.01

b> 0.01. 1202

In cases in which the gate pulse sequence is randomand not periodic, Vn given by Eq. 1192 is the meanbaseline shift, but it is advisable to consider an evenmore stringent limitation because of the randomfluctuations around the mean.It is also important to take into account that the

charge of the avalanche pulse is stored in Cg, causingthe voltage applied to the SPAD to decay with timeconstant

Tgq 5 1Cg 1 Cd 1 Cs2RdRL

Rd 1 RL> Cg

RdRL

Rd 1 RL

. 1212

The voltage recovery that follows has the timeconstant Tgr of Eq. 1172, so that

Tgq 5 Tgr

Rd

Rd 1 RL5 Tgg

Rd

Rd 1 RL

, 1222

and we can define

h 5Tgq

Tg5 g

Rd

Rd 1 RL

. 1232

A thorough analysis of passive gated circuits has totake into account that the end of the gate pulse willterminate the avalanche current, if still flowing atthat time. We therefore have to deal not only withself-quenching passive gated circuits, but also withpassive gated circuits with quenching by gate termi-nation.

B. Passive Gated Circuits: Self-Quenching

1. Direct Current Coupled GateLoad resistor RL must be high if self-quenching isrequired, particularly in cases for which high excess


bias voltage has to be employed, as discussed inSubsection 3.B. The rise and fall times of gatevoltage 2.2Tr are thus fairly slow, from hundreds ofnanoseconds to microseconds. Therefore, these cir-cuits are unsuitable in most cases; they can workonly with fairly long gate durations, at least variousmicroseconds, and suffer significant small-pulse ef-fects.

2. Alternating Current Coupled GateThe avalanche quenches itself only if it fully chargesCg within gate time Tg, allowing the SPAD voltage todecay to VB. This can occur only if Tgq is muchshorter than Tg, typically

Tgq # Tg@5, that is, h # 1⁄5. 1242

We see from Eqs. 1182 and 1232 that the ac coupledcircuit is self-quenching only with high loadRL:Rd,typically

RL $ 5gRd $ 500Rd. 1252

It is worth stressing that, with a self-quenchingpassive circuit having an ac coupled gate, no morethan one event per gate pulse can be observed,because the voltage recovery after quenching ismuch longer than Tg. Furthermore, this recoverysets a more severe limitation on the duty cycle thaninequality 1202. At the gate end, the SPAD voltagedecays to VB, just above the quiescent bias level VA.The negative step of the gate voltage produces avoltage undershoot below VA with almost full ampli-tude Vg, followed by exponential recovery with timeconstant Tgr. To limit the baseline shift imposed onthe next gate pulse, it is necessary to wait until theundershoot amplitude decays fromVg toVg@100, thatis, ,Tgr loge 100 , 5Tgr 5 5gTg $ 500Tg. In conclu-sion, correct operation of a self-quenching passivecircuit with ac coupled gate input is possible onlywith very low duty cyclew, typically

w #Tg

Tgr loge 100>

1

5g# 0.002. 1262

A definite conclusion can be drawn about self-quenching gated passive circuits: their perfor-mance and applications are severely limited. Thedc coupled types are practically unsuitable in mostcases. The ac coupled types can be employed in fastgating with very low duty cycle for detecting notmore than one event per gate pulse.

C. Passive Gates Circuits: Quenching by GateTermination

1. Direct Current Coupled GateTo keep gate rise and fall times at the nanosecondlevel, the load resistor RL value must be 100 V orless.42–44 In correspondence with the fast gate-onand gate-off transitions the gate voltage, through thediode junction capacitance 1see Subsection 4.B.12,


injects on the output Rs fast current pulses, withpolarity equal to the avalanche pulse at the gateopening45 and opposite at the gate closing. Withlow RL values, these spurious pulses have amplitudecomparable with the avalanche pulses and compli-cate the operation of circuits employed for pulsecounting or timing. To obtain nanosecond gate du-ration, the situation must be analyzed with morecomplex equivalent circuits that better take intoaccount the distribution of resistances, capacitances,and inductances in the actual detector device andmounting. Employing microwave design tech-niques, even subnanosecond gate durations havebeen obtained.61 The following conclusions can bedrawn about SPAD’s in dc coupled gated circuitswith quenching by gate termination:

1a2 They can be well exploited for detecting asingle photon within a gate pulse of short durationTg, from subnanosecond to a few microseconds.

1b2 The limits to gate duration, repetition rate,and duty cycle are set by the thermal and trappingeffects caused in the SPAD’s by the avalanche cur-rent, which flows until the end of the gating pulse.1c2 They are totally unsuitable for cases in which

more than one photon should be detected within onegate interval.

2. Alternating Current Coupled GateIn circuits having a load resistor RL insufficient forself-quenching, the voltage drop caused by the ava-lanche is smaller than Vg and quenching occurs atthe end of the gate pulse. No more than one eventper gate pulse can be observed. When Tgq is compa-rable with Tg, the SPAD voltage decay is still consid-erable and, therefore, the amplitude of the under-shoot at the gate end is still fairly large. It dependson the time of triggering within the gate and canattainVg31 2 exp12Tg@Tgq24. With respect to the self-quenching type, the time needed for the undershootto decay to Vg@100 and the corresponding limitationto the duty cycle are reduced: in fact, the amplituderatio in the logarithm is reduced from 100 of inequal-ity 1262 to 10031 2 [email protected] Tgq : Tg, the SPAD voltage decay and the

undershoot are very small, so that this limitationthat is due to the recovery from a single avalanchepulse becomes insignificant. However, the ava-lanche pulses enhance the limitation that is due tothe linear superposition of negative tails of the gatepulses. In fact, when the avalanche is triggered, Rdis added in parallel toRL and the differentiating timeconstant is accordingly switched from Tgr to Tgq.The amplitude of the negative tail increases fromVg@g to VgTg@Tgq 5 1Vg@h2 5 11 1 RL@Rd 21Vg@g2. If Pgis the probability of having an avalanche within gatetime Tg, the mean amplitude of the negative tailfollowing a gate pulse is approximately

11 2 Pg2Vg

g1 Pgs

Vg

g 11 1RL

Rd2 5

Vg

g 11 1 Pg

RL

Rd2 . 1272

The mean baseline shift Vn is accordingly modifiedwith respect to Eq. 1192:

Vn 5 Vgwb11 1 Pg

RL

Rd2 , 1282

and to have baseline shiftVn # 0.01Vg, it is necessarythat

w #0.01

b11 1 Pg

RL

Rd2

>0.01

11 1 Pg

RL

Rd2. 1292

Inequality 1292 points out that a high factor RL@Rdcan make this limitation significantly more strin-gent than inequality 1202, notwithstanding that Pg isusually quite lower than unity. It is therefore advis-able to employ a low value for the load resistor, thatis,RL #Rd and a correspondingly higher capacitorCgto keep the time constant Tgr sufficiently long 3seeEq. 11824. These conditions appear the most advis-able for ac coupled gate circuits with quenching bygate termination. In such conditions, the ac configu-ration is an interesting alternative to the dc coupledconfiguration, particularly valuable for working withSPAD’s having high VB. For very short gate timesTg, resistive load RL can be advantageously substi-tuted or complemented by an inductive load.61 Theconclusions drawn for the dc coupled configurationwith quenching by gate termination also apply inthis case, except that duty cycle w is subject to themore severe limitation given by inequality 1292.

D. Passive Gated Circuits: Conclusions

Some general conclusions can be drawn about gatedpassive circuits. The dc or ac coupled configura-tions with quenching by gate termination are themost interesting for practical applications. Theycan be employed for detecting not more than onephoton per gate time. They are well suited for gatepulses with short duration. The dc coupled typecan work with duty cycle w limited only by thermaland trapping effects associated with the avalanche.For the ac coupled type, the circuit behavior sets afurther limitation to w. It is worth noting thatpassive gated circuits, provided they are employedwith a sufficient time interval between gate pulses,offer a feature of remarkable interest for investiga-tions of SPAD behavior and also for some practicalapplications. In fact, the avalanche triggering al-ways occurs without the interfering effects that aredue to previous pulses as described in Section 2,because only the first event is detected. Therefore,simple gated passive circuits can be reliably em-ployed to characterize the true timing accuracy of aSPAD device and to obtain uncompromised resolu-tion in some photon-timing measurements, for ex-ample, in laser ranging applications.

E. Gated Active-Quenching Circuits

Adapting AQC’s to gated operation51 is straightfor-ward: the external gate-off command and the inter-

nally generated quenching command can be appliedto the input of an OR circuit whose output goes to thequenching driver. There is no limitation to longgate times Tg and, thanks to the low output resis-tance of the driver, short transition times can beobtained for the detector voltage. It was indeedverified early51 that AQC’s are almost ideally suitedfor effective and versatile gated operation of SPAD’s.It is worth noting, however, that gated operationmakes even more strict the requirement of avoidingany spurious triggering of the AQC because of forcedtransitions of the SPAD voltage. In fact, the transi-tion from gated off to gated on is equal to the resettransition after quenching and, unless the circuit isproperly designed and operated as illustrated inSection 4, it can generate a false output pulse justwhen the gate is open.

6. Circuits with Mixed Passive–Active Features

The quenching and reset transitions do not necessar-ily have to be both passive or both active and even asingle transition can be managed partly in passiveand partly in active ways. Such mixed solutionscan be an effective approach to designing simple andcompact circuits or for satisfying specific applicationrequirements, or both.

A. Active-Quenching Circuits with Passive Reset

Looking for a simple solution to avoid overshoots andringings in the recovery of the SPAD voltage may bea motivation for resorting to a passive reset in anAQC. An example is the circuit reported by Brownet al.32 diagrammed in Fig. 13. A fast bipolar n-p-ntransistor Q1 is switched on by the comparator andquenches the avalanche by pulling current throughload RL. After a delay just longer than the quench-ing transistion, a p-n-p transistor Q2 is switched onand resets the comparator, which then switches Q1off. The fast switching diodes D1 and D2 are nowboth off and the avalanche photodiode with loadRL isisolated from the rest of the circuit. A low-resis-tance load RL 5 1 kV is employed for smoothlypulling the voltage to the quiescent level, with a

Fig. 13. Simplified diagram of the AQC with the passive resetreported in Ref. 32.


recovery time that can bemade shorter than 20 ns byaccurately minimizing the stray and detector capaci-tance. This circuit has been developed for photoncorrelation measurements to be performed withSPAD’s with excess bias voltage VE to 8 V andoperating with a short dead time of less than 50 ns.The circuit is fairly simple and has been successfullyemployed in the application devised; however, it isnot versatile. It is not suitable to work with highexcess bias voltage because of the limits to thecollector voltage and current of the fast transistorQ1. In fact, Q1 has to stand quiescently a voltagehigher than VE and must then be used to switch on acurrent that is high enough to produce a voltage dropat least equal to VE on a 500-V total resistance. Forexample, with VE 5 20 V this means at least 40 mA.Furthermore, the presence of this steady currentthrough Q1 in the quenched state complicates theintroduction of a hold-off time 1Section 22. Gatedoperation requires nontrivial further elaboration ofthe circuit design. In the gated-off condition Q1and Q2 should be both maintained on and transitionto the gated-on condition should be obtained bycutting off first Q1 and then Q2. The circuit doesnot appear suitable for remote detector operation,since it does not provide a matched termination tothe connecting cables and does not have the capabil-ity of discharging and recharging the cable capaci-tance quickly.

B. Passive Quenching with Active Reset

Starting from the PQC configuration with voltage-mode output 3see Fig. 41a24 the evolution is straightfor-ward. A circuit of this kind has been reported byLightstone and McIntyre.48 A fast voltage switch 1aFET2 is introduced between circuit ground and thenode constituted by the SPAD cathode and the lowend of ballast resistor RL. The switch is quiescentlyopen and the RL value is high enough to guaranteepassive quenching 1see Subsection 3.B.2. After ava-lanche quenching, when the detector voltage has tobe restored, the switch is closed for a short time torecharge the diode and stray capacitance. The re-set command is derived from the comparator thatsenses the avalanche pulse and is applied to theswitch with a delay just longer than the time takenby the quenching transition. It is important toemploy a FET with low capacitance and minimize allstray capacitances by placing a FET and load resis-tor close to the SPAD. Ahold-off time can be simplyenforced by introducing an additional delay afteravalanche quenching, before applying the reset com-mand. This compact circuit is not much more com-plex than the original PQC and provides a remark-ably faster voltage recovery. It has, however, variouslimitations. Like the corresponding PQC configura-tion, it is not suitable for accurate photon timingsince it exploits the voltage-mode output signal.The duration of hold off is limited to a fraction ofrecovery time constant Tr 3Eq. 1724. In gated opera-tion, the circuit suffers limitations similar to those of


PQC’s 1see Section 52. Since the gate commandshould be applied through a large coupling capacitorCg 3see Fig. 121b24, the active reset transition wouldbecome much slower because the switch should alsodischarge Cg. Remote detector operation appearsproblematic: a FET switch remote from the SPADmust also discharge the large capacitance of thecoaxial cable and provide a matched termination.An actively reset scheme derived from the PQC

configuration with current-mode output 3Fig. 41b24might be interesting for applications that requireaccurate photon timing at high counting rates.However, the introduction of a reset FET switch inthis configuration requires more complex modifica-tions in the circuit. In fact, the FET switch shouldbe connected to the SPAD terminal biased at highvoltage. Furthermore, the reset pulse would injecta spurious signal through the SPAD capacitance atthe comparator input, with the problems outlineddealing with AQC having opposite terminal configu-ration. In fact, as far as we know, no circuit of thiskind has been reported.

C. Mixed Passive–Active Quenching

Mixed passive–active quenching4,11 may be a conve-nient approach for minimizing the charge in theavalanche pulse, particularly for SPAD’s havingsmall diode resistance and small stray capacitance3see inequalities 11424. A passive load RL can providea prompt drastic reduction 1quasi-quenching2 of theavalanche current. An active loop can complete thetask after loop delay by forcing the SPAD voltagewell below the nominal VB, with sufficient margin toensure final quenching and avoid reignition that isdue to nonuniformity of VB over the SPAD activearea.4 The active loop also forces a fast reset transi-tion and makes it possible to introduce a controlledhold-off time. By minimizing the pulse charge,trapping and SPAD power dissipation can be mini-mized. Furthermore, this mixed approach appearsparticularly suitable for developing compact circuits.It is worth stressing that it gives flexibility in thechoice of the passive load. Since a quasi-quenchingaction is sufficient, load resistance RL can be smallerthan theminimumvalue required for passive quench-ing 1see Subsection 3.B.2. An inductive load can alsobe employed to enhance the reduction of the ava-lanche current for a short time, covering the delay ofthe active feedback loop. However, to obtain satis-factory results and avoid overshoots and ringing thatare due to the unavoidable combination of induc-tance and capacitances, such a circuit must beaccurately analyzed and carefully implemented.

D. Mixed Active–Passive Reset

Amixed active–passive reset can be adopted to avoidovershoots and ringing in the voltage recovery. Anactive driver can be employed to bring the voltageclose to the quiescent level swiftly and can then beswitched off, leaving the task of completing the smallresidual part of the transition to a slower but

smoother passive reset. In our laboratory solutionsof this kind have been tested with good results andare currently employed inAQC’s.

7. Conclusions

Photon-counting and time-correlated photon-count-ing techniques provide the ultimate sensitivity andaccuracy in measurements of weak and@or fast opti-cal signals. Avalanche photodiodes, called single-photon avalanche diodes 1SPAD’s2, have photon detec-tion efficiency higher than photomultiplier tubes1PMT’s2, particularly in the red and near-IR spectralrange. The spectral region covered with photondetection efficiency higher than 1% extends to,1000nm with silicon SPAD’s and to at least 1600 nm withgermanium and III–V compound semiconductor de-vices. With the available PMT photocathodes, thelong-wavelength cutoff occurs between 600 and 750nm for ordinary high-sensitivity photocathodes 1S-11, S-20, etc.2 and around 900 nm for GaAs negative-electron-affinity types. The old S-1 photocathodestill has the widest near-IR range, but its photondetection efficiency is very low: from a peak valueof ,0.2% at 850 nm it exponentially declines athigher wavelengths, falling to ,1026 at 1300 nm.3Recently, a new photocathode with photon detectionefficiency of ,0.1% to 1600 nm was announced.62In time-correlated photon counting, the neat time

response of SPAD’s, free from the secondary peaksand ringing that plague PMT’s,5,6,12,22,33–35,43 makeseasier and more accurate the reconvolution analysisof measured waveforms. Decay time constants atleast five times shorter than the FWHM resolu-tion14,15,19–21 can thus be accurately measured. TheFWHM values obtained with various SPAD types,ranging from 100 to 350 ps, compare favorably withthose of fast PMT’s. The best FWHM obtained withultrafast silicon SPAD’s5 is 20 ps, equivalent to orbetter than that of the most advanced microchannel-plate photomultipliers.3The SPAD sensitive area is much smaller than

that of PMT’s but is nevertheless sufficient for mostof the envisaged applications. In particular, thesmall area is an advantage for working with opticalfibers, since it is perfectly matched to the fiberoutput and avoids the additional dark-counting rateassociated with an unnecessarily wider area. SPADdetectors bring to photon counting the inherentadvantages of solid-state devices: ruggedness, lowsupply voltage, low power consumption, low sensitiv-ity to magnetic fields, and external disturbances ingeneral. Thanks to their tiny size, they can beeasily mounted in small receptacles within an appa-ratus, for example, in the interior of a micro-scope,14–16 and can be easily cooled to cryogenicconditions.26,42–44SPAD’s must operate in association with quench-

ing circuits. Passive, active, and gated quenchingcircuit configurations have been critically analyzed,and their relative merits in photon counting andtiming applications have been assessed.

For continuous operation of the detector, PQC’sare suitable only for low or moderate total countingrates 1optical signal plus stray light plus dark counts2.For photon counting with 1% accuracy, the counting-rate limit is at best ,200 kc@s. For photon timingthat fully exploits the SPAD resolution, the limit iseven more stringent, at best ,50 kc@s. The count-ing-rate limit is often exceeded by the backgroundalone, that is, by dark counts and stray light reach-ing the detector. It is therefore concluded thatsimple passive circuits find fairly limited application.However, they still deserve interest for simple experi-ments and for tests of initial characterization andselection of the SPAD devices. Passive circuits areattractive because they are simple, they inherentlylimit the average current in the detector device 1thuspreventing excessive power dissipation and heating2,and give easily detectable output pulses. Suitablydesigned AQC’s make it possible to exploit SPAD’sfully, which can be useful at performance levels thatare less limited by the circuit and approach theirintrinsic physical limits. The best-achieved count-ing dead times are 10 ns for low-voltage SPAD’s and40 ns for high-voltage types and operation at count-ing rates exceeding 40 and 10Mc@s, respectively, hasbeen verified. AQC’s thus open the way to wide-spread application of these detectors.For gated operation of the detector, the range of

application of PQC’s is broader. Essentially, pas-sive gated circuits provide satisfactory performancein cases for which only the first photon that arrivesin the gate interval has to be detected. They arevery interesting for cases with very short gate times,in the nanosecond and subnanosecond range. Theycan also be fairly satisfactory with somewhat longergate duration, not exceeding a few microseconds.Actively quenched gated circuits are better suited togated operations in general, and they are absolutelymandatory in applications for which more than onephoton has to be detected within a gate time.In summary, by exploiting the available features of

available quenching circuits and particularly AQC’sSPAD’s are no longer a laboratory curiosity. Theyare a solid-state alternative to PMT’s for measure-ments of very weak and@or fast light signals andprovide a higher sensitivity over a wider spectralrange, particularly in the near infrared, and a bettertime resolution.

Appendix. List of Symbols

b numeric factorCd junction capacitanceCg gate coupling capacitanceCs stray capacitanceD1 fast switching diodeD2 fast switching diodeEpd energy dissipated in the SPAD during an

avalanche pulsefa gate pulse repetition rateg ratio between Tgr and Tg


h ratio between Tgq and TgId transient diode current

Idmax peak amplitude of the diode currentIf asymptotic steady-state diode currentIq latching current levelnb dark pulse ratenp detected photon ratent pulse repetition ratePg probability of having an avalanche within

gate time TgPL probability of having one or more pulses

within time interval TpdQ1 fast bipolar n-p-n transistorQ2 fast bipolar p-n-p transistorQac total charge in the actively quenched ava-

lanche pulseQpc total charge in the passively quenched ava-

lanche pulseRd diode resistanceRL ballast resistanceRs low-value series resistanceTa time interval between a gate pulse and the

following oneTac avalanche pulse durationTad dead time of an active-quenching circuitTaq quenching pulse rise timeTar reset transistion durationTg gate pulse durationTgq time constant of the voltage decay across

the diode when a gate pulse is appliedTgr time constant of the differentiator made by

Cg in series with RLTL circulation time in the quenching loopTpd dead time of a passive-quenching circuitTq quenching time constantTr voltage recovery time constantTw width of a square pulse approximating the

actively quenched avalanche current signalVA bias voltageVB breakdown voltageVd transient diode voltageVE excess bias voltageVex transient excess diode voltageVf asymptotic steady-state diode voltageVg gate pulse amplitudeVg8 actual amplitude of the gate pulseVn negative baseline offsetVq peak amplitude of the current-mode output

signalVu peak amplitude of the voltage-mode output

signalw gate pulse duty cycle.

This paper is based on extensive research that hasbeen carried out for several years in our laboratorywith the joint support of the Italian Space Agency,the Italian National Research Council, and the Min-istry of University and Scientific and TechnologicalResearch. The stimulating discussions, construc-tive criticism, and help in carrying out experimentsgiven by various colleagues and students, in particu-


lar, G. Ripamonti and I. Dal Santo, are gratefullyacknowledged.

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Avalanche photodiodes and quenching circuits for single-photon … · 2017-10-27 · Avalanche photodiodes and quenching circuits for single-photon detection S. Cova, M. Ghioni,A