Nuclear Instruments and Methods in Physics Research A 695 (2012) 226–228

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Nuclear Instruments and Methods inPhysics Research A

0168-90

doi:10.1

n Corr

6, D-81

E-m

journal homepage: www.elsevier.com/locate/nima

New method for the determination of non-quenching regime for siliconphotomultipliers: A comparative study

Christian Jendrysik a,b,n, Ladislav Andricek a,b, Gerhard Liemann a,b, Hans-Gunther Moser a,b,Jelena Ninkovic a,b, Rainer Richter a,b

a Max-Planck-Institut Halbleiterlabor, Otto-Hahn-Ring 6, D-81739 Munich, Germanyb Max-Planck-Institut fur Physik, Fohringer Ring 6, D-80805 Munich, Germany

a r t i c l e i n f o

Available online 25 October 2011

Keywords:

Single photon counting

Silicon photomultiplier

Quench resistor

Geiger mode avalanche photodiode

02/$ - see front matter & 2011 Elsevier B.V. A

016/j.nima.2011.10.007

esponding author at: Max-Planck-Institut Hal

739 Munich, Germany. Tel.: þ49 8983940092

ail address: jendrysik@hll.mpg.de (C. Jendrysi

a b s t r a c t

In this paper a new method to determine the onset of the non-quenching condition in silicon

photomultipliers (SiPMs), limiting the maximum overbias voltage, is demonstrated. In SiPMs both,

photon detection efficiency and dark count rate (initiated by thermally generated electron-hole pairs),

increase with increasing overbias voltage, making it necessary to find a compromise. New devices with

lower dark count rates allow operation at higher overbias, now, an additional limitation comes from the

ability of the resistor to quench the avalanche in a triggered diode. By determining the ratio of

measured to calculated dark current, in which latter results from measuring the dark count rate, the

start of the non-quenching regime can be identified by a disproportionately high increase of this ratio.

First comparative studies of devices from Hamamatsu, MEPhI-Pulsar, STMicroelectronics, and the MPI

semiconductor laboratory have been carried out. The results demonstrate the capability of this method

to be used as an additional parameter for SiPM characterization.

& 2011 Elsevier B.V. All rights reserved.

1. Introduction

Silicon photomultipliers (SiPMs) are new photon-countingdevices, which have capabilities to replace conventional photo-multiplier tubes (PMTs) in future high energy physics, astrophy-sics, and medical applications [1,2]. SiPMs consist of an arrayof independent avalanche photodiodes (APDs), each having aquench resistor Rq in series. All APDs are connected in parallel,so the signal is the sum of all simultaneously fired cells. Thedevice is operated a few volts above breakdown voltage (overbias,DV). If a photon is absorbed in the sensitive volume of a micro-cell an electrical breakdown occurs. The initial charge carriers areamplified by the avalanche process, adding up to a high internalgain (G� 106). To be sensitive to successive photons the ava-lanche breakdown is stopped by the integrated quench resistor.Since the number of charge carriers is approximately constant foreach pixel, SiPMs promise an excellent photoelectron resolution.In addition, they have a low operating voltage, a small size andthey are insensitive to magnetic fields. Though, SiPMs also havesome drawbacks like high thermal noise of a few 100 kHz (darkcounts), afterpulsing and optical crosstalk (OCT) [3].

Further developments in SiPM research tend to minimize OCTand the dark count level [4], and therefore allow operation at

ll rights reserved.

bleiterlabor, Otto-Hahn-Ring

; fax: þ49 89839400 11.

k).

higher voltages above breakdown, leading to higher photondetection efficiency (PDE) and reduced influence of temperaturevariations. A limiting factor for predictable operation is the abilityof the resistor Rq to quench the avalanche breakdown.

As shown in Ref. [5], with increasing overbias the asymptoticsteady-state value If ¼DV=Rq of the declining current flowingthrough a fired APD approximates a threshold current level Iq ofabout 100 mA. If If is higher than Iq the avalanche is no longerquenched and charge carriers, continuously crossing the junction,generate self-sustaining new breakdowns. To determine the pointof transition to this non-quenching regime is important forreliable operation of the detector at high PDE. Since the recoverytime of an APD is directly proportional to the value of Rq, theresistance is kept small in order to minimize the dead time of thecell. As a rule of thumb, according to Ref. [5], quenching is safe if If

does not exceed a value of 20 mA.In order to measure the onset of non-quenching in SiPMs with

more precision a new, simple method comparing the ratio of darkcounts and dark current is presented and first results, using thisnew approach, are shown for different devices.

2. Method

The dark current of an APD is the charge per second flowingthrough the diode. For an ideal device it is given by the product ofdark counts per second (DC) and charge per pulse [6]. Latter isrepresented by the gain G of the device multiplied by elementary

Fig. 1. Normalized dark count rate calculated from amplitude spectrum of

Hamamatsu with 50 mm pitch. Integration leads to average number NX of fired

cells per trigger event.

Fig. 2. Ratio of currents for SiMPl device (pitch 130 mm, gap 11 mm) as a function

of overbias. The dotted line indicates a ratio of r¼1. A resistor dependent start of

increase of r can be observed.

C. Jendrysik et al. / Nuclear Instruments and Methods in Physics Research A 695 (2012) 226–228 227

charge e:

I¼DC � G � e: ð1Þ

For SiPMs the value of dark counts has to be corrected by a factor,which considers the contribution of optical crosstalk, since thedark count rate gives only information about number of eventsabove trigger level (here 0.5 photon equivalent, pe) but not thenumber of simultaneously fired cells. To take this into account,amplitude spectra at different overbias were measured with adigital oscilloscope (LeCroy WaveRunner). Normalizing the spec-tra and subsequently integrating it, an average number NX of firedpixels per DC trigger event can be calculated (see Fig. 1).

So, for SiPMs Eq. (1) changes to an OCT corrected dark currentgiven by

I¼DC � NX � G � e: ð2Þ

For an ideal device in normal operation the ratio r of themeasured dark current and the calculated one (using Eq. (2)) isexpected to be r¼1. The non-quenching condition should bedistinguished by a disproportional enhancement of the measuredcurrent due to the self-sustaining avalanche process, leading to ahigh increase of r. Ideal in this context means that the contribu-tion of surface leakage currents to the dark current measurementsis taken as zero. In reality an additional contribution of surfaceleakage current leads to an increase of r. But since it is notamplified by the avalanche process, the contribution is onlyrelevant for small overbias and can be neglected from about 1 Voverbias (see Fig. 2).

The current–voltage (I–V) measurements were done in darkconditions with a Keithley 4200 SCS with pA resolution. The darkcount rate was determined with a frequency counter fromAgilent, and the internal gain of the SiPMs was measured with aD5720 charge integrating digitizer from CAEN. The devices wereplaced in a light-tight climate chamber in order to use thetemperature coefficient dR=dT of the quench resistor for thevariation of Rq.

3. Results and discussion

In a comparative study the characteristics and relations of darkcurrent and dark counts of devices from Hamamatsu, MEPhI-Pulsar, STMicroelectronics (STM) and MPI semiconductor

laboratory (SiMPl [7]) were analyzed, using the new methoddescribed in the previous section, and the results are reportedbelow.

For all measurements, which are presented in this paper,corrections for afterpulsing effects were not implemented. InFig. 2, the ratio of measured to calculated current for a MPIdevice with bulk-integrated quench resistor is shown for differentoverbias. At low bias above breakdown voltage the ratio for allestimated resistor values is r� 1, implying a good estimation bythe theoretical value. Small deviations are expected to be causedby pile-up and afterpulsing effects and could be minimized byimproving the measurement setup. With increasing the biasvoltage up to 4 V above breakdown the ratio starts to increaseby a factor of 5–10. According to Ref. [5], the initiation of thisincrease depends on the value of the quench resistor via If. Thus,for smaller resistance the start of non-quenching regime shifts tosmaller overbias. In order to compare different measurements theoverbias, needed to obtain a ratio of r¼2 was chosen. For a valueof Rq ¼ 262 kO a voltage of 3.2 V above breakdown was measured,whereas for Rq ¼ 340 kO a value of 3.6 V can be applied, leading toquench currents of If ¼ 12 mA and If ¼ 11 mA, respectively (seeTable 1). Since the quench resistor of SiMPl devices is formed bynon-depleted bulk material, the mobility of carriers is increasedby less phonon scattering with decreasing temperature, thusleading to a positive temperature coefficient of resistance [8].

For comparison, the same measurement of a Hamamatsudevice with 50 mm pixel size is shown in Fig. 3. For small overbiasthe measured value is described well by the calculated one, whichis again indicated by a ratio of r� 1. At 2.75 V for Rq ¼ 139 kO(If ¼ 20 mA), respectively 2.95 V for Rq ¼ 183 kO (If ¼ 16 mA) itstarts to increase about one order of magnitude, showing thesame qualitative behavior as measured for SiMPl. As expected theHamamatsu device can only be operated at smaller overbias dueto its smaller value of Rq. Furthermore, conventional SiPMs withpolysilicon resistors have negative temperature coefficient dR=dT

(non-linear behavior at doping levels of � 1014 cm�3 [9]), leadingto an inversion of temperature dependence in comparisonwith SiMPl.

In Table 1, the pitch size, temperature dependent breakdownvoltage Vbreak, Rq, and determined current at which r¼2 are listedfor all devices tested in this study. The respective overbias, whichhas to be applied to obtain a ratio of r¼2, is shown in Fig. 4 forcomparison. For the MEPhI-Pulsar device, at T ¼ 273 K and T ¼

253 K, only a ratio of r¼1.4 could be reached due to the instable

Table 1Pitch size, temperature dependent breakdown voltage, resistance, and current at

r¼2 of all devices in this study. Sensor area was ca. 1 mm2. For conventional

SiPMs the values of Rq were determined by I–V measurements in forward bias. For

SiMPl, Rq was estimated by recovery time measurements.

Device Pitch size (mm) Vbreak (V) Rq (kO) If ðr¼ 2Þ ðmAÞ

Hama. 25 69.4 (293 K) 332 17

25 68.4 (273 K) 371 16

25 67.5 (253 K) 417 15

50 70.1 (293 K) 139 20

50 68.9 (273 K) 156 19

50 67.6 (253 K) 183 16

100 70.2 (300 K) 125 13

100 68.7 (273 K) 145 12

100 67.6 (253 K) 163 10

100 66.5 (233 K) 190 9

MEPhI 35 77.5 (293 K) 700 9

35 76.2 (273 K) 855 8

35 74.9 (253 K) 1030 7

SiMPl 130 35.2 (273 K) 340 11

130 34.5 (253 K) 302 12

130 33.9 (233 K) 262 12

STM 60 28.7 (293 K) 346 25

60 28.3 (273 K) 364 29

60 27.8 (233 K) 389 31

Fig. 3. Ratio of currents for Hamamatsu SiPM with 50 mm pitch as a function of

overbias. The measurements show the same qualitative dependence on Rq as

measured for the SiMPl device.

Fig. 4. Overbias to obtain a ratio of r¼2 for different devices as a function of

resistance. The solid line represents 20 mA, according to Ref. [5].

C. Jendrysik et al. / Nuclear Instruments and Methods in Physics Research A 695 (2012) 226–228228

performance of its measurements and the points, plotted in thegraph, are extrapolated values to r¼2. Most of the devices tend toreach the non-quenching regime at a current level, which is belowIf ¼ 20 mA. In addition, the results do not fit to one straight line sothe quenching process is probably influenced by other SiPMparameters (breakdown voltage, etc.), too. In particular, the STMdevice shows, in comparison to the other SiPMs, a differentbehavior (slope and overbias) that is not yet understood.

4. Conclusion

A new approach to determine the onset of the non-quenchingregime in SiPMs, limiting the reliable operation range, waspresented. By taking the optical crosstalk into account thecalculated values of dark current show good agreement withthe measured ones for small overbias. Small contributions ofafterpulsing were not corrected in this work. A disproportionalincrease of the ratio of measured and calculated current isobserved and shows a dependency on the quench resistor forboth, polysilicon as well as bulk-integrated. The new methodoffers a more precise way of determining the non-quenchingregime in SiPMs and indicates that the recommendation ofIf ¼ 20 mA for quenching is safe may be not sufficient. Since thefirst results of this additional characterization parameter are verypromising further studies of possible dependencies on breakdownvoltage, etc., are necessary and could lead to better understandingof the quenching condition in APD-based devices. The obtainedresults for the STM device, using the new method, are not yetunderstood.

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