606 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 60, NO. 2, APRIL 2013

A Novel Technique for the Stabilization of SiPMGain Against Temperature Variations

Francesco Licciulli, Ivano Indiveri, and Cristoforo Marzocca

Abstract—In several applications of Silicon Photo-Multipliers(SiPM), drifts of the detector gain with the temperature repre-sent a severe drawback which prevents from achieving optimalperformance. We propose an original technique to address thisissue, based upon the use of a SiPM not exposed to the light asa temperature sensor. The average amplitude of the dark pulsesproduced by this detector is measured and controlled to a constantreference value by means of a negative feedback loop, whichautomatically varies the bias voltage of the SiPM. The same biasvoltage variations generated by the feedback loop are also appliedto the sensitive SiPMs used in the specific application, thus makingconstant their gain.The effectiveness of the proposed compensation scheme has been

experimentally demonstrated by using two SiPMs from FBK-irst(1mm 1mm, 400micro-cells, breakdown voltage ),one as temperature sensor involved in the negative feedback loopand the other as light sensitive device. Both detectors have beenenclosed in a thermally isolated box with temperature varied inthe interval between 20 and 30 : the variation of the SiPMgain can be reduced from more than 20%, without compensation,to about 2%.

Index Terms—Gain control, negative feedback, SiPM, tempera-ture compensation.

I. INTRODUCTION

R EMARKABLE research efforts are devoted nowadays tothe development of applications in which the favorable

characteristics of Silicon Photo-Multiplier detectors (SiPM)[1]–[3], for instance in terms of gain, timing accuracy andruggedness, are exploited for the detection of low light levels[4], [5]. Even though, thanks to the Geiger mode of operation,the gain sensitivity of a SiPM with respect to temperaturevariations is significantly lower as compared to other kind ofsolid state detectors, such as, for example, APDs, in severalcases the effects of gain drift due to temperature changesseriously limit the optimal performance which can be achievedin the specific application. Gain variations can cause undesiredshifts in the detected photo-peaks, which may compromise theenergy resolution of the detection system. Timing accuracycan be also possibly affected by the excess timewalk generatedby variations in the amplitude of the signals provided by thedetector, caused by gain drift related to temperature changes.

Manuscript received June 07, 2012; revised September 24, 2012; acceptedFebruary 15, 2013. Date of current version April 10, 2013.F. Licciulli and C. Marzocca are with the Department of Electrical and

Electronic Engineering, Politecnico di Bari, I70125 Bari, Italy (e-mail:marzocca@poliba.it).I. Indiveri is with the Italian National Institute of Nuclear Physics (INFN),

Sezione di Bari, Bari, Italy (e-mail: ivanoindiveri@libero.it).Digital Object Identifier 10.1109/TNS.2013.2249527

Therefore, effective temperature compensation techniques mustbe devised when the requirements of the specific applicationcall for an accurate control of the detector gain, especially whendirect control of the temperature to a constant value is costly orunreliable.The gain of the SiPM, i.e., the ratio between the total chargegenerated by a single Geiger discharge and the elementary

charge, can be expressed as a function of its bias voltageby means of the well known equation:

(1)

where is the total capacitance of the elementary micro-cell of the device and is its breakdown voltage. As a con-sequence, the temperature dependence of is mainly related tothe breakdown voltage, which is a linear function of the temper-ature [6], [7].The most straightforward way to control the gain to a con-

stant value in presence of temperature variations is to modify thebias voltage of the detector accordingly, so that the overvoltage

is kept constant [8]. In the compensationschemes presented in the literature a suitable sensor provides asignal proportional to the temperature and, starting from this in-formation, the needed variation of the bias voltage is obtainedand applied to the SiPM [9], [10].We propose here a novel approach, in which the amplitude

of the dark pulses generated by a SiPM, of the same type of theones used as light detectors in the specific application, is usedto measure the variations of the detector gain as a function ofthe temperature. Based on this information, a negative feedbackloop is established, which is able to provide automatically thebias voltage variations needed to keep the gain constant.The paper is organized as follows: in Section II, the temper-

ature compensation solutions reported in the literature are dis-cussed and the proposed closed loop compensation techniqueis basically described; in Section III the details of the experi-mental setup which has been used to prove the feasibility andthe effectiveness of the proposed technique will be given, alongwith the main results obtained; last, in Section IV the conclu-sions are drawn and some future perspectives are presented.

II. TEMPERATURE COMPENSATION OF THE SIPM GAIN

As pointed out above, the main cause of the gain drift withthe temperature for a SiPM is the temperature dependence of thebreakdown voltage, which is expressed by the following equa-tion [7]:

(2)

0018-9499/$31.00 © 2013 IEEE

LICCIULLI et al.: NOVEL TECHNIQUE FOR THE STABILIZATION OF SIPM 607

Fig. 1. Schematic architecture of a classic compensation scheme for the tem-perature dependence of SiPM gain.

Typical values of the parameter are in the order of .From (1) and (2), the sensitivity of the gain with respect to thetemperature descends:

(3)

Different approaches can be found in the literature for com-pensating the gain drift [9], [10]. Essentially, they are basedon the active control of the SiPM bias voltage as a function ofthe temperature. In these schemes, a sensor provides a voltagesignal proportional to the actual temperature:

(4)

This voltage signal is then amplified by a suitable factor , sothat the thermal sensitivity of the resulting signal matchesexactly the sensitivity of the breakdown voltage . Even-tually, the variations of the amplified signal are superimposed tothe bias voltage of the SiPM, for instance by controlling a powersupply source via a GPIB interface. In this way, the breakdownvoltage variations due to temperature drift are exactly compen-sated, thus making constant the SiPM gain. Fig. 1 illustrates thebasic principle of this technique.In Fig. 1 the resistor represents the input impedance of the

DC coupled front-end electronics used to read-out the detector.The effectiveness of the described technique is limited by

some drawbacks: first of all the temperature-to-voltage char-acteristic of the used sensor must be linear, at least within theforeseen temperature range of operation. Moreover the coeffi-cients and , which define respectively the sensitivities ofthe voltage generated by the sensor and the SiPM breakdownvoltage with respect to temperature variations, must be knownwith sufficient accuracy. Also the gain of the amplifier blockmust be controlled with good precision. Last, a variation of theseparameters due, for instance, to aging, may cause a non-optimalbehavior of the compensation system. To correct these effects,long and complex calibration procedures must be applied, sinceobservation of the system behavior under temperature variationsis required to suitably adjust the tunable parameters.The same considerations hold for a similar approach, in which

a thermistor is used as temperature sensor [11]. The bias voltageof the detector, generated by a voltage divider which contains

Fig. 2. The proposed temperature compensation technique: a possibleimplementation.

the thermistor in one of its branches, is able to track the varia-tions of the breakdown voltage, thus making the gain constant.We propose an alternative solution, based on the direct mea-

surement of the temperature dependence of the SiPM gain. Ba-sically, let us consider a SiPM of the same kind of those usedin the considered application as light sensors and shield it fromany exposure to external photons. This “blind” SiPM will gen-erate only dark pulses with amplitude approximately propor-tional to its gain. In fact, the resulting waveform associated to asingle dark pulse can be approximated as the response of a linearsystem to a very short current pulse, i.e., a Dirac’s delta ,which describes the current generated by the triggering of anavalanche breakdown [12]. If the blind detector is in thermalequilibrium with the sensitive devices, the amplitude of its darkpulses will track the temperature variations according to thetemperature dependence of the SiPM gain [9].In the proposed compensation scheme, the average value of

the dark pulse amplitude is measured over an appro-priate time interval in which the temperature can be consideredconstant. Thus, a negative feedback loop is established aroundthe blind detector: the difference between and a desiredreference value is amplified and superimposed to the biasvoltage of the detector, as depicted schematically in Fig. 2. If theloop gain is adequately large, in presence of temperature varia-tions, the bias voltage is automatically adjusted by the feedbackloop so that the amplitude of the dark pulses is kept constantlyequal to the reference value, hence also the gain of the blindSiPM does not vary. The same bias voltage variations gener-ated by the feedback loop for the blind device are also appliedto the sensitive SiPMs, thus achieving the desired gain control.For example, in the ideal arrangement shown in Fig. 2 the

amplitude of the dark pulses generated by the blind SiPM isextracted by means of a peak detector and averaged by a low-pass filter, to obtain .If this kind of approach is used, the advantages of negative

feedback are fully exploited and there is no need of accuratemeasurements of the temperature sensitivity of the breakdownvoltage, which is variable considering different SiPM manufac-turers and even different lots of SiPMs of the same type. More-over no special control of the amplifier gain is necessary andthe influence of parametric drifts of the system components canbe made negligible, thus avoiding the need of long and compli-cated calibration procedures, which involve an accurate controlof the temperature. The only requirement is that the blind SiPMused as a temperature (or gain) sensor must be matched to thedetectors used as light sensors in the specific application.Since the time constants of the temperature variations to be

compensated are usually very slow, no particular requirements

608 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 60, NO. 2, APRIL 2013

must be imposed on the closed loop frequency response of thefeedback system. As a consequence, simple narrow-bandingtechniques can be easily exploited to guarantee the stability ofthe feedback loop. For instance, with reference to Fig. 2, thesystem composed by the SiPM, the pulse peak detector and thelow-pass filter can be considered linear and a transfer functionrelating to can be defined. If the cut-offfrequency of the low-pass filter is adequately reduced, the loopgain presents only a dominant pole, thus system stability isensured.The accuracy of the SiPM gain stabilization depends on the

total dc loop gain , where is the gain of the amplifierand is the dc value of the ratio , i.e., thesensitivity of the dark pulse amplitude to the variations of thebias voltage, assuming that the dc gain of the low-pass filter is 1.The feedback loop will be able to decrease the sensitivity of thedark pulse amplitude with respect to the temperature by a factor

, which can be made conveniently large simply increasingthe amplifier gain.An alternative implementation of the technique can be based

on direct measurements of the average value of the charge con-tained in the dark pulses of the SiPM used as temperature sensor.The drawback of this solution is that it would require more com-plex electronics, since at least integration of the dark pulses,management of the dc current of the blind SiPM, a reset mech-anism and output baseline control for the integrator would beneeded.

PROOF OF PRINCIPLE: EXPERIMENTAL SETUP AND RESULTS

To prove the feasibility and the effectiveness of the temper-ature compensation principle described in the previous section,an experimental system has been set up, in which the feedbackloop around the blind SiPM has been implemented in differentway with respect to the example shown in Fig. 2. This specificimplementation of the compensation technique is schematicallyillustrated in Fig. 3 and is only intended as a proof of principle.The system shown in Fig. 3 sets automatically the bias voltageof the blind SiPM to the value which yields an averageamplitude of the dark pulses equal to , so it exploits thesame principle as the system of Fig. 2.Using a power supply source equipped with a GPIB interface,

the value of the bias voltage applied to the blind SiPMis generated by a routine which runs on the host PC. For eachapplied value of , dark pulses generated by the SiPMare acquired and their amplitude is extracted and averagedby the host PC, obtaining the value . Starting from aninitial value slightly greater than the breakdown voltage, thesoftware increases the bias voltage by a constant stepup to the final value , for which reaches thereference value , corresponding to the desired SiPMgain. The STOP signal is thus generated and the procedurestarts over again from the initial value of , yielding anew value of , automatically updated according to thetemperature variations. Thanks to another output of the powersupply source, the resulting final bias voltages obtainedin each of the described measurement cycles are applied tothe sensitive SiPMs. The typical waveforms of the dark pulses

Fig. 3. Block diagram of the experimental setup used to prove the effectivenessof the proposed temperature compensation principle.

generated by the blind detector for increasing values ofare also shown in the upper right part of Fig. 3.The effectiveness of the described setup depends strongly

on the value chosen for the parameters and . Con-cerning , its value sets the minimum temperature vari-ation which can be ideally compensated. From (1) and(2) it results that, to keep the SiPM gain constant in presence ofa temperature drift , a variation of the bias voltage equal to

is required, thus we have:

(5)

At a given temperature, the estimation of the averageamplitude of the dark pulse generated by the blind SiPM is af-fected by the number of samples used to calculate its value.For instance, the effects of excess noise from the detector andelectronic noise from the measurement system can be reducedif is increased. Optical cross talk and afterpulsing are furthersources of inaccuracies, but also is this case an increase of theparameter is advantageous. In fact, neglecting all the othersources of error and considering only the effects of optical crosstalk, if the average fraction of double dark pulses can be con-sidered constant in the temperature range of operation and theamplitude of the single dark pulse is , the average valueof is

which is proportional to , i.e., to the SiPM gain. Thus, ifis conveniently increased, a good indicator of the SiPM gain isstill obtained also in presence of optical cross talk. Similar con-siderations can be done for what concerns afterpulsing, which,by the way, affects the charge associated to a dark pulse muchmore than its peak amplitude.Since, in each of themeasurement cycles of our setup, the bias

voltage can be varied only by steps , to appreciate thecorresponding variation of the dark pulse amplitude

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(where is a constant), in presence of all the men-tioned sources of noise, the parameter should be set so that agiven signal to noise ratio SNR is guaranteed:

where is the total variance of the measurement errorwhich affects . As a consequence the minimum numberof samples to be considered should be:

(6)

Thus, if is reduced to decrease , the numberof samples should be increased according to (6). In prac-tice, once has been set, the parameter must be in-creased until each measurement cycle provides the same finalvalue , at constant temperature.Two 1 mm 1 mm SiPM of the same type, manufactured

by FBK-irst and composed by 400 micro-cells 50 m 50 m,have been used in the experiments, one as blind SiPM and theother as sensitive detector. The gain of the sensitive SiPM asa function of the temperature has been also monitored via theamplitude of its own dark pulses. Both detectors have been en-closed in a thermally isolated dark box and their temperature hasbeen controlled bymeans of a Peltier cell in the interval between20 and 30 . Two AC-coupled transimpedance preampli-fiers, with gain of about 2 and bandwidth of 20 MHz, basedon discrete BJTs, have been used to read-out the detectors. Tem-perature control via the Peltier cell, instrument control via GPIBinterface and all the data transfer and processing operations havebeen managed by software routines which run on the same hostPC.Since, due to limited resolution in the control of the Peltier

cell we have used, the minimum temperature variation whichcan be reliably imposed to the system is , (5)yields , knowing that .First, the temperature has been kept constant at

and a long series of measurement cycles have been carried out,i.e., a series of ramps of have been applied to the blindSiPM, to find a suitable value for the parameter . According tothe previous considerations, the value of has been increaseduntil a constant has been achieved, yielding . InFig. 4 the values of obtained considering the first tenmeasurement cycles are shown. In these conditions, an averagevalue of 5.4 mV has been measured for , with a stan-dard deviation of 145 , so that the relative variation is about2.7%. The amplitude of the dark pulses generated by the sensi-tive SiPM has been also monitored and similar results have beenobtained.Considering Fig. 4, note that a complete measurement cycle,

which requires the acquisition of about 500 dark pulses, takesabout to be completed, due to the speed limitationsintroduced by the GPIB interface used to transfer the acquireddata from the oscilloscope to the PC. As a consequence, tem-perature variations slower than canbe efficiently tracked by the system.

Fig. 4. Average amplitude of the dark pulses generated by the blind SiPM ob-tained considering 10 measurement cycles at constant temperature .

Fig. 5. Average amplitude of the dark pulses generated by the blind SiPM as afunction of its bias voltage, for each considered value of the temperature.

After this first test, five different values of temperature havebeen considered in the range from 20 to 30 . The referencevalue for the average amplitude of the dark pulses generated bythe blind SiPM has been set to . For each tem-perature value a single measurement cycle has been considered,i.e., a single ramp of has been applied to the blind SiPM.In Fig. 5 the values of obtained for each temperature arereported as a function of the bias voltage. The final bias voltageof each ramp increases with the temperature, according to (3).The control of the Peltier cell has been varied over time to

change the temperature in steps of 2.5 in the same range be-tween 20 and 30 and the described temperature compen-sation system have been left free to evolve in time, so that mea-surement cycles are continuously applied to the blind SiPM. Thetime needed to change the temperature between two different

610 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 60, NO. 2, APRIL 2013

Fig. 6. Bias voltage applied to the sensitive SiPM as a function of thetemperature.

values is about 30 s, whereas the system is able to update thebias voltage of the sensitive SiPM in .The resulting bias voltages applied to the sensitive

SiPM at the end of the thermal transients for each temperaturestep are reported in Fig. 6 as a function of the temperature. Theresults shown in Fig. 6 confirm that the temperature sensitivityof the breakdown voltage is 40 .Finally, in Fig. 7 the average amplitude of the dark pulses gen-

erated by the sensitive SiPM is reported as a function of the tem-perature, respectively in open loop conditions (i.e., without anytemperature compensation technique) and in closed loop, whenits bias voltage is automatically adjusted by the described com-pensation system. Considering a temperature variation ofaround the center value , the measured value of themaximum relative variation of the dark pulse amplitude withouttemperature compensation is more than . The applica-tion of the proposed compensation scheme allows to achievea drastic limitation of this relative variation, which, in closedloop, has been measured to be less than 2%: this result is domi-nated by the error which affects the measurement of the averagedark pulse, due to the limited number of acquired samples. Ifintermediate values of the temperature are considered, i.e., iftemperature steps smaller than are imposed,the quantization error associated to the value chosen formust be considered. Themaximum amount of this error dependson the variation of breakdown voltage that the systemis not able to compensate, i.e., , and on the overvoltage

:

(7)

In our case, the overvoltage of the sensitive detector is about 2 Vand the maximum relative gain error given by (7) is around 5%,but this value can be easily reduced by decreasing and,consequently, , which was not possible in our setup, dueto the mentioned limitations in the temperature control system.Note also that the two detectors used in the experiments are

characterized by a large breakdown voltage mismatch, but this

Fig. 7. Average amplitude of the dark pulses generated by the sensitive SiPMas a function of the temperature, with (“closed loop”) and without (“open loop”)temperature compensation.

does not affect the successful application of the compensationtechnique, since it relies only on the matching between the tem-perature coefficients of the breakdown voltages, which is verygood.

III. CONCLUSIONS AND PERSPECTIVES

A novel technique for the compensation of the gain drift ofSiPM detectors caused by temperature variations has been pro-posed. In this approach a SiPM not exposed to incident photonsis exploited as temperature sensor and its gain is monitored bymeasuring the amplitude of the dark pulses generated by thedetector. This detector is enclosed in a negative feedback loop,which automatically modifies the bias voltage so that the ampli-tude of the dark pulses and, as a consequence, the gain are keptconstant in presence of temperature changes. One of the mainadvantages of this technique is that, since it is based on a feed-back loop, its application does not require an accurate knowl-edge of the detector parameters. The only requirement is thatthe SiPM used as temperature sensor must have the same tem-perature sensitivity of the SiPMs used as light sensors in theapplication.The effectiveness of the proposed temperature compensation

principle has been demonstrated by means of a simple experi-mental setup. The application of the technique allows a remark-able reduction of the relative variation of the detector gain withthe temperature: the main sources of error and the parameterswhich affect them have been also considered and discussed.Since several ASICs designed to read-out SiPMs allow a fine

tuning of the detector bias voltage by means of a DAC [13],[14], a possible development of the proposed technique canbe oriented to the exploitation of this feature for temperaturecompensation purposes. Another interesting scenario whichdeserves investigation is the design of SiPM arrays includingmicro-cells clusters shielded from the incident photons, to be

LICCIULLI et al.: NOVEL TECHNIQUE FOR THE STABILIZATION OF SIPM 611

used as temperature sensors within the proposed compensa-tion scheme. Furthermore, alternative implementations of thetechnique can be based on direct measurements of the detectorgain, i.e., of the average value of the charge contained in thedark pulses generated by the blind SiPM: this approach couldresults in complication of the required circuitry, but it couldpossibly guarantee more accuracy.

ACKNOWLEDGMENT

The authors would like to thank Dr. C. Piemonte, fromFBK-irst, for providing the SiPM samples used in the experi-ments, and prof. F. Corsi, DEE Politecnico di Bari, for helpfuldiscussions.

REFERENCES[1] G. Bondarenko et al., “Limited Geiger-mode microcell silicon photo-

diode: New results,” Nucl. Instr. Meth. Phys. Res. Sec. A, vol. A 442,pp. 187–192, 2000.

[2] P. Buzhan et al., “Silicon photomultiplier and its possible applica-tions,” Nucl. Instr. Meth. Phys. Res. Sec. A, vol. A 504, pp. 48–52,2003.

[3] C. Piemonte, “A new silicon photomultiplier structure for blue light de-tection,” Nucl. Instr. Meth. Phys. Res. Sec. A, vol. A 568, pp. 224–232,2006.

[4] V. Golovin and V. Saveliev, “Novel type of avalanche photodetectorwith Geiger mode operation,” Nucl. Instr. Meth. Phys. Res. Sec. A, vol.A518, pp. 560–564, 2004.

[5] J. C. Jackson, P. J. Hughes, D. Herbert, A. Stewart, and L. Wall, “Re-view of SPM low light level detectors,” in Proc. 19th IEEE LasersElectro-Optics Soc. Meeting, 2006, pp. 723–724.

[6] C. Y. Chang, S. S. Chiu, and L. P. Hsu, “Temperature dependence ofbreakdown voltage in silicon abrupt P-N junctions,” IEEE Trans. Elec-tron Devices, vol. 18, no. 6, pp. 391–393, 1971.

[7] M. Petasecca et al., “Thermal and electrical characterization of siliconphotomultiplier,” IEEE Trans. Nucl. Sci., vol. 55, no. 3, pp. 1686–1690,2008.

[8] M. Ramilli, “Characterization of SiPM: Temperature dependencies,”in Proc. 2008 IEEE Nucl. Sci. Symp. Med. Imag. Conf. Rec., 2008, pp.2467–2470.

[9] R. Bencardino and J. E. Eberhardt, “Development of a fast-neutrondetector with silicon photomultiplier readout,” IEEE Trans. Nucl. Sci,vol. 56, no. 3, pp. 1129–1134, 2009.

[10] P. S. Marrocchesi et al., “Active control of the gain of a 3 mm 3mm silicon photoMultiplier,” Nucl. Instr. Meth. Phys. Res. Sec. A, vol.A602, pp. 391–395, 2009.

[11] H. Miyamoto, M. Teshima, B. Dolgoshein, R. Mirzoyan, J. Nincovic,and H. Krawczynski, “SiPM development and application for astropar-ticle physics experiments,” in Proc. 31st Int. Cosm. Ray Conf., Lodz,Poland, 2009.

[12] F. Corsi et al., “Preliminary results from a current mode CMOSfront-end circuit for silicon photomultiplier detectors,” in Proc. IEEENucl. Sci. Symp. Med. Imag. Conf. Rec., 2007, pp. 360–365.

[13] S. Callier, F. Dulucq, R. Fabbri, C. de La Taille, B. Lutz, G. Martin-Chassard, L. Raux, and W. Shen, “Silicon Photomultiplier IntegratedReadout Chip (SPIROC) for the ILC: Measurements and possible fur-ther development,” in Proc. 2009 IEEE Nucl. Sci. Symp. Med. Imag.Conf. Rec., 2009, pp. 42–46.

[14] F. Corsi, M. Foresta, C. Marzocca, G. Matarrese, and A. Del Guerra,“CMOS analog front-end channel for silicon photo-multipliers,” Nucl.Instr. Meth. Phys. Res. Sec. A, vol. A617, pp. 319–320, 2010.