An automated system to define the optimal operating settings of cryogenic calorimeters
Krystal Alfonso, Carlo Bucci, Lucia Canonica, Paolo Carniti, Sergio Di Domizio, Andrea Giachero, Claudio Gotti, Laura Marini, Irene Nutini, Gianluigi Pessina
PPrepared for submission to JINST
A highly automated system to define the best operatingsettings of cryogenic calorimeters
K. Alfonso c C. Bucci d L. Canonica d , e , P. Carniti a , b S. Di Domizio f , g A. Giachero a , b C. Gotti a , b L. Marini h , i I. Nutini a , b , G. Pessina a , b a Dipartimento di Fisica, Università di Milano-Bicocca, Milano I-20126, Italy b INFN – Sezione di Milano Bicocca, Milano I-20126, Italy c Department of Physics and Astronomy, University of California, Los Angeles, CA 90095, USA d INFN – Laboratori Nazionali del Gran Sasso, Assergi (L’Aquila) I-67100, Italy e Massachusetts Institute of Technology, Cambridge, MA 02139, USA f Dipartimento di Fisica, Università di Genova, Genova I-16146, Italy g INFN – Sezione di Genova, Genova I-16146, Italy h Department of Physics, University of California, Berkeley, CA 94720, USA i Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
E-mail: [email protected]
Abstract: Cryogenic macro-calorimeters instrumented with NTD thermistors have been devel-oped since several decades. The choice of NTD bias current is crucial for the optimal operation ofthis type of detector. The CUORE detector, consisting of an array of 988 TeO crystals, coupled withNTD-Ge thermistors, and operated at ∼
10 mK, utilizes this technology. New automatic proceduresfor the characterization and optimization of the detector parameters were developed for CUORE inorder to address the large number of calorimeters and the intrinsic spread of their characteristics,reaching optimal signal to noise ratio and linear response for each detector.Keywords: keywords currently at Max-Planck-Institut für Physik, D-80805 München, Germany Corresponding author. a r X i v : . [ phy s i c s . i n s - d e t ] J u l ontents Cryogenic calorimeters, also called bolometers, represent one of the leading techniques for rareevent searches. This class of low temperature detectors features an excellent energy resolution,sensitivity to all kinds of particles, low energy threshold, and a wide choice of absorber materials[1]. At present, the largest implementation of the bolometric technique is the CUORE experiment,designed, constructed and operated to search for
Te neutrinoless double beta decay (0 ν ββ ) [2].The CUORE detector consists of an array of 988 TeO crystals operated as cryogenic calorimetersat ∼
10 mK. The crystals are 5 × × each and weigh an average of 750 g; thus the total detectorexperimental mass almost reaches the ton-scale. Each TeO crystal, operating as an energy absorber,is instrumented with a Neutron Transmutation Doped germanium (NTD-Ge) thermistor, acting asa phonon sensor, and a silicon heater to periodically inject a fixed amount of energy to the detectorfor gain stabilization [3–5].The NTD thermistor converts the thermal phonons, produced by any energy release in theTeO crystals, into a measurable resistance variation that is proportional to the total energy of thecollected phonons. The resistance variation can be read out by applying a bias current to the sensorand thus converting it to a voltage variation. The choice of the value of the NTD bias current iscrucial for the optimal operation of the detectors.The behaviour of the detector with respect to the applied bias is described by the characteristicI-V curve. The I-V curve measurement and the identification of the optimal bias current, or optimalworking point (optimal WP), is a standard procedure for the operation of cryogenic calorimeters.– 1 –UORE’s predecessor experiments (i.e. MiDBD, Cuoricino, CUORE-0)[6] had all a small numberof detectors and the optimization was handled manually by changing the parameters of the biascircuit and measuring the resulting voltage output with a standard oscilloscope, or data acquisitionsystem. In CUORE, the large number of calorimeters and the intrinsic spread of their characteristicsobliged to develop new automatic procedures for the characterization and optimization of variousdetector parameters [7–9]. The automatic procedure for the identification of the optimal WP permitsfaster and more precise measurements, resulting in better control over the detectors performance.In addition, it has also been the first time in which the optimal working points were identified by adedicated algorithm which takes into consideration not only the I-V curve and the voltage amplitude,but also the signal-to-noise ratio and the pulse shape variation with the bias current.In the following we will describe the procedure for measuring the NTD characteristic curvesand for identifying the optimal working point. We will first introduce the working principle ofthe NTD and the parameters that play major roles in the characterization of these devices and inthe construction of the load curves. We will give an overview of the hardware and slow controlsoftware, with which the data from the CUORE detectors are controlled and acquired. Lastly wewill provide a detailed description of the aforementioned procedures for characterizing the NTDsand of the developed analysis algorithms for identifying the optimal working point.The procedures described in this paper were applied to the CUORE and CUPID-0 experiments,setting the foundation for the scientific results they obtained [10–17]. The same automated systemcan be applied to any array of cryogenic calorimeters read by NTDs, such as CUPID [18], easingthe procedures for detector characterization and optimization. The NTD-thermistor converts thermal pulses into electrical signals through a resistance variation.The NTD-thermistors are usually germanium semiconductor slabs doped by means of thermalneutrons [19, 20]. When the doping concentration reaches a critical value, the NTD enters themetal-insulator transition (MIT) region, where its resistivity exhibits a strong dependence on thetemperature [21]. At sub-Kelvin temperature, the thermistor resistance dependence on the temper-ature is described by [22]: R ( T ) = R exp (cid:32) T T (cid:33) γ (2.1)where R is the thermistor resistance, R and T depend on the doping concentration and on thegeometry, T is the temperature, and the γ exponent depends on the conduction mechanism. Theparameters R , T and γ are usually determined using measurements of the thermistor resistance atvarious temperatures. For CUORE-like NTDs (with dimensions of 3 × × ), typical valuesare: R = 1.0 – 1.5 Ω , T = 4.0 – 5.0 K , and γ (cid:39) ∼
10 mK, typical resistance valuesfor CUORE-like NTDs are of the order of a few hundred M Ω such that an energy deposition of1 MeV in the absorber induces a resistance variation of a few M Ω . The small size of the NTD compared to the crystals allows to have a small contribution to the detector heatcapacitance, while ensuring good electrical properties in terms of resistance value. – 2 – V bias I V
NTD R NTD R L /2R L /2 I V NTD
Working Point(WP) Inversion Point(IP)Load LineLoad Curve (LC) V bias V bias /R L Figure 1 . [Left] Scheme of the biasing circuit for the thermistor readout; R
NTD corresponds to the NTDresistance R. [Right] Load curve (I-V) of an NTD, an analytical example.
To measure the NTD resistance and its variation, the sensor is biased with the circuit schemat-ically represented in Fig.1[left]. A bias voltage V bias , produced by a dedicated circuit, is appliedacross a pair of load resistors R L /
2, in series with the thermistor. The total resistance R L is chosenmuch higher than the thermistor resistance R, so that the current I flowing through the thermistor canbe considered approximately constant. The voltage across the thermistor and the power dissipationproduced by the current I flowing through the NTD are: V NT D = I · R ( T ) , P = I · V NT D (2.2)The thermistor temperature T is affected by the power dissipation P: T = T b + PG , where the basetemperature T b , is the temperature of the heat sink and G is the conductance between the NTDand the heat sink. For high power dissipation, the increase in the thermistor temperature P/G, iscomparable to T b and is not negligible. The power dissipation acts back on the NTD, decreasingits resistance since it varies with the temperature of the device. This phenomenon is called electro-thermal feedback and it is valid whenever the load impedance, either static or dynamic, is largerthan that of the thermistor impedance, see also below.The I-V curve for semiconductor thermistors is usually referred to as the currentâĂŞvoltagecharacteristic curve , or load curve . An example of a load curve (LC) is shown in Fig.1[right].Given a fixed base temperature, the slope of the load curve is nearly constant for low I . When thebias current is sufficiently high, the electro-thermal feedback causes the I-V relation to deviate fromlinearity leading to a non-ohmic behavior; beyond the “inversion point” (IP), the slope becomesnegative. Within the ohmic region, each point on the load curve is associated with a static resistance of the NTD.Each point on the I-V curve is a potential working point (WP). As shown in Fig.1[right], WP isthe point of intersection between the load line ( V NT D = V bias – I · R L ), which translates with V bias ,and the load curve. We change the NTD bias current, in order to find the detector’s best operatingconditions along the I-V curve, the optimal WP.The procedure for determining the optimal WP consists of monitoring the amplitude of a pulseof fixed energy while varying the bias current, and finding the point where the signal to noise ratio– 3 –s maximum. For this reason, not only does the amplitude of the signal pulses play an importantrole in the choice of optimal WP, but also the noise.An estimate of the noise level of the detector is evaluated from the analysis of the baseline fluc-tuations. In CUORE the resistance range of NTDs is large and the series noise of the amplifieris negligible; the intrinsic noise is dominated by the parallel Johnson noise of the load resistancesacross the impedance of the thermistor. The noise spectral density of the NTD voltage, in worstcondition, is proportional to the NTD resistance and to the temperature of both the thermistor andthe load resistors: ∆ V NT D ∝ R R L T L T , with T ∼
10 mK and T L ∼
300 K (room temperature) in our case.For cryogenic calorimeters, given an energy release in the absorber, the thermistor resistancevaries, leading to a signal pulse. The NTD pulses for a given energy deposition are quite small, ∆ V NT D ∼
100 – 400 µ V/MeV; the signals require amplification. The average voltage read after theamplification stage ( V bsl ) is used to reconstruct the NTD voltage ( V NT D ) since they are related by: V ± bsl = A V · ( V of f ± V NT D ) (2.3)where V of f is the residual input-referred offset of the electronics, A V is the gain of the amplificationstage, and the ± sign corresponds to the bias polarity. Moreover, for signal pulses, the relationshipbetween the maximum voltage variation (or pulse amplitude), A , and the energy deposition resultingin a temperature variation, ∆ T , is A ∝ ∆ TT V NT D ; this dependence holds if the thermistor logarithmicsensitivity [23] is used to correlate resistance and temperature variations. The signal amplitudeincreases with V NT D , increasing the bias. However the increase of the applied bias voltage resultsin an higher temperature and lowers the ∆ T / T ratio, therefore the A vs V bias curve will reach amaximum and then will start decreasing.The electro-thermal feedback also has an effect on the pulse shape; the non-ohmic behavior ofthe device for high bias current leads to instabilities in its dynamic response, resulting in distortedpulses or in an oscillation of the detector. In order to avoid regenerative electro-thermal feedback,semiconductor thermistors should not be loaded with an impedance smaller than the impedance ofthe thermistor itself. In CUORE, the NTDs are read out by an amplifier at room temperature andthis leads to a large parasitic capacitance of the link in parallel to the NTD. This capacitance givesthe dominant contribution to the load impedance in the bandwidth of interest.At low bias, the NTD impedance is purely resistive and equals the ratio of its bias voltage andcurrent: in this case an oscillation can start if the signal has a frequency content for which themodule of the parasitic capacitance becomes smaller than that of the thermistor impedance. Thefeedback, however, increases the power and the NTD thermistor lowers its resistance, damping theoscillation (i.e. the NTD impedance is real).At high bias, moving towards the inversion point, the NTD thermistor deviates from the resistiveregime and its dynamic impedance shows an inductive component: in this case, when the inductivecomponent gets sufficiently high, the oscillation is maintained instead of being damped [24]. Thisregion of operation must be avoided in order to have a stable detector operation.In order to measure the pulse amplitude (A) and shape variation with bias voltage, a referenceenergy injection is needed. For this purpose, either a line from a reliable radioactive source, or agiven power injection from the heater installed on the crystal, could be used. Generally, the lattersolution is chosen because of the higher precision of the energy injection and the possibility ofregulating the rate of heater pulses for each NTD bias configuration.– 4 –n conclusion, the optimal WP is chosen as a compromise between having a large SNR andensuring a stable and linear behavior of the NTD, which is crucial for the best operation of thethermal sensor.Despite the previous considerations, in real experimental conditions, we do not have ‘a priori’knowledge of all the NTD parameters and conductances. Moreover there can be further contributionsto the noise related to vibrations, pick-up noise, etc. Therefore the NTD optimal working point mustbe determined experimentally and dedicated measurements on the NTDs are necessary. Three typesof measurements, which we will refer to as characterization measurements , can be performed:• Load curve measurement: accurately reconstruct the current-voltage (I-V) curve, in order tocharacterize the NTD static behavior and identify the range of bias voltages for which thepulse amplitude is close to its maximum;•
Working point measurement: accurately build the signal-to-noise ratio (SNR) curve and studythe pulse shape variation as a function of the applied bias voltage in order to find the optimalWP;•
Resistance measurement: precisely measure the NTD static resistance at a given bias voltageto monitor its stability over time.Estimators for the NTD resistance, voltage variation for a given energy deposition, and noiseare therefore calculated for each different bias current value from the mentioned measurements.The procedures and algorithms used to reconstruct the NTD’s voltage/current/resistance ( V NT D , I , R ), noise (N), pulse amplitude (A), signal-to-noise ratio (SNR) will be described in detail in Sec.4. A dedicated procedure has been developed in order to perform characterization measurements ofthe response parameters for each of the 988 CUORE detectors. Since no NTD-TeO system isexactly the same, it is necessary to optimize each crystal’s NTD bias voltage from the analysis ofthe load curve data.In the following, we will first present the CUORE electronics systems for the readout of theNTD-Ge thermistor (R NTD ) and for power injection through a Si heater (R heat ), as represented inFig.2. We will focus on the design specifications of the CUORE front-end boards, utilized for theNTD biasing circuit (introduced in Sec.2) and amplification stage, and the capabilities of the pulserboard. Next, the function of the CUORE data acquisition system (DAQ) to identify and associateraw data from the detector with designated electronics settings will be discussed in relation to the characterization measurements on the NTDs from Sec.2. Lastly, we will describe the load curvemeasurement, including the front-end and DAQ configurations for the procedure. We emphasize thedesign considerations of each infrastructure to facilitate the operation of a large array of cryogenicdetectors. – 5 –
NTD R heat Absorber R L Bias Generator AntialiasingLow-passFilter Data AcquisitionSystem 18-bitdataPulser CAN-bus ControlFront-End BoardCryostatT B ~ 10 mK T = 300 KFaraday Cage Control SystemAmpliOffset Corrector Figure 2 . Schematic of the CUORE detectors electronics and DAQ chain.
The front-end electronics system, specifically developed for the CUORE experiment, is responsiblefor the differential signal amplification, detector biasing, and detector thermal response calibrationand stabilization. The first two functions are performed by the JFET-input preamplifier and the front-end board [25], while the calibration is handled by the pulser board [26]. Auxiliary electronicssystems provide anti-aliasing filtering [27], power supply regulation, and high-stability voltagereferences [28, 29]. The technical details of these electronics systems are described thoroughly inthe references provided above; in the following we will mainly highlight the characteristics thatinfluence any characterization measurement (load curves, working point measurement, etc.).The detector bias current is generated by applying an adjustable differential voltage to twoalternative pairs of high-value custom-made load resistors placed at room temperature, which havea designated value of 60 GΩ (2 ×
30 GΩ) or 10 GΩ (2 × Ω up to a few G Ω .The bias voltage has a maximum differential range of ±
50 V, which corresponds to 0.8 nA(5 nA) bias current with 30 GΩ (5 GΩ) load resistors, a resolution of 16 bits, and a thermal driftbetter than 80 ppm / ◦ C. Each of the two differential voltages (positive and negative) can be setindependently from the other, providing the capability of applying a bias voltage with non-zerocommon-mode voltage. This is useful when evaluating and optimizing the DC common-moderejection ratio (CMRR) of the preamplifiers, which is important for suppressing any common-modenoise source; internal trimmers are used for optimizing the CMRR. Once the bias voltage is setby the on-board circuitry, a relay is used to invert the polarity of the bias applied to the detectorwithout further adjustments. This operation provides the capability of taking the difference betweenthe two configurations (direct and inverted bias), thus canceling purely electrical offsets due to the– 6 –ignal amplification Fully differentialInput transistors InterFET NJ132 (custom pairs)Gain settings 20 V/V – 10k V/VGain stability < / ◦ COffset adjustment ±
80 mVOffset stability < µ V / ◦ CInput bias current <
100 fAInput differential current <
20 fASeries noise 3.3 nV/ √ Hz (white)8 nV/ √ Hz (1 Hz)Parallel noise < .
15 fA /√ HzCMRR (after optimization) >
120 dBBias voltage ( V bias ) range ±
50 VLoad resistors ( R L ) ×
30 GΩ or 2 × ± ± Ω Bias voltage resolution 16 bits
Table 1 . Summary of the front-end electronics specifications. preamplifier voltage offset. In the case when the load curves are acquired with a single polarity, theeffect of the offset can be minimized by adjusting it to zero before performing the measurements.Thanks to the proper custom design, the JFETs’ gate current (below 20 fA differential and below100 fA single-ended) is completely negligible with detector impedance up to a few GΩ [30]. If thegate current were not negligible, its residual power injection could still be taken into account [31].The signal amplification is fully differential and the gain is remotely programmable (from20 V/V up to 10k V/V) in order to accommodate the broad dynamic range of this type of detectorwhen it is operated at different base temperatures. The offset can be digitally adjusted up to ±
80 mV(input-referred) and its stability is calibrated to be better than 1 µ V / ◦ C, enabling reliable baselinemonitoring even for very long operating times (years).Detector thermal response stabilization is performed using a pulser board that is capable ofapplying precise (sub ppm / ◦ C), low-noise voltage pulses to a Si heater resistor glued to the detector.The response of the detector to such a heat pulse enables the monitoring of the detector behavior atdifferent base temperatures and bias currents.All the adjustments done by the front-end electronics (bias voltage, relay switching, offsetadjustment, pulse generation, etc.) are managed by the on-board firmware. In this way, eachoperation can be easily parallelized since the DAQ provides only a few slow control commands tothe front-end electronics through the CAN bus interface, while all the computation algorithms aremanaged by the on-board microcontrollers.Table1 summarizes the specifications and characteristics of the front-end systems.
The CUORE data acquisition system, described in detail in [32], consists of a core system for datadigitization and storage, and of a control interface for the analog electronic readout chain. The– 7 –etector waveforms are acquired with a 1 kHz sampling frequency by a 18-bit ADC. The relativelylow signal bandwidth (on the order of 10 Hz) makes it possible to digitize and save the continuouswaveforms of the detectors for offline processing. For the same reason, triggering can be performedin software, allowing for more flexibility and control. The data analysis is performed on triggeredevents, namely finite-length waveform windows selected in correspondence of a trigger. The defaultevent window length used in CUORE is 10 s. Events are associated with supplementary informationincluding
DetectorId (an identifier which maps the different detectors in the CUORE array), time,and the type of trigger that caused the generation of the event. Three types of events exist: signalevents , generated when the signal trigger detects a pulse in the waveform; noise events , generatedperiodically or at a random time, regardless of the presence of a pulse in the waveform; and pulserevents , whose generation is forced in correspondence to the injection of a pulse from a heaterattached to the absorber.The control software for interfacing with the analog electronics is implemented with a multi-threading approach, allowing concurrent communication with multiple target a single CAN buslink. Some digital signals are acquired synchronously with the waveforms from the calorimetersand are used to synchronize external events with the data. In particular, digital signals are generatedin correspondence to changes in the electronics configuration and when pulser-generated signalsare injected in the detectors. The synchronization mechanism enables pulser-generated events to beidentified and flagged in the offline analysis. Similarly, each acquired event can be associated withan
EleId , i.e. an identifier for a well-defined electronics configuration (which includes parameterslike V bias , R L and A V ). This capability of characterizing the measurement procedure is fundamentalfor the offline analysis because it enables events to be classified based on their EleId .Depending on the goal of the particular measurement being performed, one or more of thefollowing quantities are estimated for each electronics configuration and for each detector: thesteady-state baseline voltage, the noise power spectrum, and the parameters of the detector responsein presence of pulses. As discussed in Sec.2, these quantities are used to estimate the values ofthe detector parameters that help determine the optimal configuration of the NTDs. Quantitiesrelated to the steady-state performance of the detector are estimated from the noise events, whilequantities related to the detector response in presence of pulses are estimated from pulser events.The pulser-based approach enables control over the timing and amplitude of the heat-injected pulsesand avoids relying on the trigger settings, which would need to adapt for any change in the electronicsconfiguration.From a procedural point of view, any characterization measurement consists of applying asequence of electronics settings to the detectors, and to acquire, for each of these configurations, n noise events and p pulser events. All the following data processing is left to the offline analysis, seeSec.4. The configurable numbers n and p of noise and pulser events are usually chosen larger thanone, so that events that do not pass quality cuts can be discarded in the analysis, and the estimatedquantities can be averaged over multiple events.The characterization measurements introduced in Sec.2 are implemented as:• Load curve measurement.
In the current-voltage (I-V) curve, both positive and negative biaspolarity configurations are measured for a large range of bias voltage values. In this case,the main purpose is to measure the thermistor voltage as a function of the bias current. An– 8 –xample of the detector output for this type of measurement is reported in Fig.3.•
Working point measurement.
In the signal-to-noise ratio (SNR) curve, only unipolar biasconfigurations (e.g. negative) are measured for a sub-range of bias voltage values. The biasvoltage values are concentrated around the maximum of the pulse amplitude identified in theI-V curve. A large number of noise and pulser events, much more than those taken during the load curve measurement , are acquired in order to improve the accuracy of the measurement.The preamplifier output is offset, such that we can maximize the signal gain of the readoutchain for the negative polarity configurations. In this way, we can fully exploit the digitizerADC dynamic range, increasing the precision in the reconstruction of all the pulse-relatedparameters.•
Resistance measurement.
The NTD resistance value for a given applied bias voltage isobtained from measuring a single point of the I-V curve in the linear region. The NTDsvoltage, current (and resistance) are obtained from two configurations with opposite polarityand the same bias voltage, which is usually the one chosen for physics measurements.All these characterization measurements are usually performed in parallel on a large number ofdetectors. Their duration is determined by the number of electronics configurations, the number ofnoise and pulser events acquired for each configuration, and by the time needed for the detectors tostabilize after an electronics configuration is applied. For example a resistance measurement per-formed in parallel over all the CUORE detectors lasts about 3 hours, while an I-V curve measurementperformed over 3 CUORE towers takes about 12 hours.
The three characterization measurements introduced in Sec.2 and in Sec.3.2, share a similar ded-icated sequence in the data acquisition, whose procedure is illustrated in the following. Thissequence has been specifically designed to measure the characteristic parameters for each of theCUORE detectors, but can also be adapted to any cryogenic macro-calorimetric experiment usingNTDs as phonon sensors.The load curve measurement is the most general procedure since it is partially comprised ofthe working point and resistance measurement procedures. The first step consists of adjusting thepreamplifier gain and offset in order to exploit, at best, the entire ADC dynamic range to avoidsaturation and to ensure that, during the measurement, the output signal takes values in a rangealmost symmetric around zero.Each load curve point, identified by an
EleId , is set by applying the required bias voltage at negativebias polarity, waiting some time to reach a steady output, and acquiring the baseline voltage forthe chosen number of noise/pulser events. Bias polarity is then inverted and the measurement isrepeated.The purpose of measuring the output signal at both positive and negative bias voltage polarity isto cancel the contribution of the residual input offset when measuring the average value of the outputsignal. Since the only use of positive polarity step is the cancellation of the residual input offset,its duration is determined only by the number of noise events required. A reference heater pulse,– 9 – ime [s]5000 10000 15000 20000 25000 30000 350000-80000-400040008000 A c qu i r e d S i gn a l [ m V ] S i gn a l [ V ] S i gn a l [ V ] (a) (b) -5.5-4.5-3.5 S i gn a l [ V ] -5.0-4.0-3.0 34164 34166 3416834163 34165 34167Times [s] (c) Figure 3 . Continuous waveform output during a
Load curve measurement for one CUORE detector. Foreach bias configuration,
EleId , the data are acquired both for negative and positive polarity. In zoom (a),we see two different bias configurations, with data taken at negative and positive polarities in which it isclearly visible the baseline inversion. Zoom (b) shows the transient time spent in configuring the electronics,waiting for the detectors to stabilize and for performing the actual measurement for each polarity for a given
EleId . In the last high-bias configurations, the detector output is oscillating, as reported in zoom (c). with fixed energy of ∼ pulser events from only the negative bias polarity, where eachsignal is characterized by a fast upward pulse; therefore the duration of each negative polarity stepis driven by the number of pulses that are required to obtain a good estimate of their amplitudeand shape parameters. Once one point of the load curve is completed, the polarity is switchedagain to negative and a new higher value of the bias is set (see Fig.3 - zoom (a)). This procedureis repeated with increasing bias voltage, as shown in Fig.3, until a pre-determined maximum biasvalue is reached. It is worth noting that between each configuration there is a transient region ofthermal origin, as shown in Fig.3 (b). Writing any electronics parameter, and in particular changingthe bias voltage value, has a thermal effect on the output signal which can last up to a few hundredsof seconds. This region is not assigned to any valid EleId in order to discard corresponding eventsin the reconstruction and analysis phases.The maximum bias is set just below the point a prompt oscillation starts. An example of theoscillating effect described in Sec.2 is shown in the bottom right insertion of Fig.3 (c). The valuesof the maximum bias voltage for each NTD are specified in a configuration file. Similarly, thenumber of steps, the duration of each step, the number of pulses in the negative polarity and thenumber of noise events to be acquired in the positive polarity, are all specified in a configuration– 10 –le, making the procedure flexible and easy to adapt to the different characterization measurements .For each
EleId , the typical number of noise events is between 5 and 15, while the typical numberof pulsers events is between 10 and 30, depending on the required accuracy.
In the following, we will discuss the procedures to construct the load curves and derive the relevantparameters for the selection of the optimal WP, namely pulse amplitude (A), noise (N), and signal-to-noise ratio (SNR).We emphasize the new analysis techniques, accounting for pulse-shape quality checks toidentify good detector operating conditions, as a crucial consideration in selecting the WP. Moreover,a regular monitoring of NTD resistance during the data-taking ensures the detectors are operatingin a stable condition. All data shown in the first parts of this section were acquired by CUORE at abase temperature of 11.8 mK.This section concludes with a discussion of the characterization procedures applied to a widerange of temperatures, further demonstrating their versatility. The study of the temperature depen-dence of the detector parameters is important to model and optimize their response.
Once a characterization measurement has been acquired, the reconstruction of the raw data isperformed through a sequence of event-based analysis modules [33].The goal of the reconstruction software is to obtain all the parameters (V
NT D , SNR, A and N) as afunction of the NTD current I , for each point of the load curve measurement ( EleId ). The analysissteps necessary to compute the above mentioned parameters are repeated for each pair of
EleId with similar electronics configuration: same bias current, but opposite polarity. In this section,we plot V
NT D as a function of I instead of the canonical way to represent the load curve (seeFig.1), in order to coalign the related (independent) variables on the horizontal axes with respectto the curves for the A, N and SNR variables. In Fig.4, there is an example for each of the curvesbuilt for a single NTD sensor. These curves are used to determine the configuration that maxi-mizes the pulse amplitude while minimizing the noise level, thus to select the optimal working point.In order to compensate for the effects of the electronics offset, the NTD voltage V NT D iscalculated as: V NT D = V + bsl − V − bsl · A V (4.1)while the current is: I = V bias − V NT D · R L (4.2)where V ± bsl is the baseline value, read at the amplifier output and scaled by the voltage gain„ at eachpolarity for a given EleId , as reported in Eq.2.3.Accordingly, each NTD resistance is obtained from the ratio of V NT D and I .The reconstruction software aims to compute event-based variables and to select a cleansample of events, where clean sample refers to events that do not show drifting output signal,particle induced pile-up, etc. – 11 – + bsl and V − bsl are obtained directly from clean samples of noise events . V NT D is then calculatedusing the
EleId parameters ( A V , R L and V bias ). Similarly, the signal noise N and the pulseamplitude A are obtained from a clean sample of noise events and pulser events , respectively.Among the variables computed from the waveform of the noise events , the most important arethe baseline and the noise. The baseline is defined as the average waveform value evaluated froma linear fit of the samples in the event window. All the baseline values of events with the same EleId -NTD are averaged, in order to obtain each time a unique value for V ± bsl .The noise level of each configuration is evaluated exploiting the optimum filter [34]. N is thereforecomputed as the integral of the noise power spectrum of each noise event , weighting each frequencybased on its contribution to the average pulse, resulting in the resolution of the optimum filter. Analternative and simpler method consists of computing for each noise event the standard deviationof the NTD output samples; the average of these values is taken as N for each EleId -NTD.We preferred to use the first method, although more complicated, since it suppresses frequenciesirrelevant to the detector signal bandwidth.The pulser events are employed to compute the amplitude of each heater pulse and a numberof pulse-shape parameters used as indicators of possible distortion of the pulse itself. The detaileddescription of the distortion indicator is provided in Sec.4.2. The amplitude of a pulse is usuallydefined as the difference between the maximum of the pulse and the baseline value in the regionbefore the trigger. Instead of evaluating this quantity for each pulser event and defining the amplitudeestimator A as the amplitudes average, we directly average all the pulser event waveforms and define A as the amplitude of the averaged pulse. This allows to reduce the effect of incoherent noise.Eventually, the signal to noise ratio SN R is computed as the ratio of the amplitude and noiseestimator.
From the analysis of the curves constructed for each detector in a working point measurement , theoptimal WP is chosen following two basic requirements: maximize the signal to noise ratio andavoid pulse deformation. An automated algorithm was developed to find the optimal bias voltagefor each detector.The shape of the heater pulses at the different bias voltages has been investigated as a figureof merit for identifying unstable conditions, which could appear when the NTD is operated in thenon-ohmic regime.The detector response is modeled with an empirical function whose Laplace transform has 4 realnegative poles and one negative zero in the complex plane, and the pulse is considered as distortedif a pair of poles departs significantly from the real axis, becoming complex conjugate [35].A fit of the heater pulses with the empirical template is performed and a global shape parameterS is constructed from the fit results. Given a pole P in the complex plane, the parameter S is definedas S = | Im ( P )| − | Re ( P )|| P | (4.3)and its value changes with the applied bias voltage; this is correlated with the ability to reconstructand predict the pulse deformation.For low bias values, the pulse shape is well-described by one time constant on the rising edge and– 12 –ias Voltage ( V bias ) 1.8 V 2.4 V 3.8 VPulse Amplitude (A) 0.148 V 0.144 V 0.130 VSignal-to-noise Ratio (SNR) 300 mV/mV 330 mV/mV 360 mV/mVShape parameter (S) -0.35 -0.20 0.05 Table 2 . Summary of the parameters for the three LC configurations identified by the three pulses in Fig.5. three time constants on the falling edge, thus the 4 real poles detector response model is satisfactoryand the parameter S is negative. Increasing the applied bias, the non-linear effects from the electro-thermal feedback start to be relevant and the pulse starts showing a damped-oscillation shape. Theseconfigurations are characterized by a positive value of S, meaning the value of the imaginary termof the pair of complex conjugate poles of the detector response function is higher than its real term,thus the oscillatory part will dominate the shape of the falling edge of the pulse.When the configuration corresponding to the maximum of SNR is in a region of high bias, thepulse shape can become slightly deformed. A threshold on the S parameter can then be set toidentify bias configurations leading to deformed pulses. The threshold is typically around S = 0,however its exact value can be optimized based on the specific experimental configuration and canbe slightly different for measurements at different base temperatures. For CUORE data at 11.8 mK,the threshold is set as S ≤ -0.2.If the maximum SN R corresponds to non ideal pulses, the algorithm iteratively takes the pre-vious points on the load curve and applies the same shape checks. Eventually the optimal WP ischosen, among the points with no deformation, as the point with the highest SNR.Characterization curves produced for one CUORE detector from the working point mea-surements and analyzed in order to find the optimal WP for the NTD are shown in Fig.4. Thecorresponding heater pulses at three different bias voltages (under-biased, optimal, over-biased) forthe same detector are shown with the effective fit superimposed in Fig.5.In Fig.4, the pulse amplitude reaches its maximum for V bias = 1.8 V and has an ideal shape; howeverthe SNR is not maximized in this configuration, due to higher noise RMS for lower bias voltage.On the contrary, the SNR is maximized for V bias = 3.8 V; the position of this point on the I-V curveis far from the linear region and the pulse shows a strong damped-oscillation shape. Thereforethe working point V bias = 2.4 V is chosen as a compromise between having a high SNR and nondeformed pulse.A summary of the parameters ( V bias , A, SNR, S) for the three configurations corresponding to thepulses in Fig.5 is reported in Tab.2.In general, with the addition of the pulse shape condition, the SNR at the chosen WP is onlyslightly lower than the maximum SNR (see in Tab.2, the SNR difference is ∼ bias [mV]900 1000 I [pA]02468101214 V N T D [ m V ] A m p lit ud e [ V ] N o i s e [ m V ] S N R Selected optimal WPUnstable region
Figure 4 . Characterization curves produced in a working point measurement for one CUORE detector. Theblack dashed line indicates the point corresponding to the bias chosen as the optimal WP. V bias = 3.8 V V bias = 2.4 V V bias = 1.8 V A m p lit ud e [ m V ] A m p lit ud e [ m V ] A m p lit ud e [ m V ] Figure 5 . Heater pulses, and their effective fit, for three different bias configurations acquired in the workingpoint measurement, for the same CUORE detector whose I-V, SNR and other plots are reported in Fig.4.[Top] V bias = 1.8 V, maximum pulse amplitude. [Center] V bias = 2.4 V, selected optimal WP. [Bottom] V bias = 3.8 V, maximum SNR. [35] – 14 – A m p lit ud e [ m V ] Figure 6 . Heater pulses at different energies for the same CUORE detector as in Fig.5, when the NTD isoperated at the optimal WP, ensuring the pulse shape to be uniform with energy.
After setting the optimal working points identified by the algorithm discussed in the section above,a further check of the pulses quality and the stability of the NTD operating conditions is performed.Dedicated measurements are performed, firing several pulsers of different amplitudes (200keV - 3.5 MeV). Average pulses for all the different amplitudes are produced for each detector andcompared to verify the shape uniformity with energy. A fit of the average pulses is performed withthe same template discussed in Sec.4.2 and the global shape parameter S is evaluated. For eachdetector, if S is consistent among the several energies, the shape uniformity is considered verified.We observed that for approximately 2-5% of the CUORE NTDs the algorithm provides an optimalWP for which the pulse shape slightly changes with energy; these are usually very noisy detectors,for which the evaluation of SNR and shape parameters from a standard load curve measurementare not accurate. For these cases, a tuning of the bias voltages optimal WP is performed manually.Afterwards, another dedicated run with multiple heater pulses is taken, to perform final qualitychecks on the detectors’ pulse shape, especially for those for which the bias has been manuallychanged and optimized. The final optimal WP ensures a uniform pulse shape at the several pulserenergies, see Fig.6.The optimal WP bias voltage values applied to the CUORE detectors at an operating temperatureof 11.8 mK are reported in Fig.7[left]. The values cluster around voltages of 1.5 - 2.0 V. Thiscorresponds to an average WP resistance of R wp ∼ G Ω , see Fig.7[right].During the standard CUORE data-taking, given an operational temperature and fixed biasvoltages, the effective NTD resistance at the optimal WP ( R wp ) is measured for each detectorseveral times per month, in order to monitor the devices’ thermal stability over time; this is the resistance measurement described in Sec.3.2. In Fig.8 the stability of the NTD working pointresistance for all the detectors during the CUORE data taking at 11.8 mK is reported . Each The plot reports the main features of the distributions of the relative variation of R wp for the CUORE detectors – 15 –
200 400 600 800 10000 200 400 600 800 1000 DetectorId0.51.52.53.54.5 R w p [ G Ω ] V b i a s [ m V ] DetectorId
Figure 7 . 11.8 mK base temperature. [Left] Distribution of the bias voltages applied to the NTD as a functionof the CUORE
DetectorId . [Right] Distribution of the NTD resistance at the selected WP as a function ofthe CUORE
DetectorId . element in the plot corresponds to the distribution of the relative variation of the values of R wp forthe CUORE detectors in two years. The procedure for characterization measurements and optimal working point identification can beapplied at different base temperatures.A dedicated set of load curve measurements from 11 mK to 27 mK base temperature wasperformed in CUORE. The data were acquired and analyzed with the procedures described above.From the load curve measurements at the different temperatures, the variables( V NT D , I, R) at each V bias were calculated. An instructive visualization of the variation at the NTD static behaviour withbias and temperature is provided by the R-P curve (resistance vs. injected power) at the differenttemperatures, as reported in Fig.9 [Left] for one CUORE detector. These curves show the combinedeffect of variation of the NTD base resistance with temperature, R( T | P = 0), and its dependence onthe power dissipation due to the electro-thermal feedback for increasing bias voltages V bias . Curveswith lower base resistance correspond to higher base temperatures. Incidentally, we can see thatthe minimum bias current used to bias the thermistor is of a few pA, which proves that the effect ofthe amplifier differential input current of a few tens of fA has a completely negligible effect.From the analysis of the mentioned load curve measurements , we defined a set of optimal WPsfor each temperature; these were optimized for each detector-temperature. The variation of theSNR with temperature was then analyzed. Runs with multiple pulser amplitudes (as described inSec.4.3) were acquired on a subset of CUORE detectors. The SNR was calculated at the differentpulser amplitudes. For each pulser amplitude at a given temperature, the average and width ofthe distribution of SNR values for each detector were evaluated. We observed that the SNR, aswell as the optimum filter resolution, improves for lower temperatures. We ascribed this behaviour measured for each resistance measurement . The circle corresponds to the median; the solid box around the medianindicates the 50% of the distribution of the data. The dashed lines extending vertically from the boxes indicate the widthof 95% of the data distribution. – 16 – / / / / / / / / / / / / / / / / / / / /
12 2020 / / R e l a ti v e r e s i s t a n ce v a r i a ti on Figure 8 . CUORE resistance stability over 2 years operation at 11.8 mK. We evaluate the relative variationwith time of the R wp for each single detector compared to a reference measurement (from August 2019).Time intervals with no points correspond to periods of cryogenics maintenance and no data-taking. The dataare more spaced in 2018, since resistance measurements were performed bi-weekly or monthly. Since 2019,we performed resistance measurements once a week and this allows for a continuous and more accuratemonitoring of the thermal stability of the detectors and the overall system. The average resistance variationdiffers for the data of late 2019 and early 2020 and that is correlated with a slight change in the operatingtemperature; since the applied bias voltages on the NTDs have been always the same, a colder temperaturelead to larger values of the NTD resistance. to the larger absorber internal gain for lower temperatures, which over-compensates the increasein the noise RMS due to larger NTD resistance values. An example of the SNR variation withtemperature, evaluated as the ratio of the amplitude of the higher pulser (at ∼ In conclusion, a dedicated procedure for performing automatic load curve measurements on a largenumber of cryogenic calorimeters read by NTDs has been developed. The specific algorithm an-alyzes the load curve data and identifies the optimal bias voltage (optimal WP), for each NTD. The absorber internal gain, in case of cryogenic calorimeters, is considered as the conversion factor from depositedenergy to temperature variation. It is inversely proportional to the lattice heat capacity ( C lat ∝ T ), for a fixed energyrelease. Therefore, a lower heat capacity C lat , obtained for lower base temperatures, is preferred in order to have a largersignal amplitude. – 17 – -4 -3 -2 -1 Power [pW]
11 mK15 mK18 mK19 mK21 mK24 mK27 mK R [ M Ω ] S N R Figure 9 . [Left] P-R curves on one CUORE NTD for several values of base temperature, from 11 mK to 27mK. [Right] Variation of the (average) SNR evaluated over a subset of detectors for several values of basetemperature.
Furthermore, the addition of the information related to the pulse shape dependence with the ap-plied bias constitutes an upgrade of the standard approach of choosing optimal WP bias voltagescorresponding to either only the maximum amplitude or maximum SNR.This is the first time that an automatic procedure is utilized for setting the optimal WP foralmost one thousand NTDs coupled to TeO crystals and can be reproduced for load curve dataacquired at any base temperature. This was crucial to find the best operating settings of the CUOREdetector.Any cryogenic experiment employing macro-calorimeters coupled with NTDs, could profitfrom the highly automated system presented in this paper, for easing the procedures to optimize thedetectors’ operating settings. Acknowledgments
This work was sponsored by the Istituto Nazionale di Fisica Nucleare (INFN). In addition we wouldlike to acknowledge the support from the DOE Office of Science, Office of Nuclear Physics. Theauthors thank the CUORE Collaboration, the directors and staff of the Laboratori Nazionali delGran Sasso.
References [1] C. Enss and D. McCammon,
Physical principles of low temperature detectors: Ultimate performancelimits and current detector capabilities , Journal of Low Temperature Physics (2008) 5–24.[2] CUORE collaboration, D. R. Artusa et al.,
Searching for neutrinoless double-beta decay of
Te withCUORE , Adv. High Energy Phys. (2015) 879871, [ ].[3] CUORE collaboration, C. Alduino et al.,
CUORE-0 detector: design, construction and operation , JINST (2016) P07009, [ ]. – 18 –
4] E. Andreotti, C. Brofferio, L. Foggetta, A. Giuliani, B. Margesin, C. Nones et al.,
Production,characterization, and selection of the heating elements for the response stabilization of the CUOREbolometers , Nuclear Instruments and Methods in Physics Research Section A: Accelerators,Spectrometers, Detectors and Associated Equipment (2012) 161 – 170.[5] A. Alessandrello, C. Brofferio, C. Bucci, O. Cremonesi, A. Giuliani, B. Margesin et al.,
Methods forresponse stabilization in bolometers for rare decays , Nucl. Instrum. Meth. A (1998) 454 – 464.[6] C. Brofferio and S. Dell’Oro,
Contributed review: The saga of neutrinoless double beta decay searchwith
T eO thermal detectors , Review of Scientific Instruments (2018) 121502,[ https://doi.org/10.1063/1.5031485 ].[7] CUORE collaboration, I. Nutini et al., The CUORE Detector and Results , J. Low Temp. Phys. (2020) 519–528.[8] C. Alduino et al.,
The CUORE cryostat: An infrastructure for rare event searches at millikelvintemperatures , Cryogenics (2019) 9–21, [ ].[9] A. D’Addabbo, C. Bucci, L. Canonica, S. Di Domizio, P. Gorla, L. Marini et al.,
An active noisecancellation technique for the CUORE Pulse Tube Cryocoolers , Cryogenics (2018) 56–65,[ ].[10] O. Azzolini et al., CUPID-0: the first array of enriched scintillating bolometers for ν ββ decayinvestigations , The European Physical Journal C (May, 2018) 428, [ ].[11] O. Azzolini et al., Search for Neutrino-less Double Beta Decay of Zn and Zn with CUPID-0 , .[12] CUORE collaboration, D. Adams et al., Improved Limit on Neutrinoless Double-Beta Decay in
Tewith CUORE , Phys. Rev. Lett. (2020) 122501, [ ].[13] O. Azzolini et al.,
Evidence of Single State Dominance in the Two-Neutrino Double- β Decay of Sewith CUPID-0 , Phys. Rev. Lett. (2019) 262501, [ ].[14] CUPID collaboration, O. Azzolini et al.,
Final result of CUPID-0 phase-I in the search for the SeNeutrinoless Double- β Decay , Phys. Rev. Lett. (2019) 032501, [ ].[15] CUPID collaboration, O. Azzolini et al.,
Search of the neutrino-less double beta decay of Se into theexcited states of Kr with CUPID-0 , Eur. Phys. J. C (2018) 888, [ ].[16] O. Azzolini et al., First Result on the Neutrinoless Double Beta Decay of Se with CUPID-0 , .[17] CUORE collaboration, C. Alduino et al., First Results from CUORE: A Search for Lepton NumberViolation via ν ββ Decay of Te , Phys. Rev. Lett. (2018) 132501, [ ].[18] CUPID collaboration, W. R. Armstrong et al.,
CUPID pre-CDR , .[19] E. E. Haller, N. P. Palaio, M. Rodder, W. L. Hansen and E. Kreysa, NTD germanium: A novel materialfor low temperature bolometers , in
Neutron Transmutation Doping of Semiconductor Materials (R. D.Larrabee, ed.), pp. 21–36. Springer US, 1984. DOI.[20] N. Wang, F. C. Wellstood, B. Sadoulet, E. E. Haller and J. Beeman,
Electrical and thermal propertiesof neutron-transmutation-doped Ge at 20 mK , Phys. Rev. B (Feb, 1990) 3761–3768.[21] N. F. Mott and J. H. Davies, Metal-insulator transition in doped semiconductors , Philos. Mag. B (1980) 845–858.[22] A. Miller and E. Abrahams, Impurity Conduction at Low Concentrations , Phys. Rev. (1960)745–755. – 19 –
23] D. McCammon,
Thermal equilibrium calorimeters – an introduction , in
Cryogenic Particle Detection (C. Enss, ed.), pp. 1–34. Springer US, 2005. arXiv:physics/0503045 .[24] C. Arnaboldi, C. Bucci, S. Capelli, P. Gorla, E. Guardincerri, A. Nucciotti et al.,
The temperaturestabilization system of CUORICINO: An array of macro bolometers , Nuclear Science, IEEETransactions on (11, 2005) 1630 – 1637.[25] C. Arnaboldi, P. Carniti, L. Cassina, C. Gotti, X. Liu, M. Maino et al., A front-end electronic systemfor large arrays of bolometers , JINST (2018) P02026, [ ].[26] K. Alfonso, L. Cassina, A. Giachero, C. Gotti, G. Pessina and P. Carniti, A High Precision PulseGeneration and Stabilization System for Bolometric Experiments , JINST (2018) P02029,[ ].[27] C. Arnaboldi, M. Cariello, S. Di Domizio, A. Giachero and G. Pessina, A programmable multichannelantialiasing filter for the CUORE experiment , Nucl. Instrum. Meth. A (2010) 327 – 328.[28] C. Arnaboldi, A. BaÃź, P. Carniti, L. Cassina, A. Giachero, C. Gotti et al.,
Very low noise ac/dcpower supply systems for large detector arrays , Review of Scientific Instruments (2015) 124703.[29] P. Carniti, L. Cassina, C. Gotti, M. Maino and G. Pessina, A low noise and high precision linearpower supply with thermal foldback protection , Review of Scientific Instruments (2016) 054706.[30] C. Arnaboldi and G. Pessina, The design of the input stage for the very front-end of the cuoreexperiment , Journal of Low Temperature Physics (2008) 964–970.[31] A. Alessandrello, C. Brofferio, D. Camin, O. Cremonesi, A. Giuliani, A. Nucciotti et al.,
Measuringthermistor resistance with very low d.c. power dissipation , Cryogenics (1997) 27 – 31.[32] S. Di Domizio, A. Branca, A. Caminata, L. Canonica, S. Copello, A. Giachero et al., A dataacquisition and control system for large mass bolometer arrays , JINST (2018) P12003,[ ].[33] CUORE collaboration, C. Alduino et al., Analysis techniques for the evaluation of the neutrinolessdouble- β decay lifetime in Te with the CUORE-0 detector , Phys. Rev. C (2016) 045503,[ ].[34] E. Gatti and P. F. Manfredi, Processing the Signals From Solid State Detectors in Elementary ParticlePhysics , Riv. Nuovo Cim. (1986) 1–146.[35] I. Nutini,
The CUORE experiment: detector optimization and modelling and CPT conservation limit .PhD thesis, SISSA, Trieste, 2019..PhD thesis, SISSA, Trieste, 2019.