Towards Energy-Dispersive Particle Detection withsub-eV Energy Resolution: Metallic Magnetic

Calorimeters with Direct Sensor ReadoutMatthaus Krantz∗, Andreas Fleischmann∗, Christian Enss∗, and Sebastian Kempf∗

∗ Kirchhoff-Institute for PhysicsHeidelberg UniversityHeidelberg, Germany

Email: sebastian.kempf@kip.uni-heidelberg.de

Abstract—Metallic magnetic calorimeters are energy-dispersive cryogenic particle detectors providing an excellentenergy resolution, a fast signal rise time, a high quantumefficiency as well as an almost ideal linear detector response.To surpass the present record resolution of 1.6 eV (FWHM) for6 keV photons, we have started to develop integrated detectorsfor which the paramagnetic temperature sensor monitoringthe temperature rise of the detector is integrated directly intothe pickup loop of the superconducting quantum interferencedevice. Due to the greatly enhanced magnetic flux coupling andconsequently the reduced contribution of SQUID noise to theoverall noise spectrum, this kind of devices should push theresolution to a value well below 1 eV. Here, we discuss the designand performance of a prototype 64 pixels metallic magneticcalorimeter based detector array with integrated detectorsthat rely on first-order parallel gradiometric SQUIDs with twomeander-shaped pickup coils onto which planar temperaturesensor made of Ag:Er are deposited.

Index Terms—SQUIDs, X-ray detectors, Superconducting pho-todetectors, Ionizing radiation sensors

I. INTRODUCTION

Metallic magnetic calorimeters (MMCs) are calorimetriclow-temperature particle detectors that are presently stronglyadvancing the state-of-the-art in energy-dispersive single par-ticle detection [1]. They are typically operated at temperatureswell below 100 mK and make use of a metallic, paramagnetictemperature sensor to transduce the temperature rise of anabsorber upon the impact of an energetic particle into a changeof sensor magnetization. The latter can be precisely measuredas a change of magnetic flux using a superconducting pickupcoil that is coupled to a superconducting quantum interferencedevice (SQUID). This outstanding interplay between a highly-sensitive magnetic thermometer and a near quantum-limitedamplifier results in a fast signal rise time, an excellent energyresolution, a large energy dynamic range, a high quantumefficiency and an almost ideal linear detector response.

The temperature sensor of state-of-the-art MMCs is coupledto the SQUID via a superconducting flux transformer that is

We would like to thank T. Wolf and D. Nagler for technical support duringdevice fabrication. The work was performed within the framework of theEuropean Microkelvin Platform EMP and was supported by the BMBF grant05P15VHFAA.

formed by a pickup coil inductively coupled to the sensor andthe input coil of a current-sensing SQUID. However, parasiticinductances within this circuit as well as transformer lossesdue to a non-ideal magnetic coupling between different coils(the magnetic coupling factor k is usually below 100 %) lead toa reduction of the actually measured signal size. In addition,SQUID noise becomes the dominant noise contribution forfrequencies above several kilohertzes [1]. Both effects impairthe achievable energy resolution of MMCs. A possible route totackle these impairments is to use detectors with direct sensorreadout for which the temperature sensor and the SQUID arecombined in an integrated device, i.e. the sensor is placedinside the SQUID loop. This approach has already been shownvery promising results [2]–[4]. However, these former deviceshad not been fully optimized, e.g. with respect to the detectorgeometry, and both the temperature sensor and the particleabsorber were not fully microfabricated, thus significantlycomplicating to build large detector arrays.

II. DETECTOR GEOMETRY

Fig. 1 depicts the detector geometry used for the prototypedetector array. It relies on a first-order parallel gradiometricSQUID those inductance is formed by two meander-shapedcoils that are connected in parallel. A planar paramagnetictemperature sensor is placed onto each of these coils such thatthe change of sensor magnetization is directly changing themagnetic flux threading the SQUID loop. For both pixels, theparticle absorber is placed above the temperature sensor andis connected to the sensor via normal conducting stems. Theabsorbers are hence free-standing and are supported only bytiny normal conducting structures in order to prevent a loss ofathermal phonons during signal formation [1]. To generate thebias magnetic field required to induce a temperature dependentsensor magnetization, a persistent current is injected into ameander-shaped coil placed below the SQUID inductance.Utilizing two separate coils for bias and magnetization pickupallows to connect different field generating coils in seriesin order to inject a persistent current simultaneously in alldetectors within the array. The use of a first-order parallelgradiometric SQUID cancels on one hand fluctuations of ho-

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absorber

stems

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Fig. 1. Schematic of the detector geometry used for the prototype detectorarray. The SQUID is a first-order parallel gradiometer whose inductance isformed by two meander-shaped pickup coils onto which planar paramagnetictemperature sensors are placed. The particle absorbers are connected vianormal conducting stems to underlying temperature sensor. A persistentcurrent I0 running inside meander-shaped coil underneath the SQUID loop isgenerating the bias magnetic field. For clarity, the temperature sensor, stemsand absorber of the lower right meander-shaped coil as well as a feedbackcoil used for flux biasing the SQUID are not shown.

mogeneous magnetic background fields and on the other handcancels temperature fluctuations, e.g. of the heat bath, thataffect both temperature sensors simultaneously. In addition,this detector configuration allows to read out two pixels byusing only one SQUID since events in the different absorberscan be distinguished by the signal polarity.

III. PROTOTYPE DETECTOR ARRAY

Fig. 2 shows an SEM picture of one of the 32 detectorsof the prototype array. The linewidth, pitch and area of eachmeander-shaped coil forming the SQUID inductance are 4µm,10µm, and 50µm × 50µm. The inductance of each coilwas numerically calculated and is 160 pH, resulting in a totalSQUID inductance of about 80 pH. Each Josephson junctionhas a critical current of Ic = 6.3µA and is shunted by a4.5 Ω resistor made of AuPd. For thermalizing the shuntscooling fins are attached. A 9 Ω washer shunt is connected inparallel to both pickup coil to damp the SQUID LC resonance.A feedback coil is wound around the SQUID inductance toprovide a flux bias and feedback.

The linewidth and pitch of the field generating meander-shaped coils are 6µm and 10µm. They are separated from theSQUID inductance by a 300 nm thick insulation layer madeof sputtered SiO2. For injecting the persistent current, the coilhas two extensions. On top of one these extensions, a resistoris placed that allows to drive the extension normal conductingto inject the persistent current into the coil.

The temperature sensor is made of Ag:Er with an erbiumconcentration of 450 ppm and is 1.2µm thick. It is separatedfrom the SQUID by a 300 nm thick insulation layer madeof sputtered SiO2. For sensor thermalization, an on-chip heatbath made of sputtered Au is connected via a small normal

50 µm

feedback coil

shunt resistor

washer shunt

persistent currentswitch

meander-shapedSQUID inductance

JosephsonJunctionthermal

bath

Fig. 2. a) Colored SEM picture of one of the detectors of the prototypedetector array. The function of the different components is explained in thetext. For making the picture, the paramagnetic temperature sensor, the stemsas well as the particle absorbers of both pixels were not deposited.

conducting stripe to each sensor. The dimensions of the stripesare chosen such that the decay time of the detector signals isabout 0.6 ms.

IV. PERFORMANCE OF DETECTOR ARRAY

For characterizing the detector array we mounted the arrayon a custom-made detector platform that was installed atthe experimental platform of a commercial 3He/4He dilutionrefrigerator (BF-LD250, BlueFors Oy). Each of the detectorSQUIDs was connected to a home-made 16-SQUID seriesarray to form a two-stage SQUID setup. The SQUID arrayswere read out using a directly coupled commercial SQUIDelectronics (XXF-1, Magnicon GmbH). The use of a two-stage SQUID setup first allows to voltage bias the detectorSQUIDs to minimize the on-chip power dissipation of theSQUID that might affect the detector operation temperatureand simultaneously allows to minimize the influence of thenoise contribution of the SQUID electronics. At the sametime, it increases the slew rate and the system bandwidthas compared to a flux modulation based SQUID readout. Aflux-locked loop with flux feedback to the detector SQUIDwas used for linearizing the relation between the magneticflux coupled into the SQUID loop and the output voltage ofthe SQUID electronics. For measuring the signal shape andheight as well as to determine the energy resolution of thearray, we irradiated the detector with X-ray photons emittedby an 55Fe calibration source having two characteristic linesat about 5.9 keV and about 6.5 keV. For all measurementsdiscussed here, we used a field-generation persistent currentof I0 = 160 mA and the temperature of the experimentalplatform was 7 mK.

Fig. 3 shows the change of magnetic flux ∆Φs within theSQUID loop of one of the detectors versus time for a singledetector event caused by the absorption of a 5.9 keV photon.The signal height is about 0.6 Φ0 and the signal decay can bedescribed by an exponential decay with a decay time constant

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0. 0 0. 5 1. 0 1. 5time t / ms

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Fig. 3. Change of magnetic flux ∆Φs within the SQUID loop versus timefor a single detector event caused by the absorption of a 5.9 keV photon. Thedecay of the signal follows an exponential decay with a decay time constantof τdecay = 240µs. The inset shows a zoom into the signal rise which islinear rather than exponential. This indicates that slew rate of the SQUIDreadout limits the signal rise.

of τdecay = 240µs. Both, the signal height as well as therather short decay time indicate that the operation temperatureof the detector is higher than the cryostat temperature. By sub-sequently switching on and off neighboring detector channelsas well as by varying the bias conditions of each detector wedetermined that Joule heating of the detector SQUIDs preventsthe detector array to reach the cryostat temperature. We aretherefore presently redesigning the array and particularly thethermalization of the shunt resistors to minimize the effect ofSQUID Joule heating on the temperature sensor. Fig. 3 alsoshows that the signal rise is linear rather than exponential asexpected from the thermodynamic model describing an MMC[5]. This indicates that slew rate of the SQUID readout limitsthe signal rise for the present setup.

Fig. 4 shows the energy distribution of baseline signalsas well as the spectrum of the 55Mn Kα line. By fittinga Gaussian function to the measured lines we extracted anenergy resolution of 4.2 eV at 0 keV and 17.7 eV at 5.9 keV.The baseline resolution is consistent with the independentlymeasured detector temperature of about 50 mK and indicateit can be improved by enhancing the thermalization of thedetector (see above). The degradation of the energy resolutionfor 5.9 keV photons is related to reaching the slew rate limit ofthe SQUID setup, temperature fluctuations of the experimentalplatform as well as a remaining athermal phonon loss due tothe need for using stems with a rather large diameter. Allthese issues are address during the present phase of detectorredesigning.

0-2 0energy / eV

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Fig. 4. Baseline spectrum as well as spectrum of the 55Mn Kα line. Themeasurements were performed at a cryostat temperature of T = 7 mKusing field generating persistent current of I0 = 160 mA. Each solid linesrepresents a Gaussian energy distribution with a FWHM width that is givenin the figure for both histograms.

V. SUMMARY

We have developed a prototype 64 pixels detector arraybased on metallic magnetic calorimeter with direct sensorreadout for which the temperature sensor is placed directlyinto the SQUID loop. Each detector relies on a first-orderparallel gradiometric SQUID formed by two meander-shapedcoils onto which planar temperature sensor made of Ag:Eras well as particle absorbers made of electroplated Au aredeposited. The measured pulse height for a 5.9 keV photonis 0.6 Φ0 at a cryostat temperature of 7 mK. The measuredbaseline resolution is about 4 eV (FWHM). It is limited bythe detector temperature which is increased compared tothe cryostat temperature due to SQUID Joule heating. Themeasured instrumental energy resolution at 5.9 keV is about18 eV (FWHM) and is degraded compared to the baselineresolution due to temperature fluctuations, athermal phononsloss and reaching the slew-rate limit of the SQUID readout.Presently, a revised detector version is under developmenthaving the potential to reach sub-eV energy resolution.

REFERENCES

[1] S.Kempf, A. Fleischmann, L. Gastaldo, and C. Enss, J. Low Temp.Phys., vol. 193, pp. 365–379, 2018.

[2] V. Zakosarenko, R. Stolz, L. Fritzsch, H.-G. Meyer, A. Fleischmann,and C Enss, Supercond. Sci. Technol., vol. 16, pp. 1404–1407, 2003.

[3] R. Stolz, V. Zakosarenko, L. Fritzsch, H.-G. Meyer, A. Fleischmann, andC. Enss, IEEE Trans. Appl. Supercond., vol. 15, pp. 773–776, 2005.

[4] S. T. P. Boyd, R. Cantor, V. Kotsubo, P. Blumenfeld, and J. A. Hall, J.Low Temp. Phys., vol. 151, pp. 369-374, 2008.

[5] A. Fleischmann, C. Enss, G. M. Seidel, in C. Enss (eds) CryogenicParticle Detection, Topics in Applied Physics, vol. 99. Springer, Berlin,Heidelberg, 2005.

IEEE CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), September 2019. Invited presentation 4-SQ-I-3 given at ISEC, 28 July-1 August 2019, Riverside, USA.

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