1 In tro ducti on - inspirehep.netinspirehep.net/record/1482830/files/Hall_Goddard_NSF_Oct31.pdf1 In tro ducti on The ob serv ation of ßa vor os cillati ons in atmo-spheri c, solar,

1 Introduction

The observation of flavor oscillations in atmo-spheric, solar, and reactor neutrino data in re-cent years has revolutionized our understandingof the leptonic sector of fundamental particles.One profound implication of neutrino oscillationphenomenology is that it requires that at leastsome of the neutrino masses are non-zero. Thisrevelation has resolved several outstanding ex-perimental anomalies, such as the solar and at-mospheric neutrino deficits, but it has also gen-erated a new set of intriguing puzzles. One ofthe first questions which must now be addressedis the origin of neutrino mass. In order to gaininsight into the physics of grand unification itis imperative that we understand the neutrinomass spectrum and a number of experimentshave been proposed and are being developed[1].It is believed, by some, that this current genera-tion of experiments to determine neutrino massis close to reaching the limits of the technolo-gies being used. In order to break through tolower sensitivities, we believe that superconduct-ing low temperature calorimeters should be de-veloped.

This proposal is to develop low temperaturemicrocalorimeter technology that is crucial forfacilitating the next generation of neutrino massexperiments. In particular, we propose to makethe key developments that are necessary to en-able two types of neutrino mass experiments : (i)a measurement of the beta endpoint spectrum of187Re, and (ii) a measurement of the neutrino-less double beta decay of 100Mo or 116Cd. Whilethese two experiments would be very different inthe way that they determine neutrino mass, theresearch that is necessary in order to develop thedetectors, is very similar.

A quantum calorimeter senses the energy ofindividual quanta as a thermal signal at low tem-peratures (typically <0.1K). It consists of a pho-ton or particle absorber, and a sensor to deter-mine the temperature rise due to the energy de-posited. In neutrino mass experiments, the ab-

sorber is the element that contains the isotopethat is decaying. Superconducting absorbers canbe applied to both types of neutrino mass ex-periment. It has been demonstrated that fast,complete thermalization of superconducting ab-sorbers is possible, but difficult to achieve. Someexperiments have shown that very high resolu-tion spectroscopy is indeed achievable using su-perconductors [2, 3], however other experimentshave also shown that energy can get “trapped”within the superconducting absorber withoutcoming into thermal equilibrium on reasonabletimescales for neutrino mass experiments. Thus,while there have been several demonstrations ofhigh resolution spectroscopy, it is not yet clearwhether a microcalorimeter can be designed tohave the desired properties for the two types ofneutrino mass experiments. Although a num-ber of different microcalorimeter technologies forvarious fields in science have now been broughtto a relatively advanced state of development,there are relatively few that use superconductingabsorbers. We still have a relatively poor under-standing of the thermalization processes in su-perconductors. This proposal finally focuses onnot just understanding the thermalization in su-perconductors, but how to use this understand-ing to optimize and improve performance of realdetector systems.

To date, most research into developing lowtemperature detectors for neutrino mass experi-ments have taken place in Europe, in particularin Genoa and Milan [16]. For the past 3 years, wehave been collaborating at a relatively low levelwith these groups, helping them by providingsamples of detector arrays, mostly without ab-sorbers attached, that were developed by us forx-ray astronomy. These groups now have a planfor a new very large 187Re beta endpoint exper-iment called MARE, and we are involved in theformulation of this experiment [16]. The field oflow temperature detectors has been growing forthe past 20 years, and our group at NASA’s God-dard Space Flight Center in co-operation withthe University of Maryland has been at the fore-

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front of this development. We are now in an idealposition to diversify the scope of our researchby developing the foundations for future deepunderground experiments to determine neutrinomass within the US. Our laboratories at GSFChave substantial and unique capabilities for car-rying out the proposed effort. These include aworld class fabrication facility, a well equippedlow temperature laboratory for device testing,and calibration equipment for evaluating deviceperformance. These facilities are complete andavailable for use in this program. Carter Hall hasrecently joined the faculty at the University ofMaryland and brings to this program the broadunderstanding of the needs of neutrino mass ex-periments to enable this new program.

In this proposal we describe our strategy forstudying the physical processes in superconduct-ing absorbers, and our detailed plan for demon-strating the potential of new approaches to im-proved thermalization. We are poised to makea significant advancement in neutrino mass mea-surement through the use of high spectral reso-lution superconducting detectors.

Broader Impact This research has a greatpotential for broader impact. The techniques de-veloped here span a broad range of experimentalscience including low temperature physics, de-vice physics, superconductivity, particle physics,and x-ray astrophysics. These detectors are alsobeing applied towards basic atomic and nuclearphysics, and are finding applications in nuclearnon-proliferation. The research will also promoteeducation directly by supporting the studies of agraduate student.

2 Absolute Neutrino MassMeasurements

In the standard model, the charged fermionmasses are determined by their coupling to theHiggs field. Although the standard model doesnot predict what these coupling should be, the

orderly mass hierarchy of the charged leptonsand quarks, makes it plausible that such a mech-anism might be at work.

The neutrino sector, however, does not fit veryeasily into this picture. Prior to the observa-tions of neutrino oscillation, it was possible toexplain the lightness of neutrinos by removingthe right handed neutrino fields from the the-ory. In this scenario, the Higgs mechanism failsto produce a neutrino mass because it requiresboth left-handed and right-handed chiral fields.This results in a massless neutrino. However, theobservation of a small but finite neutrino masshas eliminated this possibility and sent model-builders back to the drawing board.

The large hierarchy between the neutrinomasses and the charged fermion masses stronglysuggests that a new mass generating mecha-nism is at work. Theories of grand unification,which unite the strong, weak, and electromag-netic forces at very high energies, have had somesuccess in providing an explanation for the small-ness of neutrino mass. Many of these theories in-voke a new mass generating mechanism at veryhigh energies, which results in neutrino fieldswith a mass on the order of the GUT scale.These new fields mix with the light neutrinos,and result in physical neutrino states which havemasses suppressed from their ”natural” mass bya factor of 1/MGUT . In this model, which iscalled the see-saw mechanism, the smallness ofthe neutrino masses is a reflection of the grandunification scale.

It is imperative, then, that we understandthe neutrino mass spectrum in order to gain in-sight into the physics of grand unification. Someinformation on the mass spectrum has alreadybeen extracted from neutrino oscillation studies.However, oscillation data cannot tell us the ab-solute mass scale, since the oscillation frequencydepends on the mass differences only.

Three techniques are available to study theabsolute neutrino mass spectrum: beta end-point spectrum, neutrinoless double beta de-cay, and cosmological measurements. To extract

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the maximum amount of information about neu-trino mass, we need to advance all three tech-niques, because they provide complementary in-formation. The research into superconductingcalorimetry proposed here has potential applica-tions to the first two methods.

2.1 β-endpoint measurements withTritium

Beta endpoint experiments attempt to detect thedistortion of the beta spectrum of an unstablenucleus due to the rest mass of the neutrino.This distortion appears as a cut-off in the betaspectrum near the Q value for the decay. Forneutrino masses on the order of 1 eV, and Q val-ues of several keV, this requires measuring theenergy of the beta with a precision of less thanone part in one thousand. Hence the energy res-olution of the experiment must be extremely pre-cise.

The most recent beta endpoint measurements(the Mainz and Troisk experiments) have usedtritium as the beta source, and have set limitsof 2.3 eV [7] and 2.5 eV [8], respectively, on theelectron neutrino mass, which is defined as

mnue =√∑ |Uei|2m2

i (1)These experiments rely on capturing the beta inan electrostatic spectrometer where its energycan be measured precisely. Consequently, thebeta must be extracted from the tritium sourcewithout undergoing any unexpected energy losslarger than one eV. This means that atomic andmolecular effects must be considered since thetritium molecule could be left in an excited statewhich would distort the energy spectrum. In the1990’s these experiments suffered from system-atic problems which made it appear that the neu-trino mass squared was negative. These prob-lems were later attributed to unexpected sourceeffects and have since been resolved.

The KATRIN experiment [9], which will begintaking data in 2009, aims to extend the sensitiv-ity of tritium endpoint neutrino mass searchesdown to 0.2 eV. To achieve this goal, the ex-

periment will utilize the world’s largest tritiumsource and a 10 m diameter beta spectrometer.As such, KATRIN likely represents the ultimatetritium neutrino mass experiment.

2.2 Neutrinoless double beta decay

Neutrinoless double beta decay is a hypotheti-cal decay mode of a heavy nucleus where twoneutrons convert to two protons while emittingtwo electrons. This process, which can be me-diated by a massive neutrino, violates leptonnumber conservation, and therefore it is only al-lowed in models where the neutrino is its ownanti-particle (Majorana). For Majorana neutri-nos, the neutrinoless double beta decay half-lifeis given by

(T 0νββ1/2 )−1 = G0νββ × |NME|2 × |〈mν〉|2 (2)

where G0νββ is a phase space factor, which canbe calculated accurately, |NME|2 is the nuclearmatrix element, which can be calculated withtheoretical errors of about 200% to 300%, and〈mν〉 is the effective neutrino mass given by

|〈mν〉| =∑3

i=1 U2eimieiαi . (3)

In this last expression the sum is over the threeneutrino mass eigenstates, U is the leptonic mix-ing matrix, mi are the neutrino masses, and αi

is a CP-violating phase which may exist for Ma-jorana neutrinos.

Three factors make it difficult to extract theabsolute neutrino masses from neutrinoless dou-ble beta decay. First, the large theoretical er-rors on the nuclear matrix element translate di-rectly into an error on the extracted neutrinomass. Secondly, the above relationship betweenthe neutrino masses and the double beta decayhalf-life assumes that only the neutrino massmechanism is responsible for the decay. Manymodels, such as supersymmetry, predict addi-tional sources of lepton number violation. Thosemechanisms may contribute to the neutrinolessdouble beta decay rate, and they must be un-derstood and accounted for seperately. Finally,the Majorana phases αi are unknown, and in-troduce additional uncertainty into the neutrino

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mass scale. Current Majorana neutrino masslimts from double beta decay range from about0.2 eV to 1.1 eV, depending on the nuclear ma-trix element calculation [4]. The discovery thatneutrons are Majorana particles (or not) is fun-damental to our understanding of unification.

3 Experimental ApproachesUsing Microcalorimeters andUltimate Sensitivity

3.1 Beta endpoint searches with mi-crocalorimeters

In recent years it has been proposed to perform abeta endpoint spectrum search for neutrino massusing 187Re as the beta source rather than tri-tium [16]. The 187Re experiments rely on lowtemperature calorimetry to measure the energydeposited in the rhenium crystal by the beta de-cay. The crystals, which typically have masses ofa few hundred micrograms, are cooled to below100 mK. At such low temperatures, the decayproduces a heat pulse in the crystal that can bemeasured with very high precision using a semi-conductor thermistor or a superconducting tran-sition edge sensor.

There are three primary advantages to thethermal detection technique compared to thetraditional tritium experiments. First, in ther-mal experiments the beta source is used as thecalorimeter itself. This resolves the issue of ex-tracting the beta from the source without anyunexpected energy losses. In fact, using low tem-perature calorimetery, we expect that all energydeposited in the crystal will eventually be con-verted to heat which can be measured. This fea-ture makes the thermal experiments highly com-plementary to the tritium experiments, whichhave been plagued by source effects in the past.As mentioned above, the KATRIN experimentwill have to control systematic effects 100 timessmaller than previous tritium experiments in or-der to achieve its neutrino mass goals. It remains

to be seen whether new and unexpected sourcesof systematic error will manifest themselves atthat level of precision. Therefore it is advanta-geous to invest in other experimental techniqueswhich show the potential to achieve comparableresults.

Secondly, the half-life of 187Re is 4.4 ×1010

years, resulting in a natural abundance on earthof 65%. This large abundance means that arhenium source can be assembled without theneed for isotopic enrichment. Furthermore, theQ value for the rhenium decay, at 2.47 keV, isthe lowest known Q value for any beta decay.This means that the fraction of the betas emit-ted in the physically interesting region (within 1eV of the Q value) in a rhenium decay will be350 times larger than that for tritium, which hasa Q value of 17 keV.

Finally, the solid-state nature of rhenium sim-plifies considerably the safety issues surroundingsource handling compared to tritium. In fact,due to the low Q value, the rhenium beta decaywas only observed for the first time in the 1960’s.

The main drawback to the micro-calorimetertechnique is the fact that the detector necessar-ily measures the complete energy spectrum of thebeta decay, rather than just the physically inter-esting region near the Q value. This leads toevent pile-up as the size of the source becomeslarge. Therefore to scale-up the experiment itis necessary to replicate the micro-calorimetermany times, rather than simply increase the sizeof the crystal. This is also required to obtainhigh spectral resolution.

Two techniques have been pursued by the Ital-ian groups that have pioneered this research.The first group, based in Genoa, has developedmicro-calorimeters using metallic rhenium crys-tals. Metallic rhenium is a superconductor be-low 1.69 K, and at temperatures far below thiscritical temperature the specific heat is smallenough to produce good energy resolution. En-ergy deposited in the crystal at these tempera-tures generates both prompt phonons, and alsobroken Cooper pairs. The broken Cooper pairs

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result in a large number of quasi-pariticles be-ing produced, and this energy is also convertedto phonons on a time scale characterized by theCooper pair recombination time. One of theaims of this research proposal is to understandand control this process.

The Genoa group has published the results oftheir initial experiments with calorimeters usingmetallic rhenium. Three crystals with a totalmass of 2.08 mg were used to set a neutrino masslimit of 19 eV at 90% confidence level[11]. Theenergy resolution in this experiment was between60 eV and 93 eV. In more recent devices, a res-olution of 11 eV at 5.9 keV has been achieved,and additional improvements are expected [13].With a resolution of 10 eV, a sensitivity of lessthan 1 eV (90% C.L) should be reachable in oneyear of integration. The Genoa group has alsomeasured the 187Re half-life and Q value, andmade the first observation of the Beta Environ-ment Fine Structure [12].

A second technique has been pursued by thegroup in Milan. They have chosen to avoid thequestion of the recombination of quasi-particlesby using silver perrhenate (AgReO4), a dielectriccompound of rhenium. The Milan experimentused 10 crystals with a total effective mass of2.174 mg, and measured the temperature signalwith silicon thermistors. In a five month datarun, they achieved an energy resolution of 28.4eV at the β endpoint energy, and set a limit onthe neutrino mass of 15 eV [41]. They also madethe most precise measurements to date of the Qvalue and half-life of the decay.

3.2 Neutrinoless double beta decaywith low temperature calorimetry

Low temperature techniques have already beenapplied to the study of neutrinoless double betadecay. An important feature of this approachis the high spectral resolution afforded by thecalorimeter that can be used to increase the de-tection sensitivity by reducing the energy band-width over which the background can contribute

Figure 1: Example of a typical laboratory backgroundspectrum up to 3.5 MeV

to the line detection.The Cuoricino collaboration[4] utilizes 130Te

in the dielectric form of tellurium oxide. 130Tewas chosen as the isotope of interest by Cuori-cino largely because of its high isotopic abun-dance (30%), which reduces the need for isotopicenrichment and makes the experiment inexpen-sive. Similar methods could be applied to otherisotopes, however.

We propose to investigate the feasibility ofsearching for double beta decay with 100Mo and116Cd at low temperatures. Since both of thesemetals are superconductors, this research inte-grates well into our proposed investigation of Remicrocalorimeters.

100Mo and 116Cd have a significantly higher Qvalue for double beta decay compared to 130Te(3304 keV and 2802 keV versus 2533 keV). Thehigher Q value has two beneficial effect. First,it places the double beta decay above most ofthe naturally occuring radioactive backgrounds,which drop off dramatically above 2615 keV asshown in Fig.1. Secondly, the phase space for thedouble beta decay increases as the fifth power ofthe Q value, making the half-life of the decayshorter and easier to observe.

Numerous searches for double beta decay with100Mo have been carried out, mostly recentlyby the NEMO-3 collaboration[15]. NEMO-3uses thin foils of 100Mo at room temperature,and measures the energy of the emerging betawith magnetic tracking and scintillation detec-

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tors. While this technique has been successful inthe past, it suffers from poor energy resolution(14% FWHM), which partially cancels out theadvantage of the higher Q value. Molybdenumin particular has an unusually short half life fortwo neutrino double beta decay (7.1×1018 years),which then becomes a significant background it-self when the energy resolution of the detector ismodest. Low temperature calorimetry promisesto solve this problem, allowing the experimental-ists to take full advantage of the high Q value.

3.3 Relationship to DUSEL

As mentioned in section 1, the Italian groupswhich have pioneered the application of low tem-perature techniques to neutrino mass have pro-posed to build a large scale rhenium experimentcalled MARE. In its first phase, MARE will in-clude both superconducting and dielectric Retechnology, and will achieve a sensitivity equalto current direct neutrino mass searches with tri-tium (2 eV). This will provide the first labora-tory check on the results of the Mainz and Troiskexperiments. In phase 2 the MARE experimentcould compete with the KATRIN experiment interms of neutrino mass sensitivity, and on a sim-ilar time scale[16]. Phase 1 primarily requiresscaling up previous experiments from a few crys-tals to several hundred crystals. Phase 2 willrequire tens of thousands of crystals, and an im-proved energy resolution beyond that achievedto date.

Previous Re neutrino mass searches have oc-curred in shallow sites. But as the experimentsbecome larger, backgrounds near the Q valuedue to cosmic rays and environmental radioac-tivity will become increasingly important, mak-ing a deep underground site increasingly attrac-tive. The MARE proposal envisions a large ex-periment being carried out at multiple laborato-ries around the world, taking advantage of theequipment and facilities available to the variouscollaborators. By pursuing reseach into low tem-perature superconducting calorimeters now, the

Figure 2: Plot of the beta-decay sensitivity for a 1 eVmicrocalorimeter and a pulse pile-up rejection of 10−5

United States will be able to present a crediblecase to be a host site for the full MARE experi-ment, possibly at a new facility such as DUSEL.Furthermore, since the superconducting technol-ogy could also be applied towards a low tem-perature double beta decay experiment in 100Moor 116Cd, the techniques we propose to developcould significantly impact the current US effortin Cuoricino and lead to a similar experimentlocated at DUSEL.

3.4 β-decay sensitivity

The experimental approach for the direct end-point measurement using 187Re has received alot of study [16]. The central issue with this ap-proach is that the calorimeter is sensitive to thefull beta spectrum and thus unrejected pile-upevents near the endpoint can distort the endpointand create a background component. Decreasingthe pulse rise time is thus essential and is a ma-jor thrust of this proposal. In figures 2 and 3we show the sensitivity for mass determinationfor a variety of detector parameters. To achievea mass sensitivity (90% C.L) of 0.2 eV, about1 × 1014 decays are required to produce enoughcounts at the end point to do the spectral fittingfor mass for a residual pulse pile-up fraction of10−5. For an assumed ultimate pulse risetime of1 µs, this allows an event rate of 10 cps/detector.This then requires about 60,000 detectors oper-ating for five years. The activity of Re is about 1decay/s/mg, so each detector would have a mass

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Figure 3: Sensitivity to neutrino mass as a function ofmicrocalorimeter energy resolution and pile-up fraction.

of about 10 mg. Given the density of Re, eachdetector element would be about 0.8 mm on aside, which is quite amenable to microelectronicfabrication techniques that will be described insubsequent sections.

3.5 ββ-decay sensitivity

There are a number isotopes that are ββ emit-ters present among superconducting elements.These are 100Mo, 116Cd and 124Sn. This opensup the possibility of searching for 0νββ-decay us-ing these elements coupled to calorimeters andsearching for the events at the Q value. Themeasurement approach is challenging in that oneis looking for a weak line in the presense of abackground, and experimental investigations arerequired deep underground to get the residualbackground rates acceptably low. The high spec-tral resolution afforded by the micrcalorimetercan help significantly in the detection sensitivityby lowering the background signal over the linedetection bandwidth.

There are many ways in which such an ex-periment might be realized, and the optimal ap-proach can’t really be developed until the goalsof this proposal are carried out. But even inthe absence of a detailed analysis, we alreadyexpect an enormous improvement in the radioac-tive backgrounds compared to current 76Ge ex-periments such as Heidelberg-Moscow for tworeasons. First, as mentioned previously, the Qvalue for 100Mo at 3.03 MeV is far above mostnatural radioactivity, which falls off dramatically

Figure 4: The basic concept behind a microcalorimeterfor β-decay detection.

above 2615 keV. From Figure 1, we expect an im-provement of a factor of 50 compared to the 76GeQ value of 2039 keV. Secondly, an energy resolu-tion of better than 100 eV is expected for leadingmicrocalorimeter technologies, an improvementof a factor of 20 over 76Ge experiments. There-fore this technology seems capable of achievingthe factor of 1000 reduction in backgrounds com-monly assumed to be necessary for next genera-tion double beta decay experiments.

4 Microcalorimeter TechnologyBackground

4.1 Quantum calorimetry

Calorimetry has been a standard physical mea-surement since the time it was first realized thatheat is a form of energy, but it is only in thepast two decades that the extremely high sensi-tivity afforded by operating at millikelvin tem-peratures has been applied to the thermal de-tection of individual photon and particle events[19]. Cryogenic calorimeters have several uniqueproperties that have enabled their application toa variety of experiments. Because of the exceed-ingly small specific heats of many materials atvery low temperatures, quite large detectors canbe constructed that still have sensitivity to smallamounts of deposited energy. Since this energy issensed after it has been converted to heat, inter-actions that produce little or no ionization canbe detected. Another useful property of ther-

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Figure 5: Array of 8x8 TES microcalorimeters with goldabsorbers

mal detection is that it does not depend on thecharge transport properties of the absorber, un-like ionization detectors, where the compositionis limited to a very few materials such as highpurity silicon or germanium. This makes it pos-sible, in many cases, to construct the detectorout of the source - confining all of the productsof a reaction and measuring the total energy. Itis this capability that makes quantum calorime-ters attractive for beta spectrum end-point andneutrinoless double-beta-decay experiments. Acalorimeter with the source incorporated directlymeasures exactly the quantity needed: the totaldecay energy minus whatever is carried away bythe neutrino. The only requirement is that therebe no metastable states created with lifetimeslonger than the thermal integration time of thedetector. This requirement, however, is not oftenreadily realized, and its achievement in materialssuitable for precise neutrino mass measurementsis the goal of this proposal.

The field of x-ray astronomy has been one ofthe most consistent drivers of the development ofquantum calorimeters for high-resolution spec-troscopy, and the Goddard x-ray calorimetergroup has been a leading contributor to this de-velopment since our pioneering work in 1984.This DUSEL proposal is an extension of ourlongstanding and successful research program indeveloping x-ray calorimeters for astrophysics.Among our more recent accomplishments is

Figure 6: Best energy resolution achieved at 6 keV withhigh quantum eficiancy and high filling factor absorber.The light blue line shows the intrinsic line profile forMnKα, the darker blue line gives the best fit to the datafitting for the gaussian broadening of the microcalorime-ter.the development of the 36-pixel, ion-implantedsilicon-thermistor array of the XRS instrumenton the space-borne Suzaku observatory whichachieved better than 6 eV FWHM energy resolu-tion at 6 keV [20]. We are also among the lead-ing groups advancing the technology of supercon-ducting transition-edge sensor (TES) calorime-ters; we routinely fabricate close-packed 8x8 ar-rays of TES pixels[21] and have recently demon-strated a design that achieves 2.5 eV resolutionat 6 keV. (See Figures 5 & 6.) We are in anexcellent position to apply these revolutionarydevices to the next generation of detectors forneutrino-mass determination.

4.2 Detection principles, thermaliza-tion, and absorber coupling

A microcalorimeter measures a small amount ofheat in a weakly heatsunk thermal mass by sens-ing a temperature change in the presence of ther-modynamically unavoidable temperature fluctu-ations. Low temperature operation is requiredin order to minimize this thermal noise and toreduce the heat capacity. The most advancedmicrocalorimeter technology to date is based onusing a temperature-dependent resistance for the

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Figure 7: Schematic representation of the heat flow in themicrocalorimeter

thermometer element, either a semiconductorthermistor or a TES thermometer. The designof a calorimeter typically includes an absorber,a thermometer, and an engineered thermal linkto a heat sink, as depicted in Fig.4. An essen-tial assumption about calorimeter operation isthat the energy is detected when the device is ina low-temperature equilibrium state where non-thermal excitations have negligible populations.Thus, to the extent that it can be regarded as aclosed system, the event-to-event statistical fluc-tuations that limit the resolution of ionizationdetectors do not occur. It is the job of the ab-sorber to thermalize the initial excitation, be itan x-ray photon or a nuclear beta particle, con-verting the initial quantum of energy into a dis-tribution of occupied energy levels that can bemeaningfully described as a change in tempera-ture. The absorber must also comply with re-strictions on the heat capacity and opacity re-quirements.

The physics is the same for the thermal-ization of a nuclear beta particle or a photo-electron, and a number of theoretical treat-ments of the problem have been published [22,23, 24, 25]. In the basic scenario, in the firstphase, the energetic electron loses energy primar-ily through electron-electron interaction, pro-ducing secondary ionization on the time scaleof pico-seconds. In the second phase, electron-phonon scattering dominates; energy starts be-

ing transferred to the lattice, but the energy dis-tribution in both the electrons and the phononsis still highly non-thermal. In the third phase,the electrons and phonons assume a thermal dis-tribution. Although simplified, the preceding ex-planation already points out one problem withthe “closed-system” view of a calorimeter - atthe very least we have two systems, the elec-trons and the phonons, and we need to con-sider how well coupled the two systems are, andwhich one is better coupled to the thermometer.Even in materials with a bandgap, for which,in equilibrium at low temperature, all thermalenergy is in the phonons, we can’t neglect theelectron system. Electron-hole pairs in a semi-conductor that fail to recombine due to trappingintroduce thermalization noise. Likewise, in asuperconductor, quasiparticles produced in theearlier phases of thermalization must recombineinto Cooper pairs in order for the full potential ofa calorimetric measurement to be realized. Forthis reason, the most reliable microcalorimeterabsorbers have been metals and semimetals (Bi,HgTe, and Au). But superconductors with highDebye temperatures hold the promise for equiv-alent spectral resolution with much larger ab-sorber masses due to their relatively small spe-cific heat and potential for fast thermalization.Thus there is great interest in characterizing andengineering the thermalization in superconduc-tors such as 187Re (for the MARE neutrino-massexperiment) or 100Mo or 116Cd (for neutrino-lessdouble-beta decay).

The first stages of thermalization in a super-conductor depend on the specific materials char-acteristics, but are typically completed in un-der a nano-second. At that time, there is afraction of energy that has already thermalizedinto sub-gap phonons, and the ratio of energy insub-gap phonons, energy less than the supercon-ducting gap 2∆ to that in quasiparticles scalesas ∆2/T 3

Debye for a number of superconductors[26, 27]. The rest of the energy is in quasiparti-cles at the superconducting gap edge. At tem-peratures far below Tc, the quasiparticle recom-

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bination times become quite long, and their ef-fective lifetime can be lengthened even furtherby the bottleneck described by the Rothwarf-Taylor equations[28]; when quasiparticles com-bine, they emit a 2∆ phonon that can break an-other Cooper pair.

Indeed many groups have reported anomaloustwo-time-constant pulse shapes when supercon-ducting absorbers are used. The secondary timeconstant can be hundreds of milliseconds long.(e.g. [29]) The behavior is notoriously sample-dependent, which suggests that final-stage ther-malization can be engineered once all the vari-ables are controlled. Fig.7 is a schematic of thefinal stages of thermalization.

4.3 Superconducting absorbers andcurrent results

Despite the concerns raised by theoretical treat-ments of thermalization, several benchmark reso-lutions have been achieved in microcalorimetersusing superconducting absorbers. As we notedalready, Gatti’s group at Genoa has obtained11-eV resolution at 6 keV using a 0.2-mg Re ab-sorber [30] with a TES sensor. Irwin’s groupat NIST has achieved 24.6-eV resolution at 103keV using a 1.5-mg Sn absorber with a TES [31].Silver’s group at SAO has achieved 3.1-eV reso-lution at 6 keV using an 8.2 µg Sn absorber withan NTD Ge sensor [3]. These proofs-of-conceptillustrate the feasibility of getting good energyresolution with detectors operating at practicaltimescales (100 µs in Sn). Good resolution byitself does not, however, indicate that all of theenergy has been measured in these devices, onlythat any energy that is not measured does notpresent an unacceptable level of event-to-eventvariation. Research is needed to prove the feasi-bility at shorter time scales and larger volumesin materials relevant to neutrino mass investiga-tions, and to gain understanding that will enableengineering the absorber to eliminate sample-to-sample variations.

There are two illustrative series of experiments

that we wish to summarize before proceedingwith our proposed plan of research. The first,conducted at Goddard in the early 90’s, used sil-icon thermistors to study thermalization in pureSn films [32]. We compared the pulse shapesdue to x-rays absorbed in the Sn to those thatresulted from x-rays absorbed in a silver-epoxythermalization reference affixed to the Sn. Sig-nal pulses resulting from the absorption of 6keV photons in the Ag epoxy rose faster, peakedhigher, and decayed to baseline more quicklythan those resulting from absorption in the Sn.Taking the Ag pulse shape as the impulse re-sponse, we deconvolved it from the Sn pulseshape to obtain the thermalization function. Thedeconvolution revealed an initial impulse, fol-lowed by thermalization that proceeds increas-ingly slowly. Nearly the same thermalizationfunction was produced at different detector tem-peratures and bias and for more than one de-vice. Subsequently, the detectors were heatedand allowed to cool through the Sn supercon-ducting transition in the presence of a magneticfield. Upon cooling back to operating temper-ature, the Ag events could no longer be distin-guished from the Sn events, and the new dis-tribution was slightly displaced to lower pulseheights than the former Sn distribution. We con-cluded that trapped flux enhanced thermaliza-tion in the Sn, at the expense of increasing theheat capacity.

The second illustration is even more relevantto the substance of this proposal. The Genoagroup performed a series of thermalization ex-periments on a variety of superconducting crys-tals, including rhenium, also in the early 90’s.[33] In these experiments the absorbers wereglued to NTD Ge thermistors. Heat pulses inthe Ge were used as thermalization references.Their main result was a “universal” thermaliza-tion law that indicated complete thermalizationwas achieved (on the tens of milliseconds of themeasurement) when the operating temperaturewas at least 2×10−4 of TDebye. In the interveningyears, the study has not be repeated, but their

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recent results supports that complete thermal-ization in rhenium crystals is achievable at 0.1 Kon time scales as short as 5 ms. [34] Since we canachieve high resolution in TES sensors with 0.1K transition temperatures, it might appear as ifthe case is settled, but there are several practi-cal (and one academic) reasons that this researchmust be resumed. In order for a neutrino-masslimit of 0.2 eV to be attained, faster signals needto be realized in order to reduce the systematicerrors associated with pile-up. Secondly, the em-pirical good thermalization limit for Re is veryclose to the highest operating point of interest,and it would add design flexibility if tempera-tures several tens of mK lower were also acces-sible. From an academic perspective, a thermal-ization law that scales as temperature relativeto TDebye, without regard to the superconduct-ing transition temperature, is hard to explain,thus further study is warranted.

5 Theory of SuperconductingAbsorbers

The critical tasks for TES development forMARE are the study and optimization of ther-malization in massive superconducting absorbersand the study and design of fast thermal con-tact between the absorbers and sensors. Thefast contact ideally should be developed first be-cause it is required in order to study the thermal-ization at the relevant time scales. Decouplingthe absorber can minimize the effects of multi-ple thermalization time scales (e.g. from diffu-sion from different positions in the absorber), butthe MARE pile-up requirements do not give usthe latitude to slow down the coupling. How-ever, it will be useful to commence thermaliza-tion experiments before the absorber coupling isentirely worked out. Because similar thermaliza-tion issues need to be addressed for a neutrino-less double-beta-decay experiment using 100Mo,we propose working with Mo absorbers as wellas the Re absorbers needed for the 187Re ex-

Figure 8: Table T1. Superconducting parameters of thekey superconductors in our proposed study. τr calculatedfrom Kaplan, et al. [42]; parameter values taken fromKaplan, et al. [42], Kozorezov , et al. [22] , and Kittel[43]. * indicates τ0 was not available; in the case of Re,an estimate was made from the Mo value by using scalingarguments.

periment that is the foundation for MARE. Wealso propose to include a few experiments withlower Debye temperature superconductors suchas Sn and Pb (TDebye equal to 200 and 105 K,respectively, compared with 430 and 450 K forRe and Mo) in order to enhance our physical un-derstanding of the thermalization mechanisms.

Table T1 lists the relevant superconductingproperties for the superconductors we proposeto study. It includes a column indicating an es-timate of the fraction of thermalized energy thatis in subgap phonons after the initial stages ofthermalization. We calculated this by fixing theratio of phonon energy to quasiparticle energy forSn at 1 (consistent with Zehnder [24] and Stahle[32]) and scaling by ∆2/T 3

Debye for the other ma-terials. This is just a thought guide; and the truesituation is substantially more complicated. Inone of the more recent theoretical investigationsof thermalization in superconductors, Kozorezovet. al. [22] determined that superconductors fallinto three categories with respect to thermaliza-tion, and such scaling laws can not be appliedbroadly. They estimate that the fraction of en-ergy in sub-gap phonons in Mo is 38%.

Table T1 also includes τ0, which representsa characteristic time scale that is derived fromthe physical properties of a given superconduc-tor; theoretical determinations of quasiparticlerecombination times and scattering times arequoted in terms of this fundamental time con-stant. The quasiparticle recombination time τr

is calculated from [42]:τ0τ−1

r ≈ π1/2( 2∆kTc

)5/2(T/Tc)1/2e−∆/kT .

In the case of Re, a value of τ0 was not avail-

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able in the literature. τ0 is derived from theelectron-phonon coupling, the low-temperaturedensity of phonon states, and T−3

c [42]. Sincethe electron-phonon interaction terms [44] andthe Debye temperatures are similar between Reand Mo, we have scaled the Mo value by T−3

c toestimate the Re value. The final two columns oftable T1 calculate τr for 0.1 K and for 0.1*Tc.The last column is included to show that mostof the variation in the values for τr at 0.1 is dueto the different values of Tc across the metals onthe list. The conclusion one draws from thesetheoretical values is that at any reasonable tem-perature for calorimeter operation, the energyput into the quasiparticle system is essentiallylost forever. This inspires the following ques-tions: Can we make a good detector anyway?Can we recover that energy and make a betterdetector?

There are several aspects to our investigation.One is simply to characterize thermalization inpure superconductors on much faster time scales(down to tens of microseconds) than previousmeasurements. We seek to test the universalthermalization law of Cosulich, et al. [33], whichspecifies that complete thermalization occurs inpure superconductors at T/TDebye > 2 × 10−4.Another is to investigate approaches to engineer-ing the superconductor to stimulate quasiparti-cle recombination yet circumvent the Rothwarf-Taylor bottleneck. The last is to lay the foun-dation for building devices with 10-mg Re ab-sorbers (this is a cube of 0.78 mm on a side, asize appropriate, per pixel, for a full scale exper-iment) that have fast coupling between the ab-sorber and the thermometer. A 10-mg absorberof pure Re at 0.1 K would have a heat capac-ity comparable to our Au-absorber devices thathave 2.5-eV resolution. (The 187Re endpoint en-ergy is 2.5 keV, which is within the x-ray rangefor which we typically design our devices, mak-ing x-ray photoelectrons appropriate surrogatesfor nuclear beta particles in our thermalizationtests.) The full MARE experiment would require105 such pixels.

6 Detailed plan for studying su-perconducting absorbers

Below we list the three approaches we intend tofollow in order to study the key properties of thesuperconductors that will enable the next gener-ation of neutrino mass experiments. Within ourgroup we have developed the three most sensi-tive sensor technologies: Semiconducting ther-mistors, transition edge thermistors, and mag-netic thermistors. Achieving greater sensitivityin all types of sensors is a goal within our group,and indeed the wider low temperature detectorcommunity. However, it is our view that worktowards greater sensor sensitivity should not bethe first priority for the community interested infuture experiments in the deep underground fa-cility. Progress in sensitivity has been supportedfor the past two decades, and continues to besupported by other communities. It is our viewthat all three of these technologies already havethe required sensitivity for future neutrino massexperiments. The need for superconducting ab-sorbers, however, is unique to this community.

In devising this research plan, we have triedto exploit the strengths of each thermistor type,in order to most easily obtain the thermaliza-tion parameters on superconducting absorbers.In general, semiconducting thermistors and mag-netic calorimeters have the advantage over TESsensors in that they can operate sensitively overa wide temperature range (∼ 20 - 150 mK). Thisallows us to study how the transport propertieschange as a function of temperature. TES sen-sors and magnetic calorimeters have the advan-tages of greater speed since they can be designedto be entirely metallic, as well as the advan-tage of potentially greater sensitivity for higherheat capacities. Semiconducting thermistors andTES sensors have the advantage of being farmore developed technically, and also do not re-quire the application of a magnetic field to makethem work. The presence of a magnetic field inthe proximity of the superconducting absorbermay be desirable, however it can also compli-

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cate the study of the superconducting properties.We have concluded that, for now, a complimen-tary approach using previously designed arraysof semiconducting and TES sensors is currentlythe simplest and most cost-effective way proper-ties of superconducting absorbers.

6.1 Depositing/plating onto existingabsorber structures

We propose to start our investigations by incor-porating superconducting absorbers onto our ex-isting TES devices. We have successfully elec-troplated Au absorbers and are in the processof refining an electroplating technique for Bi; weare confident that we can electroplate any metal-lic absorber for which there is established elec-troplating chemistry, including Re, Cd, Sn, andPb [45]. The use of existing photolithographicmask sets and processes, for which only minormodifications are needed, enables a quick startto our investigation and a ready comparison tohistorical devices. The main challenge with thisapproach is that our basic pixels are designedaround a particular x-ray telescope concept, andare squares that are only 0.24 mm on a side. Thesuperconducting transition width and the totalheat capacity set the dynamic range of a TEScalorimeter. Given the low specific heat of a su-perconductor operated far below its Tc, we willnot be able to make the absorbers thick enoughto achieve a useful dynamic range; therefore, wewill need to add substantial heat capacity to theabsorber with an underlying Au layer. This layercan also act as the electroplating seed.

We have two standard detector designs. Inone, we fabricate 8x8 arrays of individual pixelsthat consist of TES sensors capped by absorbers.We have engineered the contact between the TESand the absorber such that the absorber does notform an electrical short for the signal current;the contacts also avoid making a direct inter-face to the active area of the TES, contactingonly normal-metal features [21]. By incorporat-ing superconducting absorbers into such designs,

Figure 9: Position sensitive calorimeter for investigatingthermal diffusivity. There is a TES at each end of a longabsorber and comparison of the two signals yields the en-ergy and position and provides the time-scale for thermaltransport in the absorber.

we can study the pulse shapes, pulse variation,and energy resolution for various superconduc-tors plated on top of Au. The other design con-sists of an absorber strip between two TES sen-sors [46, 47], as shown in Fig.9. Originally con-ceived as an imaging TES, the design has alsoproven useful for measuring diffusion times inabsorber materials. We propose to plate super-conducting absorbers onto these devices to studytheir transport properties. In these designs, wecan vary the distribution of the added heat ca-pacity. For example, we can use the minimal Authickness required for plating, and split the bulkof the added heat capacity between the two endsso that, to the greatest extent possible, we canstudy the time scales intrinsic to the supercon-ductor.

The Au itself may enhance thermalization byproviding a reservoir of free electrons with whichdiffusing quasiparticles (and the occasional 2∆phonon) can interact. The application of normalmetal films to superconductors to aid thermal-ization has often been proposed and occasionallytried [48], largely with null results; some promis-

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ing results have not been reproduced. Mostof these attempts have used rolled supercon-ducting foils. A systematic study has not yetbeen attempted on high-quality superconduct-ing absorbers. Andreev scattering has been in-voked to explain this apparent failure. This isa process by which a quasiparticle approachinga region of lower superconducting gap (such ascreated by the proximity effect at the normal-superconducting interface) scatters as a quasi-hole at the boundary, with charge, but not en-ergy, carried forward into the region of smallergap via a Cooper pair. Quasiparticle trap-ping, however, seems to work in superconductingtunnel junctions [49], and this process requiresquasiparticles to diffuse into regions of lower gapand scatter into lower energy states there, be-coming trapped. When application of a normalmetal layer to a superconducting absorber hasnot changed the detector response, this judgmenthas been made on the basis that a long secondarytime constant persisted in the pulse shape. Weassert now that the presence of a finite secondarytime constant in the untreated superconductor isitself an indication that some internal trappingprocess, such as might result from internal de-fects or magnetic impurities, was dominating therecombination physics, and quasiparticles neverreached the films applied to the surface. Theexperiment we propose, with high-purity filmsgrown in a microelectronics clean room, will al-low greater understanding of the relevant effects.

An important aspect of our earlier studies ofSn absorbers had been the addition of a normal-metal, complete-thermalization reference on theabsorber to permit separation of the detectorthermal response from the thermalization signa-ture. We can achieve this end in the new devicessimply by limiting the thickness of the supercon-ducting layer such that a reasonable fraction ofthe incident x-rays will be absorbed in the un-derlying Au layer. This will be essential for de-termining whether all of the energy deposited ismeasured on the time scale of a pulse.

6.2 Attaching single crystals to TESand silicon pixels

We also propose a parallel quick-start route thatwill enable study of bulk absorbers that do notneed to be ballasted by a large added heat ca-pacity whose source may influence the thermal-ization we aim to study. We will attach bulkabsorber crystals to existing devices, both TESand silicon thermistor, using minute quantitiesof epoxy and a technique developed for assemblyof the XRS/Suzaku array. TES devices have afixed operating temperature, but the silicon ther-mistors can be used to study thermalization as afunction of temperature. With such devices, wecan probe the Cosulich universal thermalizationlaw down to time scales of ∼ 1 ms. The semicon-ductor devices are also better suited to studiesthat involve the application of a magnetic field tothe absorber to trap magnetic flux, as the prop-erties of a TES will change in response to sucha field. The TES, however, are better suited forstudying larger volumes (because they achievethe same sensitivity with higher heat capacities)and shorter time scales at a particular tempera-ture.

6.3 Patterning devices onto crystals

Lastly, we propose to address the shortcomingsof the two quick-start approaches, and work to-wards devices that could be implemented in alarge scale experiment, by inverting the process-ing order and developing procedures for pattern-ing the TES sensors on top of superconductingcrystals. Such an approach enables direct metal-lic contact between the TES and the crystal.

The following is a possible scheme for completefabrication of large arrays of TES calorimeterswith bulk absorbers:1. Start with an absorber crystal of the thick-ness and area needed for an array and mount iton handle wafer.2. If normal metal layers are needed to enhancethermalization, pattern these on one or bothsides of the crystal,

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3. Passivate absorber surface.4. Open holes in passivation where metalliccontact will be made with normal metal regionsof the TES thermometers.5. Deposit TES films on absorbers (standardGoddard Mo/Au bilayer TES)6. Deposit bump-bond pads on TES.7. Dice absorber material into individualabsorbers, each with a TES patterned on it.8. Fabricate fan-out array of bump bondcontacts and leads9. Bump bond absorber/TES pieces to fan-outarray using pick-and-place machine

- Indium is radioactive, but we could use goldbumps to a solid substrate.

- Au/Si Kapitza resistance can be used as thecalorimeter weak link

For the present program, we propose to inves-tigate the first steps of such a scheme: the pat-terning of a TES directly on a planarized super-conducting crystal. We can characterize the TESproperties by making simple wire-bond connec-tions to the TES contacts. When the TES char-acteristics are satisfactory, we will test devicesvia aluminum wire-bond suspensions. The ear-liest microcalorimeters were tested in this way;the device is supported with a temporary ad-hesive during the wirebonding and subsequentlyreleased so that the wirebonds provide the ther-mal link as well as the electrical contact. Withthese devices, we can simultaneously probe thesize scale and times scale of interest to a next-generation neutrino-mass experiment.

7 Workplan

7.1 Schedule

Year 1 Fabricate pixel arrays with electroplatedsuperconducting absorbers (2 runs). Fabricatestrip devices with superconducting absorbers (2runs). Evaluate candidate substrate crystals forpost-facto absorber attachment and/or invertedprocess (TES’s deposited on absorber). Lay out

photolithography mask set for inverted process.Year 2 Continue pixel and PoST (PositionSensitive TES calorimeters) experiments (2 fabruns), Test bulk absorbers glued to silicon ther-mistors and TES’s. Build and test thick-absorber devices using inverted process.Year 3 Build and test thick-absorber devices us-ing inverted process (2 fab runs). Extend tech-niques to improve thermalization. Expand stud-ies to different superconductors.

7.2 Personnel

Prof. Carter Hall is the principal investigatorand will be responsible for co-ordinating all theactivities outlined in this proposal. He will par-ticipate in the design of devices, and will analyzeand report on the results obtained.Dr. Simon Bandler is a Co-investigator. Hewill contribute to the design of the experimentson superconducting absorbers, and will be re-sponsible for measurements made on devices us-ing transition edge sensors.Dr. Richard Kelley is a Co-Investigator andthe NASA/GSFC institutional PI. He will con-tribute to the design of the experiments and willcoordinate the activities with Carter Hall.Dr. Caroline Kilbourne is a Co-Investigator.She is responsible for the design of all the exper-iments and is responsible for the team’s effortsto analyze and understand the properties of su-perconductors.Dr. F. Scott Porter is a Co-Investigator. Hewill contribute to the design of experiments andis responsible for the measurements on devicesusing silicon thermistors.Prof. George Seidel is a collaborator. Hewill be advising in the design of experiments tostudy superconducting absorbers, and will helpto analyze data and link it to theory.Prof. Massimiliano Galeazzi is a collabora-tor. He will advise on the design and analysis ofexperiments, and in the collaboration with therest of the MARE team.

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