Calorimetric observation of single He2* excimers in a 100 mK He bath
F. W. Carter, S. A. Hertel, M. J. Rooks, P. V. E. McClintock, D. N. McKinsey, D. E. Prober
CCalorimetric observation of single He ∗ excimers in a 100 mK He bath F.W. Carter,
1, 2, a) S.A. Hertel,
3, 4, 2
M.J. Rooks, P.V.E. McClintock, D.N. McKinsey,
3, 4, 2 and D.E. Prober Argonne National Laboratory, High Energy Physics, Lemont, IL, 60439 Yale University, Department of Physics, New Haven, CT 06511 University of California Berkeley, Department of Physics, Berkeley, CA 94720 Lawrence Berkeley National Laboratory, Berkeley, CA 94720 Yale Institute for Nanoscience and Quantum Engineering, New Haven, CT 06520 Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom Yale University, Department of Applied Physics, New Haven, CT 06520 (Dated: 23 October 2018)
We report the first calorimetric detection of individual He ∗ excimers within a bath of su-perfluid He. The detector used in this work is a single superconducting titanium transitionedge sensor (TES) with an energy resolution of ∼ ∗ excimers are produced in the surrounding bath using an external gamma-ray source.These excimers exist either as short-lived singlet or long-lived triplet states. We demonstratedetection (and discrimination) of both states: in the singlet case the calorimeter records theabsorption of a prompt ≈
15 eV photon, and in the triplet case the calorimeter records adirect interaction of the molecule with the TES surface, which deposits a distinct fractionof the ≈
15 eV, released upon decay, into the surface. We also briefly discuss the detectorfabrication and characterization.Keywords: Superconductivity, Superfluidity, Nanophysics
I. INTRODUCTION
Superfluid helium, when subjected to ionizing radia-tion, produces metastable diatomic He molecules in boththe singlet and triplet states, emitting a ≈
15 eV pho-ton upon decay. The singlet He ∗ (A Σ + u ) decays withinnanoseconds, while the triplet He ∗ (a Σ + u ) exhibits a re-markably long lifetime of 13 seconds in superfluid helium(McKinsey et al. , 1999). The long-lived triplet state canserve as an observable tracer particle in a liquid heliumbath, tagging the flow of the normal-fluid component or,at colder temperatures, tagging quantized vortices in thesuperfluid component (Guo et al. , 2014). Efficient de-tection of helium excimers may also enable the use ofa superfluid helium bath in a search for dark matter-induced nuclear recoils, given that a recoil’s resulting sin-glet:triplet excimer ratio distinguishes between electron-and nuclear-recoils. Additionally, high-sensitivity detec-tion of electronic excitations may be used to veto electronrecoil backgrounds when searching for low energy nuclearrecoils, since nuclear recoils predominantly produce heatin the form of rotons and phonons (Guo and McKinsey,2013).These applications require an efficient technique forobserving and differentiating between the two excimerstates. Two techniques have been employed previouslyfor triplet excimer detection: observation through laserfluorescence (Rellergert et al. , 2008; Guo et al. , 2009),and observation of Auger electrons produced throughquenching on a surface (Zmeev et al. , 2013b,a). Low-temperature calorimetry offers near-unity efficiency fordetecting any energy deposition above some energythreshold, making both the ≈
15 eV singlet decay pho-tons and the triplet surface quench process observable a) Electronic mail: [email protected]
TABLE I. Characteristics of the Ti TES with Al leads and anintegrated 100 nm thick Al/Cu thin-film aperture.
Physical External
Width 10 µ m L total
50 nHLength 15 µ m R shunt
200 mΩThickness 15 nm R parasitic R Normal T bath
100 mK T c
345 mK I bias µ A with the same sensor. Here we report success at thishigh-efficiency detection of both excimer states by a sin-gle sensor.In this work, we employ a single Transition Edge Sen-sor (TES) with resolution of ∼ et al. ,2014). The detector is immersed directly in a superfluidhelium bath at 100 mK (the Kapitza resistance betweenthe sensor and liquid helium allows the sensor to functioneven while in contact with the superfluid helium), andexcimers are created by exposing the bath to gamma-rays from a 100 µ Curie Na source located outside thecryostat. The superfluid reservoir, the cryostat, and theelectronics are described in Carter (2015).
II. THE TRANSITION EDGE SENSOR
The TES consists of a 15 nm film of evaporated tita-nium with 300 nm thick evaporated aluminum leads andan integrated 100 nm thick Cu/Al aperture. Table I givesbasic device parameters. The dominant cooling mecha-nism, which sets the detector time constant of ≈
800 ns,is electron-phonon coupling in the Ti (electron outdiffu-sion is blocked by Andreev reflection in the superconduct- a r X i v : . [ c ond - m a t . o t h e r] J u l Aluminum ! Titanium ! Cu/Al bilayer ! PMMA ! Substrate ! (a) (b) (c) FIG. 1. (a) Cross-sectional diagram of TES configuration (not to scale, dimensions in table I). (b) SEM image of TES withaperture. (c) Optical image of TES with aperture. Leads are just visible extending to the left underneath the Cu/Al shieldlayer (outlined in dashed white). ing Al leads). The TES is operated in negative electro-thermal feedback mode by wiring it in parallel with asmall shunt resistor (see table I) and providing a currentbias (Irwin, 1995). The current through the TES is readout with a SQUID amplifier and room-temperature elec-tronics from Magnicon (Drung et al. , 2007), which arecoupled to a fast (6 GHz) digitizing oscilloscope. Energydeposited in the voltage-biased TES results in a negativecurrent pulse with an integrated charge that is propor-tional to the energy absorbed. Henceforth, we refer tothese pulses as ‘events’. Event pulses are recorded, fil-tered, and fit to a model-pulse derived from the TESresponse to several thousand single blue photon events.The integral of the resulting best-fit pulse is then scaledby the TES efficiency to give our best estimate of theincident energy.The TES is protected by a thin-film aperture intendedto absorb and diffuse energy deposited near, but notdirectly into the TES. The aperture is fabricated byevaporating a 100 nm thick Cu/Al bi-layer on top of athick 1 µ m layer of insulating polymethylmethacrylate(PMMA) spun directly onto the wafer, and then etchinga window directly over the TES. The full fabrication pro-cess of the TES is detailed in the appendix and Fig. 1ashows a side view of the layers. Figures 1c and 1b showoptical and SEM images respectively.We characterized our detector response with a pulsedblue (2.6 eV) laser, in the same manner as in Carter et al. (2014). By illuminating the TES with a pulsed source oflow average photon number and making a histogram ofthe measured TES pulse-areas, one may calculate theTES energy resolution and efficiency by fitting the his-togram with a Gaussian-broadened Poisson distribution. III. EXPERIMENTAL SETUP
The TES was mounted on the inner wall of a 5 × × helium-filled chamber, held at a temperature of100 mK. The helium was pure He (less than 1 part in10
12 3
He) produced at Lancaster University using theheat-flush technique (McClintock, 1978). Excimers werecreated in the helium bath in two ways. The first methodemployed a Na gamma-ray source external to the cryo-stat. Compton scattering in the helium produces elec- tron recoils extending to hundreds of keV. These high-energy electrons lose their energy to the surrounding Heatoms by exciting and ionizing He atoms, which uponelectron-ion recombination produce a mixture of singletand triplet excimers. The second method for excimerproduction was to apply a large negative voltage ( ∼ -1.5 kV) to a sharp tungsten tip immersed in the Hebath. Electrons emitted from the tip lose energy to thebath, producing atomic excitations, rotons, and quan-tized vortex rings. Both production methods were em-ployed with consistent results. Here we report resultsfrom the Na method, which allowed a cleaner timingselection (through the use of a coincidence trigger as ex-plained below) and lower electronic readout noise.When using the Na source some fraction of thegamma-rays will Compton scatter within the Si substraterather than in the He. Such substrate energy depositionswere observed, and excluded from the analysis using apulse shape selection, which takes advantage of the rel-atively slow diffusion of phonons within the substrate,and their relatively weak coupling to the TES. Figure 2shows two scatter plots of pulse height vs. pulse area forevents measured under Na irradiation. The events inFig. 2a were recorded with the chamber empty of helium,and the events in Fig. 2b were recorded after condensingHe. In both sets of data, a population corresponding tolarge pulse energies (10—1000 eV) and large pulse heights(30—1000 nA) was observed; this is the substrate absorp-tion signal (the cutoff near 1000 nA is due to detector sat-uration). Random noise triggers are included as a blob inthe lower left of each plot. In Fig. 2b, two populations ofmuch faster (larger height-to-energy ratio), lower-energypulses may be observed. The upper population (coloredin blue) results from direct absorption of energy in theTES from either a singlet photon or a triplet quench.The lower population is due to events near the TES (i.e.the leads, the substrate below the TES, etc.) All of thefollowing data analysis focuses solely on the ‘direct hits’(blue), which are selected by windowing on events withtime-constants that match the intrinsic TES time con-stant.Each Na decay produces two counter-propagating511 keV gamma-rays and a single 1.3 MeV gamma-ray.Thus, by adding a standard NaI scintillator coupled to aphoto-multiplier tube (PMT) opposite the helium cham- (a) No helium(b) With helium
FIG. 2. (a) Pulse heights vs. collected energy recorded withthe TES while an empty chamber was subject to a Nagamma-ray source. (b) The same, except in this case thechamber was filled with superfluid helium. Blue points cor-respond to direct excimer detection events in the TES (bothsinglet and triplet). The “extra” population located just be-low the blue points, but not present in (a), is due to energydeposited near the TES, but not directly in it (i.e. leads,substrate nearby, etc.). ber, we may tag TES events coincident with a Na de-cay. Figure 3a illustrates the geometry for this setup.Singlet-decay photons are emitted promptly (ns scale)after the gamma-ray/electron recoil, whereas triplet ex-cimers arrive at the TES delayed by a ballistic prop-agation time measured by Zmeev et al. (2013b) to be ∼ µ m from the TES.The chamber is big enough that this small population oftriplets will contribute fewer than one out of every fiftydetection events and may thus be neglected.The PMT output is continuously monitored by thesame oscilloscope that monitors the TES. Whenever aTES signal triggers the oscilloscope, it collects 5 µ s ofdata before the trigger and 45 µ s after the trigger. Therising edge of any pulses observed in the PMT channelare recorded as delay times relative to the trigger timeat t = 0. Figure 3b shows a histogram of delay times Cryostat
PMT+NaI Na
511 keV 511 keV
Helium Chamber (a) C oun t s -1.0 -0.5 0.0 0.5 1.0Time from trigger ( µ s) (b) FIG. 3. (a) Experimental setup for coincidence measurementswith a Na source. The PMT+NaI detector and the heliumchamber are aligned relative to the radiation source such thatthe solid angles of illumination are matched. Any 511 keVgamma-ray that is incident on the chamber, will also producea 511 keV gamma-ray that is incident on the PMT+NaI de-tector. (b) Histogram of the time difference between pulsesdetected in the PMT channel and pulses detected in the TESchannel; substrate events have been removed. The shadedregion is the cut used to make the red curve in Fig. 4. between TES events (at t = 0) and PMT events. Thelarge peak near zero delay is due to photon absorptionevents in the TES that were coincident with a gamma-ray detection in the PMT. The ≈
100 ns offset from zeroreflects the combined effects of cable-length delay and theplacement of the TES trigger partway up the rising edgeof the TES pulse.
IV. RESULTS
Figure 4 shows two energy spectra created by binning ∼
13 000 single excimer detection events by the energymeasured with the TES. The blue curve is a spectrum ofall the TES events due to irradiation by the Na source(the population of events colored blue in Fig. 2b). Thered curve shows a spectrum consisting of only the coin-cident events (the events in the shaded region of the his-togram in Fig. 3b), which must arise from detecting sin-glet photons (plus a 3% contribution from non-coincidentevents due to random coincidence). The shaded area in-dicates the error, calculated as the square-root of thenumber of counts in each bin. The two curves have beenscaled such that their areas are each equal to unity. We
FIG. 4. Red curve: detected emission spectrum of singletHe ∗ decays (683 counts). Blue curve: total spectrum of alldetected events (13 256 counts). Shaded area between linesindicates error, calculated as ± the square-root of the countsin each bin. hypothesize that the large peak in the blue curve near3.5 eV arises mostly from the detection of triplet stateexcimer quenches on the TES surface, although it is clearthat the photon-only signal (red curve) also has a smallcontribution in that energy range. A. Discussion1. Coincident spectrum (red curve)
The primary feature of the helium scintillation spec-trum as measured previously by Stockton, Keto, andFitzsimmons (1970) is a peak centered at 15.5 eV with afull-width-half-maximum of about 3 eV. One would ex-pect the red spectrum in Fig. 4 to look qualitatively sim-ilar, as it is due almost entirely to scintillation photons.Instead, the coincident spectrum peaks somewhat lower,near 10 eV, and shows a tail towards lower energies. Itis possible that the detector response may not be lin-ear from 2.65 eV (the calibration energy using blue pho-tons) to this higher 15.5 eV range. We investigated TESlinearity at low-energy experimentally by comparing our2.65 eV calibration with a separate 0.8 eV calibration;results were consistent with linearity in this range (anidentical fraction of photon energy appeared in the TESelectron system during the absorption of a single photon:67 %). Calibration at higher photon energies was notperformed as we did not have access to such a photonsource.In order to estimate the efficiency of our TES at higherenergies we calculated the energy lost during a photonabsorption according to Kozorezov et al. (2013). Whenthe detector absorbs a single photon all of the energyis initially contained in a single excited photo-electron.This excited electron transfers its energy to the elec-tron system, which arrives at a thermal distribution andthen cools off through phonon-scattering. This is a four-step process. Step 1: The initial photo-electron sharesits energy with other electrons within a radius of about20 pm via electron-electron interactions until the meanelectron energy in the hot spot is about 800 meV, inde- pendent of initial energy (this is a material property ofTi). This process takes of order 100 fs. Step 2: Theathermal electrons then shed phonons until the rate ofphonon emission roughly matches the rate of phonon ab-sorption, which happens at a mean energy per electronof about 4 meV for titanium and takes a time of order afew picoseconds. Step 3: The hot spot of electrons sharesits energy with the rest of the system through electronicinteractions and arrives at a thermal distribution withina few nanoseconds. Step 4: The thermal electrons coolthrough phonon scattering over a time-scale of order 1 µ sfor our device. This characteristic time is shortened toabout 700 ns in our experiment through electro-thermalfeedback due to the voltage bias. During Step 2 of thisprocess a large amount of the initial photon energy isconverted into athermal phonons. For a thin film device(thinner than the athermal phonon mean-free-path) thechance of energy loss due to phonons escaping into thesubstrate is high. We have calculated that for our de-vice this loss should be about 30 % of the initial energy,a value that is consistent with our experimentally de-termined device energy efficiency of 67 %. However, wefind that this efficiency does not depend on initial pho-ton energy (unless the initial photon energy is smallerthan 800 meV in which case the energy loss will be less),and so can not explain the apparent non-linear effect weobserve at 15 eV.There are at least three remaining possible additionalchannels for energy loss during a photon event. At thebeginning of Step 4, the hot electrons have a mean energyof about 4 meV, which is roughly 20 times higher than thealuminum superconducting energy gap (∆). The time foran electron to diffuse from the center of the TES to theedge ( τ = L /D , where L is the distance to the contactand D is the diffusion coefficient) is about 80 ns, whichis of the same order as the time it takes the hot spotto settle into a thermal distribution below the Al energygap. This allows for the possibility that some hot elec-trons could escape out the Al leads prior to thermaliza-tion. The energy lost in this process should be a linearfunction of the initial number of hot electrons present,and so a linear function of photon energy. Our two-pointcalibration (0.8 eV and 2.6 eV) does not exhibit any sig-nificant efficiency variation and so we discount this lossmechanism.The second energy loss channel is the photo-electriceffect. At the beginning of Step 1, a photo-electron withenergy greater than the Ti work function (4 eV) maysimply escape the TES entirely. This can happen eitherimmediately or after sharing some of its energy with theelectron system. Mancini, Giaquinta, and Pennisi (1981)show that for thin films, the escape probability is pro-portional to 1 /d where d is the film thickness. Studies ofphoto-electron yield for micron-thick Ti films give yieldsas large as 20 % (Cairns and Samson, 1966), suggestingthat a 100 % yield for a very thin film is not unreason-able. When a photo-electron escapes, it leaves a holebelow the Fermi surface that is filled by an electron fromthe Fermi level, releasing the remainder of the energyinto the TES according to the four step process above.Walker and Weissler (1962) studied the energy spectrumof photo-electrons emitted from a gold film during illumi-nation from a 14 eV source and found a large fraction ofescaping photo-electrons with very low energies ( ∼ + is about 4 eV,so for a 15 eV photon, 11 eV would be deposited in theTES. We expect the occurrence of this phenomenon tobe quite low, but include it here for completeness.Finally, we note that Cabrera et al. (1998) character-ized a thin-film tungsten TES at energies from near-IRup to 3.5 eV and found that while their device was lin-ear up to 3 eV, it experienced an onset of decreased ef-ficiency above 3 eV (see Fig. 4, inset, in their paper).This motivates further study of the energy loss of thin-film TES devices in the vacuum-ultraviolet energy rangewhere photo-electric and Auger processes may be impor-tant.
2. Total spectrum (blue curve)
The total spectrum (collected without regard to coin-cidence in the PMT channel) also shows the 10 eV peakthat we attribute to absorption of singlet-state excimerdecay photons; the coincidence trigger efficiency was lowso we could not construct a data selection free from thisprompt contribution. A second peak is observed near3.5 eV, and we conclude that this peak represents thedirect detection of triplet-state excimers after a propaga-tion delay.Deexcitation of single He ∗ atoms through interactionwith solid surfaces has been studied for the purpose ofprobing the electron density of states in a material’s sur-face (metastable deexcitation spectroscopy). See, forexample, Harada, Masuda, and Ozaki (1997), Bonini,Brivio, and Trioni (2003), or Trioni et al. (2005). He ∗ deexcitation (or quenching) at a surface is expected toproceed in a similar fashion. Figure 5 depicts the man-ner in which an excimer quenches at the surface throughelectron exchange, coupling a fraction of its 15.5 eV ex-citation energy into the TES surface. The process is asfollows:1. As the excimer comes within angstrom-scale dis-tance of the TES surface, the excited electron res-onantly tunnels into an empty state (at energy E )above the metal’s Fermi level ( E F ), leaving the ex-cimer charged as He ∗ +2 . This electron at E thenscatters down to the Fermi energy, releasing an en-ergy ( E − E F ) into the TES. For this ‘resonant ion-ization’ process to occur, the work function of theTES surface must be greater than E v − E where E v is the vacuum energy. It should be noted that boththe surface and He ∗ electron energies vary as a func-tion of surface-He ∗ separation (excimer electron en-ergies increase slightly as distance decreases). 2. An electron from the metal surface then tunnelsin the opposite direction, filling the vacancy in theground state to neutralize the He ∗ +2 . The dimerseparates.3. An electron from within the Fermi sea gains the en-ergy released in the previous step ( E − E g ) throughan Auger process. This may be enough energy tocause the electron to escape the TES. This and theprevious step are often termed ‘Auger neutraliza-tion’.4. Finally, electrons from the Fermi surface cascadedown to fill the two holes left by the neutralizingelectron and the Auger electron. These two en-ergies are E F − E and E F − E . If the Augerelectron from the previous step remains withinthe TES, it will deposit the rest of its energy,( E − E g ) − ( E F − E ), in the TES as it relaxesto the Fermi level.In this process, E − E F is always deposited in the TES.For a Ti TES, this energy is very nearly zero. The twoelectrons from steps 2 and 3 can come from any filledstate in the TES, and so the density of states plays alarge role in determining E and E . There is also noreason why E should be larger than E . This processeffectively maps out the density of states near the Fermilevel, and is nearly the inverse of metastable deexcitationspectroscopy. In that process the Auger electron is col-lected when it escapes from the surface, whereas in thiscase, the TES collects the energy that does not escape.Thus, the spectral shape will be heavily influenced byboth the density of states near the Fermi surface of theTES and the detector’s response to input energy.This explanation relies on the efficient escape of Augerelectrons from their origin in the outermost atomic layerof the TES. While there are no measurements of thisescape probability specifically for He ∗ metastable de-excitation on Ti, there are a variety of measurementson other metals for the similar He ∗ deexcitation pro-cess. The Auger electron escape probability has beenobserved to range from ≈ > V. CONCLUSION
We have demonstrated the calorimetric detection ofindividual He ∗ excimers in two distinct channels with aTES immersed directly in superfluid helium. The short-lived singlet states are visible through their ≈
15 eV scin-tillation photons, well above threshold of the device. Thelong-lived triplet states are also detectable through theirfew-eV energy deposition upon arrival at the TES sur-face. The two signals are distinguishable (in aggregate)by their spectral shapes.The energy deposited during the interaction of thetriplet excimer with the TES surface is expected to behighly dependent on the TES surface’s electronic den-sity of states. In our case, we posit that the oxidized Ti
TES He E v E E g E F (a) Just before coupling E v E E TES He E E g E F (b) Just after coupling FIG. 5. (a) The triplet state excimer is to the right of the dashed line (one He atom in the ground state, and one in an excitedstate) and the TES is to the left of the dashed line. The horizontal axis is distance, and the vertical axis is energy. E v is thevacuum energy and E F is the Fermi energy of the TES. E g is the ground-state energy of the excimer. The gradient regiondepicts an arbitrary non-uniform density of states below the Fermi level in the TES. E − E g is the excimer energy and is about15 eV. E is roughly 4 eV below E v , but shifts upwards as the excimer approaches the TES surface. (b) The processes involvedin the excimer quenching on the detector (blue arrows) is numbered in order of occurrence 1: the excited electron tunnels intoa free state in the TES, and relaxes to the Fermi surface. 2: An electron from the TES Fermi sea fills the empty ground stateof the helium molecule, and the molecule splits into two atoms. 3: An Auger electron is promoted from within the TES Fermisea, and has energy E − E g . Finally, electrons relax from the Fermi surface to fill the two empty states in the TES (this isnot pictured). Energies E and E are arbitrary as these two electrons may source from anywhere in the TES Fermi sea. surface allowed the efficient transfer of a fraction of theexcimer energy into the surface by taking advantage ofbands located between 2 eV and 5 eV below the Fermienergy. In a future version of this experiment, this den-sity of states could be engineered to generate a signalof higher efficiency or fidelity. The eventual applica-tion of these new excimer detection principles towardsinstrumenting a large volume with high excimer detec-tion efficiency will depend on applying them to larger-area calorimeters (see Angloher et al. (2005) or Pyle,Feliciano-Figueroa, and Sadoulet (2015)).One promising application for our detector conceptlies in studies of quantum turbulence. Given the large(96 nm) trapping diameter for He ∗ molecules on quantumturbulence vortices (Zmeev et al. , 2013a), high-efficiencydetection of these excimers should enable sensitive mon-itoring of quantum turbulence density by measuring theHe ∗ flux passing through a superfluid helium-filled vol-ume. This technique would also allow for independentmonitoring of the He ∗ production from sharp tungstentips held at a high voltage and used to decorate quan-tum turbulence with He ∗ excimers.Finally, we note that there is a considerable uncer-tainty as to the exact physics underlying the spectralshapes presented in Fig. 4. We have put forward a hy-pothesis that appeals to the surface electron density ofstates, the photo-electric effect, and Auger processes, butthere is no detailed model. A full understanding is not possible within the limits of the current data, and a newset of experiments and devices will be required to obtaina detailed theoretical explanation of these promising firstresults. ACKNOWLEDGMENTS
We would like to thank Prof. M. Devoret for the loan ofa dilution refrigerator; J. Cushman for drafting expertise;C. Matulis for circuit-board design; Dr. L. Frunzio forfabrication advice; Prof. R. Schoelkopf and Prof. M. Ha-tridge for cryogenics expertise; Dr. C. McKitterick,Dr. Z. Leghtas, and S. Touzard for helpful discussions;and the Gibbs Machine Shop for making experimentalhardware. Facilities use was supported by YINQE andNSF MRSEC DMR-1119826. We also acknowledge sup-port from the National Science Foundation under NSFDMR-1007974.
Appendix: Fabrication
The TES was fabricated on a bare (unoxidized) high-resistivity silicon wafer. All the metal depositions wereaccomplished using electron beam (E-beam) evaporationin a commercial evaporator from Plasma Systems. Thepatterning was done using electron-beam lithography ina Raith EBPG 5000+ system.1.
Alignment marks:
The wafer is cleaned, anda bilayer of polymethylmethacrylate (PMMA) E-beam resist is applied. A pattern of 20 × µ m squares are written via E-beam, and then 400 nm ofCu is evaporated and lifted-off to define the align-ment marks. These marks are used to preciselyposition the etch window over the region destinedto become the TES.2. Ti/Al bilayer:
A bilayer of PMMA is applied.The outline of the detectors, wiring, and absorbersis written via E-beam. Then a bilayer of 15 nm ofTi and 300 nm of Al is evaporated and lifted-off.3.
Al etch:
A single layer of PMMA is applied. Win-dows are opened in the resist via E-beam lithogra-phy directly over the areas that are to become theTES. The exposed Al is then etched down to theTi, defining the detectors (Ti is a natural etch stopfor the etchant used).4.
Aperture:
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