Transition-edge sensor detectors for the Origins Space Telescope
TTransition-edge sensor detectors for the Origins Space Telescope
Peter C. Nagler a,* , John E. Sadleir a , Edward J. Wollack a a NASA Goddard Space Flight Center, Greenbelt, Maryland, 20771 USA
Accepted by the Journal of Astronomical Telescopes, Instruments, and Systems.
Abstract.
The Origins Space Telescope is one of four flagship missions under study for the 2020 AstrophysicsDecadal Survey. With a 5.9 m cold (4.5 K) telescope deployed from space,
Origins promises unprecedented sensitivityin the near-, mid-, and far-infrared, from 2.8 – 588 µ m. This mandates the use of ultra-sensitive and stable detectorsin all of the Origins instruments. At the present, no known detectors can meet
Origins’ stability requirements in thenear- to mid-infrared, or its sensitivity requirements in the far-infrared. In this work, we discuss the applicability oftransition-edge sensors, as both calorimeters and bolometers, to meet these requirements, and lay out a path towardimproving the present state-of-the-art.
Keywords:
Transition-edge sensors, single-photon detectors, calorimeters, bolometers, infrared astrophysics. * Corresponding author: [email protected]
The Origins Space Telescope (
Origins ) traces our cosmic history, from the formation of the firstgalaxies and the rise of metals to the development of habitable worlds and present-day life.
Origins does this through exquisite sensitivity to infrared radiation from ions, atoms, molecules, dust, watervapor and ice, and observations of extra-solar planetary atmospheres, protoplanetary disks, andlarge-area extragalactic fields.
Origins operates in the wavelength range 2.8 to 588 µ m and is morethan 1000 times more sensitive than its predecessors due to its large, cold (4.5 K) telescope andadvanced instruments.A complete description of Origins , its science goals, and its instrumentation is provided by theOrigins Space Telescope Mission Concept Study Report. We reproduce some key details here.
Origins has three instruments, each with a variety of observing modes. The Origins Survey Spec-trometer (OSS) is designed to perform extra-galactic surveys of far-infrared (FIR) line emission1 a r X i v : . [ a s t r o - ph . I M ] D ec rom 25 – 588 µ m, probing galaxy evolution out to z ∼ . . OSS uses a series of grating mod-ules to disperse incident light into six logarithmically-spaced bands, each with spectral resolvingpower R ∼ . A Fourier transform spectrometer (FTS) can be inserted into the optical path toachieve R ∼ , , and the FTS can be used in conjunction with a scanning etalon to achieve R ∼ , in the 100 – 200 µ m band. In order to make background-limited observations offar-infrared spectral lines at R ∼ , OSS requires instrument sensitivity of . × − W / m inan hour of observing at 200 µ m. This corresponds to a required detector noise equivalent power(NEP) of × − W / √ Hz and per-pixel saturation power of ∼ . − . fW, a level of sensi-tivity that has yet to be achieved in a FIR detector. OSS has six focal planes, each with ∼ , pixels.The Far-Infrared Imager Polarimeter (FIP) instrument will perform wide-field photometric sur-veys of astrophysical objects, bridging the gab between observations by James Webb Space Tele-scope ( JWST ) and the Atacama Large Millimeter/sub-millimeter Array (ALMA). FIP has polar-ized imaging capability at both 50 µ m and 250 µ m. It requires ∼ , pixels, a per-pixel NEP of × − W / √ Hz , and per-pixel saturation power of ∼ − fW.The Mid-Infrared Spectrometer Camera Transit spectrometer (MISC-T) will make spectralmeasurements of transiting exoplanets in the 2.8 – 20 µ m band with exquisite photometric pre-cision, looking for biosignatures in the atmospheres of Earth-like exoplanets that orbit M stars.MISC-T uses a series of grisms to disperse light into three bands. The short wavelength bands (2.8– 5.5 µ m and 5.5 – 11 µ m) will have R = 50 − and require ∼ ppm stability over 60 transits,and the long wavelength band (11 – 20 µ m) will have R = 165 − and requires ∼ ppmstability over 60 transits. Bright targets of K magnitude ∼ will be observed, leading to photonarrival rates of up to a few hundred thousand photons per pixel per second. Detector systems that2eet these stringent stability requirements in the MISC-T band do not exist today.The choice of detector used for each instrument will have tremendous impact on the devel-opment, construction, and eventual operation of Origins . The sensitivity requirements of the FIRinstruments mandate the use of sub-Kelvin detectors. There are several detector technologies thathave the potential to meet the requirements of the FIR instruments. Among them are microwavekinetic inductance detectors (MKIDs), quantum capacitance detectors (QCDs), and transition-edgesensors (TESs), the subject of this paper. MKIDs and QCDs will be discussed elsewhere in thisissue. The MISC-T instrument’s stability requirement does not mandate the use of a low temper-ature detector. As a result the baseline detectors under consideration for MISC-T (HgCdTe arraysfor wavelengths shorter than 10 µ m and Si:As arrays for wavelengths longer than 10 µ m) do notrequire sub-Kelvin coolers. They operate at T (cid:39) K and T (cid:39) K, respectively. Neither detectortype has shown that it can meet the stability requirements of MISC-T, so in this paper we alsopresent a TES calorimeter option for MISC-T. TES bolometers are also considered as candidatesfor MISC-T, but we argue that operation in a calorimetric mode provides an ideal choice.This paper is organized as follows. In Section 2, we introduce the TES and its most commonimplementations: calorimeters and bolometers that use a superconductor as a resistive thermome-ter. Then we present a path toward meeting the requirements of each
Origins instrument usingTESs. In Section 3 we present the use of a photon-counting TES calorimeter for MISC-T. In Sec-tion 4, we discuss how TES bolometers can be designed to meet the requirements of OSS and FIP.Since no detector systems currently satisfy
Origins ’ requirements, we describe how TESs can. Ourconclusions are in Section 5. 3 ig 1
Left: Basic architecture of a TES detector. The variable resistor is a superconductor biased in its transition,employed as a resistive thermometer. The pixel has heat capacity C and is isolated from the thermal bath via a thermalconductance G . Right: Basic TES readout circuit that uses a superconducting quantum interference device (SQUID)amplifier. The shunt resistor value R s is chosen to be much smaller than the TES operating resistance R TES in orderto achieve voltage bias in the device. The SQUID amplifier is employed as an ammeter that measures changes in TEScurrent due to absorption of energetic particles (calorimeter) or flux (bolometer).
Transition-edge sensors detectors measure incident power or energy using the temperature depen-dence of a superconductor’s resistance. First realized by Andrews in 1941, TESs are now the mostsensitive detectors to radiation from the gamma-ray through the millimeter wave.TESs can operate as calorimeters or bolometers. A calorimeter is designed to measure discretedepositions of energy, and a bolometer is designed to measure quasi-static power dissipated bya flux of photons. Both implementations share the same basic architecture. Figure 1 shows acartoon of a TES and its basic readout circuit. The detector consists of a thermal mass of heatcapacity C at a temperature T , isolated from a thermal bath at temperature T b across a thermal linkwith conductance G . The thermometer - a superconductor biased in its transition - measures thetemperature of the isolated thermal mass, which can consist of electrons or electrons and phonons.The device is operated at near-constant voltage bias to stabilize the device in the superconducting4ransition via negative electrothermal feedback. A shunt resistor whose resistance is much smallerthan the TES’s at its operating point is typically used to achieve voltage bias. The shunt resistancevalue, in conjunction with the device and bias circuit inductance, sets the electrical time constant.The TES is readout/multiplexed out using one or more superconducting quantum interferencedevice (SQUID) amplifiers. A range of SQUID multiplexing options currently exist for TESreadout ( e.g. , time-division multiplexing (TDM), frequency-division multiplexing (FDM), mi-crowave SQUID multiplexing ( µ mux), and code-division multiplexing (CDM) ). Many TDMschemes are deployed in the field for reading out kilopixel-scale arrays of TES bolometers. Pro-viding more bandwidth per pixel, microwave multiplexing shows the most promise for reading outlarge arrays of TES calorimeters; the Lynx mission is baselining arrays of ∼ TES calorimetersthat are read out with µ mux.For simplicity, the thermal conductance and heat capacity are commonly assumed to be in-dependent of temperature over the range of operation, however, extension of this limiting case isnecessary to model the full dynamic range and temporal response of the device in practical set-tings. TESs are amendable to production entirely by available micro-fabrication techniques andare suitable for realization as large format detector arrays ( e.g. , see for examples et cetera ).Both TES bolometers and TES calorimeters have achieved measured performance consistentwith a linear near-equilibrium thermodynamics model of the system, with no hidden variables orunaccounted-for noise sources. This TES model is a powerful tool used to design detectors thatmeet the combined requirements for an application. It gives confidence in the ability to predictperformance, help identify sources of unwanted characteristics, and make necessary changes thataccelerate development programs. 5
TES calorimeters
TES calorimeters are designed to measure discrete depositions of energy. In this case, when anincident energetic particle of energy E is absorbed by the TES, the temperature of the detectorrises by ∆ T = E/C . This sudden temperature increase yields a corresponding increase of thesuperconductor’s resistance, shunting current through the shunt resistor and reducing the currentflowing through the SQUID input coil. The device then relaxes to its steady state temperature withan exponential decay time constant τ = C/G e , where G e accounts for electrothermal feedbackgain. This process yields a pulse in the time domain (Fig. 5). In the X-ray band, where TEScalorimeters are most commonly deployed, typical time constants are ∼ . ms. TES calorimetersdesigned for the near- to mid-infrared have time constants faster than ∼ µ s. TES calorimetersare most commonly operated linearly where the pulse height is proportional to the deposited en-ergy. In this way each TES pixel is a spectrometer, and an array of TES calorimeters is an imagingspectrometer on a chip ( i.e., an integral field spectrograph (IFS) that does not need dispersive op-tics). The energy scale of linear device operation is set by the heat capacity; the saturation energy– the maximum deposited energy in the linear regime – is defined as E sat = CT /α , where α is the logarithmic temperature sensitivity of the device. With non-linear data analysis techniques,TES calorimeters can also be effectively operated non-linearly with little negative impact on deviceperformance.
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TES calorimeter development for astronomy applications has concentrated in development ofX-ray calorimeter arrays. The X-ray work, along with complementary development of bolometersfor microwave applications, has led to significant advancement in TES understanding and per-formance. In this band TESs have achieved the highest resolving power of any non-dispersive6pectrometer, measuring the energy of photons to better than a part in 3400. Some notable ad-vancements in both TES understanding and performance include: 1) identification of sources ofexcess noise in TESs;
2) identification of the resistive mechanisms in TES sensors and waysto control the shape of the resistive transition surface;
3) improved understanding of energylosses from athermal phonons and quasiparticle excitations;
4) improved fabrication methodsand understanding of the thermal conductance of MEMs membranes and leg structures;
5) im-proved coupling to radiation at longer wavelengths using tuned optical stacks;
13, 35 and 6) improvedsignal processing including methods for nonlinear signals.
14, 15, 36, 37
Fundamental thermodynamic noise limits a TES calorimeter’s achievable energy resolution ∆ E FWHM . For a TES, the known thermodynamic fluctuations are associated with electrical re-sistance (Johnson noise in the TES resistance R and in the bias shunt resistor R sh ) and thermalimpedance (phonon noise across the thermal link G that couples the sensor to the bath). The ex-pression for ∆ E FWHM simplifies to a compact form under the assumptions of negligible amplifiernoise, negligible shunt resistor Johnson noise, and large loop gain: ∆ E FWHM = 2 (cid:112) (cid:115) k B T C (cid:112) n/ (cid:112) − ( T b /T ) n (cid:114) βα . (1)Here T and T b are the temperature of the TES and bath respectively, n is a thermal exponentdescribing the power through the thermal link G , C is the total heat capacity, and α and β areboth dimensionless parameters characterizing the sensitivity of the resistive transition to changesin temperature and current respectively. More precisely, α and β are defined as the logarithmicderivative of the resistance with respect to temperature and current, respectively: α = ( T /R ) × ( ∂R/∂T ) and β = ( J/R ) × ( ∂R/∂J ) . The spectral resolving power R is the ratio of the photon7nergy to the energy resolution: R = E/ ∆ E FWHM (for R of a few or more, R = E/ ∆ E FWHM (cid:39) λ/ ∆ λ FWHM ). A detector with smaller ∆ E FWHM is a higher resolution detector.Work by Bandler et al. , 2008 and Iyomoto et al. , 2008 are early examples that demonstratea TES calorimeter’s measured noise spectrum and energy resolution agree with those calculatedfrom the model thermodynamic system (Eq. 1). Assuming near-equilibrium thermodynamicsand modeling the calorimeter system as one heat capacity C connected through a single thermalconductance G to a heat bath at temperature T b , the calculated energy resolution departs from themeasured value by less than 30%. If rather than the TES resistance being ohmic, it is assumed to benear-equilibrium with a linear current dependence, then the first order non-equilibrium correctionterm to the Johnson noise is shown to account for all the measured excess noise at the operatingpoint. Measurements providing inputs to Eq. 1 include impedance measurements and current-voltage (I-V) curves at different bath temperatures and bias currents, and measurements of thenatural decay time τ of a pulse with no electrothermal feedback ( τ = C/G ). Together with Eq.1, these measurements predicted an energy resolution ∆ E FWHM = 1 . eV. The measured energyresolution fitting to the Mn-k α complex at 5.9 keV agrees, giving ∆ E FWHM = 1 . ± . eV.TES calorimeters have been designed to give high detection efficiency and constant energyresolution over a large spectral range. In the visible, TES calorimeters exhibited uniform energyresolution from 0.3 eV to > eV. TES calorimeters developed for quantum information sci-ence applications have achieved detection efficiencies of 99%, the highest of any detector in theoptical.
13, 35 ig 2 Illustration of the advantage to photon counting. The top frame shows how power is measured bolometricallywith an ideal instrument. Incident optical power is manifested as a shift in the “baseline” TES current in the timedomain. In the frequency domain, one would observe a higher white noise level due to incident photon noise. Thecenter frame illustrates how system drift can be confused with an optical signal; the long time constants of bolometersplace stringent requirements on system stability. The bottom frame shows how drift is mitigated if individual photonevents are resolved (as opposed to just measuring a flux of photons.) In this case system drift has no effect on themeasurement.
In this section, we describe how a TES operated as a calorimeter, instead of a bolometer, can beused for the MISC-T instrument, reducing the requirements on instrument stability while maxi-mizing effective throughput and overall observing time.A bolometer is unable to distinguish various external factors from the optical signal and there-fore puts more stringent requirements on control of instrumental systematics, stability of the sys-tem, and the length of time over which such stability must be maintained. Compared to a calorime-ter, a bolometer is more negatively impacted by system drift, stray power coupling into the detector,changes in ambient operating conditions including the local magnetic field environment, low fre-quency ( /f ) noise, and array non-uniformities. These effects manifest as a shift or drift in thebaseline signal, the measured current flowing in the TES. Because the drift can be confused with9 ig 3 Example of our minimal criterion for noiseless single photon counting. Left: TES model simulated TES currenttime series records of a photon pulse with spectral resolving power R = 5 (red) and a noise record with no photon(black). Right: distribution of filtered energy of individual records with 1 or 0 photons. Even with sensitivity of only R = 5 it is extremely unlikely to falsely report a 0-photon record (noise record) as an in-band photon. an optical signal (Fig. 2), the burden to account for any drifts rests on the instrument as a whole.Especially as bolometers become more sensitive and therefore slower, commonly employed tech-niques to push the optical signal into a higher frequency band ( e.g. , by chopping) are more difficultto execute. By contrast, as long as the intrinsic resolution of the detector is high enough, this shiftor drift in the baseline signal has negligible impact on a calorimeter’s ability to detect a photonevent. Moreover, photon-counting observations are more efficient. No external modulation is re-quired and no observation time is spent observing a calibrator. From a sensitivity perspective, ithas been shown in several previous studies that TES calorimeters can be realized with sufficientintrinsic energy sensitivity to count THz photons.
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A TES dark count analog occurs when no photon is incident upon the detector and an anoma-lous noise trace triggers an event acquisition and application of the optimal filter to this noiserecord results in the energy of an in-band photon. One finds that if you have a TES in its steadystate operating bias collecting noise records at 50 MHz continuously in the dark with an energyresolving power of 4 for the lowest photon energy of the band of interest, the dark count eventrate is of order one per age of the universe. We use this R > criterion for a “noiseless” detector10effectively no detector false positives). In Fig. 3 we show an example for conditions that are justbarely satisfying our criterion for noiseless photon counting with R = 5 . In red and black are TEScurrent time series plotted for a 1 photon event with R = 5 (red) and a corresponding record forthe TES at its operating point with a no photon record (black). To the right is the distribution ofmany such records after application of an optimal filter to extract the energy of each record. We seeeven for only R = 5 the population of 0 and 1 photon records are well separated. The likelihoodof mistaking a noise record for a photon record is extremely low. This can also be seen as the 0photon distribution at an energy of 1 is very small. As R increases beyond R = 5 the dark countrate remains negligible. Since the energy resolution ∆ E FWHM is constant, as the photon energyincreases the height of the pulse signal proportionally increases, leading to a proportionally-higher R measurement.The energy sensitivity in the X-ray is used to determine the energy of an incident photon withhigh accuracy. In this application, the high energy sensitivity of a TES can be used to push noiselesssingle photon detection down to lower photon energies and into the MIR for Origins . The combi-nation of high speed, noiseless single photon detection, and sensitivity are used to unambiguouslydistinguish in-band photon events from noise and identify and remove out-of-band events causedby cosmic rays or background. In grating-based dispersive spectrometers, the energy sensitivityalso enables rejection of higher-order photons that correspond to a different spectral channel, acapability unique to energy-resolving single photon detectors and not found in other single pho-ton technologies ( e.g., electron multiplying charge coupled devices (EMCCDs), superconductingnanowire single photon detectors (SNSPDs), avalanche photo diodes (APDs), quantum dot de-tectors (QDs), et cetera .)For the MISC-T instrument the TES calorimeter design for the lowest photon energy of the11 ig 4 MISC-T TES spectral resolving power R at λ = 20 µ m versus log α operating at 70 mK. The TES modelpredicts this device designed for high absorption efficiency at λ = 20 µ m gives sufficient energy sensitivity fornoiseless photon counting with margin. Even very modest values of α give sufficient sensitivity to count photons withample tolerance for system instabilities, which for realistic values only lead to minor degradation of energy resolution(see Chiao et al. ) band ( λ = 20 µ m) is most challenging. It requires the lowest ∆ E FWHM for noiseless photoncounting, while also needing the largest absorbing area for an absorber-coupled strategy (see Sec-tion 4.3; λ × λ is sufficient
46, 47 ). We therefore focus our discussion on the λ = 20 µ m detector,which uses a × µ m resistive Bi absorber coupled to a TES sensor. We find applying theTES model to our MISC-T TES design achieves the required photon count rates, sensitivity, andabsorption efficiency with known materials parameters. In Fig. 4 we plot resolving power R for λ = 20 µ m versus log α over a range of typical α values. We find that internal thermal fluctuationnoise (ITFN) in the absorber is not negligible and departs from the simple analytic single bodyexpression in Eq. 1. The ITFN limits sensitivity and shows that increasing α much above 20 pro-vides limited improvement in sensitivity. The key take away is that even accounting for ITFN, thesensitivity is greater than the photon counting criterion (over 6 times larger). This gives signifi-cant sensitivity margin even at the lowest photon energy of the MISC-T band. Noiseless photoncounting becomes easier (even greater margin) for the rest of the MISC-T band.The thermal recovery time of TES calorimeters designed for the optical are typically of order12 µ s, accommodating count rates of ∼
35, 49–51
During the thermalrecovery time, the TES is still able to receive and detect a photon, and therefore has no dead time,a feature unique among single photon detectors. If an additional absorption event occurs duringthe detector recovery signal pile-up occurs. In such a case the ability to extract the energy ofeach event is degraded below the maximum resolving power of the detector. For spectroscopyapplications with no dispersive optics, such records are tagged as lower resolution events anddifferent processing is employed to extract the event energies. For MISC-T where the TESs aredistributed over a spectral channel, pulse pile-up can be tolerable and the single photon eventsare identified by the fast rise of the leading edge provided the detector stays below the saturationenergy. Even for λ = 20 µ m we see in Fig. 4 the sensitivity is over 6 times larger than requiredto photon count and an increase in rate will not impact the ability to count photons. The energysensitivity margin increases further as the wavelength decreases. As the rate increases furtherthe calorimeter operation begins to become more bolometer-like and the advantages of photoncounting start to diminish.Increasing the number of spectral channels increases the spectral information of the measure-ment and decreases the photon rate per channel. Increasing the event rate per spectral channel muchabove 1 million counts per second is achievable by : (1) decreasing the pulse recovery time; (2)increase the number of TES pixels per spectral channel (oversampling the point spread function);and (3) implementing photon counting algorithm for high count rates. The faster pulse recoverytime is achievable by operating the TES at higher temperatures (see Fig. 5 right) or by engineeringa TES’s thermal coupling. Calkins et al. have demonstrated engineering of the thermal couplingof the TES to achieve a thermal recovery time of less than half a microsecond. In Fig. 5 we showthe MISC-T TES response to a λ = 20 µ m (60 meV) photon. In this TES model simulation 6013 ig 5 Simulated time domain signals of the MISC-T TES microcalorimeter response to λ = µ m photons (60 meV).The bath temperature in this simulation is 50 mK, α = 10 , and the absorber consists of a 10 nm-thick Bi film.Left: Series of pulses absorbed at nine different points in a × µ m absorber at 70 mK. The 9 different pulsescorresponds to 60 meV of energy deposited at 9 different positions in the absorber (increasing distance from TESwith increasing hue). The different colors show that there is some positional dependence to the pulse shape due tofinite thermal conductance of the absorber structure. Right: A similar simulation, but at a 100 mK. This speeds up thedetector response at the cost of energy resolution. meV of energy is deposited at 9 different locations in a high efficiency absorber. The simulationon the left is at 70 mK and on the right 100 mK. By raising the temperature we increase the speedof the detector. The faster pulses at higher temperatures show positional dependence of absorptionwhich impacts the energy resolution. But even here the sensitivity is sufficient for noiseless photoncounting with margin. The maximum count rate expected for MISC-T is ∼ . × photonsper second incident on the detector, thus we do not expect as-demonstrated device speeds to belimiting. TES bolometers operate similarly to TES calorimeters, but as quasi-steady state devices, wherepower balance is achieved between sources of power dissipation (Joule heating of the sensor andincident radiation) and heat flow out the thermal link. Instead of being sensitive to single photonevents, bolometers are sensitive to a quasi-steady flux of photons absorbed by the detector and14anifested as deposited power. Bolometric operation of the TES has many of the traditional ad-vantages of a transducer with large negative feedback including improved linearity, device speed,and immunity to parameter non-uniformity. When operated under negative electrothermal feed-back, TES bolometers are highly linear devices. Thermal conductance to the bath sets the devicesaturation power and upper range of linear operation as a detector.TES bolometers are the most sensitive detectors used to measure millimeter and sub-millimeterradiation. For applications requiring background-limited sensitivity, they are also the most widelydeployed, with arrays of thousands of pixels operating from ground ( e.g.,
BICEP/Keck ), air-craft ( e.g., SOFIA/HAWC+ ) and balloon ( e.g., SPIDER and EBEX ) platforms. Due to boththeir high sensitivity and the comparative ease of reading out large arrays, TES bolometers havelargely replaced bolometers that use high-impedance thermistors as thermometers. At the present,however, no bolometers have demonstrated the ultimate sensitivity required for Origins . In thefollowing, we discuss what dictates a bolometer’s sensitivity, the state-of-the art achieved, andsome of the strategies being employed and natural tradeoffs that occur when designing a bolome-ter to meet
Origins requirements. These include thermal isolation techniques, radiation couplingtechniques, and strategies to mitigate the impact of cosmic ray events.
A bolometer’s sensitivity is parametrized by its NEP. In the dark, a bolometer’s NEP is ideallylimited by phonon noise ( N p ), the fundamental thermodynamic noise that arises due to the randomexchange of energy across the thermal link coupling the bolometer pixel to the thermal bath (seeFig. 1). In this limit, NEP (cid:39) N p . Under optical bias, a background-limited detector is limited byphoton noise, with N p as the leading sub-dominant noise term. Thus N p is the figure of merit for15 bolometer’s sensitivity (see Mather, 1982 for a complete treatment of bolometer noise). Thepower spectral density of the phonon noise |(cid:104) N p (cid:105)| , is given by |(cid:104) N p (cid:105)| = γ k B T G, (2)where k B is Boltzmann’s constant, T is the temperature of the bolometer pixel, G is the thermalconductance between the pixel and the thermal bath, and γ is a constant that accounts for potentialnon-equilibrium effects. In the equilibrium case, where the pixel temperature T is equal to thetemperature of the thermal bath T b , γ = 1 . In the extreme non-equilibrium case, where T (cid:29) T b , γ = 1 / . Bolometers are usually designed to operate somewhere between these extrema; e.g.,bolometers designed for cosmic microwave background studies typically operate with γ (cid:39) . .Thus to make a more sensitive detector, one must reduce the operating temperature and/or reducethe thermal conductance. The former must meet practical constraints of available cryostats (spacequalified cryostats can achieve a minimum operating temperature of ∼ mK), so once a minimumoperating temperature is reached, reductions in NEP are accomplished by reducing G .NEP can be expressed in several ways that represent different measurements and device char-acteristics. It is important to note the distinctions between them. First is the thermal fluctuationnoise NEP (NEP TFN ). NEP
TFN is calculated from Eq. 4.1 using a value for G extracted fromI-V curve measurements. It represents a theoretical limit where there is no significant contributionto the noise from other known or unknown noise sources (e.g., Johnson noise, amplifier noise,or excess noise). Next is the electrical NEP (NEP el ). NEP el is calculated from the measuredcurrent noise spectral density i n and frequency-dependent electrical responsivity S el ( ω ) , where S el ( ω ) = S el / (1 + iωτ ) . Here S el is the DC electrical responsivity to dissipated Joule power,16 ig 6 Left: Illustration of the relationship between a bolometer’s operating temperature, time constant, and NEP when G is dominated by electron-phonon conduction ( n = 5 , solid), Kapitza conduction ( n = 4 , dashed), and phononconduction ( n = 3 , dotted). The blue lines correspond to the axis on the left, and the red lines to the axis on the right.This plot assumes each bolometer has the same NEP and time constant at 300 mK. Real bolometers typically haveexponents that take a value between 3 and 5, indicating multiple conduction mechanisms. Right: The impact on timeconstant if the most sensitive bolometer demonstrated to date were modified to meet Origins requirements by simplyreducing G . To make the device the required 10x more sensitive requires a 100x reduction in G , which in turn makesthe device 100x slower. extracted from the I-V curve, and τ is the time constant of the device. Finally there is the opticalNEP (NEP opt ). In contrast to NEP TFN and NEP el , NEP opt is necessarily derived from optical mea-surements and is calculated from the measured current noise spectral density i n and the device’sresponsivity to incident optical power S opt . In a background-limited detector NEP opt would bedominated by photon noise. Both NEP el and NEP opt account for all noise sources, but only NEP opt accounts for potential inefficiencies and loss mechanisms associated with photon absorption.Reductions in operating temperature T and thermal conductance G to achieve higher sensi-tivity both impact the bandwidth of a bolometer. Recall that the response time of a bolometer isproportional to C/G . At low temperatures, both C and G scale with temperature; C ∝ T and G ∝ T n . Bolometers are engineered to achieve a specific n value depending on the physics ofthe heat transfer. Typical values include n = 3 , , or , corresponding to ballistic phonon conduc-tion, Kapitza conduction, or electron-phonon conduction, respectively. In a realized bolometer, the17easured n value may take on intermediate values if there are multiple seres/parallel conductionpaths through differing means or if there are few propagating modes.
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Figure 6 illustrates thenatural tradeoffs that occur between operating temperature, time constant, and NEP. In short, amore sensitive bolometer is also slower, thus introducing more stringent requirements on overallinstrument stability.Engineering G to achieve a certain value also impacts the saturation power of a bolometer P sat , defined as the power required to heat the bolometer to a temperature T sat above which theresponsivity of the device falls below some critical level. The relationship between G and P sat can be understood from the power balance requirement of steady-state operation, where the powerflowing out the thermal link equals the sum of absorbed optical power and Joule power dissipatedby the TES resistance. Note that stray power can manifest itself as either optical power or Joulepower. For G = AT n , where A is a constant and n is the exponent of the thermal conductance, P sat is given by: P sat = (cid:90) T sat T b G ( T ) dT = An + 1 (cid:0) T n +1sat − T n +1 b (cid:1) . (3)Thus for a given bath temperature and sensor transition temperature ( T c (cid:39) T sat ), the saturationpower of the device scales with the thermal conductance. As G is reduced to achieve highersensitivity, the stray power requirements of the experimental platform – electrical and optical –become proportionally more stringent. In particular, implementation of techniques to mitigatestray power, like filtered connectors at the cryostat vacuum feedthroughs, thermal blocking andpowder filters in close proximity to the detectors, and single-point grounding, are necessary toachieve a sufficiently quiet experimental space.In the dark, the most sensitive bolometer demonstrated to date was developed by SRON and18 ig 7 Examples of bolometers that use the thermal isolation techniques most likely to meet
Origins sensitivity require-ments. Left: long-legged bolometer with micromachined SiN legs. Here the bolometer pixel is ∼ × µ m , whilethe required per-pixel area is ∼ × µ m . Devices like this have achieved excellent sensitivity, but suffer from alow fill fraction. Center left: Ballistic leg bolometer developed for the HIRMES instrument (image credit: A. Brown).Compared to the long-legged bolometer at left, the fill fraction offered by this type of bolometer is much higher. Themembrane is micromachined from Si and is ∼ × µ m in area. Center right: Phononic leg supporting a bolome-ter membrane (image credit: K. Denis and K. Rostem). A realized phononic filter bolometer resembles the ballisticleg bolometer at center left, except nano-machined legs like the one pictured replace simpler dielectric beams. Right:Hot electron solid-substrate bolometer that accompishes thermal isolation via weak e-p coupling in the W sensor film.This device is ∼ × µ m in area. This device was designed for dark measurements and is not coupled to an antenna,however antenna coupling would be appropriate for optical characterization (see Section 4.3). is described by Khosropanah et al. , Ridder et al. , and Suzuki et al. It uses a TiAu TES on aleg-isolated SiN membrane, achieving NEP
TFN of < × − W / √ Hz and NEP el of ∼ × − W / √ Hz , with a phonon noise-limited bandwidth of ∼ Hz and a saturation power below afew fW. Figure 6 illustrates the impact on this detector’s time constant if G were reduced by thenecessary factor of ∼ to meet Origins sensitivity requirements. Under optical bias, Karasik etal. measured NEP opt of × − W / √ Hz using a Ti hot electron bolometer, the lowest opticalNEP demonstrated to date in a TES bolometer. There are several thermal isolation techniques that show promise toward enabling
Origins -typesensitivities in bolometers. In no particular order, these fall into four basic categories (Fig. 7):isolation via long (diffusive) legs, short (ballistic) legs, phononic filter/bandgap legs, and weak19lectron-phonon (e-p) coupling in the sensor material (a “hot electron” bolometer).
Long (diffusive) leg bolometers generate thermal isolation via diffuse phonon transport acrossthe legs that support a membrane-isolated bolometer. The legs and the membrane are typically mi-cromachined from Si or SiN. Conduction via diffuse phonon transport follows Fourier’s law ofthermal conduction: G = κA/(cid:96) , where κ is the material’s bulk thermal conductivity, A is the crosssectional area of the leg, and (cid:96) is the length of the leg. As has been pointed out in the literature,
64, 65 the Fourier limit is an oversimplification of the physics. κ is not a bulk property, but rather a prop-erty that depends on the details of the leg’s fabrication process, which can lead to non-uniformconductance across an array or between fabrication runs. In addition, the G ∝ (cid:96) − behavior onlyholds for legs longer than a certain threshold; (cid:96) > µ m has been reported. Bolometers thatuse long-leg isolation are exemplified in practice by the SPICA/SAFARI bolometers developedby SRON
58, 61, 62 (see Section 4.1). A representative optical micrograph of a long-leg bolometer isshown in Fig. 7. Despite the excellent achieved sensitivity of long-legged bolometers, an obviouslimitation is the low fill fraction achieved. By area, the SPICA/SARARI bolometers have a fillfraction of ∼ . SPICA/SAFARI has three bands with between 600 and 2000 pixels per band,yielding far fewer pixels than the ∼ , required for OSS. With G ∝ A/(cid:96) , reducing the con-ductance by 100x to meet OSS requirements would necessarily reduce the fill fraction. For FIP,however, these bolometers already meet the sensitivity requirement and the arrays size is similar toSPICA/SAFARI. An added complication to longer legs is that as the leg length increases, the heatcapacity of the legs can become non-negligible, leading to measurable ITFN degrading device per-formance. Long-legged bolometers lend themselves most naturally to resistive absorber coupling.Antenna coupling would likely have to incorporate the legs themselves, and further investigation isrequired to determine whether the electromagnetic requirements of an antenna could be consistent20ith the thermal requirements of the legs.
Short (ballistic) leg bolometers achieve thermal isolation by minimizing the solid angle be-tween the radiating sensor and legs that support a membrane. The ballistic limit occurs when thelength of the leg is shorter than the phonon mean free path (cid:96) mfp in the material, so it is assumed thatphonons that pass through the leg aperture escape to the bath. For very small cross sectional areas,ballistic legs have been shown to approach the so-called “quantum limit” of thermal conductance,where only four phonon modes can propagate. The bolometers developed for the HIRMES in-strument used this technique to achieve kilopixel arrays with NEP el < . × − W / √ Hz , in good agreement with the targeted value of NEP < × − W / √ Hz for background-limitedoperation. Compared to long-legged bolometers, ballistic leg bolometers can achieve much higherarray fill fractions, and the achieved thermal conductance of realized legs is both calculable fromreal bulk material properties and is much more tolerant of fabrication non-idealities and non-uniformities.
66, 68, 69
Phononic filter bolometers use nano-machined legs to generate coherent phonon scatteringthat suppresses propagated phonon modes to below the quantum limit.
34, 68–70
Like ballistic legbolometers, phononic filter bolometers promise short legs that enable high array filling fractions,but with the additional advantage of reduced thermal conductivity relative to ballistic leg designs.Theoretical work by Rostem et al. indicates that a factor of 5 improvement over the quantumlimit is possible with phononic filter legs that are just 10 µ m long and are machinable using knowntechniques. Devices presented by Williams et al. achieved a factor of ∼ reduction in thermalconductance below the quantum limit using phononic filter legs. Fabrication of phononic filtersis challenging as sub- µ m lithography techniques are required, but recent work by Denis et al. demonstrates reliable and robust fabrication of phononic leg-isolated TESs.21 ot electron bolometers (HEBs) use the inherent decoupling of electrons and phonons incertain metals at low temperatures for thermal isolation. The conductance between electrons andphonons at low temperature is given by G ep = Σ V T n , (4)where Σ is the electron-phonon coupling constant (material property), V is the volume of thesensor, T is temperature, and n is the thermal exponent (typically n = 5 for e-p coupling). Atable of measured coupling constants for superconducting metals that would act as the hot electronbolometer is provided by Karasik et al. Among superconductors, W has the weakest known e-pcoupling and therefore the greatest potential as a hot electron bolometer sensor material. Karasik et al.
63, 72, 73 have achieved NEP el below × − W / √ Hz and NEP opt of × − W / √ Hz using Ti as the hot electron sensor; we have performed simulations that indicate W-based HEBscan exceed OSS requirements at 70 mK. A significant advantage of HEBs over the other bolometertypes described above is that HEBs do not require any membranes, thus fabrication is simplified,large fill fractions can be realized, and the final devices are mechanically robust. The fabricationproblems that can occur in HEBs ( e.g. , inconsistent transition temperatures or interface problems)are shared among all TES bolometer types and ultimately are not limiting. Note that while there arecomparatively few examples of realized hot electron bolometers in the literature, calorimeters arefrequently designed to operate in the electron-phonon decoupled limit using materials that wouldalso yield exceptional sensitivity in a bolometer ( e.g. , see Calkins et al. , 2011 ).22 .3 Radiation coupling techniques Antenna-coupling can be used to define the sensor’s angular acceptance and coupling to the elec-tromagnetic radiation field. It converts the incident fields (photons) into electronic excitationsin the absorber media which are dissipated and subsequently detected as heat. To achieve highantenna coupling efficiency requires transforming the modal symmetry and impedance scales en-countered by the wave in free space to that present in the circuit elements employed to absorbthe radiation. A wide variety of techniques exist to carry out these functions; however, due to theneed to realize large arrays of sensors – in particular – methods amendable to implementation asplanar lithographic structures are primarily of interest. Consideration of the overlap in the angu-lar response of the individual antenna elements in a multi-beam array can provide insights intothe inter-pixel isolation and maximum achievable power coupling. Similarly, care is warrantedin providing isolation between the detector bias/readout and the optical signal paths. Rejectionof out-of-band radiation sources, which can potentially load a bolometric sensor and degrade theachievable response, also needs to be realized. These functions are typically achieved throughthe use of choke circuits on the sensor wafer and cooled thermal blocking filters at appropriatelocations in the instrument system.A qualitative survey of commonly encountered planar antennas such as resonant and traveling-wave line- and slot-structures is provided in Fig. 8. The angular response (or “antenna pattern”)as well as the impedance scales of complementary line- and slot-like aerial structures are linkedby Babinet’s principle in its vector form. Extension of these symmetry concepts to antennageometries which are only a function of angle enables the realization of frequency independentantenna structures. Examples of frequency-independent traveling-wave structures include planar23ogarithmic spiral and log-periodic antennas, which have continuous and discrete scaling symme-tries respectively. In practice, such antennas exhibit deviations from frequency independence fromtruncation at the inner and outer length scales ( i.e., set by the feed network and and the maximumextent of the aerials). While this tends to simplify impedance matching to the detector’s absorbercircuit, these structures tend to have a low filling-fraction when used in arrays over a wide spectralrange. The operation of planar antenna arrays in an immersion lens configuration has enabledgreater control over electromagnetic substrate losses and has allowed a natural separation of theradiation and readout functions of the focal plane.While antenna coupled arrays have found utility in instrument applications where high spatial-sampling presents a driving consideration, an alternative approach to achieve full sampling ispresented by “absorber coupled” sensor arrays. In this limit, the “antenna response” of the sen-sor is essentially uniform over the range of interest and the telescope optics in concert with a coldLyot stop is used to specify and limit radiation presented to the focal plane. In this configura-tion a homogeneous thin film for each pixel’s absorber has resonant (quarterwave) or frequencyindependent back-termination
83, 84 depending on the desired spectral range and coupling. Incorpo-ration of frequency selective surfaces (FSS) in the absorber structure
85, 86 provides an alternativepath to achieving the desired impedance scales for high in-band-coupling and improved out ofband rejection in bolometric sensor settings.Prior discussions of antenna coupling for bolometer implementations can be found in the lit-erature.
72, 87, 88
It is important to note that for a bolometric sensor, the detailed thermal mode ofoperation can place practical constraints on how the device is electromagnetically coupled to theradiation field. For example, in hot-electron bolometers, the antenna has direct electronic cou-pling and appropriate material selection enables operation of the device. Similarly, in phononic24 ig 8
Planar slot aerials and their relation to complementary wire aerials (Babinet’s principle). filter, ballistic leg, and diffusive leg bolometers, direct electrical contact would thermally shortthe detector and reactively electromagnetically coupling the antenna to a resistive absorber ele-ment on a thermally isolated element is typically employed. Either approach can be employedfor calorimeter applications, though the device we present in Section 3 uses a resistive absorberelement. In all cases, the choice of absorber strategy should reflect that array fill fraction is a param-eter which should be maximized in large array applications like Origins . For completeness, relatedantenna-coupled sensors at infrared wavelengths employing other physical detection mechanismsare also conveyed. These non-cryogenic implementations have included integrated dipole anten-nas, bowtie antennas,
91, 92 log-periodic/spiral antennas, microstrip patch antennas, microstripdipole antennas, and Yagi-Uda arrays. The interaction between energetic charged particles and the materials used in the detector systemlead to a stochastic background of energetic events observed by the sensors in the focal plane25ver the course of a space mission. Consider for example the
Planck Surveyor mission whichreported a rate of 80 cosmic ray related events per minute for the High Frequency Instrument arrayduring operations in its L2 orbit. Even with template fitting of its radiometric data, a sciencedata loss of ∼ − was experienced due to these “glitch”-like temporal events.
96, 97
Beyondimpacting observational efficiency, non-ideal detector responses associated with these energeticevents can lead to instrumental stability and calibration issues which reduce imaging fidelity ifunmitigated.
Origins will require higher sensitivity and by extension a lower focal plane operatingtemperature than used in previously deployed systems and thus increase the relative importanceof the sensor’s thermal bus implementation on minimizing the impact of cosmic rays. Extensionof the detector design techniques employed for calorimetry provide a viable path to addressthis instrumentation need. Mitigating cosmic rays is one particular advantage of a device knownas the ideal integrating bolometer (IIB), which combines leg isolation (diffusive, ballistic, orphononic) with a switchable thermal short. Upon an upset ( e.g., cosmic ray hit), the device can bereset quickly to mitigate the data losses that
Planck experienced.
The unprecedented sensitivity enabled by
Origins ’ large, cold, and space-based telescope placesstringent requirements on its instruments. In particular, the detector systems employed by eachinstrument must be designed to enable background-limited observations, contributing negligiblenoise to the overall instrumental budget. Detectors that enable background-limited observationsin each channel do not exist today. For MISC-T, the most difficult specification the detector sys-tem must meet is stability. While bolometers and semiconducting detectors have many sourcesof instability ( e.g. , environmental drifts for bolometers, dark current and read noise for semicon-26uctors), all these terms go to zero if a TES calorimeter is employed. The TES calorimeter wedesigned using well-established physical models and measured material parameters can overcomemany of the other challenges associated with the MISC-T detector system, such as high photonflux and the large required bandwidth, delivering all the advantages of photon-counting using anenergy-resolving detector. For OSS and FIP, the most challenging requirement the detector subsys-tems must meet is sensitivity, with radiation coupling and cosmic ray immunity also leading designdrivers. There are multiple promising paths toward achieving the required sensitivity using TESbolometers, with demonstrated sensitivities now approaching the OSS requirement and improving.For all the instruments, the TES detector options benefit from strong heritage in astrophysics in-strumentation and well-understood physics that enables the design and implementation of devicesthat operate at the thermodynamic limit across the
Origins band.
Disclosures
The authors declare no conflicts of interest.
Acknowledgments
Research supported by the National Aeronautics and Space Administration (NASA) under theGoddard Space Flight Center (GSFC) Internal Research and Development (IRAD) program. Theauthors are grateful for figures and technical feedback provided by Ari Brown, Kevin Denis, andKarwan Rostem of the GSFC. We are also grateful for the feedback provided by the referees, whichimproved the quality of this paper. 27 eferences et al. , “Origins Space Telescope Mission ConceptStudy Report,” arXiv e-prints , arXiv:1912.06213 (2019).2 C. M. Bradford, B. Cameron, B. Moore, et al. , “The Origins Survey Spectrometer (OSS):revealing the hearts of distant galaxies and forming planetary systems with far-IR spec-troscopy,”
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IEEE Transactions on AppliedSuperconductivity , 2664830 (2017). Peter C. Nagler is an experimental physicist in the Instrument Systems and Technology Division39t NASA’s Goddard Space Flight Center. His research focuses on low temperature detectors andcustom instrumentation for astrophysics applications.
John E. Sadleir is a condensed matter physicist in the Detector Systems Branch at NASA’s God-dard Space Flight Center. His research focuses on cryogenic detectors for particle physics, cos-mology, and astrophysics applications.
Edward J. Wollack is a research astrophysicist in the Observational Cosmology Laboratory atNASA’s Goddard Space Flight Center. His interests include cosmology, astronomical instrumen-tation, and electromagnetics.