Transition-edge sensor detectors for the Origins Space Telescope

The Origins Space Telescope is one of four flagship missions under study for the 2020 Astrophysics Decadal Survey. With a 5.9 m cold (4.5 K) telescope deployed from space, Origins promises unprecedented sensitivity in the near-, mid-, and far-infrared, from 2.8 - 588 $\mu$m. This mandates the use of ultra-sensitive and stable detectors in all of the Origins instruments. At the present, no known detectors can meet Origins' stability requirements in the near- to mid-infrared, or its sensitivity requirements in the far-infrared. In this work, we discuss the applicability of transition-edge sensors, as both calorimeters and bolometers, to meet these requirements, and lay out a path toward improving the present state-of-the-art.


Fig 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 thermal conductance 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 order to achieve voltage bias in the device. The SQUID amplifier is employed as an ammeter that measures changes in TES current due to absorption of energetic particles (calorimeter) or flux (bolometer).

Transition-edge sensors
Transition-edge sensors detectors measure incident power or energy using the temperature dependence of a superconductor's resistance. First realized by Andrews in 1941, 3 TESs are now the most sensitive detectors to radiation from the gamma-ray through the millimeter wave.
TESs can operate as calorimeters or bolometers. A calorimeter is designed to measure discrete depositions of energy, and a bolometer is designed to measure quasi-static power dissipated by a flux of photons. Both implementations share the same basic architecture. Figure 1 shows a cartoon of a TES and its basic readout circuit. The detector consists of a thermal mass of heat capacity C at a temperature T 0 , isolated from a thermal bath at temperature T b across a thermal link with conductance G. The thermometer -a superconductor biased in its transition -measures the temperature 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 superconducting transition via negative electrothermal feedback. 4 A shunt resistor whose resistance is much smaller than the TES's at its operating point is typically used to achieve voltage bias. The shunt resistance value, 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 interference device (SQUID) amplifiers. A range of SQUID multiplexing options currently exist for TES readout (e.g., time-division multiplexing (TDM), 5 frequency-division multiplexing (FDM), 5 microwave SQUID multiplexing (µmux), 6 and code-division multiplexing (CDM) 7 ). Many TDM schemes are deployed in the field for reading out kilopixel-scale arrays of TES bolometers. Providing more bandwidth per pixel, microwave multiplexing shows the most promise for reading out large arrays of TES calorimeters; the Lynx mission is baselining arrays of ∼ 10 5 TES calorimeters that are read out with µmux.
For simplicity, the thermal conductance and heat capacity are commonly assumed to be independent of temperature over the range of operation, however, extension of this limiting case is necessary to model the full dynamic range and temporal response of the device in practical settings. 8 TESs are amendable to production entirely by available micro-fabrication techniques and are suitable for realization as large format detector arrays (e.g., see for examples [9][10][11][12] et cetera).
Both TES bolometers and TES calorimeters have achieved measured performance consistent with a linear near-equilibrium thermodynamics model of the system, with no hidden variables or unaccounted-for noise sources. This TES model is a powerful tool used to design detectors that meet the combined requirements for an application. It gives confidence in the ability to predict performance, help identify sources of unwanted characteristics, and make necessary changes that accelerate development programs.

TES calorimeters
TES calorimeters are designed to measure discrete depositions of energy. In this case, when an incident energetic particle of energy E is absorbed by the TES, the temperature of the detector rises by ∆T = E/C. This sudden temperature increase yields a corresponding increase of the superconductor's resistance, shunting current through the shunt resistor and reducing the current flowing through the SQUID input coil. The device then relaxes to its steady state temperature with an exponential decay time constant τ = C/G e , where G e accounts for electrothermal feedback gain. 4 This process yields a pulse in the time domain (Fig. 5). In the X-ray band, where TES calorimeters are most commonly deployed, typical time constants are ∼ 0.5 ms. TES calorimeters designed for the near-to mid-infrared have time constants faster than ∼ 1 µs. 13 TES calorimeters are most commonly operated linearly where the pulse height is proportional to the deposited energy. In this way each TES pixel is a spectrometer, and an array of TES calorimeters is an imaging spectrometer on a chip (i.e., an integral field spectrograph (IFS) that does not need dispersive optics). 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 0 /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 device performance. 14,15 TES calorimeter development for astronomy applications has concentrated in development of X-ray calorimeter arrays. The X-ray work, along with complementary development of bolometers for microwave applications, has led to significant advancement in TES understanding and performance. In this band TESs have achieved the highest resolving power of any non-dispersive spectrometer, measuring the energy of photons to better than a part in 3400. 16 Some notable advancements in both TES understanding and performance include: 1) identification of sources of excess noise in TESs; [17][18][19][20][21][22] 2) identification of the resistive mechanisms in TES sensors and ways to control the shape of the resistive transition surface; [23][24][25][26][27][28][29] 3) improved understanding of energy losses from athermal phonons and quasiparticle excitations; 30 4) improved fabrication methods and understanding of the thermal conductance of MEMs membranes and leg structures; 31-34 5) improved coupling to radiation at longer wavelengths using tuned optical stacks; 13, 35 and 6) improved signal 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 resistance (Johnson noise in the TES resistance R 0 and in the bias shunt resistor R sh ) and thermal impedance (phonon noise across the thermal link G that couples the sensor to the bath). The expression for ∆E FWHM simplifies to a compact form 18 under the assumptions of negligible amplifier noise, negligible shunt resistor Johnson noise, and large loop gain: Here T 0 and T b are the temperature of the TES and bath respectively, n is a thermal exponent describing the power through the thermal link G, C is the total heat capacity, and α and β are both dimensionless parameters characterizing the sensitivity of the resistive transition to changes in temperature and current respectively. More precisely, α and β are defined as the logarithmic derivative 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 photon  In the frequency domain, one would observe a higher white noise level due to incident photon noise. The center frame illustrates how system drift can be confused with an optical signal; the long time constants of bolometers place stringent requirements on system stability. The bottom frame shows how drift is mitigated if individual photon events are resolved (as opposed to just measuring a flux of photons.) In this case system drift has no effect on the measurement.

Photon-counting TES for the mid-infrared
In this section, we describe how a TES operated as a calorimeter, instead of a bolometer, can be used for the MISC-T instrument, reducing the requirements on instrument stability while maximizing effective throughput and overall observing time.
A bolometer is unable to distinguish various external factors from the optical signal and therefore puts more stringent requirements on control of instrumental systematics, stability of the system, and the length of time over which such stability must be maintained. Compared to a calorimeter, 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 frequency (1/f ) noise, and array non-uniformities. These effects manifest as a shift or drift in the baseline signal, the measured current flowing in the TES. Because the drift can be confused with 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 techniques to push the optical signal into a higher frequency band (e.g., by chopping) are more difficult to execute. By contrast, as long as the intrinsic resolution of the detector is high enough, this shift or drift in the baseline signal has negligible impact on a calorimeter's ability to detect a photon event. Moreover, photon-counting observations are more efficient. No external modulation is required and no observation time is spent observing a calibrator. From a sensitivity perspective, it has been shown in several previous studies that TES calorimeters can be realized with sufficient intrinsic energy sensitivity to count THz photons. 40,41 A TES dark count analog occurs when no photon is incident upon the detector and an anomalous noise trace triggers an event acquisition and application of the optimal filter to this noise record results in the energy of an in-band photon. One finds that if you have a TES in its steady state operating bias collecting noise records at 50 MHz continuously in the dark with an energy resolving power of 4 for the lowest photon energy of the band of interest, the dark count event rate is of order one per age of the universe. We use this R > 4 criterion for a "noiseless" detector (effectively no detector false positives). In Fig. 3 we show an example for conditions that are just barely satisfying our criterion for noiseless photon counting with R = 5. In red and black are TES current time series plotted for a 1 photon event with R = 5 (red) and a corresponding record for the TES at its operating point with a no photon record (black). To the right is the distribution of many such records after application of an optimal filter to extract the energy of each record. We see even for only R = 5 the population of 0 and 1 photon records are well separated. The likelihood of mistaking a noise record for a photon record is extremely low. This can also be seen as the 0 photon distribution at an energy of 1 is very small. As R increases beyond R = 5 the dark count rate remains negligible. Since the energy resolution ∆E FWHM is constant, as the photon energy increases 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 with high accuracy. In this application, the high energy sensitivity of a TES can be used to push noiseless single photon detection down to lower photon energies and into the MIR for Origins. The combination of high speed, noiseless single photon detection, and sensitivity are used to unambiguously distinguish in-band photon events from noise and identify and remove out-of-band events caused by cosmic rays or background. In grating-based dispersive spectrometers, the energy sensitivity also enables rejection of higher-order photons that correspond to a different spectral channel, a capability unique to energy-resolving single photon detectors and not found in other single photon technologies (e.g., electron multiplying charge coupled devices (EMCCDs), 42 superconducting nanowire single photon detectors (SNSPDs), 43 avalanche photo diodes (APDs), 44  band (λ = 20 µm) is most challenging. It requires the lowest ∆E FWHM for noiseless photon counting, while also needing the largest absorbing area for an absorber-coupled strategy (see Sec- 46,47 ). We therefore focus our discussion on the λ = 20 µm detector, which uses a 40 × 40 µm 2 resistive Bi absorber coupled to a TES sensor. We find applying the TES model to our MISC-T TES design achieves the required photon count rates, sensitivity, and absorption efficiency with known materials parameters. In Fig. 4 we plot resolving power R for λ = 20 µm versus log α over a range of typical α values. We find that internal thermal fluctuation noise (ITFN) in the absorber is not negligible and departs from the simple analytic single body expression in Eq. 1. The ITFN limits sensitivity and shows that increasing α much above 20 provides limited improvement in sensitivity. The key take away is that even accounting for ITFN, the sensitivity is greater than the photon counting criterion (over 6 times larger). This gives significant sensitivity margin even at the lowest photon energy of the MISC-T band. Noiseless photon counting 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 order 1 µs, accommodating count rates of ∼ 1 million counts per second. 35,[49][50][51] During the thermal recovery time, the TES is still able to receive and detect a photon, and therefore has no dead time,

Bolometer sensitivity
A bolometer's sensitivity is parametrized by its NEP. In the dark, a bolometer's NEP is ideally limited by phonon noise (N p ), the fundamental thermodynamic noise that arises due to the random exchange of energy across the thermal link coupling the bolometer pixel to the thermal bath (see Fig. 1). In this limit, NEP N p . Under optical bias, a background-limited detector is limited by photon noise, with N p as the leading sub-dominant noise term. Thus N p is the figure of merit for a bolometer's sensitivity (see Mather, 1982 56 for a complete treatment of bolometer noise). The power spectral density of the phonon noise | N p | 2 , is given by where k B is Boltzmann's constant, T 0 is the temperature of the bolometer pixel, G is the thermal conductance between the pixel and the thermal bath, and γ is a constant that accounts for potential non-equilibrium effects. In the equilibrium case, where the pixel temperature T 0 is equal to the temperature of the thermal bath T b , γ = 1. In the extreme non-equilibrium case, where T 0 T b , γ = 1/2. Bolometers are usually designed to operate somewhere between these extrema; e.g., bolometers designed for cosmic microwave background studies typically operate with γ 0.62.
Thus to make a more sensitive detector, one must reduce the operating temperature and/or reduce the thermal conductance. The former must meet practical constraints of available cryostats (space qualified cryostats can achieve a minimum operating temperature of ∼ 50 mK), so once a minimum operating temperature is reached, reductions in NEP are accomplished by reducing G.
NEP can be expressed in several ways that represent different measurements and device characteristics. It is important to note the distinctions between them. First is the thermal fluctuation noise NEP (NEP TFN ). NEP TFN is calculated from Eq. 4.1 using a value for G extracted from I-V curve measurements. It represents a theoretical limit where there is no significant contribution to 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 measured current noise spectral density i n and frequency-dependent electrical responsivity S el (ω), where S el (ω) = S el / (1 + iωτ ). 57 Here S el is the DC electrical responsivity to dissipated Joule power,  Figure 6 illustrates the natural tradeoffs that occur between operating temperature, time constant, and NEP. In short, a more sensitive bolometer is also slower, thus introducing more stringent requirements on overall instrument 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 the responsivity 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 power flowing out the thermal link equals the sum of absorbed optical power and Joule power dissipated by the TES resistance. Note that stray power can manifest itself as either optical power or Joule power. For G = AT n , where A is a constant and n is the exponent of the thermal conductance, P sat is given by: Thus for a given bath temperature and sensor transition temperature (T c T sat ), the saturation power of the device scales with the thermal conductance. As G is reduced to achieve higher sensitivity, the stray power requirements of the experimental platform -electrical and opticalbecome proportionally more stringent. In particular, implementation of techniques to mitigate stray power, like filtered connectors at the cryostat vacuum feedthroughs, thermal blocking and powder filters in close proximity to the detectors, and single-point grounding, are necessary to achieve a sufficiently quiet experimental space.
In the dark, the most sensitive bolometer demonstrated to date was developed by SRON and

Thermal isolation techniques
There are several thermal isolation techniques that show promise toward enabling Origins-type sensitivities 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 weak electron-phonon (e-p) coupling in the sensor material (a "hot electron" bolometer).

Long (diffusive) leg bolometers generate thermal isolation via diffuse phonon transport across
the legs that support a membrane-isolated bolometer. The legs and the membrane are typically micromachined from Si or SiN. Conduction via diffuse phonon transport follows Fourier's law of thermal conduction: G = κA/ , where κ is the material's bulk thermal conductivity, A is the cross sectional area of the leg, and 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 property that depends on the details of the leg's fabrication process, which can lead to non-uniform conductance across an array or between fabrication runs. In addition, the G ∝ −1 behavior only holds for legs longer than a certain threshold; > 400 µm has been reported. 65 Bolometers that use long-leg isolation are exemplified in practice by the SPICA/SAFARI bolometers developed by SRON 58, 61, 62 (see Section 4.1). A representative optical micrograph of a long-leg bolometer is shown in Fig. 7. Despite the excellent achieved sensitivity of long-legged bolometers, an obvious limitation is the low fill fraction achieved. By area, the SPICA/SARARI bolometers have a fill fraction of ∼ 4%. SPICA/SAFARI has three bands with between 600 and 2000 pixels per band, yielding far fewer pixels than the ∼ 60,000 required for OSS. With G ∝ A/ , reducing the conductance 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 to SPICA/SAFARI. An added complication to longer legs is that as the leg length increases, the heat capacity of the legs can become non-negligible, leading to measurable ITFN degrading device performance. Long-legged bolometers lend themselves most naturally to resistive absorber coupling.
Antenna coupling would likely have to incorporate the legs themselves, and further investigation is required to determine whether the electromagnetic requirements of an antenna could be consistent with the thermal requirements of the legs.
Short (ballistic) leg bolometers achieve thermal isolation by minimizing the solid angle between the radiating sensor and legs that support a membrane. The ballistic limit occurs when the length of the leg is shorter than the phonon mean free path mfp in the material, so it is assumed that phonons 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. 66  Phononic filter bolometers use nano-machined legs to generate coherent phonon scattering that suppresses propagated phonon modes to below the quantum limit. 34,[68][69][70] Like ballistic leg bolometers, 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. 68 indicates that a factor of 5 improvement over the quantum limit is possible with phononic filter legs that are just 10 µm long and are machinable using known techniques. Devices presented by Williams et al. 69 achieved a factor of ∼ 2 reduction in thermal conductance below the quantum limit using phononic filter legs. Fabrication of phononic filters is challenging as sub-µm lithography techniques are required, but recent work by Denis et al. 71 demonstrates reliable and robust fabrication of phononic leg-isolated TESs.
Hot electron bolometers (HEBs) use the inherent decoupling of electrons and phonons in certain metals at low temperatures for thermal isolation. The conductance between electrons and phonons at low temperature is given by where Σ is the electron-phonon coupling constant (material property), V is the volume of the sensor, T is temperature, and n is the thermal exponent (typically n = 5 for e-p coupling). A

Radiation coupling techniques
Antenna-coupling can be used to define the sensor's angular acceptance and coupling to the electromagnetic radiation field. It converts the incident fields (photons) into electronic excitations in the absorber media which are dissipated and subsequently detected as heat. To achieve high antenna coupling efficiency requires transforming the modal symmetry and impedance scales encountered by the wave in free space to that present in the circuit elements employed to absorb the radiation. A wide variety of techniques exist to carry out these functions; however, due to the While antenna coupled arrays have found utility in instrument applications where high spatialsampling presents a driving consideration, 80 an alternative approach to achieve full sampling is presented by "absorber coupled" sensor arrays. 81 In this limit, the "antenna response" of the sensor is essentially uniform over the range of interest and the telescope optics in concert with a cold Lyot stop is used to specify and limit radiation presented to the focal plane. 82 In this configura-

Susceptibility to cosmic rays
The interaction between energetic charged particles and the materials used in the detector system lead to a stochastic background of energetic events observed by the sensors in the focal plane over the course of a space mission. Consider for example the Planck Surveyor mission which reported a rate of 80 cosmic ray related events per minute for the High Frequency Instrument array during operations in its L2 orbit. Even with template fitting of its radiometric data, a science data loss of ∼ 10 − 15% was experienced due to these "glitch"-like temporal events. 96,97 Beyond impacting observational efficiency, non-ideal detector responses associated with these energetic events can lead to instrumental stability and calibration issues which reduce imaging fidelity if unmitigated. Origins will require higher sensitivity and by extension a lower focal plane operating temperature than used in previously deployed systems and thus increase the relative importance of the sensor's thermal bus implementation on minimizing the impact of cosmic rays. Extension of the detector design techniques employed for calorimetry 98-101 provide a viable path to address this instrumentation need. Mitigating cosmic rays is one particular advantage of a device known as the ideal integrating bolometer (IIB), 102-105 which combines leg isolation (diffusive, ballistic, or phononic) with a switchable thermal short. Upon an upset (e.g., cosmic ray hit), the device can be reset quickly to mitigate the data losses that Planck experienced.

Conclusions
The unprecedented sensitivity enabled by Origins' large, cold, and space-based telescope places stringent requirements on its instruments. In particular, the detector systems employed by each instrument must be designed to enable background-limited observations, contributing negligible noise to the overall instrumental budget. Detectors that enable background-limited observations in each channel do not exist today. For MISC-T, the most difficult specification the detector system must meet is stability. While bolometers and semiconducting detectors have many sources of instability (e.g., environmental drifts for bolometers, dark current and read noise for semicon-ductors), all these terms go to zero if a TES calorimeter is employed. The TES calorimeter we designed using well-established physical models and measured material parameters can overcome many of the other challenges associated with the MISC-T detector system, such as high photon flux and the large required bandwidth, delivering all the advantages of photon-counting using an energy-resolving detector. For OSS and FIP, the most challenging requirement the detector subsystems must meet is sensitivity, with radiation coupling and cosmic ray immunity also leading design drivers. There are multiple promising paths toward achieving the required sensitivity using TES bolometers, with demonstrated sensitivities now approaching the OSS requirement and improving.
For all the instruments, the TES detector options benefit from strong heritage in astrophysics instrumentation and well-understood physics that enables the design and implementation of devices that operate at the thermodynamic limit across the Origins band.

Disclosures
The authors declare no conflicts of interest.  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 order to achieve voltage bias in the device.

List of Figures
The SQUID amplifier is employed as an ammeter that measures changes in TES current due to absorption of energetic particles (calorimeter) or flux (bolometer).
Illustration of the advantage to photon counting. The top frame shows how power is measured bolometrically with an ideal instrument. Incident optical power is manifested as a shift in the "baseline" TES current in the time domain. In the frequency domain, one would observe a higher white noise level due to incident photon noise. The center frame illustrates how system drift can be confused with an optical signal; the long time constants of bolometers place stringent requirements on system stability. The bottom frame shows how drift is mitigated if individual photon events are resolved (as opposed to just measuring a flux of photons.) In this case system drift has no effect on the measurement. were modified to meet Origins requirements by simply reducing G. To make the device the required 10x more sensitive requires a 100x reduction in G, which in turn makes the device 100x slower.