Demonstration of ultra-low noise equivalent power using a longitudinal proximity effect transition-edge sensor
DDemonstration of ultra-low noise equivalent power using alongitudinal proximity effect transition-edge sensor
Peter C. Nagler, John E. Sadleir and Edward J. WollackNASA/Goddard Space Flight Center, Greenbelt, MD USA
Abstract
Future far-infrared astronomy missions will need large arrays of detectors with ex-ceptionally low noise-equivalent power (NEP), with some mission concepts calling forthousands of detectors with NEPs below a few × − W/ √ Hz . Though much progresshas been made toward meeting this goal, such detector systems do not exist today. Inthis work, we present a device that offers a compelling path forward: the longitudinalproximity effect (LoPE) transition-edge sensor (TES). With a chemically-stable andmechanically-robust architecture, the LoPE TES we designed, fabricated, and char-acterized also exhibits unprecedented sensitivity, with a measured electrical NEP of × − W/ √ Hz . This represents a >100x advancement of the state-of-the-art, push-ing TES detectors into the regime where they may be employed the achieve to goals ofeven the most ambitious large and cold future space instruments. Experiments employing incoherent low temperature detectors have made significant contri-butions to astronomy from the X-ray through the millimeter-wave. Offering superior noiseperformance compared to detectors that operate at higher temperatures, the earliest widely-deployed detectors of this type were based on doped semiconductors cooled below theirmetal-insulator transition, where a temperature-dependent conduction mechanism (variablerange hopping) enables the material to act as a thermometer sensitive to deposited energy orpower. Space-based instruments flying on
COBE [1],
Planck [2], and
Astro-H/Hitomi [3] useddetectors based on this technology. More recently, both equilibrium and non-equilibriumsuperconducting detectors have largely replaced semiconducting detectors, offering highersensitivity, simpler fabrication, and multiplexed readout schemes for large numbers of de-tectors. Many thousands of superconducting detectors are currently deployed from ground(e.g., SCUBA-2 [4], BICEP-3 [5], ACTpol [6], and Subaru [7]), aircraft (e.g., HAWC+[8]),and balloon (e.g., Spider [9], EBEX [10], PIPER [11], and PICTURE-C [12]) platforms.Future space telescopes - particularly those with large and/or cooled apertures - are likelyto require the use of superconducting detectors to achieve background-limited sensitivity.Despite considerable effort, demonstrating detector systems achieving the ultimate sensitiv-ity and scale required for these future missions remains elusive. For example, the OriginsSpace Telescope concept (
Origins ), which features a 6.5 m primary mirror cooled to <5 K,requires more than 10,000 far-infrared (FIR) detectors with noise-equivalent power below × − W/ √ Hz in order to make background-limited observations of far-infrared (FIR)spectral lines [13]. Superconducting transition-edge sensor (TES) bolometers have beenidentified by the mission as the baseline detectors capable of meeting this requirement, butpublished performance is still an order of magnitude away [e.g., 14–18]. Microwave kinetic in-ductance detectors (MKIDs) [19] - another superconducting detector technology - also show1 a r X i v : . [ a s t r o - ph . I M ] D ec romise, but the best measured MKID performance is similar to that achieved by TESs [20].Recently quantum capacitance detectors (QCDs) have emerged as a technology able to meetthe sensitivity requirements of missions like Origins [21], but uniform arrays of the scaleenvisioned for future space telescopes ( > pixels), along with a practical large-formatreadout scheme, have yet to be shown.In this work, we present a TES bolometer with a measured electrical NEP of < × − W/ √ Hz in the signal band from 1 Hz to 1 kHz, representing a >100x improvement over thestate-of-the-art. The device is fabricated from chemically-stable materials on a mechanically-robust solid substrate and uses the longitudinal proximity effect (LoPE) from attached Nbleads to induce superconductivity in a Au sensor film. We refer to this new type of TES as a“LoPE TES.” We present both measurements and a complete theoretical model that explainthe breakthrough performance of this device, and discuss the implications of its sensitivityfor astronomy and other applications. Superconductivity is a thermodynamic phase that exists below a critical temperature T c ,current I c , and magnetic field B c . Transitioning through a material’s normal phase (non-superconducting) to the superconducting phase, while carrying a finite DC bias current, theelectrical resistance undergoes an abrupt decrease from its normal state resistance R N tozero. Superconducting transition-edge sensors (TESs) exploit this steep resistive transitionto precisely measure deposited energy (as in TES quantum calorimeters) or deposited powers(as in TES bolometers). The change in TES resistance results in a change in current throughthe device, measured by a superconducting quantum interference device (SQUID) amplifieremployed as an ammeter (Fig. 1).In Sadleir et al. [22], measurements of a bilayer TES’s critical current versus temperature,magnetic field, and over a range of geometries showed excellent agreement with a Ginzburg-Landau (GL) model for the TES and the hallmarks of a superconducting Josephson weak-link: exponential temperature dependence, Fraunhofer-like oscillations with applied mag-netic field, and a Josephson current-phase relation [23–25]. This GL model and microscopictheoretical treatment of the system both showed that superconducting order from the higher T c superconducting leads diffused longitudinally into the variable resistor region of the TESeffectively raising the TES’s transition temperature. This longitudinal proximity effect wasobserved over remarkably long distances, in excess of 1000 times the electron mean free path (cid:96) mfp .These results point to the intriguing possibility of a LoPE TES where the sensor need not be asuperconductor at the device’s operating temperature and can even be made of materials thatare not superconducting at any temperature [26, 27]. This greatly expands the TES materialdesign space and provides opportunities to extend state-of-the-art performance for a widerange of applications, enabling materials and designs that can offer combinations of reducednoise, higher responsivity, higher speed, higher quantum efficiency, and improved spectralresolving power. Additionally, it enables making smaller sized TESs. This can both reducenoise and allow higher density arrays across the electromagnetic spectrum. Importantly itcan offer a simplified fabrication procedure with fewer layers and steps.Here we present the first results on a Au LoPE TES. The device is designed such thatquantum wavefunction governing the superconducting pairs in the Nb leads penetrates intothe Au region that constitutes the variable resistor. For a given Au film composition andthickness, and for given interface properties between Au and Nb, the T c of the LoPE TES2 igure 1: Left: Basic TES bias and readout circuit. Changes in the TES resistance R TES change thecurrent flowing through the input coil to the SQUID amplifier, which serves as a sensitive ammeter. Right:SEM of a representative detector. The leads are Nb and the TES sensor is Au. This particular sensoris 6 µ m × µ m. The on-chip Nb field coil is capable of applying a few 10s of mT before exceeding thecritical current of the Nb traces. In the measurements presented in this paper, it is used to null the ∼ µ T ambient magnetic field in the detector package and also to measure the dependence of critical currenton applied field. An off-chip coil could also be used for this purpose, but the on-chip version is useful forlaboratory characterization. depends on the longitudinal separation (cid:96) between the Nb leads. In this case (cid:96) is chosen togive an operating temperature below 150 mK.
The detector employed is a TES that uses a Au sensor film connected to Nb leads. The devicewas fabricated using standard microfabrication techniques and optical photolithography.This material combination was chosen for its relative ease of fabrication, chemical stability,and ability to achieve high sensitivity on solid substrates. Additionally, the properties ofthe material constituents are well understood in thin film form. Figure 1 shows a scanningelectron micrograph (SEM) of a representative detector.The detectors feature on-chip magnetic field coils that use a superconducting Nb winding.The field coils can be employed to null the ambient magnetic field in the test platform orenable electrical measurements taken as a function of applied magnetic field. The devicespresented in this paper have measured critical fields (field at which no critical current is mea-surable) of a few hundred µ T; the coil itself is capable of supplying fields of >10 mT beforeexceeding the critical current of the Nb windings. Critical current versus field measure-ments for these devices reproduce the familiar Fraunhofer-like diffraction pattern measuredpreviously in MoAu TESs [e.g., see 22, 28] and anticipated in weak-link TESs [29].The TESs are read out using series arrays of superconducting quantum interference devices(SQUIDs). Each TES sensor has its own readout channel. The devices are cooled witha two-stage adiabatic demagnetization refrigerator (ADR) backed by a pulse tube cooler.3 I in [A] -8 DC r es pon s i v i t y [ A / W ] Measured dataSimulated data
Figure 2:
Left: Measured and simulated current-voltage (I-V) curves at 135 mK, showing excellent agree-ment between measurement and simulation throughout the superconducting-normal transition. The yellowshaded region is expanded in the inset plot. It details the region where we biased the device for noise mea-surements. Both the measured and simulated data are computed by taking one second averages of the TEScurrent at a given bias point. Right: DC current responsivity of the device computed from the measuredand simulated I-V curves at left. This plot details the region where we biased the device for noise measure-ments. The strong agreement between the measured and simulated I-V curves yields strong agreement inthe calculated responsivities.
With the TES characterization package and associated wiring installed, the ADR can reachtemperatures as low as 36 mK.
We measured current-voltage (I-V) curves in the dark. The on-chip field coil was employed inthese measurements to null the ambient magnetic field normal to the sensor films, estimatedto be ∼ µ T. An example I-V curve measured at 135 mK is shown in Fig. 2. From theI-V curves, we determined the device’s DC current responsivity R using the dual of Jones’expression [30], where R = ( R − Z ) / (2 V ( R s + Z )) . Here Z is the dynamic resistance dV /dI , R is the resistance V /I , V is the voltage across the TES, and R s is the shuntresistance. The maximum responsivity is ∼ × A/W and occurs near the peak of theI-V curve, however estimates of the responsivity in that region are limited by system noise.We also measured noise spectra of the devices. To do so, we collected timestreams of theSQUID output at a given bias point. We then took the discrete Fourier transform of a giventimestream and computed the power spectral density (PSD). The noise spectrum at the biaspoint near the maximum measured responsivity is shown in Fig. 3. Shown are the average of32 PSDs (“32x average”) and 10,000 PSDs (“10,000x average”). Both are processed from thesame 32 seconds of timestream data; for n averages, we divide the full timestream equallyinto n shorter timestreams, calculate the PSD of each, then take their average.We computed the device’s electrical noise-equivalent power (NEP) spectrum from the DCresponsivity and noise spectrum. With an approximate single-pole response, the frequency-dependent responsivity R ( f ) is given by R ( f ) = R / (1 + 2 πif τ ) , where we τ is the timeconstant of the device inferred from the noise spectrum and f is the device signal frequency.The NEP spectrum is then obtained by dividing the current spectral density by the modulusof the responsivity, | R ( f ) | . The result measured at 135 mK is shown in Fig. 3.4 Frequency [Hz] -12 -11 -11 -10 -10 C u rr e n t s p ec t r a l d e n s i t y [ A / H z ] Measured data: 32x averageSimulated data: 32x averageMeasured data: 10,000x average
Figure 3:
Left: Measured and simulated noise spectra. The measured 32x average current noise traceshown here is the average of 32 consecutive traces, each 1 second in duration. The simulated noise trace isprocessed in the same way. When the measured traces are instead concatenated, the device’s /f knee isvisible at a frequency of ∼ . Hz; this is due to the SQUID’s contribution. Right: electrical NEP spectracomputed using the measured and simulated noise spectra and frequency-dependent electrical responsivity.At the bias point where the data were measured the DC responsivity is . × A/W. This device achievesa broadband electrical NEP of × − W/ √ Hz across the signal band from 1 Hz to 300 Hz, and remainsbelow × − W/ √ Hz for frequencies up to 1 kHz. We use the resistively shunted junction (RSJ) model [31, 32] to model our device. The RSJmodel is commonly used to describe Josephson junctions and Josephson weak-links generally,and has also been previous applied to TESs [33–37]. In this model the TES current iscomposed of: (1) quasiparticle current through the shunt resistor; and (2) Josephson current I through the weak-link. Equivalently, the variable resistor representing the TES in Fig. 1is replaced by a shunt resistor in parallel with a weak-link. We apply this model to our TESwhere the weak-link current I is proportional to the sine of the phase, consistent with theGL theory LoPE TES model result [28] with I = I c sin φ , and the voltage is proportionalto the time derivative of the phase difference V = (Φ / π ) ˙ φ , where Φ is the magneticflux quantum, and φ and I c are the phase difference and critical current across the weak-link, respectively. We numerically solve the RSJ model in the time domain following themethod presented by [38]. Thermal fluctuation noise at the device temperature of operationis explicitly incorporated in the model. The model outputs TES current as a function oftime for a given bias point sampled at 40 MHz. We find excellent agreement between themodeled and the measured data, as seen in both the I-V relation (Fig. 2) and the noisespectrum (Fig. 3). To generate these plots, the time domain output of the simulation isanalyzed with the same analysis procedure as the measured data. The I-V curve uses theaverage of a 1 second long timestream, and the noise spectrum is generated by averaging 32separate noise spectra, with each individual PSD computed from 1 second of time domaindata. We point out that the agreement is achieved with no free undetermined parameters,no hidden variables, and with no unknown noise sources. All inputs to the RSJ model areindependently measured physical parameters.Operating as a bolometer, the useful signal bandwidth of the device is from ∼ − Hz.The bandwidth is limited at low frequency by the SQUID’s /f noise and at high frequenciesby the resonant feature in the noise spectrum visible near 4 kHz. This feature looks similar5o the signature of a slightly underdamped TES biased near an electrothermal instability.Our bias point is electrothermally stable, overdamped, and not near an instability. Thisfeature is purely electrical, arising from the Josephson limit cycle frequency. Its shape andfundamental frequency are determined by the electrical circuit, bias condition, and thermalfluctuation noise.We may also consider the sensitivity of the device when operated as a calorimeter [39]. In thiscase the important figure of merit is the detector’s energy resolution (or equivalently spectralresolution). Under the assumption that the noise is approximately Gaussian-distributed,the following expression relates the full width half maximum (FWHM) energy resolution ∆ E FWHM to the NEP: ∆ E FWHM = 2 (cid:112) (cid:18)(cid:90) ∞ f ) df (cid:19) − / , (1)where f is signal frequency [40]. Solving this equation using our measured NEP and band-width, we find ∆ E FWHM (cid:39) . meV. Using spectral resolving power R = 4 as the criteriafor noiselessly counting single photons [41], the calculated ∆ E FWHM implies that this devicehas the intrinsic sensitivity to count single 180 GHz photons.In addition to reproducing the measured data, the model we developed gives us the abilityto predict the ultimate sensitivity of an optimized LoPE TES based on this design. Bychanging the bias point and/or reducing the operating temperature, we expect the electricalNEP can improve by more than a factor of 10 while retaining a similar signal bandwidth.
We designed, fabricated, and characterized a LoPE TES that exhibits exceptionally-lowelectrical NEP, advancing the sensitivity achieved by TESs by >100x. The device’s behavioris well explained by a finite-temperature RSJ model, which reproduces both the measured I-V relation and noise spectrum. Importantly, the device presented here is simple to fabricate,chemically stable, and mechanically robust. The use of a sensor material with no knownintrinsic T c is a paradigm shift in TES design.While the readout circuit used here is not multiplexed, the full range of SQUID multiplexingoptions developed for TES readout can be used with this device. For the envisioned scale ofarrays for a mission like Origins , we expect microwave SQUID multiplexing [42] to be mostappropriate, though other techniques (e.g., time-division multiplexing [43]) can be used forlaboratory characterization of modestly sized arrays.To confirm the utility of this device as a radiation detector, its optical NEP needs to beimplemented and measured. Antenna coupling [44] is likely to be the most suitable radiationabsorption technique for this device at FIR frequencies. We plan to add antennas to ournext generation of devices, and future laboratory measurements will focus on measuring theoptical response. We point out that we can meet the sensitivity requirement of a missionlike
Origins even if the optical NEP is degraded relative to the electrical NEP.Beyond the application of FIR space missions, the intrinsic sensitivity of this device may en-able broad utility in applications needing single photon sensitivity at lower energies than hasbeen demonstrated before, such as quantum photonics, quantum information, and quantumsensing – or in detection of small energy processes more generally, including particle physicsand dark matter searches. 6
Acknowledgements
This work was funded by the NASA/Goddard Space Flight Center Internal Research andDevelopment (IRAD) program. 7
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