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At SRON we have been developing X-ray TES micro-calorimeters as backup technology for the X-ray Integral Field Unit (X-IFU) of the Athena mission, demonstrating excellent resolving powers both under DC and AC bias. We also developed a frequency-domain multiplexing (FDM) readout technology, where each TES is coupled to a superconducting band-pass LC resonator and AC biased at MHz frequencies through a common readout line. The TES signals are summed at the input of a superconducting quantum interference device (SQUID), which performs a first amplification at cryogenic stage. Custom analog front-end electronics and digital boards take care of further amplifying the signals at room temperature and of the modulation/demodulation of the TES signals and bias carrier, respectively. We report on the most recent developments on our FDM technology, which involves a two-channel demonstration with a total of 70 pixels with a summed energy resolution of 2.34 +/- 0.02 eV at 5.9 keV without spectral performance degradation with respect to single-channel operation. Moreover, we discuss prospects towards the scaling-up to a larger multiplexing factor up to 78 pixels per channel in a 1-6 MHz readout bandwidth., Comment: Under publication in Journal of Low Temperature Physics

SRON (Netherlands Institute for Space Research) is developing the Focal Plane Assembly (FPA) for Athena X-IFU, whose Demonstration Model (DM) will use for the first time a time domain multiplexing (TDM)-based readout system for the on-board transition-edge sensors (TES). We report on the characterization activities on a TDM setup provided by NASA Goddard Space Flight Center (GSFC) and National Institute for Standards and Technology (NIST) and tested in SRON cryogenic test facilities. The goal of these activities is to study the impact of the longer harness, closer to X-IFU specs, in a different EMI environment and switching from a single-ended to a differential readout scheme. In this contribution we describe the advancement in the debugging of the system in the SRON cryostat, which led to the demonstration of the nominal spectral performance of 2.8 eV at 5.9~keV with 16-row multiplexing, as well as an outlook for the future endeavours for the TDM readout integration on X-IFU's FPA-DM at SRON., Comment: Under publication in Journal of Low Temperature Physics

We present a detailed analysis of the fundamental noise sources in superconducting transition-edge sensors (TESs), ac voltage biased at MHz frequencies and treated as superconducting weak links. We have studied the noise in the resistive transition as a function of bath temperature of several detectors with different normal resistances and geometries. We show that the excess noise, typically observed in the TES electrical bandwidth, can be explained by the equilibrium Johnson noise of the quasiparticles generated within the weak link. The fluctuations at the Josephson frequency and higher harmonics contribute significantly to the measured voltage noise at the detector bandwidth through the nonlinear response of the weak link with a sinusoidal current-phase relation., Comment: 9 pages, 7 figures

The X-IFU is the cryogenic spectrometer onboard the future ATHENA X-ray observatory. It is based on a large array of TES microcalorimeters, which works in combination with a Cryogenic AntiCoincidence detector (CryoAC). This is necessary to reduce the particle background level thus enabling part of the mission science goals. Here we present the first joint test of X-IFU TES array and CryoAC Demonstration Models, performed in a FDM setup. We show that it is possible to operate properly both detectors, and we provide a preliminary demonstration of the anti-coincidence capability of the system achieved by the simultaneous detection of cosmic muons., Comment: Accepted for publication in the Journal of Low Temperature Physics for LTD-19 special issue

We report on the development and demonstration of a MHz frequency domain multiplexing (FDM) technology to read out arrays of cryogenic transition edge sensor (TES) X-ray microcalorimeters. In our FDM scheme, TESs are AC-biased at different resonant frequencies in the low MHz range through an array of high-$Q$ LC resonators. The current signals of all TESs are summed at superconducting quantum interference devices (SQUIDs). We have demonstrated multiplexing for a readout of 31 pixels using room temperature electronics, high-$Q$ LC filters and TES arrays developed at SRON, and SQUID arrays from VTT. We repeated this on a second setup with 37 pixels. The summed X-ray spectral resolutions $@$ 5.9 keV are $\Delta E_{\rm 31 pix ~MUX}=2.14\pm0.03$ eV and $\Delta E_{\rm 37 pix ~MUX}=2.23\pm0.03$ eV. The demonstrated results are comparable with other multiplexing approaches. There is potential to further improve the spectral resolution and to increase the number of multiplexed TESs, and to open up applications for TES X-ray microcalorimeters., Comment: 6 pages, 3 figures, accepted for publication on Applied physics letters

Transition Edge Sensors (TESs) are the selected technology for future spaceborne X-ray observatories, such as Athena, Lynx, and HUBS. These missions demand thousands of pixels to be operated simultaneously with high energy-resolving power. To reach these demanding requirements, every aspect of the TES design has to be optimized. Here we present the experimental results of tests on different devices where the coupling between the x-ray absorber and the TES sensor is varied. In particular, we look at the effects of the diameter of the coupling stems and the distance between the stems and the TES bilayer. Based on measurements of the AC complex impedance and noise, we observe a reduction in the excess noise as the spacing between the absorber stem and the bilayer is decreased. We identify the origin of this excess noise to be internal thermal fluctuation noise between the absorber stem and the bilayer. Additionally, we see an impact of the coupling on the superconducting transition in the appearance of kinks. Our observations show that these unwanted structures in the transition shape can be avoided with careful design of the coupling geometry. Also the stem diameter appears to have a significant impact on the smoothness of the TES transition. This observation is still poorly understood, but is of great importance for both AC and DC biased TESs., Comment: 9 pages, 8 figures

We are developing large TES arrays in combination with FDM readout for the next generation of X-ray space observatories. For operation under AC-bias, the TESs have to be carefully designed and optimized. In particular, the use of high aspect ratio devices will help to mitigate non-ideal behaviour due to the weak-link effect. In this paper, we present a full characterization of a TES array containing five different device geometries, with aspect ratios (width:length) ranging from 1:2 up to 1:6. The complex impedance of all geometries is measured in different bias configurations to study the evolution of the small-signal limit superconducting transition parameters, as well as the excess noise. We show that high aspect ratio devices with properly tuned critical temperatures (around 90 mK) can achieve excellent energy resolution, with an array average of 2.03 +- 0.17 eV at 5.9 keV and a best achieved resolution of 1.63 +- 0.17 eV. This demonstrates that AC-biased TESs can achieve a very competitive performance compared to DC-biased TESs. The results have motivated a push to even more extreme device geometries currently in development., Comment: 11 pages, 10 figures

Large format arrays of transition edge sensor (TES) are crucial for the next generation of X-ray space observatories. Such arrays are required to achieve an energy resolution of $\mathrm{\Delta}E<$3 eV full-width-half-maximum (FWHM) in the soft X-ray energy range. We are currently developing X-ray microcalorimeter arrays as a backup option for the X-IFU instrument on board of ATHENA space telescope, led by ESA and foreseen to be launched in 2031. In this contribution, we report on the development and the characterization of a uniform 32$\times$32 pixel array with (length$\times $width) 140$\times$30 $\mu$m$^2$ TiAu TESs, which have \textcolor{black}{a 2.3 $\mu$m} thick Au absorber for X-ray photons. The pixels have a typical normal resistance $R_\mathrm{n}$ = 121 m$\Omega$ and a critical temperature $T_\mathrm{c}\sim$ 90 mK. We performed extensive measurements on 60 pixels out of the array in order to show the uniformity of the array. We obtained an energy resolutions between 2.4 and 2.6 eV (FWHM) at 5.9 keV, measured in a single-pixel mode at AC bias frequencies ranging from 1 to 5 MHz, with a frequency domain multiplexing (FDM) readout system, which is developed at SRON/VTT. We also present the detector energy resolution at X-ray with different photon energies generated by a modulated external X-ray source from 1.45 keV up to 8.9 keV. Multiplexing readout across several pixels has also been performed to evaluate the impact of the thermal crosstalk to the instrument's energy resolution budget requirement. This value results in a derived requirement, for the first neighbour, that is less than 1$\times$10$^{-3}$ when considering the ratio between the amplitude of the crosstalk signal to an X-ray pulse (for example at 5.9 keV)

Transition-edge sensors (TESs) are used as very sensitive thermometers in microcalorimeters aimed at detection of different wavelengths. In particular, for soft X-ray astrophysics, science goals require very high resolution microcalorimeters which can be achieved with TESs coupled to suitable absorbers. For many applications there is also need for a high number of pixels which typically requires multiplexing in the readout stage. Frequency Domain Multiplexing (FDM) is a common scheme and is the baseline proposed for the ATHENA mission. FDM requires biasing the TES in AC at MHz frequencies. Recently there has been reported degradation in performances under AC with respect to DC bias. In order to assess the performances of TESs to be used with FDM, it is thus of great interest to compare the performances of the same device both under AC and DC bias. This requires two different measurement setups with different processes for making the characterization. We report in this work the preliminary results of a single pixel characterization performed on a TiAu TES under AC and afterwards under DC bias in different facilities. Extraction of dynamical parameters and noise performances are compared in both cases as a first stage for further AC/DC comparison of these devices.

We are developing X-ray microcalorimeters as a backup option for the baseline detectors in the X-IFU instrument on board the ATHENA space mission led by ESA and to be launched in the early 2030s.5$\times$5 mixed arrays with TiAu transition-edge sensor (TES), which have different high aspect ratios and thus high resistances, have been designed and fabricated to meet the energy resolution requirement of the X-IFU instrument. Such arrays can also be used to optimise the performance of the Frequency Domain Multiplexing (FDM) readout and lead to the final steps for the fabrication of a large detector array. In this work we present the experimental results from tens of the devices with an aspect ratio (length-to-width) ranging from 1-to-1 up to 6-to-1, measured in a single-pixel mode with a FDM readout system developed at SRON/VTT. We observed a nominal energy resolution of about 2.5 eV at 5.9 keV at bias frequencies ranging from 1 to 5 MHz. These detectors are proving to be the best TES microcalorimeters ever reported in Europe, being able to meet not only the requirements of the X-IFU instrument, but also those of other future challenging X-ray space missions, fundamental physics experiments, plasma characterization and material analysis.

The next generation of Far-infrared and X-ray space observatories will require detector arrays with thousands of transition edge sensor (TES) pixel. It is extremely important to have a tool that is able to characterize all the pixels and that can give a clear picture of the performance of the devices. In particular, we refer to those aspects that can affect the global energy resolution of the array: logarithmic resistance sensitivity with respect to temperature and current ($\alpha$ and $\beta$ parameters, respectively), uniformity of the TESs and the correct understanding of the detector thermal model. Complex impedance measurement of a TES is the only technique that can give all this information at once, but it has been established only for a single pixel under DC bias. We have developed a complex impedance measurement method for TESs that are AC biased since we are using a MHz frequency domain multiplexing (FDM) system to readout an array. We perform a complete set of AC impedance measurements for different X-ray TES microcalorimeters based on superconducting TiAu bilayers with or without normal metal Au bar structures. We discuss the statistical analysis of the residual between impedance data and fitting model to determine the proper calorimeter thermal model for our detectors. Extracted parameters are used to improve our understanding of the differences and capabilities among the detectors and additionally the quality of the array. Moreover, we use the results to compare the calculated noise spectra with the measured data.

Uniform large transition-edge sensor (TES) arrays are fundamental for the next generation of X-ray space observatories. These arrays are required to achieve an energy resolution $\Delta E$ < 3 eV full-width-half-maximum (FWHM) in the soft X-ray energy range. We are currently developing X-ray microcalorimeter arrays for use in future laboratory and space-based X-ray astrophysics experiments and ground-based spectrometers. In this contribution we report on the development and the characterization of a uniform 32$\times$32 pixel array with 140$\times$30 $\mu$m$^2$ Ti/Au TESs with Au X-ray absorber. We report upon extensive measurements on 60 pixels in order to show the uniformity of our large TES array. The averaged critical temperature is $T_\mathrm{c}$ = 89.5$\pm$0.5 mK and the variation across the array ($\sim$1 cm) is less than 1.5 mK. We found a large region of detector's bias points between 20\% and 40\% of the normal-state resistance where the energy resolution is constantly lower than 3 eV. In particular, results show a summed X-ray spectral resolution $\Delta E_\mathrm{FWHM}$ = 2.50$\pm$0.04 eV at a photon energy of 5.9 keV, measured in a single-pixel mode using a frequency domain multiplexing (FDM) readout system developed at SRON/VTT at bias frequencies ranging from 1 to 5 MHz. Moreover we compare the logarithmic resistance sensitivity with respect to temperature and current ($\alpha$ and $\beta$ respectively) and their correlation with the detector's noise parameter $M$, showing an homogeneous behaviour for all the measured pixels in the array.

In the frequency-domain multiplexing (FDM) scheme, transition-edge sensors (TES) are individually coupled to superconducting LC filters and AC biased at MHz frequencies through a common readout line. To make efficient use of the available readout bandwidth and to minimize the effect of non-linearities, the LC resonators are usually designed to be on a regular grid. The lithographic processes however pose a limit on the accuracy of the effective filter resonance frequencies. Off-resonance bias carriers could be used to suppress the impact of intermodulation distortions, which nonetheless would significantly affect the effective bias circuit and the detector spectral performance. In this paper we present a frequency shift algorithm (FSA) to allow off-resonance readout of TES's while preserving the on-resonance bias circuit and spectral performance, demonstrating its application to the FDM readout of a X-ray TES microcalorimeter array. We discuss the benefits in terms of mitigation of the impact of intermodulation distortions at the cost of increased bias voltage and the scalability of the algorithm to multi-pixel FDM readout. We show that with FSA, in multi-pixel and frequencies shifted on-grid, the line noises due to intermodulation distortion are placed away from the sensitive region in the TES response and the X-ray performance is consistent with the single-pixel, on-resonance level., Comment: Accepted for publication on Review of Scientific Instruments

Frequency domain multiplexing (FDM) is the baseline readout system for the X-ray Integral Field Unit (X-IFU) on board the Athena mission. Under the FDM scheme, TESs are coupled to a passive LC filter and biased with alternating current (AC bias) at MHz frequencies. Using high-quality factor LC filters and room temperature electronics developed at SRON and low-noise two-stage SQUID amplifiers provided by VTT, we have recently demonstrated good performance with the FDM readout of Mo/Au TES calorimeters with Au/Bi absorbers. We have achieved a performance requested for the demonstration model (DM) with the single pixel AC bias ($\Delta E=$1.8 eV) and 9 pixel multiplexing ($\Delta E=$2.6 eV) modes. We have also demonstrated 14-pixel multiplexing with an average energy resolution of 3.3 eV, which is limited by non-fundamental issues related to FDM readout in our lab setup., Comment: 7 pages, 5 figures. Published on Journal of Low Temperature Physics (2020)

Transition Edge Sensors are ultra-sensitive superconducting detectors with applications in many areas of research, including astrophysics. The device consists of a superconducting thin film, often with additional normal metal features, held close to its transition temperature and connected to two superconducting leads of a higher transition temperature. There is currently no way to reliably assess the performance of a particular device geometry or material composition without making and testing the device. We have developed a proximity effect model based on the Usadel equations to predict the effects of device geometry and material composition on sensor performance. The model is successful in reproducing I-V curves for two devices currently under study. We use the model to suggest the optimal size and geometry for TESs, considering how small the devices can be made before their performance is compromised. In the future, device modelling prior to manufacture will reduce the need for time-consuming and expensive testing.

Athena is a space-based X-ray observatory intended for exploration of the hot and energetic universe. One of the science instruments on Athena will be the X-ray Integrated Field Unit (X-IFU), which is a cryogenic X-ray spectrometer, based on a large cryogenic imaging array of Transition Edge Sensors (TES) based microcalorimeters operating at a temperature of 100mK. The imaging array consists of 3800 pixels providing 2.5 eV spectral resolution, and covers a field of view with a diameter of of 5 arc minutes. Multiplexed readout of the cryogenic microcalorimeter array is essential to comply with the cooling power and complexity constraints on a space craft. Frequency domain multiplexing has been under development for the readout of TES-based detectors for this purpose, not only for the X-IFU detector arrays but also for TES-based bolometer arrays for the Safari instrument of the Japanese SPICA observatory. This paper discusses the design considerations which are applicable to optimise the multiplex factor within the boundary conditions as set by the space craft. More specifically, the interplay between the science requirements such as pixel dynamic range, pixel speed, and cross talk, and the space craft requirements such as the power dissipation budget, available bandwidth, and electromagnetic compatibility will be discussed.

The X-ray integral field unit for the Athena mission consists of a microcalorimeter transition edge sensor pixel array. Incoming photons generate pulses which are analyzed in terms of energy, in order to assemble the X-ray spectrum. Usually this is done by means of optimal filtering in either time or frequency domain. In this paper we investigate an alternative method by means of principle component analysis. This method attempts to find the main components of an orthogonal set of functions to describe the data. We show, based on simulations, what the influence of various instrumental effects is on this type of analysis. We compare analyses both in time and frequency domain. Finally we apply these analyses on real data, obtained via frequency domain multiplexing readout., Comment: SPIE Astronomical Telescopes and Instrumentation; conference contribution

The Athena+ mission concept is designed to implement the Hot and Energetic Universe science theme submitted to the European Space Agency in response to the call for White Papers for the definition of the L2 and L3 missions of its science program. The Athena+ science payload consists of a large aperture high angular resolution X-ray optics and twelve meters away, two interchangeable focal plane instruments: the X-ray Integral Field Unit (X-IFU) and the Wide Field Imager (WFI). The X-IFU is a cryogenic X-ray spectrometer, based on a large array of Transition Edge Sensors (TES), offering 2.5 eV spectral resolution, with ~5" pixels, over a field of view of 5 arc minutes in diameter. In this paper, we briefly describe the Athena+ mission concept and the X-IFU performance requirements. We then present the X-IFU detector and readout electronics principles, the current design of the focal plane assembly, the cooling chain and review the global architecture design. Finally, we describe the current performance estimates, in terms of effective area, particle background rejection, count rate capability and velocity measurements. Finally, we emphasize on the latest technology developments concerning TES array fabrication, spectral resolution and readout performance achieved to show that significant progresses are being accomplished towards the demanding X-IFU requirements., Comment: Supporting paper for the science theme "The Hot and Energetic Universe" to be implemented by the Athena+ X-ray observatory (http://www.the-athena-x-ray-observatory.eu). 17 pages, 19 figures

We present the performances and the strain sensitivity of the first spherical gravitational wave detector equipped with a capacitive transducer and read out by a low noise two-stage SQUID amplifier and operated at a temperature of 5 K. We characterized the detector performance in terms of thermal and electrical noise in the system output sygnal. We measured a peak strain sensitivity of $1.5\cdot 10^{-20} Hz^{-1/2}$ at 2942.9 Hz. A strain sensitivity of better than $5\cdot 10{-20}Hz{-1/2}$ has been obtained over a bandwidth of 30 Hz. We expect an improvement of more than one order of magnitude when the detector will operate at 50 mK. Our results represent the first step towards the development of an ultracryogenic omnidirectional detector sensitive to gravitational radiation in the 3kHz range., Comment: 8 pages, 5 figures, submitted to Physical Review D

ATHENA is a European led x-ray observatory due for launch in the early 2030s. The X-ray Integral Field Unit (X-IFU) instrument on ATHENA will have an array of 3168 TES microcalorimeters, 2.5 eV resolution (at 7 keV), 5 arc second angular resolution and a 5 arc minute field of view. As one example, will allow unprecedented views of composition and dynamics of galaxy clusters.

The X-ray integral field unit (X-IFU) for ESA's Athena X-ray observatory will consist of 3840 AC-biased transition edge sensors (TESs), read out using frequency domain multiplexing (FDM). In this paper we describe details of the latest pixels geometries that are being designed for the current baseline array configuration. This includes details on how important TES properties (transition parameters, thermal design of the pixels, absorber composition) are being optimized to meet the target energy resolution, count-rate and quantum efficiency. We also present the latest design optimizations specifically targeted at mitigating AC-bias phenomena in Mo/Au TESs that can degrade performance.