We present finite element simulations of the transition-edge sensor (TES) microcalorimeter behavior using COMSOL Multiphysics. The simulated detector has a large absorber with a size of 990×990μm2. The simulation calculates the TES response after x-ray impact for a single pixel with a known, realistic, current-dependent resistive transition R(T,I). The simulation includes the full electrothermal feedback effects and heat conduction through the multiple contact points of the absorber to the TES thermometer and supporting membrane. The presented model, especially the 2D model, has been optimized for high accuracy, making it suitable for simulating the detector response when incident photons hit different positions on the absorber. We study the effects of position dependence using Principal Component Analysis with the aim of extracting correct photon energies from the pulses. The simulations show that the degradation, i.e., the FWHM broadening, due to the pulse variations will be less than 0.7 eV at below 2 keV, while it can be significant (>1 eV) at a higher energy band. The simulation result for position dependence can guide the design of large-absorber detectors for future x-ray missions, such as the Hot Universe Baryon Surveyor.

The electromagnetic spectrum in the terahertz frequency region is of significant importance for understanding the formation and evolution of galaxies and stars throughout the history of the universe and the process of planet formation. Within the star forming clouds the constituent atoms and molecules are excited to produce characteristic emission and absorption lines, many of which happen at the terahertz frequencies. Thus, detecting the spectral signatures as unique fingerprints of molecules and atoms require terahertz spectrometers, which need to be operated in a space observatory because of the water vapor absorption in the earth atmosphere. However, current terahertz spectrometers face several challenges that limit their performances and applications, including a low resolution, limited bandwidth, large volume, and complexity. In this paper, we address the last two issues by demonstrating a concept of a compact terahertz spectrometer using metasurface. We start by modelling, designing, and fabricating a metasurface, aiming to optimize its performance within a band from 1.7 to 2.5 THz. Next, we make use of an array of quantum cascade lasers that operate at slightly different frequencies around 2.1 THz to validate the performance of the spectrometer. Finally, we apply the spectrum inversion method to analyse the measured data to confirm a resolution R of at least 273. Our results demonstrated a miniaturized terahertz spectrometer concept successfully.

We design, fabricate, and measure a novel spectrometer based on meta-surface structures, aiming to optimize its spectroscopic resolution within a band from 1.7 to 2.5 THz. The latter corresponds to a bandwidth of 38%, being comparable with a grating spectrometer. The meta-surfaces apply unit cells that consist of double-anchor structures based on gold, polyimide and gold triple layers. Several quantum cascade lasers that operate at slightly different frequencies around 2.1 THz were used to validate the spectrometer. We have measured a resolving power R of 273 and an efficiency of 78 %. Our results demonstrate for the first time a centimeter-sized, light weight FIR spectrometer with a promising resolution, which has potential to replace the half meter-sized, heavy grating based spectrometers in this wavelength band.

With applications in cosmology, infrared astronomy and CMB survey, frequency-division multiplexing (FDM) proved to be a viable readout for transition-edge sensors (TESs). We investigate the occurrence of out-of-band resonances (OBR) which could constrain the bandwidth of the FDM readout of TES bolometers. The study includes SPICE modeling of the entire setup including the cryogenic harness, LC filters, Superconducting Quantum Interference Device (SQUID) and room-temperature amplifier. Simulation results show that the long harness (for flight model) could cause multiple reflections that generate repetitive spikes in the spectrum. Peaks of the OBR are mainly due to the parasitic capacitances at the input of SQUID. Implementing a low-pass RC circuit (snubber) at the input of the SQUID dampened the OBR. As a result, the first peak only appears around 20 MHz which is a safe margin for the 1 MHz - 3.8 MHz FDM in use in the prototype readout. Using a spectrum analyzer and broadband LNAs, we also measured the OBR for the prototype FDM readout in the laboratory up to 500 MHz. The measurement was conducted at temperatures of 50 mK and 4 K and for various biasing of the DC SQUID. It turns out that OBRs are more intense at 50 mK and are caused by the harness impedance mismatch rather than the SQUID. Simulation codes and supporting materials are available at https://github.com/githubamin/LT-Spice-Simulation-of-FDM-readout .

Large arrays of transition edge sensors (TESs) are the baseline for a number of future space observatories. For instance, the X-ray integral field unit (X-IFU) instrument on board the ATHENA space telescope will consist of $$\sim$$ ∼ 3000 TESs with high energy resolution ( $$2\,{\mathrm{eV}}$$ 2 eV at X-ray energies up to 7 keV). In this contribution we report on the development of an X-ray TES array as a backup detector technology for X-IFU. The baseline readout technology for this mission is time domain multiplexing where the detectors are DC biased. Specifically, we report on the characterization of four different Ti/Au TESs with the following dimensions ( $$\hbox {L}\times \hbox {W}$$ L × W ): $$30\times 15$$ 30 × 15 , $$30\times 30$$ 30 × 30 , $$50\times 25$$ 50 × 25 and $$50\times 50\,\mu \hbox {m}^2$$ 50 × 50 μ m 2 , all of which are coupled to a $$2.3\,\mu \hbox {m}$$ 2.3 μ m thick Au absorber of area $$240\times 240\,\mu \hbox {m}^2$$ 240 × 240 μ m 2 . We have performed our characterization using our standard frequency domain multiplexing readout connecting only pixels at low frequencies, where nonlinear effects due to the AC biasing are negligible. Promising energy resolution has been obtained, for instance $$1.78\pm 0.10\,\hbox {eV}$$ 1.78 ± 0.10 eV and $$1.75\pm 0.10\,\hbox {eV}$$ 1.75 ± 0.10 eV at 5.9 keV for the $$50\times 25$$ 50 × 25 and $$50\times 50\,\mu \hbox {m}^2$$ 50 × 50 μ m 2 detectors respectively. Uniformity over a kilo-pixel array (of detectors with the same geometry) has been also studied, confirming the high quality of our fabrication process.

Transition edge sensor (TES) microcalorimeters and bolometers are used for a variety of applications. The sensors are based on the steep temperature-dependent resistance of the normal-to-superconducting transition, and are thus intrinsically sensitive to magnetic fields. Conventionally the detectors are shielded from stray magnetic fields using external magnetic shields. However, in particular for applications with strict limits on the available space and mass of an instrument, external magnetic shields might not be enough to obtain the required shielding factors or field homogeneity. Additionally, these shields are only effective for magnetic fields generated external to the TES array, and are ineffective to mitigate the impact of internally generated magnetic fields. Here we present an alternative shielding method based on a superconducting groundplane deposited directly on the backside of the silicon nitride membrane on which the TESs are located. We demonstrate that this local shielding for external magnetic fields has a shielding factor of at the least ~ 75, and is also effective at reducing internal self-induced magnetic fields, as demonstrated by measurements and simulation of the eddy current losses in our AC biased detectors. Measurements of 5.9 keV X-ray photons show that our shielded detectors have a high resilience to external magnetic fields, showing no degradation of the energy resolution or shifts of the energy scale calibration for fields of several microTesla, values higher than expected in typical real-world applications.

We present a characterization of the sensitivity of TES X-ray micro-calorimeters to environmental conditions under frequency-domain multiplexing (FDM) readout. In the FDM scheme, each TES in a readout chain is in series with a LC band-pass filter and AC biased with an independent carrier at MHz range. Using TES arrays, cold readout circuitry and warm electronics fabricated at SRON and SQUIDs produced at VTT Finland, we characterize the sensitivity of the detectors to bias voltage, bath temperature and magnetic field. We compare our results with the requirements for the Athena X-IFU instrument, showing the compliance of the measured sensitivities. We find in particular that FDM is intrinsically insensitive to the magnetic field because of TES design and AC readout.

Future astronomical space missions in the far-infrared will utilize compact and wideband grating spectrometers. These grating spectrometers are inherently sensitive to a single polarization, enabling an efficient bandsplitting scheme, without spectral gaps, providing a large continuous wavelength coverage. The key component required is a broadband half-waveplate. In this paper we present our results of a broadband resonant halfwave plate, which satisfies the needs for such spectometers.

We have measured and characterized the thermal crosstalk in two different arrays of transition-edge sensor (TES) X-ray microcalorimeters with frequency-domain multiplexing (FDM) readout. The TES arrays are fabricated at SRON and are a 8 × 8 and a 32 × 32 “kilo-pixel” uniform array. The amount of crosstalk is evaluated as the ratio between the averaged crosstalk signal and the X-ray pulse amplitudes. The crosstalk ratios (CRs) for our detectors are compliant with the requirements for future X-ray space missions, such as Athena X-IFU (CR $< 10^{-3}$ for first-neighbor pixels): We measured a nearest neighbor thermal CR at a level of $10^{-4}$, with a highest CR of $4\times 10^{-4}$ for the kilo-pixel array (worst case, center of array) and $1\times 10^{-4}$ for the 8 × 8 array, with a margin of improvement achievable by optimizing the Cu metallization and the width of the Si supporting structures (muntins) in the backside of the TES array chip. Based on the measured CRs, we have estimated the impact on the spectral resolution by means of noise equivalent power considerations and a Monte Carlo simulation, finding an average degradation in quadrature of less than 40 meV, compliant with the <0.2 eV requirement for Athena X-IFU.

We demonstrate multiplexed readout of 43 transition edge sensor (TES) bolometers operating at 90 mK using a frequency division multiplexing (FDM) readout chain with bias frequencies ranging from 1 to 3.5 MHz and a typical frequency spacing of 32 kHz. We improve the previously reported performance of our FDM system by two important steps. First, we replace the coplanar wires with microstrip wires, which minimize the cross talk from mutual inductance. From the measured electrical cross talk (ECT) map, the ECT of all pixels is carrier leakage dominated. Only five pixels show an ECT level higher than 1%. Second, we reduce the thermal response speed of the TES detectors by a factor of 20 by increasing the heat capacity of the TES, which allows us to bias all TES detectors below 50% in transition without oscillations. We compare the current-voltage curves and noise spectra of the TESs measured in single-pixel mode and multiplexing mode. We also compare the noise equivalent power (NEP) and the saturation power of the bolometers in both modes, where 38 pixels show less than 10% difference in NEP and 5% difference in saturation power when measured in the two different modes. The measured noise spectrum is in good agreement with the simulated noise based on measured parameters from an impedance measurement, confirming that our TES is dominated by phonon noise.

In the early 2030s, ESAs new X-ray observatory, Athena, is scheduled to be launched. It will carry two main instruments, one of which is the X-ray Integral Field Unit (X-IFU), an X-ray imaging spectrometer, which will consist of an array of several thousand transition-edge sensors (TESs) with a proposed energy resolution of 2.5 eV for photon energies up to 7 keV. At SRON we develop the backup TES array based on Ti/Au bilayers with a transition temperature just below 100 mK. In this contribution we will give a broad overview of the properties and capabilities of these state-of-the-art detectors. Over the years we have fabricated and studied a large number of detectors with various geometries, providing us with a good understanding of how to precisely control the properties of our detectors. We are able to accurately vary the most important detector properties, such as the normal resistance, thermal conductance and critical temperature. This allows us to finely tune our detectors to meet the demands of various applications. The detectors have demonstrated excellent energy resolutions of below 1.8 eV for 5.9 keV X-rays. By tuning the properties of the devices, they can be optimally matched to various read-out schemes using both AC and DC biasing. The next step is to increase the size of our TES arrays from our current kilo-pixel arrays towards the full-sized array for X-IFU.

We report measured $$T_\mathrm{c}$$ of superconducting Ti/Au bilayer strips with a width W varying from 5 to 50 µm. The strips were fabricated based on a Ti/Au bilayer that consists of a 41-nm-thick Ti layer to which a 280-nm-thick Au layer was added. We find that the $$T_\mathrm{c}$$ drops as W decreases and the declining trend almost perfectly follows $$T_\mathrm{c}/[\mathrm{mK}] =-738.4[{\upmu } \mathrm{m}]^{2}/W^{2}+91.0$$ , where $$T_\mathrm{c}(W=\infty )$$ of 91 mK is consistent with the intrinsic $$T_\mathrm{c}$$ of the bilayer. The result is interpreted as a consequence of the lateral inverse proximity effect originated in normal-metal microstructures, namely Au overhangs that exist at the edges of the Ti/Au bilayer. The $$T_\mathrm{c}$$ shift from the intrinsic $$T_\mathrm{c}$$ should be anticipated in addition to the longitudinal proximity effect from superconducting Nb leads when one designs Ti/Au TESs.

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.

We are developing a kilo-pixels Ti/Au TES array as a backup option for Athena X-IFU. Here we report on single-pixel performance of a 32 × 32 array operated in a Frequency Division Multiplexing (FDM) readout system, with bias frequencies in the range 1–5 MHz. We have tested the pixels response at several photon energies, by means of a $^{55}$ Fe radioactive source (emitting Mn-K $\alpha$ at 5.9 keV) and a Modulated X-ray Source (MXS, providing Cr-K $\alpha$ at 5.4 keV and Cu-K $\alpha$ at 8.0 keV). First, we report the procedure used to perform the detector energy scale calibration, usually achieving a calibration accuracy better than $\sim$ 0.5 eV in the 5.4–8.9 keV energy range. Then, we present the measured energy resolution at the different energies (best single pixel performance: $\Delta$ E $_{\mathrm{FWHM}}$ = 2.40 $\pm$ 0.09 eV @ 5.4 keV; 2.53 $\pm$ 0.10 eV @ 5.9 keV; 2.78 $\pm$ 0.16 eV @ 8.0 keV), investigating also the performance dependency from the pixel bias frequency and the count rate. Thanks to long background measurements ( $\sim$ 1 d), we finally detected also the Al-K $\alpha$ line at 1.5 keV, generated by fluorescence inside the experimental setup. We analyzed this line to obtain a first assessment of the single-pixel performance also at low energy ( $\Delta$ E $_{\mathrm{FWHM}}$ = 1.91 eV $\pm$ 0.21 eV @ 1.5 keV), and to evaluate the linearity of the detector response in a large energy band (1.5–8.9 keV).

In the frequency-domain multiplexing (FDM) scheme, transition-edge sensors (TESs) 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 TESs, while preserving the on-resonance bias circuit and spectral performance, demonstrating its application to the FDM readout of an 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 the 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.

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 × 32 pixel array with (length × width) 140 × 30 $\mu$m$^2$ TiAu TESs, which have 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).

We demonstrate multiplexing readout of 60 transition edge sensor (TES) bolometers operating at 90 mK using a frequency division multiplexing readout chain with bias frequencies ranging from 1 to 3.5 MHz and with a typical frequency spacing of 32 kHz. The readout chain starts with a two-stage SQUID amplifier and has a noise level of 9.5 pA/Hz. We compare current–voltage curves and noise spectra of TESs measured in a single-pixel mode and in a multiplexing mode. We also map the noise equivalent power (NEP) and the saturation power of the bolometers in both modes, where there are 43 pixels that do not show more than 10% difference in NEP and 5% in saturation power when measured in single pixel and multiplex modes. We have read out a TES with an NEP of 0.45 aW/Hz in the multiplexing-mode, which demonstrates the capability of reading out ultra-low noise TES bolometer arrays for space applications.

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.