The current noise at the output of a microcalorimeter with a voltage biased superconducting transition edge thermometer is studied in detail. In addition to the two well-known noise sources: thermal fluctuation noise from the heat link to the bath and Johnson noise from the resistive thermometer, a third noise source strongly correlated with the steepness of the thermometer is required to fit the measured noise spectra. Thermal fluctuation noise, originating in the thermometer itself, fully explains the additional noise. A simple model provides quantitative agreement between the observed and calculated noise spectra for all bias points in the superconducting transition.

We studied the phonon transport in free-standing 1μm thick silicon-nitride membranes at temperatures around 100 mK. By varying the geometry of the membranes and the dimensions of the heater element, we are able to distinguish between radiative and diffuse phonon transport. The data indicate that the transport is radiative ballistic with a lower limit to a phonon mean-free path of about 1 mm and that the probability for specular reflection from the surface is at least 0.99. The tested silicon-nitride membranes were grown on Si(100), Si(110), and polycrystalline-Si and the transport properties show no dependency on the substrate.

The SAFARI instrument is a far-infrared imaging Fourier transform spectrometer for JAXA's SPICA mission. Taking advantage of the low emission of SPICA's 5 K telescope, SAFARI will provide sky background-limited, Nyquist-sampled spectroscopic imaging of a 2 2 field-of-view over 34-210 m, creating significant new possibilities for far-infrared astronomy. SAFARI's aggressive science goals drive the development of a unique detector system combining large-format Transition Edge Sensor arrays and frequency division multiplexed SQUID readout with a high 160 multiplexing factor. The detectors and their cold readout electronics are packaged into 3 focal plane arrays that will be integrated into SAFARI's focal plane unit. Here we present the preliminary system design and current development status of the SAFARI detector system.

High-T c GdBa 2 Cu 3 O 7Ϫ␦ superconductor bolometers with operation temperatures near 89 K, large receiving areas of 0.95 mm 2 and very high detectivity have been made. The bolometers are supported by 0.62 m thick silicon nitride membranes. A specially developed silicon-on-nitride layer was used to enable the epitaxial growth of the high-T c superconductor. Using a gold black absorption layer an absorption efficiency for wavelengths between 70 and 200 m of about 83% has been established. The noise of the best devices is fully dominated by the intrinsic phonon noise of the thermal conductance G, and not by the 1/f noise of the superconducting film. The temperature dependence of the noise and the resulting optimum bias temperature have been investigated. In the analysis the often neglected effect of electrothermal feedback has been taken into account. The minimum electrical noise equivalent power ͑NEP͒ of a bolometer with a time constant of 95 ms is 2.9 pW/Hz 1/2 which corresponds with an electrical detectivity D* of 3.4ϫ10 10 cm Hz 1/2 /W. Similar bolometers with ϭ27 ms and NEPϭ3.8 pW/Hz 1/2 were also made. No degradation of the bolometers could be observed after vibration tests, thermal cycling and half a year storage. Measurements of the noise of a Pr doped YBa 2 Cu 3 O 7Ϫ␦ film with T c ϭ40 K show that with such films the performance of air bridge type high-T c bolometers could be improved.

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We report the experimental evidence of the ac Josephson effect in a transition edge sensor (TES) operating in a frequency domain multiplexer and biased by ac voltage at MHz frequencies. The effect is observed by measuring the non-linear impedance of the sensor. The TES is treated as a weakly-linked superconducting system and within the resistively shunted junction model framework. We provide a full theoretical explanation of the results by finding the analytic solution of the non-inertial Langevian equation of the system and calculating the non-linear response of the detector to a large ac bias current in the presence of noise.Superconducting transition-edge sensors (TESs) are highly sensitive thermometers widely used as radiation detectors over an energy range from near infrared to gamma rays. In particular we are developing TESbased detectors for the infrared SAFARI/SPICA 1 and the X-ray XIFU/Athena 2 instruments. TESs are in most cases low impedance devices that operate in the voltage bias regime while the current is generally read-out by a SQUID current amplifier. Both a constant or an alternating bias voltage can be used 3,4 . In the latter case changes of the TES resistance induced by the thermal signal modulate the amplitude of the ac bias current. The small signal detector response is modelled in great details both under dc and ac bias 5,6 . Those models however do not fully explain all the physical phenomena recently observed in TESs. It has been recently demonstrated that TES-based devices behave as weak-links due to longitudinally induced superconductivity from the leads via the proximity effect 7 and a detailed experimental investigation of the weak-link effects in dc biased x-ray microcalorimeters has been reported 8 . Evidence of weaklink effects in ac biased TES microcalorimeters has been given 9 , but an adequate experimental and theoretical investigation is still missing. We previously proposed a theoretical framework 10 based on the resistively shunted junction model (RSJ) that can be used to describe the resistive state of a TES under dc bias. In this letter, we extend the model to calculate the stationary non-linear response of a TES to a large ac bias current in the presence of noise and we compare it to the experimental data obtained with a TES-based bolometer. We report a clear signature of the ac-Josephson effect in the TES biased at MHz frequencies.The general equation for the Frequency Domain Multiplexing (FDM) electrical circuit, simplified for a single a) Electronic mail: l.gottardi@sron.nl resonator is 6(1) where V (t) is the total voltage across the TES, L and C are respectively the inductance and the capacitance of the bias circuit, r s is the total stray resistance in the circuit and Z T ES is the TES impedance, which depends on temperature T and current I(t). As previously reported 8,11 , the superconducting leads proximitize the TES bilayer film over a distance defined by the coherence length ξ. As a result, the superconducting order parameter |Ψ| is spatially dependent over the ...

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 α and β , 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.

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