Simon R. Bandler

Impedance measurements and modeling of a transition-edge-sensor calorimeter

We describe a method for measuring the complex impedance of transition-edge-sensor (TES) calorimeters. Using this technique, we measured the impedance of a Mo/Au superconducting transition-edge-sensor calorimeter. The impedance data are in good agreement with our linear calorimeter model. From these measurements, we obtained measurements of unprecedented accuracy of the heat capacity and the gradient of resistance with respect to temperature and current of a TES calorimeter throughout the phase transition. The measurements probe the internal state of the superconductor in the phase transition and are useful for characterizing the calorimeter.

Longitudinal Proximity Effects in Superconducting Transition-Edge Sensors

We have found experimentally that the critical current of a square thin-film superconducting transition-edge sensor (TES) depends exponentially upon the side length L and the square root of the temperature T, a behavior that has a natural theoretical explanation in terms of longitudinal proximity effects if the TES is regarded as a weak link between superconducting leads. As a consequence, the effective transition temperature T{c} of the TES is current dependent and at fixed current scales as 1/L{2}. We have also found that the critical current can show clear Fraunhofer-like oscillations in an applied magnetic field, similar to those found in Josephson junctions. We have observed the longitudinal proximity effect in these devices over extraordinarily long lengths up to 290 microm, 1450 times the mean-free path.

Emission-Line Intensity Ratios in Fe XVII Observed with a Microcalorimeter on an Electron Beam Ion Trap

We report new observations of emission line intensity ratios of Fe XVII under controlled experimental conditions, using the National Institute of Standards and Technology electron beam ion trap (EBIT) with a microcalorimeter detector. We compare our observations with collisional-radiative models using atomic data computed in distorted wave and R-matrix approximations, which follow the transfer of the polarization of level populations through radiative cascades. Our results for the intensity ratio of the 2p6 1S0-2p53d 1P1 15.014 A line to the 2p6 1S0-2p53d 3D1 15.265 A line are 2.94 ± 0.18 and 2.50 ± 0.13 at beam energies of 900 and 1250 eV, respectively. These results are not consistent with collisional-radiative models and support conclusions from earlier EBIT work at the Lawrence Livermore National Laboratory that the degree of resonance scattering in the solar 15.014 A line has been overestimated in previous analyses. Further observations assess the intensity ratio of the three lines between the 2p6-2p53s configurations to the three lines between the 2p6-2p53d configurations. Both R-matrix and distorted wave approximations agree with each other and our experimental results much better than most solar and stellar observations, suggesting that other processes not present in our experiment must play a role in forming the Fe XVII spectrum in solar and astrophysical plasmas.

Close-packed arrays of transition-edge x-ray microcalorimeters with high spectral resolution at 5.9 keV

We present measurements of high fill-factor arrays of superconducting transition-edge x-ray microcalorimeters designed to provide rapid thermalization of the x-ray energy. We designed an x-ray absorber that is cantilevered over the sensitive part of the thermometer itself, making contact only at normal-metal features. With absorbers made of electroplated gold, we have demonstrated an energy resolution between 2.4 and 3.1 eV at 5.9 keV on 13 separate pixels. We have determined the thermal and electrical parameters of the devices throughout the superconducting transition and, using these parameters, have modeled all aspects of the detector performance.

Proximity effects and nonequilibrium superconductivity in transition-edge sensors

We have recently shown that normal-metal/superconductor (N/S) bilayer superconducting transition-edge sensors (TESs) exhibit weak-link behavior.(1) Here, we extend our understanding to include TESs with added noise-mitigating normal-metal structures (N structures). We find that TESs with added Au structures also exhibit weak-link behavior as evidenced by the exponential temperature dependence of the critical current and Josephson-like oscillations of the critical current with applied magnetic field. We explain our results in terms of an effect converse to the longitudinal proximity effect (LoPE),(1) the lateral inverse proximity effect (LaiPE), for which the order parameter in the N/S bilayer is reduced due to the neighboring N structures. Resistance and critical current measurements are presented as a function of temperature and magnetic field taken on square Mo/Au bilayer TESs with lengths ranging from 8 to 130 mu m with and without added N structures. We observe the inverse proximity effect on the bilayer over in-plane distances many tens of microns and find the transition shifts to lower temperatures scale approximately as the inverse square of the in-plane N-structure separation distance, without appreciable broadening of the transition width. We also present evidence for nonequilbrium superconductivity and estimate a quasiparticle lifetime of 1.8 x 10(-10) s for the bilayer. The LoPE model is also used to explain the increased conductivity at temperatures above the bilayers steep resistive transition.

Advances in Small Pixel TES-Based X-Ray Microcalorimeter Arrays for Solar Physics and Astrophysics

We are developing small-pixel transition-edge sensor microcalorimeters for solar physics and astrophysics applications. These large format close-packed arrays are fabricated on solid silicon substrates and are designed to have high energy resolution, and also accommodate count-rates of up to a few hundred counts per second per pixel for X-ray photon energies up to ~ 8 keV. We have fabricated kilo-pixel versions that utilize narrow-line planar and stripline wiring. These arrays have a low superconducting transition temperature, which results in a low heat capacity and low thermal conductance to the heat sink. We present measurements of the performance of pixels with single 65-μm absorbers on a 75-μm pitch. With individual single pixels of this type, we have achieved a full-width at half-maximum energy resolution of 0.9 eV with 1.5 keV Al K X-rays, to our knowledge the first X-ray microcalorimeter with sub-eV energy resolution. We will discuss the properties of these arrays and their application to new solar and astrophysics mission concepts.

Laboratory Astrophysics Survey of Key X-Ray Diagnostic Lines Using A Microcalorimeter on an Electron Beam Ion Trap

Cosmic plasma conditions created in an electron beam ion trap (EBIT) make it possible to simulate the dependencies of key diagnostic X-ray lines on density, temperature, and excitation conditions that exist in astrophysical sources. We used a microcalorimeter for such laboratory astrophysics studies because it has a resolving power ≈1000, quantum efficiency approaching 100%, and a bandwidth that spans the X-ray energies from 0.2 keV to 10 keV. Our microcalorimeter, coupled with an X-ray optic to increase the effective solid angle, provides a significant new capability for laboratory astrophysics measurements. Broadband spectra obtained from the National Institute of Standards and Technology EBIT with an energy resolution approaching that of a Bragg crystal spectrometer are presented for nitrogen, oxygen, neon, argon, and krypton in various stages of ionization. We have compared the measured line intensities to theoretical predictions for an EBIT plasma.

The X-Ray Surveyor Mission: A Concept Study

NASAs Chandra X-ray Observatory continues to provide an unparalleled means for exploring the high-energy universe. With its half-arcsecond angular resolution, Chandra studies have deepened our understanding of galaxy clusters, active galactic nuclei, galaxies, supernova remnants, neutron stars, black holes, and solar system objects. As we look beyond Chandra, it is clear that comparable or even better angular resolution with greatly increased photon throughput is essential to address ever more demanding science questions—such as the formation and growth of black hole seeds at very high redshifts; the emergence of the first galaxy groups; and details of feedback over a large range of scales from galaxies to galaxy clusters. Recently, we initiated a concept study for such a mission, dubbed X-ray Surveyor. The X-ray Surveyor strawman payload is comprised of a high-resolution mirror assembly and an instrument set, which may include an X-ray microcalorimeter, a high-definition imager, and a dispersive grating spectrometer and its readout. The mirror assembly will consist of highly nested, thin, grazing-incidence mirrors, for which a number of technical approaches are currently under development—including adjustable X-ray optics, differential deposition, and new polishing techniques applied to a variety of substrates. This study benefits from previous studies of large missions carried out over the past two decades and, in most areas, points to mission requirements no more stringent than those of Chandra.

Implications of weak-link behavior on the performance of Mo/Au bilayer transition-edge sensors

Understanding the physical properties of the superconducting-to-normal transition is fundamental for optimizing the design and performance of transition-edge sensors (TESs). Recent critical current IC measurements of square Mo/Au bilayer structures show that they act as weak superconducting links, exhibiting oscillatory, Fraunhofer-like behavior with applied magnetic field. In this paper, we investigate the implications of this behavior for TES x-ray detectors operated in the resistive transition. These devices include normal metal features used for absorber attachment and suppression of detector noise. We present extensive measurements of IC as a function of temperature T and field B, which show a complex temperature and current evolution when compared with the behavior expected from a simple geometry. We introduce a resistively shunted junction model for describing the TES resistive transition as a function of current I, temperature T, and magnetic field B. From this model, we calculate the R(T,I,B) tra...

Transition-Edge Sensor Pixel Parameter Design of the Microcalorimeter Array for the X-Ray Integral Field Unit on Athena

The focal plane of the X-ray integral field unit (X-IFU) for ESA’s Athena X-ray observatory will consist of ~ 4000 transition edge sensor (TES) x-ray microcalorimeters optimized for the energy range of 0.2 to 12 keV. The instrument will provide unprecedented spectral resolution of ~ 2.5 eV at energies of up to 7 keV and will accommodate photon fluxes of 1 mCrab (90 cps) for point source observations. The baseline configuration is a uniform large pixel array (LPA) of 4.28” pixels that is read out using frequency domain multiplexing (FDM). However, an alternative configuration under study incorporates an 18 × 18 small pixel array (SPA) of 2” pixels in the central ~ 36” region. This hybrid array configuration could be designed to accommodate higher fluxes of up to 10 mCrab (900 cps) or alternately for improved spectral performance (< 1.5 eV) at low count-rates. In this paper we report on the TES pixel designs that are being optimized to meet these proposed LPA and SPA configurations. In particular we describe details of how important TES parameters are chosen to meet the specific mission criteria such as energy resolution, count-rate and quantum efficiency, and highlight performance trade-offs between designs. The basis of the pixel parameter selection is discussed in the context of existing TES arrays that are being developed for solar and x-ray astronomy applications. We describe the latest results on DC biased diagnostic arrays as well as large format kilo-pixel arrays and discuss the technical challenges associated with integrating different array types on to a single detector die.