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.

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

Superconducting transition-edge sensor (TES) microcalorimeters have demonstrated the Constellation-X requirements for spectral resolution, speed, and pixel size in a close-packed geometry. We will present our recent breakthrough energy resolution with sensors that have all gold and bismuth-gold absorbers. This has been enabled by cantilevered absorbers that make contact to the TES only in regions that are not part of the active thermometer. With this approach, rapid thermalization of the x-ray energy is achieved and interaction between the absorber and TES sensor films is avoided. This design allows us to obtain uniform high performance and is compatible with large-format, high fill-factor arrays. We will discuss this design, the results we have achieved in 8×8 arrays of these pixels, and the dependence of the performance on the geometry of the absorber contact area and on stress within the sensor.

Performance of TES X-ray Microcalorimeters with a Novel Absorber Design

Development of a cryogen-free continuous ADR for the constellation-X mission

We present results on wavelength division multiplexing of radio-frequency single-electron transistors. We use a network of resonant impedance matching circuits to direct applied rf carrier waves to different transistors depending on carrier frequency. A two-channel demonstration of this concept using discrete components successfully reconstructed input signals with small levels of crosscoupling. A lithographic version of the rf circuits had measured parameters in agreement with electromagnetic modeling, with reduced crosscapacitance and inductance, and should allow 20–50 channels to be multiplexed.

Multiplexing of Radio-Frequency Single Electron Transistors

We report on the structural and electrical characterization of Mo thin films deposited at room temperature by RF magnetron sputtering. The effect of RF power on the morphology and residual stress of the films is analyzed. The films are under compressive stress and consist of densely packed columns with a lateral size on the order of 20 nm. The stress, critical temperature, and resistivity of the films are found to rise when increasing the ejected ion energy during the sputtering process. The changes in critical temperature and resistivity are discussed in terms of the observed morphology and stress changes.

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Effects of Stress and Morphology on the Resistivity and Critical Temperature of Room-Temperature-Sputtered Mo Thin Films

We are developing superconducting transition-edge sensor (TES) microcalorimeters for astronomical x-ray spectroscopy We have obtained very high energy resolution (24 eV at 15 keV and 37 eV at 33 keV) in large, isolated TES pixels using Mo/Au proximity-effect bilayers on silicon-nitride membranes several mm wide In order to be truly suitable for use behind an x-ray telescope, however, such devices need to be arrayed with a pixel size and focal-plane coverage matched to the telescope focal length and spatial resolution For the Constellation-X mission, this requires fitting the TES, its thermal link, and contact wiring into a 025 mm square, a far more compact geometry than has previously been investigated We have demonstrated that the weak thermal link can be restricted to a narrow (∼10 micron) perimeter of membrane around the TES and still provide a thermal conductance in the acceptable range Varying the size and placement of slits in that nitride perimeter, we can tune that value

Arraying compact pixels of transition-edge microcalorimeters for imaging x-ray spectroscopy

We are developing X-ray calorimeters to meet the specifications of the Constellation-X mission. Each calorimeter consists of a transition-edge-sensor (TES) thermometer, which is suspended on a silicon-nitride membrane. Our TES thermometers are Mo/Au bilayer films that are biased in the sharp phase transition between the superconducting and normal-metal states. These calorimeters have demonstrated very good energy resolutions: 2.4 eV at 1.5 keV and 3.7 eV at 3.3 keV. The energy resolutions are limited by thermal noise and Johnson noise (which are intrinsic to any resistive calorimeter) plus excess noise. The excess noise, which is several times larger than the Johnson noise, is consistent with frequency-independent voltage noise in the TES. Detailed measurements of one Mo/Au TES demonstrate that the excess noise is independent of the voltage applied to the TES over a range of biases at the same TES resistance. The magnitude of the excess noise is smallest at the high-resistance end of the phase transition. We also compared noise in square Mo/Au TES’s ranging in size from 300 microns to 600 microns to learn how the excess noise is affected by the geometry of the TES.

Performance of Mo/Au TES microcalorimeters

We present fabrication details of our Mo/Au X-ray microcalorimeters, which are being developed as one of the candidate high resolution spectrometers for the Constellation-X mission. We have reproducibly fabricated Mo/Au transition-edge sensors with Tc's of /spl sim/100 mK on etched silicon nitride membranes and connected via superconducting Nb leads. Our single pixel devices have, so far, attained resolution of 3.7 eV at 3.3 keV. We also discuss our plans for fabrication and testing of fully functional multi-pixel array of X-ray microcalorimeters.

Fabrication of Mo/Au transition-edge sensors for X-ray spectrometry

We are optimizing Mo/Au transition-edge-sensor (TES) calorimeters to meet the specifications of NASA’s Constellation-X mission. Our calorimeters have already demonstrated very good energy resolution of X rays (2.4 eV at 1.5 keV). We wish to further improve the energy resolution by reducing excess noise in the calorimeters. Development of a detailed model and understanding of the noise is instrumental to reaching this goal. Towards that end, we employ a linear model that describes the response of a calorimeter to signal and various sources of noise. The model is based on detailed measurements of the parameters that affect the calorimeter’s performance, such as current-voltage characteristics of the TES, thermal conductance of our silicon-nitride membranes, and inductance in the electronic circuit used to bias the TES. We determine the sharpness of the superconducting phase transition by fitting the model to the measured responsivity of the calorimeter. The model relates sources of noise, such as phonon noi...

Detailed characterization of Mo/Au TES microcalorimeters

In the X-ray astrophysics community, the desire for wide- field, high-resolution, X-ray imaging spectrometers has been growing for some time. We present a concept for such a detector called a Position-Sensing Transition-edge sensor (PoST). A PoST is a calorimeter consisting of two Transition- Edge Sensors (TESs) on the ends of a long absorber to do one dimensional imaging spectroscopy. Comparing the rise time and energy estimates obtained from each TES for a given event, the position of that event in the PoST is determined. Energy is inferred from the sum of the two signals on the TESs. We have designed 7, 15, and 32 pixel PoSTs using our Mo/Au TESs and bismuth absorbers. We discuss the theory, modeling, operation and readout of PoSTs and the latest results from our development.

Nilesh Tralshawala

Papers

Arraying compact pixels of transition-edge microcalorimeters for imaging x-ray spectroscopy

Performance of Mo/Au TES microcalorimeters

Fabrication of Mo/Au transition-edge sensors for X-ray spectrometry

Detailed characterization of Mo/Au TES microcalorimeters

Position-sensing transition-edge sensors for large-field high-energy-resolution x-ray imaging spectroscopy