Microcalorimetry and the transition-edge sensor

Abstract

Many scientific and industrial applications call for quantum-efficient high-energy-resolution microcalorimeters for the measurement of x rays. The applications driving the development of these detectors involve the measurement of faint sources of x rays in which few photons reach the detector. Interesting astrophysical applications for these microcalorimeters include the measurement of composition and temperatures of stellar atmospheres and diffuse interstellar plasmas. Other applications of microcalorimeter technology include xray fluorescence (XRF) measurements of industrial or scientific samples. We are attempting to develop microcalorimeters with energy resolutions of several eV because many sources (such as celestial plasmas) contain combinations of elements producing emission lines spaced only a few eV apart. Our microcalorimeters consist of a metal-film absorber (250 µm × 250µm × 3 µm of copper) coupled to a superconducting transitionedge-sensor (TES) thermometer. This microcalorimeter demonstrated an energy resolution of 42 eV (FWHM) at 6 keV, excellent linearity, and showed no evidence of position dependent response. The response of our microcalorimeters depends both on the temperature of the microcalorimeter and on the electrical current conducted through the TES thermometer. We present a microcalorimeter model that extends previous microcalorimeter theory to include additional current dependent effects. The model makes predictions about the effects of various forms of noise. In addition, the model helps us to understand what measurements are useful for characterizing TES microcalorimeters. While the energy resolution we obtained was quite good (twice as good as conventional semiconductor-based x-ray detectors), the obtained resolution was not as good as expected, due to excess noise from fluctuations in the TES thermometer. The energy resolution of future TES microcalorimeters can be improved by redesigning the calorimeters to minimize the noise due to these fluctuations.

Complex Impedance and Equivalent Bolometer Analysis of a Low Noise Bolometer for SAFARI

“…The thermal conductances of the links G and G TES in the model combine is to give G 0 . The remaining parameters, including, and heat capacities can be found by measuring the complex impedance of the TES bolometer [3]. In impedance measurements, a small ac stimulus is added to the bias of the bolometer and the resulting current through the TES is measured as a function of frequency.…”

“…Coefficients of the linearized differential equations of the model are represented using the usual matrix formulation [3,4]. (1) The heat capacity of the electrons in the TES is represented by C TES .…”

“…The temperatures of bodies are evenly distributed between the bath, typically at 30 mK, and the temperature of the TES, typically near 100 mK. Noise due to the thermal couplings, resistors, and other sources can be easily added to the model, and the matrix can be inverted to find the response of the bolometer to these [3,4].…”

Thermal models and noise in transition edge sensors

“…A key feature of our approach to modeling TES noise is the small-signal matrix formulation described by Lindeman 5,6 and Figueroa-Feliciano. 7 We have previously used the same scheme to interpret frequency-dependent impedance data, and thus to understand responsivity and response saturation.…”

Modelling and reduction of noise in transition edge sensor detectors

“…A key feature of our approach to modelling non-ideal noise has been the small-signal matrix formulation described by Lindeman 6,7 and Figueroa-Feliciano. 8 We have previously used the scheme to interpret impedance data and thus to understand responsivity and response-saturation.…”