edfas.org ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 25 NO. 4 6 TES. Negative electrical-thermal feedback then balances the device at the desired point on the superconducting transition. A heating event such as the absorption of an x-ray photon causes a brief reduction in the electrical current through the device, lasting typically a few milliseconds or less. Figure 3 shows the operating concept of a TES. Pulses in the TES current are the signatures of a photon detection; the amplitude of the pulse indicates the photon’s energy. TESs with energy-resolving powers of 2000 and higher have been demonstrated at x-ray energies from near 1 keV[5] up to at least 12 keV,[6] as well as for gamma rays in the range of 100 keV[7] and even for alpha particles with energies of several MeV.[8] (An energy resolving power of 2000 implies a relative uncertainty of 0.05 %.) Once fabricated, a TES operates only at a specific temperature, that of its superconducting phase transition. Thanks to the properties of metallic thin films, it is possible to select the transition temperature of materials that combine a superconductor with a normal metal. Thin-film bilayers of molybdenum with either gold or copper can be produced having a range of transition temperatures up to 1K (the transition temperature of bulk Mo), with the temperature engineered to match the available cryogenic cooling system. A layer of high-Z material such as gold or bismuth is often placed near (and thermally connected to) the TES to improve the calorimeter’s efficiency for absorption of x-ray photons. Thermal fluctuations are the dominant source of noise in a well-designed TES, so the energy resolution is optimized by designing them for the coldest achievable operating temperature. We typically work with detectors in the range of 20 to 140 mK, temperatures accessible to some commercial refrigerators that offer automated operation without using liquid cryogens. The fundamental advantage of a microcalorimeter such as the TES over other technologies for x-ray detection is its extremely high energy resolution. The resolution is as good as that of any but the best diffraction-based wavelength-dispersive spectrometers. In addition, the ability to measure the entire spectral band at once means that measurement throughput exceeds that of most highresolution analyzers. TESs must be made small, however, to minimize their heat capacity and maximize their resolving power. To accelerate measurements with TESs, we employ arrays of hundreds of sensors (Fig. 2, right). Considerations of both thermal loading and system complexity mean we cannot realisti- cally connect thousands of wires from room temperature directly to a sensor array at subKelvin temperatures. Instead, multiplexing readout systems must be used. Many TES applications have used time-division multiplexing: an amplifier chain based on superconducting quantum interference devices (SQUIDs),[9] Fig. 2, left, cycles through dozens of sensors in a time-shared manner. In a more recent development, a frequency-domain multiplexing system built upon microwave SQUIDs delivers even higher multiplexing factors and/or wider readout bandwidth for each detector. Such systems have been demonstrated to multiplex 250 TESs onto a single radio-frequency transmission line.[10] Arrays of TES microcalori- meters have been developed Fig. 3 The TES detection concept. Top left: Photons are absorbed on a microcalorimeter, a small island of low heat capacity containing the TES thermometer. Top right: In the transition, the TES resistance is a very steep function of its temperature. Bottom left: Absorption of a photon causes a transient pulse in the temperature and a corresponding reduction in the bias current. Bottom right: This dip in current is the signal; the size of the pulse indicates the x-ray energy.
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