We have found experimentally that the critical current of a square superconducting transition-edge sensor (TES) depends exponentially upon the side length L and the square root of the temperature T . As a consequence, the effective transition temperature Tc of the TES is current-dependent and at fixed current scales as 1/L 2 . We also have found that the critical current can show clear Fraunhoferlike oscillations in an applied magnetic field, similar to those found in Josephson junctions. The observed behavior has a natural theoretical explanation in terms of longitudinal proximity effects if the TES is regarded as a weak link between superconducting leads. We have observed the proximity effect in these devices over extraordinarily long lengths exceeding 100 µm.PACS numbers: 74.78.Bz,74.25.Op A superconductor cooled through its transition temperature T c while carrying a finite dc bias current undergoes an abrupt decrease in electrical resistance from its normal-state value R N to zero.Superconducting transition-edge sensors (TESs) exploit this sharp transition; these devices are highly sensitive resistive thermometers used for precise thermal energy measurements. 1 TES microcalorimeters have been developed with measured energy resolutions in the X-ray and gamma-ray band of ∆E = 1.8±0.2 eV FWHM at 6 keV, 2 and ∆E = 22 eV FWHM at 97 keV, 3 respectively-with the latter result at present the largest reported E/∆E of any non-dispersive photon spectrometer. TESs are successfully used across much of the electromagnetic spectrum, measuring the energy of single-photon absorption events from infrared to gamma-ray energies and photon fluxes out to the microwave range. 1 Despite these experimental successes, the dominant physics governing TESs biased in the superconducting phase transition remains poorly understood. 1 To achieve high energy resolution it is important to control both the TES's T c and its transition width ∆T c . Because the energy resolution of calorimeters improves with decreasing temperature, they are typically designed to operate at temperatures around 0.1 K. For a TES, this requires a superconductor with T c in that range. While there exist a few suitable elemental superconductors, the best results have been achieved using proximitycoupled, superconductor/normal-metal (S/N) bilayers 2,3 , for which T c is tuned by selection of the thicknesses of the S and N layers. 4 There have been a variety of models 4-8 used to explain the noise, T c , and ∆T c in TES bilayers, all assuming spatially uniform devices. Though some have been shown to be consistent with certain aspects of particular devices, they do not explain measured T c and ∆T c in S/N bilayer TESs generally.In this paper we emphasize the importance of a phenomenon that so far has been neglected in previous theoretical studies of TESs: the longitudinal proximity effect.Since the square bilayers at the heart of the TES are connected at opposite ends to superconducting leads with transition temperatures well above the intrinsic transition temperatur...

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 measurements of Mol Au bilayer test structures show that they act as weak superconducting links, exhibiting oscillatory, Fraunhofer-like

We have recently shown that normal-metal/superconductor (N/S) bilayer TESs (superconducting Transition-Edge Sensors) exhibit weak-link behavior. 1 Here we extend our understanding to include TESs with added noise-mitigating normal-metal structures (N structures). We find TESs with added Au structures also exhibit weak-link behavior as evidenced by 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 µm 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 inplane 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 × 10 −10 s for the bilayer. The LoPE model is also used to explain the increased conductivity at temperatures above the bilayer's steep resistive transition.