Analysis of Impedance and Noise Data of an X-Ray Transition-Edge Sensor Using Complex Thermal Models

Abstract

The so-called excess noise limits the energy resolution of transition-edge sensor (TES) detectors, and its physical origin has been unclear, with many competing models proposed. Here we present the noise and impedance data analysis of a rectangular X-ray Ti/Au TES fabricated at SRON. To account for all the major features in the impedance and noise data simultaneously, we have used a thermal model consisting of three blocks of heat capacities, whereas a two-block model is clearly insufficient. The implication is that, for these detectors, the excess noise is simply thermal fluctuation noise of the internal parts of the device. Equations for the impedance and noise for a three-block model are also given.

Complex impedance, responsivity and noise of transition-edge sensors: Analytical solutions for two- and three-block thermal models

“…[7][8][9]14 The formalism is kept general so that we do not need to decide on the physical picture a priori.…”

“…Sometimes this thermal model is fairly adequate in describing the detector response, 3 but some detector designs have been experimentally shown to behave in a more complex manner. [4][5][6][7][8][9] Therefore, theoretical modeling has been advanced in recent years to include more complex thermal circuits. 4,5,[10][11][12][13][14][15] One way to approach the problem is to generalize the problem fully to any number of heat capacity blocks and thermal conductances, and solve the obtained (large) linearized system of equations numerically.…”

“…The goal of the present work is thus to give an extensive set of equations for the responsivity, current noise and impedance in a compact and usable form, which can easily be used to analyze real noise and impedance data of TES detectors. 8,9 We also give many example plots to show how various thermal parameters affect the detector properties. Detailed discussion on the noise equivalent power, energy resolution and other figures of merit are left for future publications.…”

Normal metal-superconductor decoupling as a source of thermal fluctuation noise in transition-edge sensors

“…The Joule power of the TES bias current is all assumed to be dissipated inside C T ES . In real X-ray and γ-ray devices with thick absorbers on top of the TES film 14,20,24 , C 1 could well be the absorber, in which case g T ES,1 describes the thermal conduction within the TES and the absorber. In devices without an absorber (most samples in this work), the idea is to model electronic degrees of freedom, thus g T ES,1 models the thermal conduction within the TES film.…”

“…This was later shown to influence the Johnson noise directly 13 , and some of the excess noise could then be explained as non-equilibrium Johnson noise. In addition, it has become clear that for many detectors, the simplest thermal circuit of one heat capacity connected to heat bath through one thermal conductance is not adequate 7,[14][15][16][17]19,20 . A more complex thermal circuit then adds new components to the thermal fluctuation part of the noise spectrum 5,21,22 .…”