Modelling the resistive state in a transition edge sensor

Abstract

We have developed a model for the resistive transition in a transition edge sensor (TES) based on the model of a resistively and capacitively shunted junction, taking into account phase-slips of a superconducting system across the barriers of the tilted washing board potential. We obtained analytical expressions for the resistance of the TES, R(T, I), and its partial logarithmic derivatives αI and βI as functions of temperature and current. We have shown that all the major parameters describing the resistive state of the TES are determined by the dependence on temperature of the Josephson critical current, rather than by intrinsic properties of the S-N transition. The complex impedance of a pristine TES exhibits two-pole behaviour due to its own intrinsic reactance.

Small Pitch Transition-Edge Sensors with Broadband High Spectral Resolution for Solar Physics

“…Figure 4b presents the measured I C (T ) for a single 35 µm TES and a 140 µm TES. Assuming a Resistively Shunted Junction R(T , I ) model of a TES [20], we can derive a simple relation for α/β [16]:…”

Proximity effect model for x-ray transition edge sensors

“…Using a proximity effect model of a TES we can calculate parameters that can be compared with experimental measurements, and the procedure for this is shown in Figure 1. Our model 20 is based on the numerical solution by iteration of the Usadel equations 21,22 in conjunction with the self-consistency equation, subject to appropriate boundary conditions. 23 The other inputs to the model are the sensor dimensions and the material parameters.…”

Modelling the Resistive State in a Transition Edge Sensor

“…It can be shown that in the range of frequencies where Z T ES (ω) significantly differs from Z 0 T ES (ω) frequency dependencies of £ 0 (ω) and τ eff (ω) can be neglected. As a result the expression (5) becomes [7] Figure 3(b) shows the calculated impedance at a constant TES current at different temperatures, illustrating the effect of the second higher frequency pole. The numbers are chosen for illustrative purposes only and the curves sequence does not reflect any experiment imposing specific constraints on TES temperature, current or bath temperature.…”

“…In our recent work [7] we proposed to describe the resistive state of TES within the model of resistively shunted conductive junction (RSJ). TES is a special kind of weak superconducting link designed with Andreev mirrors at the lead/TES interfaces to prevent energy leak into leads.…”