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

TL;DR

This paper derives analytical solutions for the complex impedance, responsivity, and noise of transition-edge sensors using two- and three-block thermal models, providing insights beyond the simple single heat capacity model.

Contribution

It introduces analytical solutions for the impedance, responsivity, and noise of TES with more complex thermal models involving multiple heat capacities.

Findings

Analytical expressions for impedance, responsivity, and noise in two- and three-block models.

Differences between simple and complex thermal models are discussed.

Implications for TES design and analysis are highlighted.

Abstract

The responsivity and noise of a voltage-biased superconducting transition-edge sensor depends strongly on the details of its thermal model, and the simplest theory for TES response assumes a single heat capacity connected to the heat bath. Here, analytical results are derived and discussed for the complex impedance, the responsivity and the noise of a transition-edge sensor, when the thermal model is not simple but consists of either two or three connected heat capacities. The implications of the differences of the models are discussed, as well.