A two-dimensional resistor network model for transition-edge sensors with normal metal features

Transition-edge sensors (TESs) can be used in high-resolution photon detection, exploiting the steep slope of the resistance in the superconducting-to-normal transition edge. Normal metal bars on the TES film are commonly used to engineer its transition shape, namely the dependence of resistance on temperature and current. This problem has been studied in one-dimension, however until now, there have been no predictive models of the influence of two-dimensional (2D) normal metal features on the TES transition shape. In this work, we approach this problem by treating the TES as a 2D network of resistors, the values of which are based on the two-fluid model. We present a study of the behavior of devices with different 2D geometric features. Our 2D network model is capable of predicting how typical TES geometry parameters, such as number of bars, bar spacing, and overall dimensions, influence device behavior and thus is a powerful tool to guide the engineering of new TES devices.