Modelling the electro-thermal response of superconducting transition-edge X-ray sensors

A two-temperature model for simulating the electrothermal response of superconducting transition-edge sensor (TES) X-ray detectors is presented. The model considers that the absorber and the superconducting layer (SL) of the detector are at different temperatures. The time constants within the absorber and the SL are assumed to be much smaller than all remaining time constants of the TES. The time dependences of the current through the SL, the temperature of the absorber, and the temperature of the SL after the absorption of single photons of different energy are found by numerically solving a set of nonlinear differential equations. In order to verify the model, a calculated current transient is compared with a previously measured pulse. Exploring the parameter space defined by appropriate ratios of electro-thermal time constants, we derive constraints for the asymptotically stable, oscillation-free operation of a TES.