Study of TES-Based Microcalorimeters of Different Size and Geometry Under AC Bias

Frequency-division multiplexing (FDM) is the current baseline read-out system for the large array of superconducting transition edge sensors (TES's) under development for the X-ray instrument XIFU (Athena). In this multiplexing scheme the sensor operates as amplitude modulator of a MHz carrier. To achieve the best performance with these and similar instruments the detector physics and its interaction with the read-out circuit needs to be better understood. In particular we need an explanation for the dependence of the TES microcalorimeter nonlinear impedance on the bias point, because it directly affects the choice of the detector optimal working point. With the TES microcalorimeters fabricated at NASA-Goddard we observe current steps in the amplitude of the uncalibrated IV characteristics when the detectors are read-out in the frequency domain and are biased in the low-resistance part of the superconducting transition. In this paper, we report on the characterization under FDM of NASA-Goddard TES microcalorimeters under development for the XIFU instrument. We have measured several pixels with different size and geometry in the bias frequency range from 1 to 4 MHz and at different bath temperatures. The results will be discussed within the recently developed weak-link theoretical framework.