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Athena is an ESA-led space telescope to be launched in the early 2030s. The X-ray Integral Field Unit (X-IFU) on board of the Athena mission is an X-ray imaging spectrometer, sensitive to 0.2-12 keV X-rays. The main sensor of the X-IFU is an array of ~3200 closely-packed superconducting transition-edge sensor (TES) microcalorimeters with X-ray absorbers. The X-IFU provides a breakthrough spectral resolution of 2.5 eV (full width at half maximum; FWHM) at 6 keV, which enables us to access unrevealed properties of the hot gases that are formed at every level of the hierarchical structure of the universe. At SRON, we are developing Frequency Division Multiplexing (FDM) readout with SQUID amplifiers as a baseline technology for the X-IFU. In the FDM system, the microcalorimeter pixels are AC-biased at different frequencies from 1 to 5 MHz. Therefore, it is crucial to minimize frequency-dependent phenomena because it causes non-linearity effects in the detector response and degrades the spectral resolution. Theoretical analyses have shown that this non-linearity is caused by weak-link behavior, induced by superconducting leads and can be mitigated by increasing the normal resistance of the TES. We are also developing TES arrays based on a superconducting Ti/Au bi-layer with an Au absorber as a sensor backup technology for the X-IFU. We have recently fabricated TES calorimeters with large variation of normal resistance from 25 to 150 mΩ by changing the width and aspect ratio of the bi-layer. The TESes with 117 and 150 mΩ have shown a promising spectral performance of below 2 eV (FWHM) at 6 keV. However, we still see that the detector response is affected by the weak-link behavior, especially at high frequency regime. In this paper, we briefly summarize our results with a focus on the spectral performance and the detector responsivity for each TES design. We also present our recent works on fabrication related to a superconducting wiring process, which would be useful for further reduction of the weak-link effects.
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