Abstract Transition Edge Sensors (TESs) are highly sensitive thermal detectors that operate across a wide frequency range, from millimeter waves to gamma rays. For optical single-photon TES detectors, a high energy resolution and large saturation energy are required, primarily limited by factors such as heat capacitance and temperature sensitivity, αI. In this study, we evaluated TES devices of varying sizes by conducting complex impedance measurements using transfer function calibration, revealing that our titanium-based TES exhibits higher heat capacities compared to theoretical values. We obtained the measured and theoretical time constants, energy resolutions, and saturation energies for the different-sized TESs, notably constructing histograms from pulse area integral analysis. Our devices achieved an optimal energy resolution of 0.2 eV, with the largest TES demonstrating an energy resolution of 0.34 eV, a saturation energy of 35 eV and the ability to discriminate up to 20 photons at 438 nm. These results provide valuable insights for optimizing TES performance in precise photon detection.
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