We have fabricated Transition Edge Sensors (TESs) whose thermal characteristics are completely characterised by few-mode ballistic phonon exchange with the heat bath. These TESs have extremely small amorphous SiN x support legs: 0.2 µm thick, 0.7 to 1.0 µm wide and 1.0 to 4.0 µm long. We show, using classical elastic wave theory, that it is only necessary to know the geometry and bulk elastic constants of the material to calculate the thermal conductance and fluctuation noise. Our devices operate in the few-mode regime, between 5 and 7 modes per leg, and have noise equivalent powers (NEPs) of 1.2 aW Hz −1/2 . The NEP is dominated by the thermal fluctuation noise in the legs, which itself is dominated by phonon shot-noise. Thus TESs have been demonstrated whose thermal characteristics are fully accounted for by an elastic noise-wave model. Our current devices, and second-generation devices based on patterned phononic filters, can be used to produce optically compact, mechanically robust, highly sensitive TES imaging arrays, circumventing many of the problems inherent in conventional long-legged designs.
The sensitivity of a low-noise superconducting transition edge sensor (TES) is determined by the thermal conductance of the support structure that connects the active elements of the device to the heat bath. Lownoise devices require conductances in the range 0.1 to 10 pW K −1 , and so have to rely on diffusive phonon scattering in long, narrow, amorphous SiN x legs. We show that it is possible to manufacture and operate TESs having short, ballistic low-dimensional legs (cross section 500 × 200 nm) that contain multi-element phononic interferometers and ring resonators. These legs transport heat in effectively just 5 elastic modes at the TES's operating temperature (< 150 mK), which is close to the quantised limit of 4. The phononic filters then reduce the thermal flux further by frequency-domain filtering. For example, a micromachined 3-element ring resonator reduced the flux to 19 % of a straight-legged ballistic device operating at the quantised limit, and 38 % of a straight-legged diffusive reference device. This work opens the way to manufacturing TESs where performance is determined entirely by filtered, few-mode, ballistic thermal transport in short, low-heat capacity legs, free from the artifacts of two level systems. arXiv:1805.09783v1 [cond-mat.mes-hall]
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