Thermal elastic-wave attenuation in low-dimensional SiN${}_x$ bars at low temperatures

Abstract

At low temperatures, < 200 mK, the thermal flux through low-dimensional amorphous dielectric bars, < 2 $\mu$m wide and 200 nm thick, is transported by a small number of low-order elastic modes. For long bars, L > 400 $\mu$m, it is known that the conductance scales as 1/L, where L is the length, but for short bars, 1 $\mu$m < L < 400 $\mu$m, the length dependence is poorly known. Although it is assumed that the transport must exhibit a diffusive to ballistic transition, the functional form of the transition and the scale size over which the transition occurs have not, to our knowledge, been measured. In this paper, we use ultra-low-noise superconducting Transition Edge Sensors (TESs) to measure the heat flux through a set of SiN${}_x$ bars to establish the characteristic scale size of the ballistic to diffusive transition. For bars supporting 6 to 7 modes, we measure a thermal elastic-wave attenuation length of 20 $\mu$m. The measurement is important because it sheds light on the scattering processes, which in turn are closely related to the generation of thermal fluctuation noise. Our own interest lies in creating patterned phononic filters for controlling heat flow and thermal noise in ultra-low-noise devices, but the work will be of interest to others trying to isolate devices from their environments, and studying loss mechanisms in micro-mechanical resonators.

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References in corpus (9)

• Quantized thermal conductance of dielectric quantum wires
• Elastic Wave Transmission at an Abrupt Junction in a Thin Plate, with Application to Heat Transport and Vibrations in Mesoscopic Systems
• Silicon nitride membrane resonators at millikelvin temperatures with quality factors exceeding $10^8$
• The "Tunneling Two-Level Systems" Model of the Low-Temperature Properties of Glasses: Are "Smoking-Gun" Tests Possible?
• Thermal Transport through a Mesoscopic Weak Link
• Surface scattering analysis of phonon transport in the quantum limit using an elastic model
• Precision control of thermal transport in cryogenic single-crystal silicon devices
• Transition Edge Sensors with Few-Mode Ballistic Thermal Isolation
• Modelling proximity effects in Transition Edge Sensors to investigate the influence of lateral metal structures

Cited by in corpus (2)

• Thermal Kinetic Inductance Detectors for millimeter-wave detection
• Superconducting transition edge sensors with phononic thermal isolation