Radiative Heat Transfer in Free-Standing Silicon Nitride Membranes

Abstract

Free-standing silicon nitride (SiN) mechanical resonators are of central interests in applications such as temperature and mass sensing, and for fundamental optomechanical reasearch. Understanding thermal coupling between a membrane resonator and its environment is required for predicting thermal noise, frequency noise, as well as sensors responses to temperature changes. In this work, we provide closed-form derivations of intrinsic thermal coupling quantities in free-standing thin films, namely total thermal conductance with the surroundings, thermal response time, and the relative contribution of thermal radiation. Our model is valid for any free-standing thin film anchored on all sides, although we particularly emphasize the specific case of SiN for which spectral emissivity is thoroughly investigated as a function of thickness and temperature. We find that radiative heat exchanges can play a non-negligible role, and even dominate thermal coupling for membranes of sizes commonly employed in optomechanics experiments. We experimentally confirm the validity of our model by measuring radiative thermal coupling between a SiN mechanical resonator and a ceramic heater in high vacuum.

References in corpus (3)

• High quality mechanical and optical properties of commercial silicon nitride membranes
• Infrared dielectric properties of low-stress silicon nitride
• Frequency and phase noise of ultra-high Q silicon nitride nanomechanical resonators

Cited by in corpus (7)

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• Silicon cantilevers locally heated from 300K up to the melting point: temperature profile measurement from their resonances frequency shift
• Annealing reduces Si${}_3$N${}_4$ microwave-frequency dielectric loss in superconducting resonators
• A Novel Architecture for room temperature microwave optomechanical experiments
• High Resolution Measurement of Near-Field Radiative Heat Transfer enabled by Nanomechanical Resonators