Radiative Heat Transfer in Freestanding Silicon Nitride Membranes

• DOI: 10.1103/physrevapplied.14.024072
• Publication Date: 2020-08-25T20:55:57Z
• Authors: Chang Zhang; Mathieu Giroux; Thea Abdul Nour; Raphael St-Gelais
• Keywords: FOS: Physical sciences; Physics - Applied Physics; Applied Physics (physics.app-ph); 02 engineering and technology; 0210 nano-technology

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.