Modeling the distribution of phonon density for designing high quality thermal resonators

An accurate theoretical model that quantifies the distribution of phonon density is indispensable for designing thermal resonators with high quality factor. This paper focuses on the modeling aspects of a generic cantilever structure excited thermally at resonance by applying Cattaneo-Vernotte hyperbolic heat conduction model. Critical analysis of the theoretical results revealed that the dynamic temperature oscillations at resonant frequencies are quantised wave responses whose characteristics ascribe to the quantum-mechanical behaviour of a particle inside a box. The theoretical predictions agree well with the experimental evaluation of the dynamic response of Al-SiXNY bimaterial cantilever structure excited electrothermally by a signal with constant power spectral density. An increase in Q by a factor of 4-5 was achieved either by increasing the resonant frequency for a given length scale or by decreasing the length scale when excited by a signal with a constant power spectral density. This will enable to design micro/nano scale resonant devices with improved performance.