Stress-dependent thermal relaxation effects in micro-mechanical resonators

Thermal relaxation is a key factor in determining the quality factor of micro and nano resonators, which controls the energy dissipation through the coupling of the mechanical and thermal domains. While the literature contains approximate, exact and computational models for quantitative analysis of thermo-elastic coupling, very few techniques are available to 'tune' it without changing the material, geometry or operating conditions. In this paper, we develop an analytical model that considers a pre-stress in a flexural resonator to modify the thermal relaxation time and thus increase the quality factor. The effects of length-scale, pre-stress and geometry on the quality factor have been analyzed. The model predicts that significant improvement in terms of dimensionless quality factors is possible by tuning the pre-stress.