Analytical model of the temperature dependent properties of microresonators immersed in a gas

A comprehensive theoretical model of microresonators immersed in a viscous gas of varying temperature is presented and verified by experiments. Analytical expressions for both the temperature dependent resonant frequency and quality factor of the first flexural eigenmode were derived extending Sader's theory of viscous damping to small temperature variations. The model provides useful implications for the thermal stabilization of microresonators immersed in a gas as well as for the reduction in the influence of the temperature dependent gas properties on the resonant frequency. Finally, an analytical expression is deduced for the mass detection capability of a microresonator that undergoes temperature variations. (C) 2011 American Institute of Physics. [doi:10.1063/1.3544345]