Thermoelastic loss in microscale oscillators

Abstract

A simple model of thermoelastic dissipation is proposed for general, free standing microelectromechanical (MEMS) and nanoelectromechanical (NEMS) oscillators. The theory defines a flexural modal participation factor, the fraction of potential energy stored in flexure, and approximates the internal friction by assuming the energy loss to occur solely via classical thermoelastic dissipation of this component of the motion. The theory is compared to the measured internal friction of a high Q mode of a single-crystal silicon double paddle oscillator. The loss at high temperature (above 150 K) is found to be in good agreement with the theoretical prediction. The importance of this dissipation mechanism as a function of scale is briefly discussed. We find that the relative importance of this mechanism scales with the size of the structure, and that for nanoscale structures it is less important than intrinsic phonon–phonon scattering.