Bulk and Surface Thermoelastic Dissipation in Micro-Hemispherical Shell Resonators

Thermoelastic dissipation (TED) is a fundamental energy loss process, which bears concern in all microelectromechanical resonators. High aspect ratio (R/h) 3-D micro-hemispherical shell resonators (μHSRs) have exceptionally low stiffness and are sensitive to dissipation forces both internally and at their surfaces. TED in μHSRs originating in the bulk of the shell and near its surfaces due to asperities (roughness) is investigated. Rayleigh´s inextensional solutions for the lowest frequency vibration modes of μHSRs in the isothermal quasistatic limit result in zero contributions to energy loss from bulk TED since no volumetric strain is generated in this approximation. After relaxing Rayleigh´s inextensional assumption, perturbational undulations of the shell´s neutral surface are found to cause non-zero bulk TED. The resulting quasi-inextensional vibration modes force the shell into an approximately anti-biaxial strain state, which stretch surface asperities along one axis and compress them along the other, generating thermal flux around the base of each asperity. Closed-form approximate analytical models are developed from the geometrical and material dependencies to predict the quality factor associated with bulk and surface TED, enabling examination of these effects across scale. Fully-coupled thermoelastic finite element models verify the above results. Finally, experimental results from fabricated μHSRs are compared with the developed models.