Thermoelastic Dissipation in Micromachined Birdbath Shell Resonators

Abstract

Many MEMS gyroscopes rely on micro mechanical resonators to measure angular rotation. Maximizing their quality factor ( $Q$ ) will help improve accuracy. There are several energy dissipation mechanisms that limit $Q$ . This paper studies the role of thermoelastic dissipation (TED) in micro birdbath shell resonators. Fully coupled thermo-mechanical equations of physical behavior are solved for these shells using a finite-element method. Furthermore, an analytical model is developed to predict TED. The effects of material properties, shell geometry, edge chipping around the shell rim, trimming approaches, thin-film coatings, and operating temperature on thermoelastic $Q$ ( $Q_{{TED}})$ are studied. It is found that the shell material properties and rim thickness have significant impact on $Q_{{TED}}$ . However, edge chipping and most of the shell geometrical parameters do not have large impact. Additionally, this paper shows that some trimming approaches, such as forming grooves along the rim, can improve $Q_{{TED}}$ . A study of the effect of metal coatings on the resonator on $Q$ shows that the coating thickness and material are important factors affecting $Q$ and $Q_{{TED}}$ . The results presented in this paper provide guidelines for the design of other similar high- $Q$ resonators. [2016–0027]