Thermoelastic Dissipation in Diamond Micro Hemispherical Shell Resonators

Abstract

Maximizing quality factor (Q) is essential to improve the performance of micro hemispherical shell resonators (μHSRs) which can be used in microelectromechanical system (MEMS) gyroscopes to measure angular rotation. Several energy dissipation mechanisms limit Q, where thermoelastic dissipation (TED) is the major one and studied in this paper. Fully coupled thermo-mechanical equations for calculating TED are formulated, and then temperature distribution in a deformed μHSR and its quality factor related to TED (QTED) are obtained by solving the equations through a finite-element method (FEM). It has been found that different fabrication process conditions can obtain various geometrical parameters in our previous studies. In order to provide guidelines for the design and fabrication of μHSRs, the effects of their geometry on resonant frequency (f0) and QTED are studied. The change of anchor height and small enough anchor radius have no effect on both f0 and QTED, but the shell size including its radius, thickness and height has significant impact on f0 and QTED. It is found that whether a μHSR has lower f0 and higher QTED or higher f0 and higher QTED can be achieved by changing these geometrical parameters. The results presented in this paper can also be applied to other similar resonators.