Finite Element Modeling of Thermoelastic Damping in Filleted Micro-Beams

In the design of micro-electromechanical systems (MEMS) such as micro-resonators, dissipation mechanisms may have detrimental effects on the quality factor (Q), which is directly related to the response amplitude of the system excited at its natural frequency. One of the major dissipation phenomena to consider in such high-Q micro-systems is thermoelastic damping. Hence, the performance of such MEMS is directly related to their thermoelastic quality factor which has to be predicted accurately. Analytical models have been developed in the literature to assess thermoelastic damping. However, these models are based on very restrictive assumptions and can only be used for simple configurations such as bending beams or bars in extension. In order to investigate structures of complex geometry, a numerical approach is required. In this paper, the finite element method is used to study the effect of the anchor on the thermoelastic quality factor of clamped-clamped silicon beams. Moreover, the effect of fillet at the anchor/beam interface is investigated. It is shown that smoothing the junction between the beam and the anchor can be benefic for some configurations while it can be detrimental in others. This study highlights the importance to have tied manufacturing tolerances for the purpose of high-Q micro-resonators fabrication.