Simulation of Anchor Loss in MEMS Resonators Using Perfectly Matched Layers

Recently, it has been shown that there is a significant pressure and temperature independent damping contribution for high-frequency modes in commercial MEMS gyroscopes. In order to investigate the contribution of anchor losses to the observed damping, perfectly matched layer (PML) simulations can be employed. This work serves as a preparatory step towards the simulation of anchor losses in complex MEMS gyroscopes. We focus on simple geometries, in order to infer general modelling rules for the setup of PML simulations. Therefore, we simulate a cantilever beam and verfiy the simulations with existing analytic results. We demonstrate a systematic approach to set up anchor loss models of MEMS resonators, which yields reliable results for various mode shapes. Furthermore, we simulate two coupled cantilever beams and show that degenerate modes, only differing in symmetries, have significantly different anchor loss quality factors. The insights gained from these simple geometries will be applied to the simulation of complex MEMS gyroscopes in the future.