Modeling support loss in SOI-based micromechanical resonators

In light of recent efforts to quantitatively evaluate the quality factor (Q) of micromechanical resonators, this paper presents an analytical-numerical model for calculating support loss in micromechanical resonators made from Silicon-On-Insulator (SOI) wafers. The time-harmonic stress due to the vibrations in a micromechanical resonator is obtained through numerical simulation, while the vibration displacement on substrate due to the stress from micromechanical resonators is analytically derived, with the assumption that the substrate is a semi-infinite medium. The combination of the time-harmonic stress from the resonator and the vibration displacement on substrate gives rise to a quantitative evaluation of support loss, which is further verified with the experimental data in the literature. This analytical-numerical combined model is general and applicable to SOI-based micromechanical resonators with different structural geometries.