Accurate Modeling of Quality Factor Behavior of Complex Silicon MEMS Resonators

The quality factor of a resonator represents the decay of vibrational energy over time, and is directly related to the frequency response and other key parameters that determine performance of inertial sensors and oscillators. Accurate prediction of the quality factor is essential for designing high-performance microelectromechanical (MEMS) devices. Several energy dissipation mechanisms contribute to the quality factor. Due to computational complexity, highly simplified models for the dominant dissipation mechanism, such as Zener’s model for thermoelastic dissipation (TED), are often employed. However, the intuition provided by these models is inadequate to predict the quality factor of more complex designs and can be highly misleading. In this paper, we construct complete, quantitative, and predictive models with finite-element methods for the intrinsic energy dissipation mechanisms in MEMS resonators using full anisotropic representation of crystalline silicon and the temperature dependence of all parameters. We find that TED is often a more significant source of damping than has been assumed, because of the previously neglected role of crystalline anisotropy and small geometric features, such as etch release holes—all of which can now be included in practical models. We show that these models, along with simpler scaling models for extrinsic dissipation mechanisms, explain measurements of quality factor in diverse sets of MEMS resonators with unprecedented accuracy. [2014-0106]