Micromechanical resonators are promising replacements for quartz crystals for timing and frequency references owing to potential for compactness, integrability with CMOS fabrication processes, low cost, and low power consumption. To be used in high performance reference application, resonators should obtain a high quality factor. The limit of the quality factor achieved by a resonator is set by the material properties, geometry and operating condition. Some recent resonators properly designed for exploiting bulk-acoustic resonance have been demonstrated to operate close to the quantum mechanical limit for the quality factor and frequency product (Q-f). Here, we describe the physics that gives rise to the quantum limit to the Q-f product, explain design strategies for minimizing other dissipation sources, and present new results from several different resonators that approach the limit.

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 finiteelement 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]

We present an uncertainty and sensitivity analysis applied to a thermo-chemical model of radiative heat loads on a capsule entering the Titan atmosphere. A one-dimensional model for the computation of the gas conditions downstream of the vehicle's bow shock is used to replace expensive CFD field simulations. The CN concentration in the shock layer is computed and fed into a simplified model for the radiative heat flux. The input reaction rates are assumed to be known only approximatively and characterized in a probabilistic framework; we perform Monte Carlo sampling to estimate the relative ranking of the various uncertainty sources. We show that linear correlation and non-linear variance decomposition techniques can lead to different estimates of the relative importance of the reaction rates uncertainties.

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