ABSTRACTWe analyze thermoelastic dissipation in composite silicon MEMS resonators that exhibit multiple mechanical and thermal modes with complex dynamics. Silicon resonators that are coated with thin films of silicon dioxide can have near-zero temperature coefficients of frequency, making them attractive for use as precision time references. The quality factor of MEMS resonators can be dominated by thermoelastic dissipation (TED), which is triggered by the relaxation of mechanically induced temperature gradients. Recently, Chandorkar et al. (2009) have shown an expression of TED based on entropy generation as a weighted sum of the modal solutions of the three-dimensional heat transfer equation. This expression was obtained for weak coupling between mechanical and thermal dynamics. Applying this same technique to a fully coupled solution to the dynamics, we show that the TED contribution of the dominant thermal modes can be inhibited in the presence of a thin silicon dioxide film. Reduction of the contribution from the dominant thermal mode is shown with increasing oxide. We studied the effects of varying oxide film thickness and beam length. The quality factor was simulated for each unique case and compared to multimode energy dissipation. Our results suggest with some variability, thin film oxide coating affects the thermal relaxation of the composite resonator in the direction of lower TED and increased quality factor.
Accurate Modeling of Quality Factor Behavior of Complex Silicon MEMS Resonators