The temperature dependence of the quality factor, Q, of encapsulated MEMS resonators is analyzed in an effort to understand the temperature regimes where different energy loss mechanisms are dominant. The effect of two limiting energy loss mechanisms for these resonators, air damping and thermo elastic dissipation, are separately analyzed to determine the Q of the system over a range of temperatures. MEMS resonators can be designed to have either strong weak dependence of Q on temperature, if the effects of the dominant loss mechanisms with temperature are well understood. Up to 1% change in quality factor per °C change of temperature was demonstrated, leading to the possibility of using quality factor as an absolute thermometer for temperature compensation in MEMS resonators.

We have developed a single wafer vacuum encapsulation for MEMS resonators, using a thick (20 µm) polysilicon encapsulation to package micromechanical resonators in a pressure < 1 Pa. The encapsulation is robust enough to withstand standard back-end processing steps, such as wafer dicing, die handling, and injection molding of plastic. We have continuously monitored the pressure of encapsulated resonators for more than 10,000 hours and have seen no measurable change of pressure inside the encapsulation at ambient temperature. We have subjected packaged resonators to > 600 cycles of-50-80°C and no measurable change in cavity pressure was seen. We have also performed accelerated leakage tests by driving hydrogen gas in and out of the encapsulation at elevated pressure. Two results have come from these hydrogen diffusion tests. First, hydrogen diffusion rates through the encapsulation at temperatures 300-400°C have been determined. Second, the package was shown to withstand multiple temperature cycles between room and 300-400°C without showing any adverse affects. The high robustness and stability of the encapsulation can be attributed to the clean, high temperature environment during the sealing process.

Thermoelastic dissipation (TED) is analyzed for complex geometries of micromechanical resonators, demonstrating the impact of resonator design (i.e. slots machined into flexural beams) on TED-limited quality factor. Clarence Zener first described TED for simple beams in 1937. This work extends beyond simple beams into arbitrary geometries, verifying simulations that completely capture the coupled physics that occur. Novel geometries of slots engineered at specific locations within the flexural resonator beams are utilized. These slots drastically affect the thermal-mechanical coupling and have an impact on the quality factor, providing resonators with quality factors higher than those predicted by simple Zener theory. The ideal location for maximum impact of slots is determined to be in regions of high strain. We have demonstrated the ability to predict and control the quality factor of micromechanical resonators limited by thermoelastic dissipation. This enables tuning of the quality factor by structure design without the need to scale its size, thus allowing for enhanced design optimization.

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