Temperature dependence of quality factor in MEMS resonators

The temperature dependence of the quality factor Q of microelectromechanical system (MEMS) resonators is analyzed and measured. For silicon MEMS resonators, there are several energy loss mechanisms that determine the quality factor. These include air-damping, thermoelastic dissipation, and anchor and surface losses. For resonators operating at a low pressure in hermetic wafer-scale encapsulation, the effect of each energy loss mechanism is discussed. The temperature dependence of each mechanism and their contribution to the total quality factor is investigated. MEMS resonators can be designed to have either strong or weak dependence of Q on temperature, which is if the effects of the temperature on the dominant loss mechanisms are well understood. The sensitivity of up to 1% changes in quality factor per degree Celsius change of temperature was demonstrated by experiment. By using Q as the thermometer for temperature compensation, a preliminary experiment demonstrated less than 4-ppm resonant frequency variation over the 0 degrees C-70 degrees C temperature range. This indicates that the quality factor can be used as an absolute intrinsic thermometer for temperature compensation in the MEMS resonators.