Energy Loss Mechanisms of Micromechanical Resonators

Quality Factor, Q:
One of the major barriers to using micromechanical resonators in high frequency filter and reference applications is Quality Factor, Q. Having a high quality factor (~105) is necessary for suppression of unwanted signals. However, typical scaling methods used to increase the resonant frequency tend to decrease Q. This work focuses on identifying and examining different ways (air damping, thermoelastic dissipation (TED), surface losses, material losses, clamping losses) that micromechanical resonant structures can lose energy and thereby limit Q.

Fig. 1 SEM cross section of encapsulated micromechanical resonator
Fig. 2 Plot of Q for resonators of 8μm wide tuning fork resonators of varying height. Clamping is shown to limit Q for very stubby beams.
Fig. 3 Q plotted against theoretical TED limit. High frequency part (10MHz) is limited by clamping loss.
Fig. 4 Quality factor vs. pressure for ~800kHz resonator (thick line shows theoretical Q limit from TED, thin diagonal line shows theoretical Q limit from air damping)

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