Abstract
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.
Highlights
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
Air damping refers to the loss of energy to the air molecules surrounding the resonating structure[5] and is the dominant energy loss mechanism in low frequency resonators that are not operated in vacuum
If the entire solid is subjected to a longitudinal elastic vibration, such as occurs during operation of a micromechanical oscillator, the periodic distortions of the solid are represented by a local variation in the dispersion relation; in effect, extension of the crystal reduces the slope of the dispersion relation, while compression of the crystal increases the slope of the dispersion relation
Summary
Shirin Ghaffari[1], Saurabh A. Chandorkar[1], Shasha Wang[2], Eldwin J. Ahn[1], Vu Hong[1], Yushi Yang1 & Thomas W.
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