Comparison of f-Q scaling in wineglass and radial modes in ring resonators

Low phase noise MEMS oscillators necessitate resonators with high f-Q. Resonators achieving high f-Q (mechanical frequency-quality factor product) close to the thermo-elastic damping (TED) limit have been demonstrated at expense of feed-through. Here we present a study comparing frequency scaling of quality factors of wineglass and radial modes in a ring resonator using an opto-mechanical two port transmission measurement. Higher harmonics of the wineglass mode show an increasing trend in the f-Q product, as compared to a saturation of f-Q for radial modes. The measured f-Q of 5.11×10
¹³
Hz at 9.82GHz in air at room temperature for a wineglass mode is close to the highest measured values in silicon resonators.