High- $Q$ UHF Spoke-Supported Ring Resonators

Abstract

A vibrating micromechanical spoke-supported ring resonator employing a central peg-anchor, balanced non-intrusive quarter-wavelength extensional support beams, and notched support attachments attains high $Q$ -factor in vacuum, posting 10 000 at 441 MHz when made of polysilicon structural material and 42 900 at 2.97 GHz when made of microcrystalline diamond. The latter marks the highest $f\cdot Q$ of $1.27\times 10^{14}$ for any acoustic resonator at room temperature, besting even macroscopic bulk-mode devices. Very high $Q$ values like these in a device occupying only 870 $\mu \text{m}^{2}$ pave a path toward on-chip realizations of RF channelizers and ultra-low phase-noise gigahertz oscillators for secure communications. With frequency determined by lithographically defined ring-width rather than radius, a capacitive transducer with a 75-nm gap allows this 2.97-GHz version to achieve a series motional resistance of 81 $\text{k}\Omega $ . Though still higher than desired, this marks a $30\times $ improvement over previous pure polysilicon surface-micromachined solid disk resonators in the gigahertz range, and if predicted performance-scaling holds true, seven such resonators constructed in a mechanically coupled array with 30-nm gap spacing, could lower this to only 300 $\Omega $ . Confidence in a prediction like this stems from the confirmed accuracy of the electrical equivalent circuit described herein that models not only the ring and its transducers, but also its supports. [2015-0132]