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 10000 at 441 MHz when made of polysilicon structural material and 42900 at 2.97 GHz when made of microcrystalline diamond. The latter marks the highest f · Q of 1.27×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">14</sup> 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 μm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> 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 kQ. Though still higher than desired, this marks a 30× 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 Ω. 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.