Aspect ratio optimization of piezoelectric extensional mode resonators for quality factor and phase noise performance enhancement

Abstract This study focuses on optimizing the resonator geometry via the aspect ratio design of a width-extensional mode resonator to improve its quality factor ( Q ), which is one of the critical performance parameters for resonators in either sensing (Allan deviation) or frequency reference (phase noise) applications. The proposed approach uses finite element analysis to reduce the strain energy at anchor supports by altering the resonator geometric structure, thereby reducing energy loss through anchors. Moreover, process limitations on feature sizes are used as constraints to find aspect ratios that can not only increase the Q but also reduce spurious modes near the targeted frequency. The devices were fabricated using AlN thin film piezoelectric on a substrate (TPoS) process. The simulated energy dissipation trends for specific length-to-width ( L / W ) ratios closely match the measured changes in the resonator Q values in vacuum. In vacuum, the highest Q -factor achieved by the device is close to 8816, with a motional resistance of a few tens of ohms. Additionally, a board-level oscillator realized using a commercial low-noise amplifier exhibits phase noise performance of −141.21 dBc Hz −1 and −164.25 dBc Hz −1 at 1 kHz and 1 MHz frequency offsets, respectively. The calculated figures of merit for these offsets are 204 and 168, respectively.