Ultra High Q Lithium Niobate Resonator at 15-Degree Three-Dimensional Euler Angle

This work presents a new approach to design microelectromechanical system (MEMS) resonators based on x-cut single-crystal lithium niobate (LiNbO ₃ ) thin film to achieve ultra high quality factor ( ${Q}$ ). By properly selecting the three-dimensional (3D) Euler angle ( $\alpha $ ) of the thin-film piezoelectric resonator body, the first-order symmetrical compression (S1) vibration mode is excited by applying horizontal electric field. When the Euler angle approaches 15°, the resonator operating at 6.5 GHz exhibits a ${Q}_{p}$ of more than 100,000 at parallel resonance, an excellent ${k}^{{2}}\cdot {Q}_{p}$ and ${f}\cdot {Q}_{p}$ product of 6,300 and ${8.6}\times {10}^{{14}}$ Hz, respectively. This result demonstrates two orders of magnitude higher ${Q}_{p}$ than the previously reported acoustic resonators in the 6 GHz range, and proves that ultra high ${Q}$ is possible for MEMS resonators operating in air and at high frequency.