Ultra High <i>Q</i> Lithium Niobate Resonator at 15-Degree Three-Dimensional Euler Angle
Zhongbin Dai, Xueyan Liu, Hengxiao Cheng, Siqi Xiao, Haiding Sun, Chengjie Zuo
Abstract
This work presents a new approach to design microelectromechanical system (MEMS) resonators based on x-cut single-crystal lithium niobate (LiNbO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> ) thin film to achieve ultra high quality factor ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula> ). By properly selecting the three-dimensional (3D) Euler angle ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> ) 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Q}_{p}$ </tex-math></inline-formula> of more than 100,000 at parallel resonance, an excellent <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${k}^{{2}}\cdot {Q}_{p}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${f}\cdot {Q}_{p}$ </tex-math></inline-formula> product of 6,300 and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${8.6}\times {10}^{{14}}$ </tex-math></inline-formula> Hz, respectively. This result demonstrates two orders of magnitude higher <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Q}_{p}$ </tex-math></inline-formula> than the previously reported acoustic resonators in the 6 GHz range, and proves that ultra high <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula> is possible for MEMS resonators operating in air and at high frequency.