Sub-GHz X-Cut Lithium Niobate <i>S</i>₀ Mode MEMS Resonators

Abstract

This paper reports on the design, fabrication, and characterization of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S_{0}$ </tex-math></inline-formula> mode X-cut Lithium Niobate Laterally Vibrating Resonators (LVRs) operating between 100 MHz and 1 GHz. In the first Section of this work, analytical and numerical models are implemented to investigate the impact of topology and geometrical features on the Electromechanical Coupling ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k_{t}^{2}$ </tex-math></inline-formula> ) and 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">$Q_{s}$ </tex-math></inline-formula> ) of this class of devices. The models are used to define the design of experiments aimed at characterizing the resonator performance. The resonators are fabricated and tested in atmospheric, vacuum, and cryogenic ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T$ </tex-math></inline-formula> = 10 K) conditions to assess their performance and identify the main sources of discrepancies in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k_{t}^{2}$ </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">$Q_{s}$ </tex-math></inline-formula> with respect to the analytical and numerical models. Under vacuum quality factors exceeding a few thousands are recorded across the investigated spectrum, with measured <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k_{t}^{2}$ </tex-math></inline-formula> as high as 28.9%. At 100 MHz, measured <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q_{s}$ </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">$k_{t}^{2}$ </tex-math></inline-formula> of 8,279 and 28.5%, respectively, combine into a record-breaking Figure of Merit ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$FOM$ </tex-math></inline-formula> ) of 2,688, while cryogenic testing highlighted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q_{s}$ </tex-math></inline-formula> as high as 26,511. In the last section, by analyzing the differences in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k_{t}^{2}$ </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">$Q_{s}$ </tex-math></inline-formula> between experiments and models, best design approaches to maximize the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$FOM$ </tex-math></inline-formula> and minimize spurious modes responses are reported, with a focus on the 100 to 550 MHz range. [2022-0081]