X-Cut Lithium Niobate Laterally Vibrating MEMS Resonator With Figure of Merit of 1560

Abstract

This letter reports on the design, fabrication, and testing of an X-cut lithium niobate laterally vibrating resonator operating around 50 MHz and exhibiting a record figure of merit–FoM = product of 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 at a resonance ( <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 1560. For practical applications, the individual resonator is arranged in a large array so as to achieve a static capacitance around 1 pF, while still preserving a high FoM of 570. Modeling of anchor losses through finite element analysis is used to guide the design of these resonators, which simultaneously exhibit high 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">$k_{t}^{2} &gt; 30$ </tex-math> </inline-formula> %) and 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">$Q_{s} &gt; 5000$ </tex-math> </inline-formula> ) in vacuum.l [2018-0097]