Accurate Extraction of Large Electromechanical Coupling in Piezoelectric MEMS Resonators

Abstract

Recent advancements in the field of piezoelectric micro-resonators have produced devices, such as lithium niobate laterally vibrating resonators, with very high electromechanical coupling factors (k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) and respectable quality factors (Q). As a result, the records of the figure of merit (FoM) for radiofrequency MEMS resonators have been broken several times in the past five years. As exciting as these high FoMs are, they impose unique caveats in accurately extracting the electromechanical coupling often due to the presence of spurious modes. It is a less noted issue for micro-resonators with moderate k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , as spurious modes either are absent or do not significantly affect the common extraction technique based on identifying resonances and anti-resonances. This paper will first theoretically analyze how disregarding spurious modes can potentially lead to inaccurate extraction of k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> of the intended mode and then offer a framework that accounts for spurious modes and accurately extracts electromechanical coupling using a multiresonance recursive fitting.