Impact of Frequency Mismatch on the Quality Factor of Large Arrays of X-Cut Lithium Niobate MEMS Resonators

Abstract

This paper investigates the impact of resonant frequency (f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> ) mismatch on the quality factor (Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">as</sub> ) of large arrays of X-cut Lithium Niobate (LN) Laterally Vibrating Resonators (LVRs) operating around 50 MHz and 400 MHz. The statistical distributions of key device parameters, including resonant frequency, quality factor (Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> ), electromechanical coupling (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 static capacitance (C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> ), are collected from replicas of identical resonators. A Monte Carlo approach is later implemented to simulate the impact of statistical variability on the quality factor of arrays of resonators. By including the effect of interconnects series resistance on the arrays, an excellent agreement between experimental and simulated Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">as</sub> is achieved, demonstrating that frequency mismatch is the major mechanism of quality factor degradation in arrays of parallel resonators. The experimental validation of the model confirms that it can be used as a predictive tool to establish the frequency tolerance requirements in order to attain high Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">as</sub> in arrays.