This paper investigates the impact of resonant frequency ( $f_{\mathrm {s}}$ ) mismatch on the quality factor ( $Q_{\mathrm {as}}$ ) 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 ( $Q_{\mathrm {s}}$ ), electromechanical coupling ( $k_{\mathrm {t}}^{2}$ ), and static capacitance ( $C_{0}$ ), 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 $Q_{\mathrm {as}}$ 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 $Q_{\mathrm {as}}$ in arrays. [2019-0210]

中文翻译：

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频率失配对 X 切割铌酸锂 MEMS 谐振器大阵列品质因数的影响

本文研究了谐振频率的影响（ $f_{\mathrm {s}}$ ) 品质因数不匹配 ( $Q_{\mathrm {as}}$ ) 的大型 X 切铌酸锂 (LN) 横向振动谐振器 (LVR) 阵列在 50 MHz 和 400 MHz 附近运行。关键器件参数的统计分布，包括谐振频率、品质因数（ $Q_{\mathrm {s}}$ ), 机电耦合 ( $k_{\mathrm {t}}^{2}$ ) 和静态电容 ( $C_{0}$ )，是从相同谐振器的复制品中收集的。后来实施蒙特卡罗方法来模拟统计可变性对谐振器阵列品质因数的影响。通过包括互连串联电阻对阵列的影响，实验和模拟之间的极好一致性 $Q_{\mathrm {as}}$ 实现了，表明频率失配是并联谐振器阵列中品质因数下降的主要机制。该模型的实验验证证实，它可以用作建立频率容限要求的预测工具，以获得高 $Q_{\mathrm {as}}$ 在数组中。[2019-0210]