Optimization of a Double-Sided Annular Dome-Like Quartz Crystal Resonator

As people's demands for the appearance, quality, and stability of various electronic devices continue to increase, quartz crystal resonators are also developing towards high frequency, miniaturization, and high stability. In order to improve frequency stability, AT-cut quartz resonators must have a high quality factor (Q factor). To achieve this goal, studying the influence of electrode shape on device performance is of great significance for sensor design. Currently, the most effective technique is to design a dome-shaped structure on the surface of the quartz resonator[1]. However, the fabrication of small dome-shaped quartz resonators requires extremely high machining accuracy, which leads to increased costs and makes large-scale production difficult to achieve. Therefore, this study proposes a novel structure to equivalent the dome-shaped quartz resonator structure and then introduces a three-dimensional finite element model to investigate the influence of quartz electrode shape on vibration coupling. Simulation results show that this double-sided annular dome-like quartz crystal resonator exhibits similar good vibration characteristics as the dome-shaped structure. Finally, based on the energy trapping effect and vibration coupling effect, the length, spacing, and height of the annular dome-like structure are optimized[2], obtaining the optimal structure with a length
$\mathbf{L}=\mathbf{1400}\boldsymbol{\mu} \mathbf{m}$
, height
$\mathbf{H}=\mathbf{3}\boldsymbol{\mu} \mathbf{m}$
, and spacing
$\mathbf{P}=\mathbf{50}\ \boldsymbol{\mu} \mathbf{m}$
. This structure provides guidance for the production of small-sized, high vibration stability, and high productivity high-frequency quartz resonators.