石英振盪器是精密計時和通訊電子中非常重要的元件，其應用對頻率準確性和穩定性要求很高。隨著振盪器未來需要越做越小，振盪區域會更接近邊界區，導致能量損耗增加，或產生其他不預期的效應。本文利用 COMSOL 進行線性與非線性模擬分析，目的是提升 Q 值並改善頻率穩定性。論文中分析的項目共有三項：能量損失過大則透過導入聲子晶體（PnC）結構來改善；溫度效應透過逐步增量法進行分析；本論文也探討了驅動強度依賴性（DLD）的非線性行為，了解其對頻率變化的影響。 模擬分析之前，需先在 COMSOL 中整合了石英的非線性彈性係數、弱式算式與應力-應變，以修改COMSOL中的模型。本文結論為：(1) 聲子晶體應用在石英震盪器上，可有效抑制不需要的振動模式，並強化能量集中，以提升 Q 值；(2) 在溫度效應之分析方面，提出一簡單的方法以有效預測主振盪模式因溫度變化而產生的頻率偏移；(3) 非線性的驅動強度依賴性分析顯示，Q 值較低的設計在高激發下更容易產生頻率偏移。;Quartz crystal oscillators are essential components in precision timing systems and communication electronics, where frequency accuracy and stability are critical. As the size of the oscillator requires to be smaller in the future, the resonant region approaches the mounting area may increase acoustic energy dissipation. This study explores linear and nonlinear numerical analysis of quartz oscillators using COMSOL Multiphysics, aiming to optimize Q-factor and improve frequency stability. In the present study, energy loss was addressed through the integration of phononic crystal (PnC) structures. The temperature effect was done by the incremental method. The nonlinear behavior of drive level dependency (DLD) were also investigated to understand the impact on performance degradation. Prior to the simulation, the integration of nonlinear coefficients for quartz elasticity, weak form, and stress-strain modification was conducted on COMSOL equation views. Phononic crystal on the quartz oscillators were then analyzed for their effectiveness in suppressing unwanted modes and improving energy confinement. These structures showed improved Q-factor and structural robustness. The temperature effect was investigated, and a method was presented for easily predicting the frequency shift of the main oscillating mode. The nonlinear analysis of drive level dependency revealed that lower Q-factor designs were more vulnerable to frequency shifts under high excitation.
