本研究主要依靠有限元素法(Finite Element Method, FEM)去分析薄膜體聲波諧振器(thin Film Bulk Acoustic wave resonator, FBAR)元件。在簡化FBAR元件模型之後，可以利用FEM 去評估FBAR元件的諧振頻率點及其各項性質已達到節省直接進行實驗所花的時間及經費。
首先，本研究會分別計算解析解以及結合FBAR元件中核心的壓電材料的壓電方程式和FEM去計算一維單層模型下的數值解，並互相比較誤差。其中，展示及討論了兩種不同利用FEM的方法去評估諧振頻率點。在兩者之中，在不解耦方程式並利用局部矩陣(local matrix)的情況下，可以利用更少的計算資源來達到更精準且接近解析解的數值解。接著，計算及分析多層的FBAR元件模型在一維情況下的差異，可以見到與預估的情況相符合。在一維模型的最後，也會利用計算結果去比較真實的實驗結果。在第二部分，本研究相同的利用壓電方程式及FEM去計算在二維情況下的單層壓電模型。透過單層的模型，可以去分析更多元FBAR元件的性質，包括面積對以及特殊邊界條件對於FBAR元件諧振頻率的影響，包括縱向模態和橫向模態。在本研究最後，數值法運算上所造成的誤差及錯誤會被簡單分析及討論。
本研究成果展示了如何利用數值方法去評估FBAR元件並給予發展及理論模型更多的協助，並期望在未來能達到更準確的評估及給予更多的支持。

This study primarily relies on the Finite Element Method (FEM) to analyze thin Film Bulk Acoustic wave resonator (FBAR) devices. After simplifying the FBAR device model, FEM can be used to evaluate various properties of the FBAR device.
Firstly, this study will separately calculate the analytical solution and the numerical solution of a one-dimensional single-layer model in the FBAR device with FEM, and compare the errors between them. Next, the differences in the one-dimensional case of a multi-layer FBAR device model are calculated and analyzed, showing the difference between single layer structure and multi-layers structure.
In the second part, the study similarly uses piezoelectric equations and FEM to calculate a single-layer piezoelectric model in a two-dimensional situation. Through the single-layer model, more properties of the FBAR device can be analyzed, including the impact of area and a special boundary condition on the resonant frequency, covering both TE and area extension modes. At the end of this study, the spurious mode caused by numerical computation are simply analyzed and discussed.
The results of this study demonstrate how to use numerical methods to evaluate FBAR devices, providing more assistance for the development and theoretical models

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