本論文找到一種方法用於計算薄膜體聲波諧振器(thin film bulk acoustic wave resonator,FBAR)受電極質量負載影響的諧振頻率，首先經由理論公式計算，再修改計算公式，基於已知的實驗結果找到最佳公式參數，並利用統計的方式提出近似計算公式作為本實驗採用的計算式，由實驗製作之FBAR元件，證明了計算方式在不同實驗的有效性，最終達到預測FBAR電極負載頻率的效果。經由計算文獻數據，發現本實驗提出的電極負載計算公式比起理論推導的計算公式，前者較能計算出實際元件頻率，且本實驗公式計算結果與文獻數據相比誤差極小，證明公式的有效性，應用上可以以此公式預測任一壓電厚度及上電極厚度組合的FBAR諧振頻率。為探討本實驗計算公式在不同實驗下的準確性，製作壓電層厚度分別為1um、1.2um、1.4um，上電極厚度分別為100nm、150nm，共六種厚度組合FBAR。製作的FBAR元件採用背向蝕刻結構，在矽基板上，沉積下電極鉑、壓電層氮化鋁、上電極鋁，反射層使用KOH濕式蝕刻製作空腔，壓電層氮化鋁薄膜由射頻磁控濺鍍機及校正後最佳沉積參數製作而成，不同厚度負載電極利用舉離法完成，元件製作完成後，使用網路分析儀進行元件的頻率響應分析，量測結果諧振頻率落在2-4GHz間，藉由ADS模擬軟體萃取MBVD等效電路的元件數值，可使模擬與量測結果fit，並運算求得元件輸入阻抗、阻抗相位與Q值。最後比較本實驗公式計算頻率與實際元件量測頻率，兩者誤差比起常用的FBAR諧振頻率計算方式降低許多，證明本實驗計算方式可行性，且可使用在不同實驗，大幅減少FBAR調頻需要的流程。

In this study, we developed a set of experimental formula which allows us to obtain FBARs' resonant frequencies closer to practical ones than the estimation from theoretical models. Along with the development of formula, we found that the mass loading effect due to bottom electrodes is negligible. Based on the known experimental results, we calculated the relationship between the relevant values of the formula and the thickness of the piezoelectric film. To confirm the ability of the proposed formula, FBARs were made with varied thicknesses of piezoelectric and top electrodes. The high C-axis-oriented piezoelectric layer of AlN with thicknesses of 1 μm,1.2um, and 1.4um was fabricated by using reactive RF magnetron sputtering. The top electrodes of Al with thicknesses of 100nm and 150nm were fabricated by using sputtering. We determined the resonant frequencies from the measured S-parameters. FBARs’ resonant frequencies are between 2 and 4GHz. That the errors are quite small about 5% for most cases means the formulas can be applied across different fabrication processes provided at least the FBARs possess similar structures. Moreover, we can diminish the error by re-fitting equations according to presently experimental data. In conclusion, the formula can provide a quick estimation with satisfactory error for most FBARs.

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