微機電系統(Micro-Electro-Mechanical System，MEMS)技術是在積體電路基礎上發展起來的。矽作為MEMS和積體電路主要材料，MEMS主要利用其機械特性，而積體電路主要利用其電學特性。因此，隨著 MEMS 的發展，以前在集成電路研究中所忽視的機械特性也得到越來越多的重視。
疲勞是機械產品與結構的最主要失效模式，也是機械強度和可靠性領域的研究熱點。MEMS中的矽質微結構長期在機械驅動下，承受非常高次數的往復載荷，因此產生累積疲勞，進而影響到整體產品的可靠性。自從1992年Connally和Brown[1]的研究探討發現矽質微結構在交變載荷下存在不同於毫米級試樣的疲勞特性，微米級試樣在製造過程中存在結構與材料的穩定性問題，均對結構強度造成影響。研究人員進行了大量研究，希望能夠探明矽微結構的疲勞失效機理。但是各個研究團隊使用了拉伸、彎曲、扭轉三種實驗方法，所得到的結果也不盡相同，直到現在矽微結構的疲勞失效影響因素仍不明確，其疲勞失效機理還存在較大爭議。
因此本文將針對既有的拉伸疲勞實驗之文獻，由基礎的力學理論出發，透過有限單元法軟體ANSYS®建構模型，並在不同文獻間施加設定一致的單元類型、網格大小、求解方式、邊界條件等，以期可以將不同文獻之應力壽命關係進行組間對比，並在此基礎上得到單晶矽薄膜在高週疲勞下的應力-壽命關係式，也即壽命預估公式。
目前，本研究已通過查閲大量期刊、會議論文和理論書籍進行了文獻回顧，已使用基於Basquin公式[2]結合歸一化(Normalization)處理，以分段函數表達式來擬合單晶矽薄膜在高週疲勞下的實驗結果。在有限單元法模擬中，根據矽為脆性材料而選擇破壞準則為最大主應力，並確定所用網格密度大小，從而對文獻結果進行驗證，並嘗試在公式中得到適用度較廣的係數。

Silicon is the most widely used material for integrated circuit (IC) and microelectromechanical systems (MEMS) which is developed based on the IC technology. The properties of silicon used in IC are its electrical properties, while the properties used in MEMS mainly are its mechanical properties. So with the development of MEMS, the silicon’s mechanical properties neglected in IC previously have got more and more attention.
　　Fatigue is the main failure mode of mechanical products and the research focus in mechanical engineering and reliability engineering. Silicon micro structures in MEMS are exposed to long-period mechanical actuation, therefore cumulative fatigue occurs under the cyclic loads, that will have effect on the overall product’s reliability. The fatigue behavior of silicon films was first reported by Connally and Brown in 1992[1], while the fatigue had not been found in the macron-sized specimens, micron-sized specimens have structural and material stability issues during the manufacturing process, all affecting the structural strength. A lot of research have been conduced to reveal the fatigue mechanism of silicon in microscale, hoping to prove the mechanism of fatigue failure of silicon micro structure. However, the research teams used three different experimental methods, which includes tensile fatigue, bending fatigue and rotation fatigue, and the obtained results are not the same. So the fatigue factors remain unclear and the fatigue mechanism is still under debate.
　　Therefore, this work will focus on the existing literature on tensile fatigue test, based on the basic mechanics theory, using finite element method software ANSYS® to build the model, and apply a consistent set of element types, mesh size, solution type, boundry conditions and so on, in order to be able to compare the stress-life relationship among different groups’ results. Finally we will get the stress-life relationship of the silicon thin film under high cycle fatigue, which is the life prediction equation.
　　This work has already complete a review of literature which includes a large number of journal papers, conference papers and published books on basic theory. It was confirmed that the Basquin’s equation [2] with normalized stress was used to fit the experimental data for high cycle fatigue life prediction. In finite element simulation, for the main constituent material in the micro-electromechanical structure is silicon which is a kind of brittle material, the failure criterion will be judged by the maximum principal stress. And the mesh size has been ensured to verify the results of the literature, also this work will try to get a couple of coefficient in Basquin’s equation[2] which is more widely applicable.

目錄
摘 要 I
Abstract III
目錄 V
表目錄 VII
圖目錄 VIII
第一章 緒論 1
1.1 研究背景 1
1.2 研究動機 2
1.3 文獻回顧 3
1.4 研究目標 11
第二章 基礎理論 13
2.1 疲勞理論 13
2.1.1 高週疲勞理論 14
2.1.2 不同平均應力負載條件 15
2.1.3 疲勞壽命預估方法 19
2.1.4 累積破壞理論[17] 24
2.2 有限單元法理論[21] 26
2.2.1 有限單元法基本思想 26
2.2.2 線性有限單元法 28
2.2.3 非線性有限單元法 32
2.2.4 全域局部有限單元法 35
2.3 歸一化理論 36
第三章 研究方法 38
3.1 模型統一處理方法 38
3.2 Bagdahn與Sharpes[11]之模型建構、修正與應力推估 39
3.2.1 模型結構尺寸設定與優化 39
3.2.2 應力收斂分析 43
3.2.3 應力推估與壽命預估 45
3.3 Namazu與Isono[13]之模型建構、修正與應力推估 48
3.3.1 模型結構尺寸設定與優化 48
3.3.2 網格劃分方法 52
3.3.3 應力結果 54
3.4 Nagai等人[14]之模型建構與應力推估 58
3.4.1 模型結構尺寸設定 58
3.4.2 應力結果 61
3.5 應力結果歸一化處理與壽命預估公式之建立 62
第四章 研究結果 67
第五章 未來工作 69
參考文獻 70

參考文獻
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