臺灣博碩士論文加值系統

本研究旨在研發一套全電信號的薄膜材料之楊氏模數與殘留應力的檢測技術。先以尤拉樑(Euler’s beam)理論以及最小能量法(Minimum energy method)的方式，推導出具初始應力之微橋狀樑承受靜電負載下的吸附電壓之解析解，再以靜電結構之吸附電壓反算薄膜材料之楊氏模數與殘留應力。在實驗製程方面，本研究採用與CMOS製程相容的面型矽微加工技術，以鋁金屬作為測試結構材料，萃取出濺鍍鋁薄膜之楊氏模數與殘留應力，與文獻中的數據比較，楊氏模數的誤差在3%以內，殘留應力的誤差在5%以內。另針對數學模型中之假設撓曲函數，本文提出三個不同的假設撓曲函數並比較之。三個假設撓曲函數為：(1) 微結構之固有模態函數(natural mode)；(2) 微結構之挫曲模態函數(buckling mode)；(3) 餘弦函數(cosine function)。其中，以微結構之固有模態為假設撓曲函數所得之結果最為準確。因為樑的固有模態不僅滿足邊界條件，且是根據樑承受橫向力(transverse forces)所推導出來的，而靜電力屬橫向力，故以微結構之固有模態為假設撓曲函數，所得之楊氏模數與殘留應力結果最為準確。

This paper presents a novel and high-precision algorithm and method for extracting the Young’s modulus and residual stress of thin films through the pull-in voltage the micro test-key at wafer level. We derives a closed form solution for the pull-in voltages of the micro fixed-fixed beam subjected to electrostatic loads and initial stress. The closed form solution is derived based on the Euler’s beam theory and the minimum energy method. The accuracy and precision of the present closed form solution is verified through comparing with the experimentally measured data conducted in the published works. Then one can use the aforesaid closed form solution of the pull-in voltage to extracted the Young’s modulus and residual stress of the test structures. The accuracy and precision of the present method for extracting the Young’s modulus and residual stress is verified through comparing with the results conducted in the published works as well as the experiment conducted by the author. The error of the extracted Young’s modulus is below 3% compared to the experimentally measured data and the error of the residual stress is below 5%. Three common assumed deflection shape functions in deriving the closed form solution of pull-in voltage are also discussed in the present work. Those are the natural mode, the buckling mode, and the cosine function. It is shown that the extracted Young’s modulus and residual stress obtained by the natural mode is more accurate than the other two. The natural modes of beam are derived based on the beams subjected to transverse forces, which is similar to the situation of the beam subjected to the transverse electrostatic force. Thus, the natural mode is the best choice.

目錄
誌謝 I
摘要 III
Abstract V
目錄 VII
表錄 X
圖錄 XIII
符號說明 XVII
第1章. 緒論 1
1.1. 研究動機 1
1.2. 文獻回顧 2
1.2.1. 薄膜材料之楊氏模數萃取 3
1.2.2. 薄膜材料之殘留應力萃取 9
1.3. 研究目標 18
第2章. 靜電結構之吸附電壓的解析解 19
2.1. 微結構系統能量式 19
2.2. 吸附電壓之解析解 25
2.3. 理論驗證 28
第3章. 以微結構之吸附電壓反算薄膜材料之楊氏模數與殘留應力 36
3.1. 相關技術簡介(M-TEST) 36
3.2. Fast M-TEST 41
3.3. Fast M-TEST與M-TEST之比較 43
3.4. Fast M-TEST之驗證 44
3.4.1. (100)單晶矽 45
3.4.2. (110)單晶矽 46
3.4.3. 複晶矽(Poly silicon) 48
第4章. 實驗驗證 51
4.1. 測試結構的製程 51
4.2. 吸附電壓量測方法 60
4.2.1. 電容-電壓量測原理 60
4.2.2. 量測儀器之參數設定 60
4.2.3. 電容-電壓靈敏度分析 64
4.3. Fast M-TEST之實驗驗證 66
4.3.1. 實驗一 66
4.3.2. 實驗二 70
4.4. 厚度誤差造成的影響 74
第5章. 不同假設撓曲函數之比較 83
5.1. 假設撓曲函數 83
5.1.1. 固有模態函數(Natural Modes) 84
5.1.2. 挫曲模態函數(Buckling Mode) 84
5.1.3. 餘弦函數(Cosine Function) 85
5.2. 以不同假設撓曲函數萃取複晶矽之材料參數 85
5.3. 以不同假設撓曲函數萃取單晶矽之材料參數 87
5.3.1. (100)單晶矽 87
5.3.2. (110)單晶矽 88
5.4. 以不同假設撓曲函數萃取鋁薄膜之材料參數 90
第6章. 結論與未來展望 92
6.1. 結論 92
6.2. 未來展望 93
參考文獻 95

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