臺灣博碩士論文加值系統

本研究旨在研發薄膜材料之楊氏模數(Young’s modulus)與殘留應力(Residual stress)的全電信號檢測技術，其方法乃是量測一承受靜電力之撓性微結構的電容-電壓變化關係，將之代入本研究推導之微結構材料性質演算法，以檢測出薄膜材料之楊氏模數與殘留應力。其輸入信號與輸出信號皆為電信號，故可利用現有之半導體量測設備，於晶圓製程線上進行即時的量測與監控。此方法優於大多數現有之微機電薄膜材料性質檢測技術。在理論推導方面首先求得微結構樑承受驅動電壓時之應變能及電位能之總能量式，後利用最小能量法(Minimum Energy Method)配合假設撓曲函數(assumed deflection shape function)推導出材料性質演算法。因單晶矽與鋁薄膜之楊氏模數已被明確定義，故本研究採用單晶矽的微懸臂樑結構(Cantilever Beam)與鋁薄膜的微橋狀樑結構(Bridge)來驗證前述之全電信號微結構材料性質演算法。以本方法所萃取之單晶矽(110)晶格面的楊氏模數約為165 GPa，與單晶矽(110)晶格面的楊氏模數168 GPa比較，誤差約為1%，至於所萃取之鋁薄膜的楊氏模數與文獻中的楊氏模數74.14 GPa比較，誤差約為2%，而所萃取之鋁薄膜的殘留應力與表面輪廓儀實際量測出的值相比較，誤差也約1%左右，故証明本演算法是非常精確的。本研究所建立之全電性信號薄膜材料性質檢測技術，可利用現有之半導體量測設備，於晶圓製程線上進行即時的量測與監控，適合大量應用在半導體與微機電製程中。

This thesis presents a novel and high-precision technology for extracting the Young’s modulus and Residual stress of thin films through measuring the capacitance-voltage variation of micro test-key at wafer level. Since the driving and response signals are all electrical, they could be accomplished using existing semiconductor testing equipments through probing on the bonding pads of devices. Because the hardware replacement could be avoided, this methodology shows substantial advantage over other property-extraction methods for large-scale implementation in semiconductor or MEMS fabs. Two algorithms are derived, One is extracting the Young’s modulus through the capacitance-voltage measurement of micro cantilever beam, and the other is extracting the Young’s modulus and Residual stress through the capacitance-voltage measurement of micro bridge. Since the Young’s modulus of single crystalline silicon and aluminum are well-defined, so a micro cantilever beam made of single crystalline silicon and a micro bridge made of sputtering aluminum were used to verify the present methodology. The extracted Young’s modulus of silicon in (110) crystalline plane by the present methodology is about 165 GPa. Compared to the well-defined value (168 GPa), the error percentage is about 1%. The extracted Young’s modulus of sputtering aluminum by the present methodology is comparable to the value (74.14GPa) published in the literature. The error percentage is about 2%. The extracted residual stress of sputtering aluminum by the present methodology comparing to the data measured by the surface profiler has the error percentage of about 1%. The precision and accuracy of the present methodology are thus verified.

誌謝 I
摘要 II
Abstract IV
目錄 VI
表錄 IX
圖錄 XI
符號說明 XVI
第1章 序論 1
1.1. 研究動機 1
1.2. 文獻回顧 2
1.2.1. 量測自然共振頻率 3
1.2.2. 直接拉伸試驗 3
1.2.3. 結構撓曲分析法 4
1.2.4. 電訊號量測法 5
1.3. 研究目標 11
第2章 以微結構之電容-電壓變化萃取楊氏模數與殘留應力之演算法 13
2.1. 微結構系統能量式 13
2.1.1. 微橋狀樑之能量式 13
2.1.2. 微懸臂樑之能量式 19
2.2. 材料性質演算法 21
2.2.1. 假設撓曲函數 21
2.2.2. 以微橋狀樑之電壓–電容變化反算楊氏模數及殘留應力 23
2.2.3. 以微懸臂樑之電容–電壓變化反算楊氏模數 24
第3章 實驗方法 27
3.1. 微結構製程 27
3.1.1. 微橋狀樑製程 31
3.1.2. 微懸臂樑製程 37
3.2. 電容-電壓量測 46
3.2.1. 電容量測原理 46
3.2.2. 量測儀器之參數設定 47
3.2.3. 量測儀器之校正 51
3.3. 寄生電容之修正 51
第4章 結果與討論 53
4.1. 微橋狀樑測試結構 53
4.2. 微懸臂樑測試結構 67
4.3. 厚度誤差造成之影響 76
第5章 結論與未來之方向 88
5.1. 結論 88
5.2. 未來方向 89
參考文獻 90
作者簡介 95

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