以往學者在量測鍍薄膜於基板的殘留應力時，皆採用Stoney's equation，並假設鍍膜於基板接觸介面上之殘留應力為均勻分布，本論文之研究目的在藉由量測矽基板上鍍不同厚度之鉻薄膜後，鍍膜殘留應力的分佈情況，以及殘留應力與鍍膜厚度的關係，以探討殘留應力為均勻分布此假設之適當性。首先在以矽基板製成之懸臂樑鍍上固定厚度之Cr薄膜，透過量測懸臂樑因薄膜殘留應力導致的面外位移後，即可用修正後之Stoney's equation計算出薄膜殘留應力。面外位移的大小是使用數位影像相關法量測，且僅需使用單一CCD鏡頭。本論文共探討了三種鍍膜厚度，分別為1 μm、2 μm和3 μm，每種厚度有三個試片，每個試片上選擇九個不同測試點來量測殘留應力，以探討殘留應力的分步情況。研究結果顯示隨著薄膜厚度增加，殘留應力大小有下降的趨勢，結合實驗結果和統計理論顯示，薄膜厚度3 μm之殘留應力值小於薄膜厚度1 μm時之可靠度為86.5%；實驗結果也顯示殘留應力並非均勻分布，薄膜厚度為1 μm時其殘留應力分布比3 μm時更不均勻之可靠度為70.98%。

In the past, if a researcher intended to measure the residual stress in a thin film coated on a substrate, the Stoney's equation was adopted and assumed that the residual stresses on the interface between film and substrate were distributed uniformity. The purpose of this thesis was to discuss the flexibility of previously mentioned uniformly distributed residual stresses assumption by investigating the distribution of residual stresses in different thickness of Cr film coated on a silicon substrate. Also, the relationship between the film thickness and the magnitude and distribution of residual stresses were studied. Firstly, a specific thickness of Cr film was coated on a cantilever beam made of silicon. Then, the residual stress can be calculated by using modified Stoney's equation and the measured out-of-plane deformation of the cantilever beam which were caused by film residual stresses. The out-of-plane deformation were measured by using digital image correlation technique with single CCD only. This thesis explored three coating thicknesses, which were 1 μm, 2 μm and 3 μm, respectively, and there were three specimens corresponded to each thickness. In order to investigate the distribution of residual stresses, the residual stresses at nine different test points on each specimen were determined. The results showed a trend that the magnitude of residual stress decreased with increasing film thickness. By combining the experimental results and statistical theory showed that the reliability of the magnitude of residual stress corresponding to 3 μm film thickness smaller than 1 μm film thickness was 86.5%. The results also showed that the residual stresses were distributed non-uniformity. The reliability of the residual stresses corresponding to 1 μm film thickness distributed more non-uniform than 3 μm film thickness was 70.98%.

謝誌 i
摘要 ii
Abstact iii
目錄 iv
表目錄 vii
圖目錄 viii
符號表 xi
第一章 緒論 1
1.1研究動機與目的 1
1.2文獻回顧 2
1.2.1數位影像相關法源起 2
1.2.2數位影像相關法三維量測之發展 4
1.2.3三維DIC之應用 5
1.2.4鍍薄膜基板薄膜殘留應力 6
1.3全文架構 9
第二章 基礎理論 10
2.1數位影像相關法 10
2.1.1影像圖片資訊 10
2.1.2影像重建 11
2.1.3物體平面變形理論 12
2.1.4影像相關原理 13
2.1.5影像特徵搜尋 14
2.1.6求取最佳位移函數 15
2.2旋轉座標理論 17
2.3鍍薄膜基板殘留應力 18
第三章 實驗方法 31
3.1實驗儀器與設備 31
3.1.1 硬體儀器 31
3.1.2 軟體設備 33
3.2實驗步驟 34
3.2.1 矽基板與鉻薄膜的規劃 34
3.2.2 矽基板表面影像擷取與分析 35
3.3三維數位影像相關法量測理論推導 36
3.3.1公式推導 36
3.3.2量測角度設定 39
3.3.3比例因子 39
3.3.4影像重建誤差 40
3.3.5量測範圍 42
3.4數位影像相關法三维位移量測誤差分析 42
3.4.1數位影像相關法的解析度和準確度 43
3.4.2剛體位移和剛體旋轉的驗證 45
3.4.3分析結果的正確性 46
3.5應用懸臂樑於鍍薄膜基板薄膜殘留應力之量測 47
3.5.1鍍薄膜基板殘留應力公式推導 47
3.5.2誤差分析 48
第四章 結果與討論 68
4.1實驗結果 68
4.2面外位移量 69
4.3殘留應力的平均值 70
4.4殘留應力的均勻度 72
第五章 結論與未來展望 88
5.1結論 88
5.2未來展望 89
參考文獻 90
附錄 99
附錄一 99
附錄二 102

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