於鍍膜製程中，常因薄膜與基板熱膨脹係數不匹配而導致殘留應力的發生，進而造成鍍膜的破壞。然而，目前所有殘留應力量測的方式都是利用Stoney方程式，僅可計算薄膜的平均縱向殘留應力，但由於鍍膜製程中結晶顆粒大小的不同或厚度不均勻等因素，皆會造成薄膜上各點的殘留應力不同，且除縱向殘留應力外，橫向殘留應力亦會發生。
本研究提出一套新的量測方法，結合三維數位影像相關法與修正過之Stoney方程式，可同時測得鍍膜任何位置之縱向殘留應力與橫向殘留應力。本研究分別利用所提方法與三維表面輪廓儀中的Istar31軟體量測於矽基板鍍鎳薄膜之殘留應力，實驗結果顯示，兩者所得到的殘留應力值誤差在7%以下，證明本研究所提方法之準確度。接著，本研究利用所提方法探討於矽基板鍍製鉻薄膜時，薄膜厚度變化對殘留應力大小與分佈均勻性的影響，此處殘留應力指的是由縱向殘留應力與橫向殘留應力組成之等效殘留應力。從實驗結果得知，隨著鍍膜厚度的增加，平均等效殘留應力會隨之降低；當薄膜厚度從1μm增到3μm時，平均等效殘留應力下降了92.47%。若厚度的變化夠大，當薄膜的厚度增加時，殘留應力分佈會越來越均勻；當薄膜厚度從1μm增到3μm時，殘留應力分佈均勻度可以提高23.91%。

During thin film deposition, the mismatching of thermal expansion coefficients between thin film and substrate may induce residual stress in the film, and damaging the coated specimen. Most researchers adopted Stoney’s equation to obtaining the residual stress at a coated thin film. However, only the average longitudinal residual stress at a coated thin film can be found. But due to variations of many parameters in the coating process, such as crystalline particle size and the unevenness of the thickness of coated film, will resulting in different residual stress at each location of a coated thin film. Also, in addition to longitudinal residual stress, the transverse residual stress will occur on the coated film.
In this study, a novel experimental technique, by combining the 3-D digital image correlation technique and the modified Stoney’s equation, is proposed, which can measure both longitudinal and transverse residual stresses at any location in a coated thin film. Considering a thin Ni-film coated on a Si-substrate, and the residual stress at the thin film was measured by using the proposed technique and 3-D surface profile with software Istar31, separately. By comparing the experimental results obtained from both approaches, it can be shown that the accuracy error of the proposed technique is less than 7%. Then, the proposed technique was adopted to study effects of thickness variations of thin Cr-film, which was coated on Si-substrate, on magnitude and distributive uniformity of residual stress at the film. Here, the residual stress means the equivalent residual stress resulted from longitudinal and transverse residual stresses. The experimental results indicate that the average equivalent residual stress decreased as the thickness of the coated thin film increased. When thicknesses of thin film increasing from 1μm to 3μm, the average equivalent residual stress was decreased by 92.47%. The results also show that if the film thickness increases enough, the distribution of equivalent residual stress will get more uniform. As the thickness increasing from 1μm to 3μm, the distributive uniformity of the equivalent residual stresses can be increased by 23.91%.

Contents

論文審定書 ……………………………………………………………… i
誌謝 …………………………………………………………….….…… ii摘要 ….................................................................................……….......... iii
Abstract ………..........………………………………………….….......... iv
Contents ...……………………………………………………….….…… vi
List of Tables …………………………………...……….……………... ix
List of Figures ………………………………...……………………. xi
Nomenclature ………………………………………………………..… xiii

Chapter 1 Introduction …………………………………………………. 1
1.1 Background ………………………….………………………. 1
1.2 Review of Literatures …………………………………………. 1
1.2.1 Digital Image Correlation………………………………... 1
1.2.2 Three-Dimensional Digital Image Correlation………… 3
1.2.3 Measurement of Residual Stress in Thin Films………… 4
1.3 Aims and Objectives ……...…….……………………………. 7
1.4 Dissertation Structure ……………………………………...…. 7

Chapter 2 Theory ………………………………………………………... 9
2.1 Longitudinal and Transverse Residual Stresses of Thin Films... 9
2.2 Measure the Radius of Curvature……..…………………….... 12
2.3 DIC Plane Deformation theory…………………….…………. 13
2.4 Theory Concerning Measurement of Three-Dimensional Displacements………………………….……………………. 15
2.5 Definition of Uniformity of Distribution of Residual Stress…. 17

Chapter 3 Experimental Method…….……….……………………… 27
3.1 Introduction ……………………………………..…………… 27
3.2 Image Information ……………………..…………………..… 28
3.3 Image Reconstruction ………………..…………………….… 28
3.4 Experimental Materials……...…………………………..…. 28
3.5 Measurements of Displacements in Thin Films……..……. 30
3.5.1 2D Digital Image Correlation Measurements…..….……. 30
3.5.2 3D Digital Image Correlation Measurements…..….…… 30

Chapter 4 Results and Discussions…………………………………… 41
4.1 Two-dimensional Digital Image Correlation Method for Residual Stress Measurement in the Nickel Coating of the Specimen..... 41
4.2 The Effects of Film Thickness Variations in Coated Cr Thin Films………………………………………………………… 43
4.2.1 Residual Stress Measurement in Coated Cr Thin Films…………………………………………………… 43
4.2.2 Residual Stress Distributions in Coated Cr Thin Films…………………………………………………… 46

Chapter 5 Conclusions and Future Prospects ……………………… 72
5.1 Conclusions ………………………………………………… 72
5.2 Future Prospects …………………………………………… 73

References …………………………………………….…….………… 74
VITA ……………………………………………………………….…... 79

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