本論文利用有限元素法以多重物理量分析模擬軟體FEMLAB，建立一以銅/鑽石/銅三層膜構成的散熱元件模型，分析銅與鑽石的介面熱應力。上層銅厚度2µm，改變中間層的鑽石厚度（20µm、50µm、100µm），及底層銅的厚度（100µm、200µm、300µm）。假設元件的製程後無殘留應力，在一般空氣對流的環境下，當元件由室溫27℃上升至溫度100℃、200℃、300℃時，以膜厚的改變，做為散熱元件的參數條件，分析散熱元件在不同膜厚對於不同的溫度，所產生的變形量及應力變化。
本論文研究模擬後發現，以銅/鑽石/銅三層膜構成的散熱元件，在固定之溫度負載下，其最大剪應力，在薄膜厚度改變時，固定上層銅厚度情況下，則最大剪應力會因為鑽石層厚度增加而變大，而且在鑽石厚度為50-70µm時，應力增加較平緩，但同時考慮鑽石熱傳隨鑽石厚度增加，在100µm時有較好的熱傳效果，而底層銅的厚度變化對於最大剪應力沒有太大的影響，所以本論文結論建議鑽石厚度在70µm時對此鑽石、銅三層膜散熱元件是較佳的選擇。其最大變形量，在薄膜厚度固定上層銅厚度及中間層鑽石厚度時，變形量會因為底層銅厚度增加而變小。

The main purpose of this research is to utilize the FEMLAB multiphysics software as to analyze the thermal stress of Cu/Diamond/Cu three-layered heat spreader device. The alteration of film thickness under different temperatures(allowing the device to increase from room temperature of 27°C to 100°C, 200°C and 300°C), with upper Cu layer of 2µm, altered middle diamond layer(20µm, 50µm 100µm), and lower Cu layer(100µm, 200µm, 300µm)(assuming that there is no residual stress produced after the manufacture of heat spreader device), is regarded as the conditional parameter of heat spreader device in analyzing the deformation rate and stress variation produced.

After simulation of the research, it was found out that a maximum shear stress is attained under a fixed temperature load. And, when the film thickness is altered and under a fixed thick of Cu layer, the shear stress will become bigger due to the thickness of the diamond layer increases, when the diamond layer is 50-70µm, stress increases slowly; but it is considered to be the greatest effect when the heat transfer of diamond is at 100µm; thus selection of 70µm would be a better option in this paper suggestion, and that the alteration of the thickness of lower Cu layer will not cause great effect to max shear stress.) After stabilizing the thickness of upper Cu layer and middle diamond layer, the maximum deformation rate will become smaller when the thickness of lower Cu layer increases.

第一章 緒論
第二章 薄膜應力
2.1前言
2.2內應力
2.3熱應力
2.4 Stoney 方程式
第三章 有限元素模擬
3.1前言
3.2有限元素方法的基本步驟
3.3有限元素模型
3.3.1 熱傳分析
3.3.2 結構分析
3.4模擬參數
3.5網格選取及取點分析
第四章 結果與討論
第五章 結 論
附錄 A 鑽石與其他材料性質比較
附錄 B 散熱元件三維(3D)模擬
參考資料

1. 宋健民, “超硬材料”,全華科技圖書,2000,p2-6,7-4－7-16,28,31,54,61
2. H.-S. Park, D. Kwon, “An energy approach to quantification of adhesion strength from critical loads in scratch tests”, Thin Solid Films 307 (1997) 156-162.
3. Y.M. Lian, K.w. Leu, S.L. Liao, W.H. Tsai, “effects of surface treatments and deposition conditions on the adhesion of silicon dioxide thin film on polymethylmethacrylate”, surface and coatings technology 71(1995) 142-150.
4. Tetsuya Hosaka, “Adhesion fracture of a two-layer Auvaporated film with C, W and Cr mixed”, Thin Solid Films 281-282 (1996) 360-363.
5. 陳心保,“鑽石散熱器的製作與分析”,國立中山大學機械與機電工程學系碩士論文,2006,p33-43.
6. Milton Ohring, “The material science of thin film”, Academic press, Inc, New York,1992,p413-429
7. Takao Hanabusa, Kazuya Kusaka, Osami Sakata, “ Residual stress and thermal stress observation in thin copper films”, Thin Solid Films 459 (2004) 245–248.
8. Chao-An Jong, Tsung-Shune Chin, Weileun Fang, “ Residual stress and thermal expansion behavior of TaOxNy films by the micro-cantilever method”, Thin Solid Films 401 (2001) 291–297.
9. Y. Nakamura, S. Sakagami, Y. Amamoto, Y. atanabe,“ Measurement of internal stresses in CVD diamond films”, Thin Solid Films 308–309 (1997) 249–253.
10. B. Gu, P.E. Phelan and S. Mei, “Coupled heat transfer and thermal stress in high-Tc thin-film superconductor devices”, Cryogenics 38 (1998) 411-418.
11. Bei Gu and P. E. phelan, “Thermal peeling stress analysis of thin-film high-Tc superconductors”, Applied superconductivity, pp. 19-20 (1998).S0964-1807.
12. M.P. Rodriguez, N.Y.A. Shammas, “Finite element simulation of thermal fatigue in multilayer structure: thermal and mechanical approach”, Microelectronics Reliability 41 (2001) 517-523.
13. 林士淵, “電漿輔助化學氣相沉積二氧化矽薄膜之內應力分析”,國立成功大學機械工程學系碩士論文,2001, p17.
14. 田春林,“光學薄膜應力與熱膨脹係數量測之研究”,國立中央大學光電所博士論文,2000,p13,19,28.
15. 白木靖寬/吉田貞史著,王建義編譯, “薄膜工程學,全華科技圖書”,2004,p4-16－4-21.
16. 陳建元,”電漿輔助化學氣相沉積二氧化矽薄膜之熱應力與破壞分析”,國立成功大學機械系碩士論文,2001,p15-17.
17. R. H. Gallagher ,“有限元素法”,茅聲燾,陳舜田,李雅榮,陳文華,姚家圻,陳永祥,楊德良,葉基棟譯，科技圖書股份有限公司, 1990, p2.
18.Moaveni,“Finite element analysis theory and application with ANSYS”, Pearson Education, Inc., New York, 2003, p6-8.
19. Daryl L. Logan ,“A First Course in the Finite Element Method using Algor”, PWS Publishing Company, Boston, 1997,p6-13.
20. “Handbook Femlab 3 user’s guide version 3.1”, Sweden COMSOL 2003.
21. “Handbook Femlab 3 modeling guide version 3.1”, Sweden COMSOL 2003.
22. Incropera, DeWitt 原著, “熱傳遞”, 杜鳳棋,張仲卿,侯順雄,張進寬譯, 高立出版社,2003,p2-7,47-50,778,782.
23. Gere and Timoshenko, “MECHANICS OF MATERIALS”, Wadsworth, Inc.1984.p404-407, 424-428.
24. Robert F. Davis ,“Diamond films and coatings : development, properties, and applications” ,Park Ridge, N.J., 1993, p9-10.
25. 陳偉斯,“滲硼之化學氣相沈積鑽石的拉曼光譜分析”,國立中山大學物理所碩士論文,2003,p47.
26. K.R. Dhawan, D.N. Singh, I.D. Gupta, “2D and 3D finite element analysis of undergroundopenings in an inhomogeneous rock mass”, International Journal of Rock Mechanics & Mining Sciences 39 (2002) 217–227.
27. K.R. Dhawan, D.N. Singh, I.D. Gupta, “Finite element-based three-dimensional stress analysis of composite bonded repairs to metallic aircraft structure”, International Journal of Adhesion & Adhesives 26 (2006) 261–273.
28. Ridha Hamabli, Alain Potiron, “Comparison between 2D and 3D numerical modeling of superplastic forming processes”, comput. Methods Appl. Mech. Engrg. 190 (2001)4871-4889.
29. Ridha Hamabli, Alain Potiron, Fabrice Guerin, Bernard Dumon, “Numerical pressure prediction algorithm of superplastic forming processes using 2D and 3D”, Jourmal of Processing Technology 112(2001)83-90.