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研究生:陳泉泰
研究生(外文):Chuan-TaiChen
論文名稱:以實驗設計法提升飛秒雷射矽通孔之孔洞真圓度
論文名稱(外文):Improving Circularity of Femtosecond Laser Drilling on Silicon Using Experimental Design Method
指導教授:賴新一
指導教授(外文):Hsin-Yi Lai
學位類別:碩士
校院名稱:國立成功大學
系所名稱:機械工程學系
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2014
畢業學年度:102
語文別:中文
論文頁數:105
中文關鍵詞:飛秒雷射矽通孔分子動力學模擬真圓度實驗設計
外文關鍵詞:Femtosecond LaserThrough-Silicon-ViaMolecular Dynamics SimulationCircularityExperimental Design
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雷射鑽孔技術挾其高精度、高加工品質之優勢,在矽通孔(Through-Silicon-Via, TSV)領域上逐漸嶄露頭角;其中又以飛秒雷射對材料周遭結構破壞小、熱影響區域小,使其最具潛力。然而影響通孔品質之研究卻尚止於逐因的定性比較,因此本研究欲以實驗設計方法,通盤考量影響通孔品質之可能因素,探討其顯著性與作用關係,再建立因子對通孔品質影響的回歸模型,並找出最佳因子組合以提升通孔品質或降低能耗成本。本研究成功以分子動力學法模擬飛秒雷射用以加工矽通孔,達到減少實驗成本之目的,並採用真圓度作為量化飛秒雷射矽通孔品質之指標,並細分為入口、出口與孔內真圓度。
透過兩階段實驗設計法規畫實驗,先以部分因子設計篩選出對通孔真圓度具顯著影響的因子,再用完全因子設計分析顯著因子之主要與交互作用,及其貢獻度;並以正向分析Yates運算法建立顯著因子對各孔洞真圓度影響的回歸模型。而計算得回歸模型之配適度均在95%以上,說明各回歸模型皆能高度反映實驗結果。
另外,本研究透過調控貢獻度,以逆向Yates運算對孔洞真圓度進行優化,考慮到業界多元的設計需求,提供兩種優化策略:(1) 依給定真圓度求最低能耗;(2)依指定能耗作最佳真圓度。成功地在指定設計需求下,求出各個真圓度在兩種優化策略中的最佳因子組合。
SUMMERY

In this study, experimental design method are used to analyze the significance and interaction of possible system factors to femtosecond laser drilled hole quality in Through-Silicon-Via (TSV). Circularity of hole is used to characterize the hole quality and is simulated by molecular dynamic simulation to reduce experimental cost. Circularity is divided into three portions including entrance, exit and in-hole circularity. Using a two-step experimental design approach, significant factors that have potential influence on hole circularity are selected via fractional factorial design. Exhaustive factorial design is then used to analyze the major and interaction effects among significant factors. Followed by that, the corresponding mathematical model is thus established via Yates analysis algorithm. The goodness of fit of three circularity models are computed and the results presenting the well fit of the model higher than 95% of the experiment results are achieved. In addition, inverse Yates method is also used to optimally design the hole circularity by readjusting the factorial contribution. To serve for various design objective, two optimization strategies are employed including (1) optimization for minimal energy cost with given circularity, and (2) optimization for best circularity with given energy cost. The results are satisfactory and can be used for innovative design project for various laser drilling processes and can be used for industrial design application.

Key words: Femtosecond Laser, Through-Silicon-Via, Molecular Dynamics Simulation, Circularity, Experimental Design.

INTRODUCTION

With high accuracy and high manufacturing quality, laser drilling has become a popular technology in Through-Silicon-Via process. Since femtosecond laser technology possesses lower damage to surrounding material structure and small heat affected zone, gives it more potential for possible higher quality.


A number of experimental investigations have been performed by researchers such as Baudach, Wang and Yu in order to obtain the effect of different laser parameters on laser drilling results. It turns out that hole quality is affect by various laser parameters. However, there’s still has little studies on the effect of interactions between manufacturing factors. On the other hand, Herrmann, Watanabe, Liu, et al. used molecular dynamics simulation to study ultrafast laser interacts with material. It is shown that molecular dynamics simulation can be an effective tool for research of femtosecond laser drilling.

In this study, circularity is used to characterize laser drilled hole quality on silicon and is simulated by molecular dynamics simulation. Experimental design methods are employed to find out significant factors, to construct mathematical model and to optimize system by improving circularity or decreasing energy cost. The result is verified by simulation using optimized combination of manufacturing factors.

MATERIALS AND METHODS

Models of two different size, 30 nm × 30 nm × 100 nm and 30 nm × 30 nm × 200 nm, as well as two different crystal orientations, (100) and (110), are established for molecular dynamics simulation. Pulse width of laser is 200fs. Tersoff potential is employed to calculate interacting force of atoms. Position and velocity are integrated by velocity Verlet algorithm. Laser energy is transformed into molecular kinetic energy by rescaling atoms’ velocity. The circularity is divided into three portions according to its position including entrance, exit and in-hole circularity.

Considering laser parameter, silicon material and geometrical effect, seven factors are selected in this study. Seven factors are x1 pulse energy, x2 pulse frequency, x3 machining time, x4 material thickness, x5 lattice direction, x6 hole diameter and x7 focus position. Fractional factorial design is used to select significant factors that have potential influence to hole circularity. Exhaustive factorial design is used to analyze significance and contribution of major and interaction effects. Yates analysis algorithm is then used to establish system mathematical model.

Two strategies to optimize laser drilling process are proposed in this study including (1) optimization for minimal energy cost with given circularity, and (2) optimization for best circularity with given energy cost. The inverse Yates method is employed to proceed optimization by readjusting factors’ contributions. To prevent missing optimal solution, factors’ contributions are readjusted through three ways including (a) enhance high contribution (above 15%), (b) enhance middle contribution (10%~15%) and (c) reduce low contribution (below 10%).

RESULTS AND DISCUSSION

Entrance Circularity
The significant factors analyzed are x1 pulse energy, x2 pulse frequency, x5 lattice direction and x6 hole diameter. The provincial mathematical model of system is

and the goodness of fit is 96.21%. The optimization for minimal energy cost with given circularity reduce energy cost form 50 mJ to 42.93 mJ. And the optimization for best circularity with given energy cost improves circularity form 2.1 nm to 1.66 nm.

Exit Circularity
The significant factors analyzed are x1 pulse energy, x2 pulse frequency, x5 lattice direction and x6 hole diameter. The provincial mathematical model of system is

and the goodness of fit is 95.39%. The optimization for minimal energy cost with given circularity reduce energy cost form 50 mJ to 44.8 mJ. And the optimization for best circularity with given energy cost improves circularity form 2.21 nm to 1.86 nm.

In-hole Circularity
The significant factors analyzed are x1 pulse energy, x2 pulse frequency, x4 material thickness and x6 hole diameter. The provincial mathematical model of system is

and the goodness of fit is 95.23%. The optimization for minimal energy cost with given circularity reduce energy cost form 50 mJ to 46.25 mJ. And the optimization for best circularity with given energy cost improves circularity form 2.16 nm to 1.91 nm.

CONCLUSION

Molecular dynamics is used for simulating femtosecond laser drilling on silicon. Entrance, exit and in-hole circularity are obtained from simulations of seven different manufacturing factors. Experimental design methods are employed to select significant factors for each circularity, to establish mathematical model of system and to optimize laser drilling process under different strategies.

The simulation result in this study is more ideal than experiment. However the error would be less than 5%, the result should be practical. Considering the interaction of significant factors, the mathematical model of system would be more accuracy and improvement would be more reasonable.
中文摘要 ......................................I
英文摘要.......................................II
致謝..........................................VI
目錄..........................................VII
圖目錄.........................................XI
表目錄.........................................XIII
符號表.........................................XVI
第一章 緒論.....................................1
1.1 研究動機....................................1
1.2 研究目的....................................2
1.3 章節回顧....................................4
第二章 文獻回顧與研究方法..........................6
2.1 飛秒雷射加工在精微通孔之回顧....................6
2.1.1 飛秒雷射在精微通孔之方法回顧..................6
2.1.2 飛秒雷射在精微通孔之應用回顧..................7
2.2分子動力學模擬在雷射通孔之回顧...................8
2.2.1分子動力學模擬在雷射通孔之方法回顧..............9
2.2.1 (a) 原子作用力之勢能函數.....................9
2.2.1 (b) 疊代步階之數值積分方法...................12
2.2.1 (c) 加速運算之鄰居表列法....................13
2.2.2 分子動力學模擬在雷射通孔之應用回顧.............15
2.3實驗設計建構真圓度模型之回顧.....................16
2.3.1 實驗設計建構真圓度模型之方法回顧...............16
2.3.1 (a) 部分因子設計步驟........................17
2.3.1 (b) 完全因子設計步驟........................24
2.3.1 (c) 順向分析正Yates運算.....................26
2.3.1 (d) 逆向分析逆Yates運算.....................29
2.3.2 實驗設計在雷射精微通孔之應用回顧...............31
2.4 本文之基本假設與研究流程........................32
第三章 研究流程與模型建構...........................35
3.1 理論架構與詳細模型建構流程......................35
3.2分子動力學模擬飛秒雷射矽通孔......................37
3.2.1 矽通孔物理模型與邊界條件......................37
3.2.2 雷射光能量轉換矽原子系統動能...................41
3.2.3 真圓度計算與飛秒雷射矽通孔分子動力學模擬流程......43
3.3 實驗設計法進行顯著分析與建立回歸模型..............47
3.3.1 飛秒雷射矽通孔可控因子水準設定.................47
3.3.2 篩選真圓度之顯著因子與建立回歸模型流程...........48
3.3.2 (a) 以部分設計篩選真圓度之顯著因子.............48
3.3.2 (b) 以完全因子設計建構系統精省回歸模型..........50
3.4 依指定條件用逆Yates運算求解矽通孔最佳因子組合......52
3.4.1 給定真圓度下求最低能耗設計流程.................53
3.4.2 指定能耗下求最佳真圓度設計流程.................56
第四章 孔洞真圓度實驗設計結果與討論...................58
4.1 入口真圓度實驗設計分析與模型建構過程..............58
4.1.1 部分因子設計篩選入口真圓度之顯著因子............58
4.1.2 完全因子設計求入口真圓度顯著因子主要與交互作用....60
4.1.3 順向分析正Yates運算建立入口真圓度精省回歸模型....62
4.1.4 入口真圓度之因子顯著關係與貢獻度討論............63
4.2 出口真圓度實驗設計分析與模型建構過程..............64
4.2.1 部分因子設計篩選出口真圓度之顯著因子............65
4.2.2 完全因子設計求出口真圓度顯著因子主要與交互作用....67
4.2.3 順向分析正Yates運算建立出口真圓度精省回歸模型....69
4.2.4 出口真圓度之因子顯著關係與貢獻度討論............70
4.3 孔內真圓度實驗設計分析模型建構過程................71
4.3.1 部分因子設計篩選孔內真圓度之顯著因子............71
4.3.2 完全因子設計求孔內真圓度顯著因子主要與交互作用....73
4.3.3 順向分析正Yates運算建立孔內真圓度精省回歸模型....75
4.3.4 孔內真圓度之因子顯著關係與貢獻度討論............76
第五章 最佳真圓度與最低能耗之優化設計.................77
5.1依給定真圓度作最低能耗設計.......................78
5.1.1給定入口真圓度求最低能耗優化結果................78
5.1.2給定出口真圓度求最低能耗優化結果................81
5.1.3給定孔內真圓度求最低能耗優化結果................84
5.2 依指定能耗作最佳真圓度設計......................87
5.2.1 指定能耗求最佳入口真圓度優化結果...............87
5.2.2 指定能耗求最佳出口真圓度優化結果...............90
5.2.3 指定能耗求最佳孔內真圓度優化結果...............93
5.3 真圓度優化結果比較與討論........................96
第六章 總結與建議 ................................98
6.1 研究總結.....................................98
6.2 建議與未來展望................................100
參考文獻.........................................102
1. Black, B., et al., 3D Processing Technology and its Impact on iA32 Microprocessors in Computer Design: VLSI in Computers and Processors. 2004, IEEE. pp. 316-318.
2. Ghoreishi, M., Statistical analysis of repeatability in laser percussion drilling, The International Journal of Advanced Manufacturing Technology, 2005, 29(1-2): pp. 70-78.
3. Jiao, L., et al., Parametric Study of Femtosecond Pulses Laser Hole Drilling of Silicon Wafer, Advanced Materials Research, 2009, 74: pp. 273-277.
4. Jiao, L., et al., Statistical Analysis of Femtosecond Pulses Laser on Hole Drilling of Silicon Wafer, Surface Review and Letters, 2011, 18(1): pp. 39-45.
5. Herrmann, R.F.W., Gerlach, J., and Campbell, E.E.B., Ultrashort pulse laser ablation of silicon: an MD simulation study, Applied Physics A, 1998, 66: pp. 35-42.
6. Wang, W., et al., Effect of two typical focus positions on microstructure shape and morphology in femtosecond laser multi-pulse ablation of metals, Applied Surface Science, 2008, 255(5): pp. 2303-2311.
7. Développement, Y., 3-D TSV interconnects - 2008 Report; Equipment & Materials, 2008.
8. Stuart, B.C., et al., Nanosecond-to-femtosecond laser-induced breakdown in dielectrics, physical Review B, 1996, 53: pp. 1749-1761.
9. Nolte, S., et al., Ablation of metals by ultrashort laser pulses, Optical Society of America B, 1997, 14: pp. 2716-2722.
10. Liu, X., Du, D., and Mourou, G., Laser Ablation and Micromachining with Ultrashort Laser Pulses, IEEE Journal of Quantum Electronics, 1997, 33: pp. 1706-1716.
11. Sundaram, S.K. and Mazur, E., Inducing and probing non-thermal transitions in semiconductors using femtosecond laser pulses, Nature Materials, 2002, 1: pp. 217-224.
12. Anisimov, S.I., Kapeliovich, B.L., and Perel'man, T.L., Electron emission from metal surfaces exposed to ultrashort laser pulses, Soviet Journal of Experimental and Theoretical Physics, 1974, 39: pp. 375-377.
13. Chichkov, B.N., et al., Femtosecond, picosecond and nanosecond laser ablation of solids, Applied Physics A, 1996, 63(2): pp. 109-115.
14. Joglekar, A.P., et al., Optics at Critical Intensity: Applications to Nanomorphing, Proceedings of the National Academy of Sciences of the United States of America, 2004, 101(16): pp. 5856-5861.
15. Venkatakrishnan, K., Tan, B., and Sivakumar, N.R., Sub-micron ablation of metallic thin film by femtosecond pulse laser, Optics & Laser Technology, 2002, 34(7): pp. 575-578.
16. Zhou, Y., et al., Near-field enhanced femtosecond laser nano-drilling of glass substrate, Journal of Alloys and Compounds, 2008, 449: pp. 246-249.
17. Baudach, S., et al., Ultrashort pulse laser ablation of polycarbonate and polymethylmethacrylate, Applied Surface Science, 2000, 154-155: pp. 555-560.
18. Ng, G.K.L. and Li, L., The efect of laser peak power and pulse width on the hole geometry repeatability in laser percussion drilling, Optics & Laser Technology, 2001, 2001(33): pp. 393-402.
19. Laakso, P., Penttilä, R., and Heimala, P., effect of shot number on femtosecond laser drilling of silicon, Journal of Laser Micro/Nanoengineering, 2010, 5(3): pp. 273-276.
20. Yu, Y.Y., et al., Ablation of silicon by focusing a femtosecond laser through a subwavelength annular aperture structure, SPIE, 2010, 7789(77890M): pp. 1-6.
21. Cleveland, C.L., Landman, U., and Barnett, R.N., Molecular dynamics of a laser-annealing experiment, Physical Review Letters, 1982, 49: pp. 790-793.
22. Jones, J.E., On the Determination of Molecular Fields. II. From the Equation of State of a Gas, Proceedings of the Royal Society of London, 1924, A: pp. 463-477.
23. Stillinger, F.H. and Weber, T.A., Computer simulation of local order in condensed phases of silicon, Physical Review B, 1985, 31(8): pp. 5262-5271.
24. Broughton, J.Q. and Li, X.P., Phase diagram of silicon by molecular dynamics, Physical Review B, 1987, 35: pp. 9120-9127.
25. Kluge, M.D. and Ray, J.R., Velocity versus temperature relation for solidification and melting of silicon: A molecular-dynamics study, Physical Review B, 1989, 39: pp. 1738-1746.
26. Daw, M.S. and Baskes, M.I., Semiempirical, Quantum Mechanical Calculation of Hydrogen Embrittlement in Metals, Physical Review Letters, 1983, 50: pp. 1285-1288.
27. Tersoff, J., New empirical approach for the structure and energy of covalent systems, Physical Review B, 1988, 37: pp. 6991-7000.
28. Tersoff, J., Empirical interatomic potential for silicon with improved elastic properties, Physical Review B, 1988, 38: pp. 9902-9905.
29. Baskes, M.I., Nelson, J.S., and Wright, A.F., Semiempirical modified embedded-atom potentials for silicon and germanium, Physical Review B, 1989, 40: pp. 6085-6100.
30. Bazant, M.Z., Kaxiras, E., and Justo, J.F., Environment-dependent interatomic potential for bulk silicon, Physical Review B, 1997, 56: pp. 8542-8552.
31. Balamane, H., Halicioglu, T., and Tiller, W.A., Comparative study of silicon empirical interatomic potentials, Physical Review B, 1992, 46(4): pp. 2250-2279.
32. Haile, J.M., Molecular Dynamics Simulation: Elementary Methods. 1992: WILEY. pp. 35-37.
33. Verlet, L., Computer 'experiments' on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules, Physical Review, 1967, 159: pp. 98-103.
34. Swope, W.C., et al., A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters, Journal of Chemical Physics, 1982, 76: pp. 637-649.
35. Watanabe, K., et al., Analysis of laser ablation process in semiconductor due to ultrashort-pulsed laser with molecular dynamics simulation, Proceedings of SPIE, 2000, 3933: pp. 46-55.
36. Nedialkov, N.N. and Atanasov, P.A., Molecular dynamics simulation study of deep hole drilling in iron by ultrashort laser pulses, Applied Surface Science, 2006, 252: pp. 4411-4415.
37. Liu, X., et al., Study of ultrashort laser ablation of metals by molecular dynamics simulation and experimental method, Journal of Materials Processing Technology, 2008, 203(1-3): pp. 202-207.
38. Yang, C.J., Wang, Y.G., and Xu, X.F., Molecular dynamics studies of ultrafast laser-induced phase and structural change in crystalline silicon, International Journal of Heat and Mass Transfer, 2012, 55: pp. 6060-6066.
39. Bharatish, A., et al., Characterization of hole circularity and heat affected zone in pulsed CO2 laser drilling of alumina ceramics, Optics & Laser Technology, 2013, 53: pp. 22-32.
40. Ivanov, D.S. and Zhigilei, L.V., Combined atomistic-continuum modeling of short-pulse laser melting and disintegration of metal films, Physical Review B, 2003, 68(064114): pp. 1-22.
41. Wang, X.W., Thermal and Thermomechanical Phenomena in Picosecond Laser Copper Interaction, Journal of Heat Transfer, 2004, 126(3): pp. 355-364.
42. Perez, D. and Lewis, L.J., Molecular-dynamics study of ablation of solids under femtosecond laser pulses, Physical Review B, 2003, 67(184102): pp. 1-15.
43. Lai, H.Y., et al., Precision modeling of form errors for cylindricity evaluation using genetic algorithms, Journal of the International Societies for Precision Engineering and Nanotechnology, 2000, 24: pp. 310-319.
44. Hayase, M., Ritzdorf, T., and Wu, B., Electronics Packaging 3. Vol. 16. 2009: The Electrochemical Society. pp. 41-42.
45. Lau, J., Through-Silicon Vias for 3D Integration. 2012: McGraw Hill Professional. pp. 94-98.
46. Garrou, P., Bower, C., and Ramm, P., Handbook of 3D Integration. Vol. 1. 2011: John Wiley & Sons. pp. 61-67.
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