近年來，由於二維積體電路(Integrated Circuit, IC)晶片將達物理上限，需朝三維空間垂直整合的方向發展，各晶片層間為達訊號連通，於矽晶圓上鑽圓形微孔，再灌入導電材質，此新互連技術稱為矽通孔(Though Silicon Via, TSV)。由Hammerstad Model 可知電阻隨矽通孔粗糙度增加而上升，而電阻增加造成功率的損失，進而造成訊號傳遞效率下降。有鑑於此，本文針對矽通孔粗糙度做進一步的探討，文中提出具體可行的飛秒雷射矽通孔模擬與改善粗糙度之方案。
本文經分子動力學模擬飛秒雷射矽通孔，並計算矽通孔孔表與孔內粗糙度，透過實驗設計法篩選出顯著之雷射加工因子，建構改善矽通孔孔表孔內粗糙度之精省模型，再依業界指定成本或指定粗糙度下，以逆Yates進行優化，優化後之粗糙度經計算，可減少訊號損失約23%，本文成功降低矽通孔粗糙度進而改善訊號傳遞損失，這正是本文研究動機。
本研究之結果可以用來再設計新型雷射通孔，降低成本與改善訊號，作為未來工業界提升品質之工具。矽通孔粗糙度與訊號完整性間尚有許多值得探討的地方，未來可進一步研究反射係數S11與矽通孔粗糙度之關聯性，藉由改善粗糙度確保訊號不受反射而失真。

SUMMARY

By using Hammerstad Model, the resistance increases with the rise of roughness of silicon hole is realized. Due to the increase of resistance, the efficiency of signal transmission can be dramatically decrease. Therefore, this thesis is intended to study the roughness of silicon hole, and in an attempt to bringing up a feasible molecular dynamics simulation of TSV by femtosecond laser. The program to improve roughness of TSV is thus launched.This thesis simulates femtosecond laser drilling of silicon holes by molecular dynamics and also computes the roughness of the surface and inside of holes. The factors significantly influence the roughness of the laser processes by experimental design is thoroughly investigated. Based upon the real conditions of specified production cost and designated roughness required by the industry, the roughness by inverse Yates are employed to design for meeting the design objectives. The optimally designed results are found to be able to reduce signal loss about 23%. The roughness of silicon holes are significantly reduced and the signal transmission loss is greatly improved. This coincide with the motivation and objectives of this study.

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

INTRODUCTION

In the passed recent years, two-dimensional IC chip production have graduating reach its physical limits. Three-dimensional space for vertically integrating is emerged as a necessitate. To enable signal connectivity between chip layers, drilling a circular hole on silicon wafer, and then filling with conductive materials is a new challenge. Research area that the interconnect technology is called “Through Silicon Via, TSV”. Current methods of drilling holes on silicon wafer are laser and etching. The requirements of accuracy have increasing, Laser processes are getting attention. Comparing with traditional long-pulsed laser, femtosecond laser have better precision, so the femtosecond laser processes will become the mainstream in drilling micro hole.

Nowadays, relevant literatures about femtosecond laser and TSV are quite rich. Chichkov and Momma. proved that heat affected zone produced by femtosecond laser is smaller than long-pulsed laser and fs laser is quite useful in processing of nano device. To better understand the interaction between femtosecond laser and materials, Herrmann, R.F.W and Heino used molecular dynamics to simulate femtosecond laser machining. In addition, Hammerstad found that the efficiency of signal transmission can be dramatically decrease due to the roughness of conductive materials inside the TSV.

Most of the studies only investigate the shape of the holes by laser processing, having no qualitative analysis of precision, and without a set of scientific and statistical methods designed after provincial downsizing. This may limits the advancement of precision for TSV processes. In view of the needs, this thesis is devoted to build the MD model of femtosecond laser drilling TSV and construct sets of rigorous experimental and practical design rule for possible modeling in order to reduce the roughness of silicon holes and improve the signal transmission loss.

MATERIALS AND METHODS

This thesis employs the molecular dynamics(MD) to investigate the transport phenomena of femtosecond laser(200fs) drilling of silicon holes and compute the roughness of the surface and inside of holes. The sizes of silicon model are 30nm*30nm*100nm and 30nm*30nm*200nm. To describe the actual phenomenon, this thesis applies tersoff potential to calculate the force between silicon atoms. By considering the computational efficiency and accuracy, velocity-Verlet is used to integrate the Newton Second Law.

This thesis employs the experimental design to research the way to improve the roughness of TSV drilling by femtosecond laser. There are seven factors to be considered into this thesis, X1 pulse energy, X2 pulse frequency, X3 machining time, X4 material thickness, X5 lattice direction, X6 hole diameter and X7 focus position. First of all, fractional factorial design is used to select notable factors. Next, using full factorial design and Anova analysis to investigate the effects of interaction between factors. Then, constructing the provincial regression model by Yates operation.

In addition, this thesis optimizes the provincial regression model by adjusting contribution of processing parameters and inverse Yates operation based upon the real conditions specified production cost and designated roughness required by industry. By Hammerstad model, the resistance decreasing with drop in roughness of silicon hole can be calculated. Due to the drop in resistance, the signal transmission loss can be dramatically decrease.

RESULTS AND DISCUSSION

Through the molecular dynamic femtosecond laser TSV model constructed by this thesis, the roughness of the surface and inside of the hole can be clearly calculated. Due to the error between simulation and experimental operation is less than5%, this thesis prove that the roughness of the holes caused by femtosecond laser is much smaller than etching.

The results of fractional factorial design show that the notable processing parameters, X1pulse energy, X2 pulse frequency, X5 lattice direction and X6 hole diameter significantly influence the roughness of the surface. The notable processing parameters, X1pulse energy, X2 pulse frequency, X4 material thickness and X5 lattice direction significantly influence the roughness inside of the hole. Through full factorial design, the provincial model of two cases, roughness of the surface and inside of the hole, are
Ys=7.78+1.86X1+1.55X2+0.85X5+0.89X6+0.38X12-0.33X16-1.06X26 [R2=556.3(96.69%),ε2=19.05(3.31%)]
and
Yh=8.3+1.35X1+2.07X2+0.95X4-0.84X5+0.93X12+1.01X14+0.91X24
[R2=546.6(93.61%),ε2=37.15(6.36%)].
Based upon the conditions of designed roughness of the surface and inside of the hole, the optimizing results of energy cost decrease 0.11mJ and 0.1 mJ respectively. Under the conditions of specified energy cost, the roughness of the surface and inside of the hole decrease 3.94nm and 1.04nm respectively.

CONCLUSION

This thesis successfully selects the notable processing parameter components and effectively decreases the roughness of silicon holes. Through signal calculating proves that the efficiency of signal transmission dramatically increase 23%.The result of this study can be used in redesigning new holes drilled by lasers, minimizing the production cost, improving signal integrity, and is instrumental for improving the quality for industry in future applications. Relationship between roughness and signal integrity are worthy for further study in the future. The study of connection between S11 (reflection parameter) and roughness are urged to further study in the near future. To ensure the signal not being distorted by reflection, the improvement on the roughness of TSV is considered to be of the first priority.

1. Reid, D.T., “Toward attosecond pulses.Science,” Laser physics, 2001,291: pp.1911-1913.
2. Chichkov, B.N., Momma, C., Nolte, S., Tünnermann, A., “Femtosecond, picosecond and nanosecond laser ablation of solids,” Applied Physics A: Materials Science & Processing,1996, 63(2): pp. 109-115.
3. Dumitru, G., Romano, V., Weber, H.P., Sentis, M., and Marine, W., “Femtosecond ablation of ultrahard materials,” Applied Physics A: Materials Science & Processing, 2002,74(6): pp. 729-739.
4. Rizvi, N.H., “Femtosecond laser micromachining: Current status and applications,” RIKEN Review,2003, 50: pp. 107-112.
5. Joglekar, A.P., Liu, H., Meyhöfer, E., Mourou, G., Hunt, A.J., and Ippen, E.P., “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.
6. Venkatakrishnan, K., Tan, B., Sivakumar, N.R., “Sub-micron ablation of metallic thin film by femtosecond pulse laser,” Optics & Laser Technology, 2002,34(7): pp. 575-578.
7. Zhou, Y., Hong, M.H., Fuh, J.Y.H., Lu, L., Lukyanchuk, B.S., and Wang Z.B., “Near-field enhanced femtosecond laser nano-drilling of glass substrate,” Journal of Alloys and Compounds,2008, 449(1-2): pp. 246-249.
8. Korte, F., Koch, J., Fallnich, C., Ostendorf, A., and Chichkov, B.N.,” Toward nanostructuring with femtosecond laser pulses,”Nanotechnology. Maspalomas, Gran Canaria, Spain: SPIE. 2003.
9. Hermmann, R.F.W.,Gerlach, J., and Campbell, E.E.B., “Ultrashort pulse laser ablation of silicon:an MD simulation study,”Applied Physics A: Materials Science & Processing, 1997,66(1): pp. 35-42.
10. Perez, D., Lewi, L.J.S., “Molecular-dynamics study of ablation of solids 158 under femtosecond laser pulses,” Phys. Rev,B,2003, 67:pp.184-102
11. Zhigilei, L.V., Leveugle, E., Garrison, B.J., Yingling, Y.G., Zeifman, M.I., “Computer simulations of laser ablation of molecular substrate.”Chem. Rev,2003,103:pp.321.
12. Sundaram, S.K., Mazur, E., “Inducing and probing non-thermal transitions in semiconductors using femtosecond laser pulses,” Nature Mat, 2002, 1: pp. 217.
13. Momma, C., Nolte, S., Chichkov, B.N., Alvensleben, F.V., and Tunnermann, A., “Precise laser ablation with ultrashort pulses,” Applied Surface Science, 1997,109-110: pp. 15-19.
14. Coyne, E., Magee, J., Mannion, P.,and Gerard, M., “A study of femtosecond laser interaction with Wafer-grade silicon,” SPIE Proceedings,2003, 4876:pp.487-499.
15. Jiao, L., Zheng H., “Parametric study of femtosecond pulses laser hole drilling of silicon wafer,” Advanced Materials Research, 2009, 74: pp.273-277.
16. David, J.H, Hee, K.P., “Femtosecond laser drilling of crystalline and multicrystalline silicon for advanced solar cell fabrication”, Applied Physics A,2012,108:pp.113-120.
17. Yang, J., Zhao, Y., Zhua, X., “Transition between nonthermal and thermal ablation of metallic targets under the strike of high-fluence ultrashort laser pulses,” Applied Physics, 2006, 88:pp. 94-101.
18. Lui, X., Du, D., Mourou, G., “Laser ablation and micromachining with ultrashort. laser pulses,” IEEE, 1997, 33:pp.1706.
19. Choi, T.Y., Hwang, D.J., Grigoropoulos, C.P., “Ultrafast laser-induced crystallization of amorphous silicon films,” Opt. Eng, 2003, 42:pp. 3383.
20. Irving, J.H. and Kirkwood, J.G., “The statistical mechanical theory of transport,” properties.IV. The equation of hydrodynamics. J.Chem.Phys, 1950,18: pp.817-829.
21. Haile, J.M., “Milecular Dynamics Simulation :Elementary methods,”John Wiley & Sons,New York,1992.
22. Tersoff, J., "New empirical approach for the structure and energy of covalent systems," Physical Review B, 1988, 37: pp. 6991-7000.
23. Tersoff, J., "Empirical interatomic potential for silicon with improved elastic properties," Physical Review B, 1988, 38: pp. 9902-9905.
24. Cleveland, C.L., Landman, U., Barnett, R.N., “Molecular dynamics of a laser-annealing experiment,” Phys. Rev, 1982, 49: pp.790.
25. Iwaki, T., “Molecular Dynamics Study on Stress-Strain in Very Thin Film (Size and Location of Region for Defining Stress and Strain),” SME Int. J. A, 1996, 39: pp. 346.
26. Kotake, S., and Kuroki, M., “Molecular dynamics study of solid melting and vaporization by laser irradiation,” Int.J.Heat Mass Transfer, 1993, 36(8): pp.2061-2067.
27. Hakkinen, H., Landman, U., “Superheating, melting and annealing of copper surfaces,”Phys. Rev, 1993, 7: pp. 1023.
28. Ohmura, E. and Fukumoto, I., “Molecular Dynamics Simulation on Laser Ablation of FCC Metal,” Int.J.Japan Soc.Prec.Eng, 1996,30(2): pp.128-133.
29. Schotz, J., Rasmussen, T., Jacobsen, K.W., Nielsen, O.H., “Mechanical Deformation of Nanocrystalline Materials,” Philosophical Magazine, 1996, 74: pp. 339 .
30. Heino, P., Hakkinen, H., Kaski, K., “Molecular-Dynamics Study of Copper with Defects under Strain,” Phys. Rev. B,1998, 58:pp.641.
31. Herrmann, R.F.W., Gerlach, J., Campbell, E.E.B.,“Ultrashort pulse laser ablation of silicon: an MD simulation study,”Appl. Phys. A,1998, 66:pp. 35-42.
32. Wang, X., and Xu, X.,“Molecular Dynamics Simulation of Heat Transfer and Phase Chang During Laser Material Interaction,”Transactions of the ASME, Journal of Heat Transfer, 2002, 124: pp. 265-274.
33. Ghoreishi, M., "Statistical analysis of repeatability in laser percussion drilling," The International Journal of Advanced Manufacturing Technology, 2005, 29(1-2): pp. 70-78..
34. Mozina, J., Dovc, M., “One-dimensional model of optically induced thermoelastic waves,” Mod. Phys. Lett. B,1994, 8:pp. 1791.
35. Siwick, B.J., Dwyer, J.R., Jordan, R.E., Miller, R.J.D., “An atomic-level view of melting using femtosecond electron diffraction,” Science, 2003,302: pp.1382.
36. Jiang, L., Tsai, H.L., “Energy Transport and Material Removal During Femtosecond Laser Ablation of Wide Bandgap Material,” International Journal of Heat and Mass Transfer, 2005, 48:pp.487-499.
37. Qiu, T.Q., Tien, C.L., “Shot-pulse laser heating on metals,” International Journal of Heat and Mass Transfer,1992, 35:pp. 719-726.
38. Qiu, T.Q., Tien, C.L., “Heat transfer mechanisms during short-pulse laser heating of metals,”J. Heat Transfer ,1993,115:pp. 835.
39. Xie, X.F, “High density plasma used in high sensitivity etching of aluminum inner connection structure with 0.22 micrometer CD of 12,”2007.
40. Tsai, J.H, “The Study of the Enhancement for Bumping Dielectric Layer Process of Wafer Level Chip Scale Packing,”2013.
41. 吳政霖，雷射對陶瓷鑽孔的特性分析及預測模式之探討，屏東科技大學，2003。
42. 劉維軒，矽晶太陽電池之雷射切割製程參數分析，國立高雄應用科技大學，2010。
43. 胡木浩，雷射切割不銹鋼之粗糙度預測模式探討，屏東科技大學，2013。