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研究生:張睿群
研究生(外文):Jui-ChunChang
論文名稱:飛秒雷射於微矽通孔表面粗糙度之建模與實驗設計精度改善之研究
論文名稱(外文):Surface Roughness Enhancement for Femtosecond Laser Silicon Drilling via Experimental Design
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:100
中文關鍵詞:飛秒雷射矽通孔分子動力學模擬實驗設計法粗糙度
外文關鍵詞:Femtosecond LaserThrough-Silicon-ViaMolecular Dynamics SimulationExperimental DesignRoughness
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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.
目錄
中文摘要 I
英文摘要 II
誌謝 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 章節導覽 4
第二章 文獻回顧與理論基礎 5
2.1飛秒雷射在通孔製程上之回顧 5
2.1.1飛秒雷射在通孔製程上之方法回顧 5
2.1.2飛秒雷射在通孔製程上之應用回顧 7
2.2分子動力學模擬飛秒雷射之回顧 8
2.2.1分子動力學模擬飛秒雷射之方法回顧 9
2.2.1(a) 基本假設與條件設定 9
2.2.1(b) 分子間作用力與勢能函數 13
2.2.1(c) 加速模擬演算法 17
2.2.1(d) velocity Verlet 20
2.2.2分子動力學模擬飛秒雷射之應用回顧 21
2.3實驗設計法建構粗糙度之順逆運算回顧 23
2.3.1建構粗糙度模型之方法回顧 23
2.3.1(a) 2k-p部分因子設計及變異數分析之原理與步驟回顧 24
2.3.1(b) 完全因子設計及精省回歸模型建構之原理與步驟回顧 29
2.3.1(c) 順向分析及逆向設計之原理與步驟回顧 33
2.3.2實驗設計法在工程上之應用回顧 38
2.4本文之基本假設與研究流程 39
第三章 飛秒雷射改善矽通孔粗糙度之理論模型建構 41
3.1理論架構與詳細模型建構流程 41
3.2 分子動力模擬飛秒雷射微矽通孔與粗糙度計算 43
3.2.1飛秒雷射矽通孔模擬流程與參數設定 43
3.2.2矽晶體模型設定 45
3.2.3飛秒雷射光能模型 46
3.2.4矽通孔粗糙度計算 47
3.3實驗設計建構矽通孔粗糙度之精省模型 49
3.3.1部分因子設計流程與粗糙度可控加工因子篩選 49
3.3.2完全因子設計流程與粗糙度精省回歸模型建構 52
3.4指定條件下之優化設計 54
3.4.1給定粗糙度下之逆向優化流程與雷射加工參數設計 54
3.4.2給定能耗下之逆向優化流程與雷射加工參數設計 56
3.5優化設計後之訊號改善計算 58
第四章 微矽通孔粗糙度之實驗設計結果與討論 60
4.1微矽通孔孔表粗糙度之顯著加工因子篩選與精省模型建構 60
4.1.1部分因子設計篩選孔表粗糙度之顯著加工因子 60
4.1.2孔表粗糙度之完全因子設計與精省模型建構 64
4.1.3雷射加工參數貢獻度對孔表粗糙度之結果與討論 68
4.2微矽通孔孔內粗糙度之顯著加工因子篩選與精省模型建構 69
4.2.1部分因子設計篩選孔內粗糙度之顯著加工因子 70
4.2.2孔內粗糙度之完全因子設計與模型建構 73
4.2.3雷射加工參數貢獻度對孔內粗糙度之結果與討論 77
第五章 改善矽通孔粗糙度與能耗之逆Yates優化設計 79
5.1.給定矽通孔粗糙度下最低能耗之雷射加工參數組合 79
5.1.1給定孔表粗糙度之逆Yates能耗優化結果 79
5.1.2給定孔內粗糙度之逆Yates能耗優化結果 82
5.2給定能耗下最佳矽通孔粗糙度之雷射加工參數組合 85
5.2.1給定能耗下之逆Yates孔表粗糙度優化結果 85
5.2.2給定能耗下之逆Yates孔內粗糙度優化結果 88
5.3優化設計後之訊號改善成果 91
第六章 結論與建議 93
6.1總結 93
6.2未來展望與建議 95
參考文獻 96

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