以離散元素法配合顆粒鍵接理論 探討矽晶圓研磨物理機制

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江晁鏷(Chao-Pu Jiang) 查詢紙本館藏

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機械工程學系

論文名稱

以離散元素法配合顆粒鍵接理論探討矽晶圓研磨物理機制

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至系統瀏覽論文 (2028-12-31以後開放)

摘要(中)

研磨是關鍵的加工步驟，廣泛應用於材料科學與半導體製造，通過消除材料表面的不均勻性來實現精密加工，其中晶圓研磨為半導體製程中的關鍵步驟，為接續先前矽晶棒切割後的加工，以確保晶圓表面的平整度與銜接後續製程。矽晶圓屬於脆性材料，研磨過程中容易造成晶圓的損傷，由於晶圓研磨涉及複雜的破壞力學問題，本研究第一次提出離散元素法(DEM)配合顆粒鍵接理論，探討晶圓研磨的破壞過程與物理機制，透過此創新模擬方法，有系統地研究加工參數對晶圓物理性質的影響，並首先探討相同速度比下，速度變化對晶圓物理性質的影響，分析研磨期間作用於研磨刀具的力量與力矩、研磨後材料的剝離率、晶圓內部體積佔有率、晶圓配位數及殘留應力，且為符合實際物理系統，進行單向度壓縮破壞實驗，並採用實驗設計法找尋可靠的微觀輸入參數。
研究結果摘入如下: (1) 研磨力量與力矩皆呈現四段落增減，且隨著刀具逐漸將顆粒磨除，研磨力量與力矩逐漸減少，直至與下一層顆粒接觸時，研磨刀具力量與力矩再次增加，研磨後九個應力分量的中，剪應力對稱，σxx與σyy遠大於其他分量。(2) 當模型試體勁度增加，整體上研磨力量減少，但研磨力矩增加。(3) 隨著旋轉速度的增加，整體上研磨力量與研磨力矩減少，顆粒剝離率增加，晶圓體積佔有率減少，配位數幾乎一致，von Mises應力先增加後減少。(4) 隨著進給速度的增加，整體上研磨力量與研磨力矩增加，隨著進給速度的增加，顆粒剝離率減少，晶圓體積佔有率增加，配位數幾乎一致，von Mises應力減少。(5) 相同速度比情況下，隨著進給速度(旋轉速度)的增加，整體上研磨力量與研磨力矩減少，顆粒剝離率、晶圓體積佔有率及配位數差異不大， von Mises應力減少。速度比採用14.41下產生的研磨力量、研磨力矩及殘留應力皆較小，且設定進給速度為0.085 nm/cycle與旋轉速度為0.94×10-3 rad/cycle下，三種速度比研磨後物理性質最為相近。(6) 隨著晶圓尺寸的增加，整體上研磨力量與研磨力矩增加，顆粒剝離率減少，晶圓體積佔有率與配位數增加，von Mises應力減少。

摘要(英)

Grinding is a crucial machining step widely applied in materials science and semiconductor manufacturing, enabling precise processing by eliminating surface irregularities. Wafer grinding, a critical process in semiconductor fabrication, follows the slicing of silicon ingots to ensure a flat surface for subsequent procedures. Due to the brittleness of silicon wafers, they are susceptible to damage during grinding. This study proposes an innovative approach using the discrete element method (DEM) combined with particle bonding theory to explore the destruction process and physical mechanisms in wafer grinding. Through this innovative simulation method, the research systematically investigates the influence of processing parameters on wafer physical properties. The impact of feed rate on the post-grinding physical properties of wafers under the same speed ratio is firstly examined. This wafer physical properties includes the forces and moments acting on the grinding tool during grinding, material removal rates post-grinding, solid volume fraction, coordination number, and residual stresses of the wafers. To reasonably predict the mechanical response in such a complex system, uniaxial compression test was conducted and design of experiment was employed to calibrate micro-scale input parameters.
The findings revealed several significant insights: (1) Both grinding forces and moments exhibit four distinct fluctuations. As the abrasive grains are gradually removed by the tool, the grinding forces and moments decrease until contact with the next layer of grains, causing an increase in forces and moments. Among the nine stress components after grinding, the shear stress is symmetrical, with σxx and σyy significantly larger than other components. (2) Increasing the stiffness of the model specimen generally reduces the grinding forces but increases the grinding moments. (3) An increase in rotational speed generally reduces both grinding forces and moments. Concurrently, grain removal rates increase, solid volume fraction decreases, coordination numbers remain nearly constant, and von Mises stress initially rises and then declines. (4) Increasing the feed rate generally increases both grinding forces and moments. With the rising feed rate, the grain removal rate decreases, solid volume fraction increases, coordination numbers remain consistent, and von Mises stress decreases. (5) Under the same velocity ratio, an increase in the feed rate (rotational speed) generally reduces both grinding forces and moments, differences in grain removal rate, coordination numbers and solid volume are minimal, and von Mises stress decreases. Employing velocity ratios of 14.41 and 28.81 results in lower grinding forces, grinding moments, and residual stresses. Additionally, configuring the feed rate at 0.085 nm/cycle and the rotational speed at 0.94×10-3 rad/cycle among these three velocity ratios yields the most closely aligned physical properties after grinding. (6) As the wafer size increases, there is a general increase in both grinding forces and moments, grain removal rates decrease, solid volume fraction and coordination numbers increase, while von Mises stress decreases.

關鍵字(中)

★ 矽晶圓研磨
★ 實驗設計法
★ 離散元素法
★ 加工參數
★ 顆粒鍵接理論
★ 單向度壓縮試驗

關鍵字(英)

★ Silicon wafer grinding
★ Design of experiment
★ Discrete element method
★ Processing parameters
★ Particle bonding theory
★ Uniaxial compression test

論文目次

摘要 ........................................................i
Abstract ...................................................iii
目錄 ........................................................v
附表目錄 ....................................................viii
附圖目錄 ....................................................ix
第一章緒論 .................................................1
1.1 當今矽晶圓研磨加工背景 ...................................1
1.2 文獻回顧 ................................................2
1.2.1 矽晶圓研磨相關文獻 .....................................2
1.2.2 離散元素法微觀參數校準相關文獻 ..........................7
1.3 研究動機 ................................................8
第二章數值架構 ..............................................9
2.1 離散元素法 ...............................................9
2.1.1 運動方程式 .............................................9
2.1.2 接觸力模型-線性接觸模型 .................................10
2.1.3 接觸力模型-赫茲接觸模型 .................................12
2.1.4 顆粒鍵接理論 ...........................................13
2.1.5 時間步的決定-密度縮放法 .................................14
2.2 實驗設計法 ...............................................16
2.3 離散元素法模型與架構 ......................................17
2.4 內部性質 .................................................19
2.4.1 晶圓體積佔有率 ..........................................19
2.4.2 平均配位數 .............................................20
2.4.3 殘留應力 ...............................................20
第三章數值模型驗證 ...........................................22
3.1 兩矽顆粒正向彈性碰撞 ......................................22
3.2 矽顆粒與剛性平面正向彈性碰撞 ...............................23
3.3 考慮不同恢復係數下矽顆粒與剛性平面正向碰撞 ..................24
3.4 考慮不同入射角下矽顆粒與剛性平面斜向碰撞 ....................24
第四章數值模型微觀參數的決定 ..................................26
4.1 矽晶柱單向度壓縮破壞物理實驗與DEM模擬 ......................26
4.1.1 矽晶柱單向度壓縮破壞物理實驗 .............................26
4.1.2 矽晶柱單向度壓縮破壞DEM模擬 ..............................27
4.2 微觀參數決定 .............................................27
4.2.1 尋找關鍵因子流程 ........................................27
4.2.2 試誤法縮小參數範圍 ......................................27
4.2.3 使用實驗設計法決定微觀參數 ...............................28
第五章結果與討論 .............................................32
5.1 三組關鍵因子的影響 .........................................32
5.1.1 setting-2 內部物理量 ....................................35
5.1.2 相同晶圓尺寸下，不同顆粒粒徑的影響 ........................36
5.3 不同旋轉速度的影響 .........................................38
5.4 不同進給速度的影響 .........................................41
5.5 相同速度比下速度的影響 ......................................44
5.6 三種速度比下速度變化的影響 ...................................45
5.7 不同晶圓尺寸的影響 ..........................................49
第六章結論 ....................................................52
6.1 結論 .......................................................52
參考文獻 .......................................................54
附表 ..........................................................59
附圖 ..........................................................68

參考文獻

[1] Z.C. Lia, Z.J. Pei, G.R. Fisher, Simultaneous double side grinding of silicon wafers: a literature review, International Journal of Machine Tools and Manufacture, 46 (2006), 1449-1458.
[2] Z.J. Pei, G.R. Fisher, J. Liu, Grinding of silicon wafers: A review from historical perspectives, International Journal of Machine Tools and Manufacture, 48 (2008), 1297-1307.
[3] G. Majumdar, M. Chakraborty, M. S. J. Hashmi, Fine Grinding of Semiconductor Materials: Review of Past and Current Practices, Materials Science and Materials Engineering, (2016), 1-13.
[4] E. Brinksmeier, Y. Mutlugünes, F. Klocke, J.C. Aurich, P. Shore, H. Ohmori, Ultra-precision grinding, CIRP Annals, 59 (2010), 652-671.
[5] J.H. Liu, Z.J. Pei, G.R. Fisher, Grinding wheels for manufacturing of silicon wafers: A literature review, International Journal of Machine Tools and Manufacture, 47 (2007), 1-13.
[6] Z.J Pei, A. Strasbaugh, Fine grinding of silicon wafers: designed experiments, International Journal of Machine Tools and Manufacture, 42 (2002), 395-404.
[7] J.A. Couey, E.R. Marsh, B.R. Knapp, R.R. Vallance, In-process force monitoring for precision grinding semiconductor silicon wafers, International Journal of Manufacturing Technology and Management, 7 (2005), 430-440.
[8] D. Pähler, Measurement of local contact zone forces in rotational grinding of silicon wafers, International Journal of Mechatronics and Manufacturing Systems, 4 (2011), 511-539.
[9] F. Qin, L. Zhang, P. Chen, T. An, Y. Dai, Y. Gong, Z. Yi, H. Wang, In situ wireless measurement of grinding force in silicon wafer self-rotating grinding process, Mechanical Systems and Signal Processing, 154 (2021), 107550.
[10] H. Tao, Y. Liu, D. Zhao, X. Lu, Prediction and measurement for grinding force in wafer self-rotational grinding, International Journal of Mechanical Sciences, 258 (2023), 108530.
[11] Z.J Pei, A. Strasbaugh, Fine grinding of silicon wafers, International Journal of Machine Tools and Manufacture, 41 (2001), 659-672.
[12] W. Sun, Z.J. Pei, G.R. Fisher, Fine grinding of silicon wafers: effects of chuck shape on grinding marks, International Journal of Machine Tools and Manufacture, 45 (2005), 673-686.
[13] H. Li, T. Yu, L. Zhu, W. Wang, Modeling and simulation of grinding wheel by discrete element method and experimental validation, The International Journal of Advanced Manufacturing Technology, 81 (2015), 1921-1938.
[14] B. Luo, Q. Yan, J. Pan, J. Lu, Z. Huang, Influences of processing parameters on metal-bonded diamond wheel wear when grinding a sapphire wafer, Diamond and Related Materials, 113 (2021), 108275.
[15] Z.J. Pei, S.R. Billingsley, S. Miura, Grinding induced subsurface cracks in silicon wafers, International Journal of Machine Tools and Manufacture, 39 (1999), 1103-1116.
[16] Z.J Pei, A study on surface grinding of 300 mm silicon wafers, International Journal of Machine Tools and Manufacture, 42 (2002), 385-393.
[17] A. Haapalinna, S. Nevas, D. Pähler, Rotational grinding of silicon wafers—sub-surface damage inspection, Materials Science and Engineering: B, 107 (2004), 321-331.
[18] H.T. Young, H.T. Liao, H.Y. Huang, Surface integrity of silicon wafers in ultra precision machining, The International Journal of Advanced Manufacturing Technology, 29 (2006), 372-378.
[19] Y. Yang, K.D. Munck, R.C. Teixeira, B. Swinnen, B. Verlinden, I.D. Wolf, Process induced sub-surface damage in mechanically ground silicon wafers, Semiconductor Science and Technology, 23 (2008), 075038.
[20] J. Sun, F. Qin, P. Chen, T. An, Z. Wang, Edge chipping of silicon wafers in rotating grinding, International Conference on Electronic Packaging Technology, (2016), 1099-1103.
[21] L. Zhang, P. Chen, T. An, Y. Dai, F. Qin, Analytical prediction for depth of subsurface damage in silicon wafer due to self-rotating grinding process, Current Applied Physics, 19 (2019), 570-581.
[22] J. Yin, Q. Bai, S. Goel, P. Zhou, B. Zhang, An analytical model to predict the depth of sub-surface damage for grinding of brittle materials, CIRP Journal of Manufacturing Science and Technology, 33 (2021), 454-464.
[23] Z. J. Pei, A. Strasbaugh, Fine Grinding of Silicon Wafers: Grinding Marks, ASME International Mechanical Engineering Congress & Exposition, (2002), 311-320.
[24] Y. Zhang, D. Wang, W. Gao, R. Kang, Residual stress analysis on silicon wafer surface layers induced by ultra-precision grinding, Rare Metals, 30 (2011), 278–281.
[25] S. Gao, Z. Dong, R. Kang, B. Zhang, D. Guo, Warping of silicon wafers subjected to back-grinding process, Precision Engineering, 40 (2015), 87-93.
[26] J. Sun, F. Qin, P. Chen, T. An, Residual stress distribution in wafers ground by different grinding parameters, International Conference on Electronic Packaging Technology, (2017), 327-331.
[27] C. J. Coetzee, Review: Calibration of the discrete element method, Powder Technology, 310 (2017), 104-142.
[28] Y.H. Wang, S.C. Leung, A particulate-scale investigation of cemented sand behavior, Canadian Geotechnical Journal, 45 (2008), 29-44.
[29] L. Benvenuti, C. Kloss, S. Pirker, Identification of DEM simulation parameters by Artificial Neural Networks and bulk experiments, Powder Technology, 219 (2016), 456-465.
[30] M. Rackl, K.J. Hanley, A methodical calibration procedure for discrete element models, Powder Technology, 307 (2017), 73-83.
[31] J. Yoon, Application of experimental design and optimization to PFC model calibration in uniaxial compression simulation, International Journal of Rock Mechanics and Mining Sciences, 44 (2007), 871-889.
[32] K.J. Hanley, C. O′Sullivan, J.C. Oliveira, K. Cronin, E.P. Byrne, Application of Taguchi methods to DEM calibration of bonded agglomerates, Powder Technology, 210 (2011), 230-240.
[33] S. Chehreghani, M. Noaparast, B. Rezai, S.Z. Shafaei, Bonded-particle model calibration using response surface methodology, Particuology, 32 (2017), 141-152.
[34] P. Zhang, X. Sun, X. Zhou, Y. Zhang, Experimental simulation and a reliable calibration method of rockfill microscopic parameters by considering flexible boundary, Powder Technology, 396 (2022), 279-290.
[35] P.A. Cundall, O.D.L. Strack, A discrete numerical model for granular assemblies, Géotechnique, 29 (1979), 47-65.
[36] D.O. Potyondy, P.A. Cundall, A bonded-particle model for rock, International Journal of Rock Mechanics and Mining Sciences, 41 (2004), 1329-1364.
[37] L. Verlet, Computer EXPERIMENTS on classical fluids. I. thermodynamical properties of lennard-jones molecules, Physical Review, 159 (1976), 98-103.
[38] PFC3D 6.0 Documentation, https://docs.itascacg.com/pfc600/pfc/docproject/index.html, Itasca, (2019).
[39] B. Durakovic, Design of Experiments Application, Concepts, Examples: State of the Art, Periodicals of Engineering and Natural Sciences, 5 (2017), 421-439.
[40] K.A.M. Said, M.A.M. Amin, Overview on the Response Surface Methodology (RSM) in Extraction Processes, Journal of Applied Science and Engineering, 2 (2015), 8-17.
[41] D.C. Montgomery, Design and analysis of experiments, 8th edition, John Wiley & Sons Inc., (2013).
[42] 葉怡成，實驗設計法-製程與產品最佳化，五南圖書版股份有限公司，台北市，民國九十年。
[43] P. Sahoo, T.K. Barman, ANN modelling of fractal dimension in machining, Mechatronics and Manufacturing Engineering, (2012), 159-226.
[44] B. Ait-Amir, P. Pougnet, A.E. Hami, Meta-Model Development, Embedded Mechatronic Systems 2, (2015), 151-179.
[45] Silicon , https://reurl.cc/7MYgjl, MatWeb.
[46] 12 inch wafer, https://www.latentek.com.tw/, 拓磊科技
[47] FCC unit cell, https://zhuanlan.zhihu.com/p/28411848.
[48] 許嘉晉，以離散元素法配合顆粒鍵接理論探討矽晶棒線切割物理機制，論文，國立中央大學機械工程學系 (2023).
[49] Y.C. Chung, Granular stresses in granular flows subjected to different obstacles, International Journal of Mechanical Sciences, 247 (2023), 108190.
[50] Y.C. Chung, C.W. Wu, C.Y. Kuo, S.S. Hsiau, A rapid granular chute avalanche impinging on a small fixed obstacle: DEM modeling, experimental validation and exploration of granular stress, Applied Mathematical Modelling, 74 (2011), 540-568.
[51] Y.C. Chung, J.Y. Ooi, Benchmark tests for verifying discrete element modelling codes at particle impact level, Granular Matter, 13 (2011), 643-656.
[52] Y.C. Chung, Z.H. Yang, C.K. Lin, Modelling micro-crack initiation and propagation of crystal structures with microscopic defects under uniaxial tension by discrete element method, Powder Technology, 315 (2017), 445-476.

指導教授

鍾雲吉(Yun-Chi Chung)

審核日期

2023-12-26

推文