本文所建立之銅晶圓CMP研磨機制模型，可分為物理、機械兩部份。物理部分探討本文所獨創的等向性碎形粗糙度理論配合不均勻非碎形處理技巧，求出比高斯分布更接近真實之研磨墊的等向性碎形粗糙峰分布，並進而利用相同原理，說明碎形理論在微小結構量測、研磨後之晶圓表面形貌檢測甚至地形地貌方面的應用。
機械部份主要探討CMP研磨過程流場分布與晶圓、粉體與研磨墊三者之接觸情形。於流場的分析，本文建立含微顆粒及粗度效應之雷諾方程式，來探討CMP混合潤滑之流場，藉由理論數值分析計算得到流場之液動壓力、液膜厚度及流場分佈。固體接觸部分則包含研磨墊粗度峰及研磨墊底材之彈性變形，以及晶圓研磨面與砥粒接觸之彈塑性變形分析。理論部分，本文中使用了等向性碎形粗度分佈，估算晶圓研磨墊間之真實接觸壓力、接觸面積半徑與變形量，再由力之作用粒與反作用粒定律，求晶圓研磨面與砥粒間之真實接觸壓力、接觸面積半徑與晶圓變形量。最後用黏附理論修正晶圓砥粒間接觸面積半徑，再代入本文所推導的的梯形面積法之砥粒刮蝕機械移除率理論與一系列有關鈍化層部分的研究與實驗，驗證理論之正確性。
實驗設備部分，分別使用了本奈米磨潤實驗室的毫微米(精度達100 )三維粗度儀、次奈米掃描式探針顯微鏡(SPM,精度達1 )對研磨墊及晶圓面做表面形貌分析、奈米微硬度實驗機(精度達10 )做鈍化層厚度與硬度、楊氏模數關係之微硬度實驗。在SPM圖像的解析部分，我們亦使用實驗設備得到晶圓研磨後的奈米刮痕與粗糙度參數，並與數值解析結果比較，驗證理論推導之正確性。最後，藉由控制自動平衡點的位置，提供非本論文實驗中，其他CMP研磨參數：研磨墊、研磨液、砥粒粒徑與背壓力最佳化設計之方向。
過去實驗室研究過的題目包括：CMP流場壓力與速度分布理論之建立、對心式與非對心式CMP機台設計與性能測試、研磨墊花樣對CMP的影響、銅膜鈍化層化學反應生成速率及濃度分布理論之建立、砥粒旋轉耦合效應理論之建立、砥粒聚集後的平均二次粒徑理論之建立、研磨液位移能理論之建立，並分別在不同晶圓、研磨墊轉速、下壓力、研磨墊花樣、二次粒徑、活化能、研磨時間的研磨參數下，討論對銅膜CMP化學生成速率的影響。
本論文主要的貢獻在於：推導出等向性碎形粗糙度分佈理論與具黏附效應之砥粒刮蝕機械移除率理論、提出砥粒機械移除率與銅膜鈍化層化學生成速率達自動平衡的示意圖、用實驗找出自動平衡點位置並求出理論相關分析數據，並用實驗驗證理論之正確性、由理論數值結果，說明自動平衡點在CMP裡扮演的角色，最後並由理論推導各研磨參數對平均移除率、不均勻度、平坦度及鈍化層殘留厚度的影響。

This dissertation aims to study the removal rate of the copper Chemical mechanical Polishing (CMP) from the viewpoint of chemical reaction in chief. The establishment of the CMP model is divided into the mechanical part、physical part and the chemical part. In mechanical part, the contact models among wafer and abrasive and polish pad are considered, they include the elastic deformation arising at asperities and substrate of polishing pad and the elastic-plastic deformation at the interface between wafer and abrasive during CMP. We also estimate the real contact pressure and the ratio of solid contact area of abrasive and asperity of pad at the same time. We develop the Reynolds equation considered the effect of micro-particle and surface roughness in the analysis of flow field between wafer and pad. We also estimate the distributions of the hydrodynamic pressure and the velocity of the fluid field by numerical analysis. In physical part, we considered the effect of abrasive aggregation of the slurry in the result of polishing to estimate the real contact pressure between wafer and aggregated abrasives with the real contact area. In the study of the chemical part, the rate constant of chemical reaction that is changed by the mechanical stresses from the viewpoint of tribochemistry is concerned. The concentration mass transfer equation was applied in the analysis of the reactant’s concentration of slurry during the CMP by numerical analysis.
In this study we considered the effect of the abrasive aggregation of the slurry in（1）the analysis of flow field between wafer and pad；（2）the contact situation between wafer and abrasives；（3）the surface roughness and contours after polishing. With the assumption of chemical reaction equivalent to the removal rate of copper CMP, we can examine the correct of theoretical model by the removal rate and surface roughness parameters from CMP experiment and wafer surface contour experiment.
Several parameters that were considered in this model include the attack angle of the wafer and the limiting strength of the copper in the slurry. They must be given in the theoretical analysis. The theoretical results obtained from the changes of these parameters are compared with the experimental removal rates. After we determined these parameters, the removal rate obtained from the theoretical analysis with the value of average secondary particle size estimated by the theory of abrasive aggregation can be compared with the results of experiment to prove the accuracy of this model. With the theoretical analysis before polishing, we can thus forecast the removal rate and non-uniformity after CMP.

[1] B. B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman, San Francisco, 1982.
[2] Q. Jiang, ‘‘Fractal Structure of Aggregates Induced by Shear Motion,’’ Ph.D. dissertation, Department of Civil Engineering and Engineering Mechanics, University of Arizona, 1993.
[3] B. E. Logan and J. R. Kilps,“Fractal dimensions of aggregates formed in different fluid mechanical environments,”Water Res. 29, 1995, pp.443-453.
[4] Majumdar, A. and Tien,C.L.(1990),”Fractal Characterization and Simulaion of Roughness Surface,”Wear,Vol.136,pp.313-327.
[5] Majumdar, A. and Bhushan, B.(1990),”Role of Fractal Geometry in Roughness Characterization and Contact Mechanics of Surfaces,”ASME J.Tribol, Vol. 112, pp.205-216.
[6] Majumdar, A. and Bhushan, B.(1991),”Fractal Model of Elastic- Plastic Contact between Roughness Surface,”ASME J.Tribol, Vol. 1., pp.231-266.
[7] F. W. Preston, “The Theory and Design of Plate Glass Polishing Machines,” J. Soc. Glass Technology, Vol. 11,1927, pp.214-247.
[8] J.S. McFarlane and D.Tabor, Relation Between Fraction and Adhesion, Proc. Roy. Soc.,Landon , Series A, Vol. 202,1950, pp.244-253.
[9] A.C. Eringen, Theory of Micropolar Fluids, J. Math.
Mech., Vol.16, 1966, pp 1-18.
[10] A.A. Kingbury, “New Oil Testing Machine and Some of its Results,” Trans. ASME, Vol.24, 1903, pp.144-150
[11] L. M. Cook, “Chemical Process in Glass Polishing,” J. Non-Crystalline Solid, Vol.120,1990, pp.152-171.
[12] T. K. Yu, C. C. Yu, M. Orlowski, “A statistical polishing pad model for chemical mechanical polish,” in IEDM Tech. Dig.,1993,pp.865-868.
[13] T. K. Yu, C. Chris and M. O. Lee, “Combined Asperity
Contact and Fluid Flow Model for Chemical Mechanical Polishing,” IEEE, 1994, pp.29-34.
[14] S. R. Runnels, L. M. Eyman, “Tribology Analysis of
Chemical Mechanical Polishing,” J. Electrochem. Soc., Vol. 141, no.6, June 1994 , pp.1698-1701.
[15] S. R. Runnels and P. Renteln, “Modeling the Effect of Polishing Pad Deformation on Wafer Surface Stress Distribution During Chemical Mechanical Polishing,” Dielectric Sci. Technil., 1993, pp.100-121.
[16] S. R. Runnels, “Feature-Scale Fluid-Based Erosion Modeling For Chemical Mechanical Polishing ,” Electrochemical Society Active Member, Vol. 141, No.7, July 1994, pp.1900-1904.
[17] S. P. Murauka and R. Gutmann, 1994 Annual Report Of The New York State Scoe, Semiconductor Research Corporation, Research Triangle Park, Nc (1994).
[18] W. Lee, D. W. Shin, M. Tomozawa, S. P. Murarka, ”The Effect of the Polishing Pad Treatments on the Chemical Mechanical Polishing of SiO2 Films,” Thin Solids Films, Vol. 270, 1995, pp.601-606.
[19] W. T. Tseng, C. W. Liu, B. T. Dai, C. F. Yeh, ”Effect of Mechanical Characteristics on the Chemical Mechanical Polishing of dielectic thin films,” Thin Solid Films, Vol. 290-291, 1996, pp.458-463.
[20] 曾偉志, VLSI-先進模組技術, VLSI-先進模組技術課程, 第二章, 1998, pp.48-51.
[21] F. Zhang and A. Busnaina, ”The Role of Particle Adhesion and Surface Deformation In Chemical Mechanical Polishing Process,” Electrochemical and Solid-State Letters, 1(4), 1998, pp.184-187.
[22] U.Mahajan, M.Bielmann, and R.K.Singh, ”In-Situ Laterial Force Technique For Dynamic Surface Roughness Measurement During Chemical Mechanical Polishing,” Electrochemical and Solid-State Letters, 2(1), 1998, pp.46-48.
[23] J. Tichy, J. A. Levert, L. Shan, S. Danyluk, “Contact Mechanics and Lubrication Hydrodynamics of Chemical Mechanical Polishing,” J. Electrochem. Soc.,146(4), 1999, pp.1523-1528.
[24] J.F.Luo. and D.A.Domfeld, “Material Removel Mechanism in Chemical Mechanical Polishing:Theory and Modeling,” IEEE,Transactions on Semiconductor Manufacturing, Vol.14, No.2, 2001, pp.112-133.
[25] F. B. Kaufman, et al, “Chemical-Mechanical Polishing for Fabricating Patterned W Metal Features as Chip Interconnects,” The Electrochemical Society, Inc,No. 11, Nov.1991, pp.3460.
[26] H. Liang, F. Kaufman, R. Sevilla, S. Anjur, “Wear Phenomena in Chemical Mechanical Polishing,” Wear, Vol.211, 1997, pp.271-279.
[27] R. Gutmann, J. Steigerwald, L. You, D.Price, J. Neirynck, D. Duquette and S. Murarka, “Chemical-mechanical polishing of copper with oxide and polymer inter-level dielectrics,” Thin Solid Film 270, 1995, pp.596-600.
[28] M. Pourbaix, Atlas of Electrochemical Equilibria in Aqueous Solutions, NACE, Houston, TX, 1975.
[29] H. Hirabayashi, M. Higuchi, M. Kinoshita, H. Hagasaka, K. Mase, J. Oshima, “Procedings of the 1st International VMIC Specialty Conference on CMP Planarization”, Santa Clara, CA, Feb. 1996, pp.119.
[30] Q. Luo, D. R. Campbell, S. V. Babu, “Proceedings of the 1st International VMIC Specialty Conference on CMP Planarization,” Santa Clara, CA, Feb.1996, pp.145.
[31] D. Zeidler, Z. Stavreva, M. Plotner, K. Drescher, “Characterization of Cu chemical mechanical polishing by electrochemical investigations,” Microelectronic Engineering 33, 1997, pp.259-265.
[32] V. Nguyen, H. VanKranenburg, P. Woerlee, “Dependency of dishing on polish time and slurry chemistry in Cu CMP, ” Microelectronic Engineering 50 , 2000, pp.403-410.
[33] M. J. Schick and A. T. Hubbard, Interfacial Forces and Fields：Theory and Applications, Marcel Dekker, New York, 1999, pp519-523.
[34] T. R. Thomas M.Sc.,Ph.D.,C.Eng.,F.Inst.p., M.I.Mech.E.,M.I.Prod.E., ROUGH SURFACE, pp.105-110.
[35] Franklin Institute Research Lab.,”NASA Contribution to Fluid-Film Lubrication – A Survey,” NASA SP-5058.
[36] G. Ahmad, “Self-similar Solution of Incompressible Micro-polar Boundary Layer Flow Over A Semi-infinite Plate,” Int. J. Engng Sci., 1976, Vol.14, pp.639-646.
[37] Mysore.N.L. Narasimhan, “ Principles of Continuum Mechanics,” 1982,John WILEY & Sons, Inc.,New York.
[38] N. Patir, H. S. Cheng, “An Average Flow Model for Determining Effects of Three-Dimensional Roughness on Partial Hydrodynamic Lubrication,” ASME J. Lubr. Techno., Vol. 100, January 1978, pp.12-17.
[39] N. Patir, “Effects of Surface Roughness on Partial Film Lubrication using An Average Flow Model Based on Numerical Simulation,” Northwestern University, June1978
[40] N. Patir, H. S. Cheng, “Application of Average Flow Model to Lubrication Between Rough sliding surfaces,” ASME J. Lubr. Techno. ,Vol. 101, April 1979, pp.220-230.
[41] E.D. Tingle, “The importance of surface oxide films in the friction and lubrication of metal, Part 2, The formation of lubrication films on metal surfaces,” Trans. Faraday Soc., Vol. 326, 1950, pp.97-102.
[42] K. L. Johnson, Contact mechanics, Cambridge University Press, Cambridge, 1989, pp.50-55.
[43] K. L. Johnson, Contact mechanics, Cambridge University Press, Cambridge, 1989, pp.406-416.
[44] J. A. Greenwood & J. B. P. Williamson, “Contact of nominally flat surfaces. Proceedings, Royal Society, A295, 1966, pp.300.
[45] J. Halling, K. A. Nuri, “Contact of rough surfaces of working-hardening materials. In The Mechanics of Contact Between Deformable Bodies,” Eds. De Pater & Kalker. Delft: University Press, 1975.
[46] A. E. H. Love, “Stress Produced in a semi-infinite solid by pressure on part of the boundary,” Phil. Trans. Royal Society, A228, 1929, pp.377.
[47] K. L. Johnson, J. A. Greenwood and S. Y. Poon, ”A Simple Theory of Asperity Contact In Elastohydrodynamic Lubrication,” Wear, Vol.19, 1972, pp.91-108.
[48] S.P. Timoshenko and J.N. Goodier, Theory of Elastic, New York, MeGraw-Hill, 1951, pp.1-404.
[49] J. Pullen and J. B. P. Williamson, ”On the Plastic Contact of Roughness Surfaces,” Proc. Roy. Soc. London, 1972, Series A327, pp. 157-173.
[50] W. R. Chang, I. Etsion, D. B. Bogy, “An Elastic-Plastic Model For The Contact Of Rough Surface,” Journal of Tribology, April 1987, Vol.109, pp.257-263.
[51] D. Tabor, The Hardness of Metals, Oxford University Press.
[52] G. W. Stachowiak, A. W. Batchelor, Engineering Tribology, 1993, pp.619-624.
[53] 呂聖章, “含微顆粒之研漿在晶圓化學機械研磨製程磨潤理論之建立與實驗印證”, 碩士論文, 國立成功大學機械工程研究所, 2000.
[54] B. Bhushan,Ph.D.,D.Sc, Handbook of Micro/Nano Tribology, CRC Press.,1986, Chap 3.
[55] 沈彥行, “銅膜化學機械研磨研磨粉體凝聚作用對膜潤化學反應速率影響知理論建立及實驗印證”, 碩士論文, 國立成功大學機械工程研究所, 2001.
[56] 陳俊達, “銅膜之化學機械研磨製程應力作用對磨潤化學反應速率之影響”, 碩士論文, 國立成功大學機械工程研究所, 2000.
[57]張營煇, “二氧化係晶圓化學研磨之拋光墊花樣對流場及膜潤性能理論分析支建立及實驗印證”, 碩士論文, 國立成功大學機械工程研究所, 2000.