化學機械研磨（CMP）中對於晶圓上不同的鍍層材料就必須使用不同的研磨墊（Pad），而相同材質的研麼墊上又可以分成各種不同的表面花樣（Pattern）。然而對於研磨墊花樣在化學機械研磨中扮演甚麼角色，由於問題十分複雜，至今很少人涉獵這部份的研究，相關文獻亦不可見。事實上研磨墊花樣在化學機械研磨中對晶圓磨除率以及均勻度具有相當的重要性。因此本研究針對同心圓花樣研磨墊進行流場理論上的模擬，且可將此理論運用於不同研磨墊花樣上，期望能對晶圓化學機械研磨磨除率與均勻度之提升有幫助，並提出一有效方法評估不同研磨墊花樣對化學機械研磨之影響。

本文所建立之銅晶圓CMP研磨機制模型，主要探討CMP研磨過程不同研磨墊花樣對流場分布與晶圓、粉體與研磨墊三者間之接觸機制。於流場的分析，本文建立含研磨墊花樣效應、微顆粒耦應力效應及研磨墊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。固體接觸部分之研究則包含研磨墊粗度峰及研磨墊底材之彈性變形計量，晶圓磨除率模型則依彈塑性變形理論建立，考慮了沙磨以及黏附磨耗行為。此磨除率模型可預測晶圓不同位置之磨除率，並與實驗結果比對，以及晶圓研磨面與砥粒接觸之彈塑性變形分析。

理論部分，由於探討研磨墊花樣效應之文獻幾乎沒有，故本文中將利用質量守恆此一原理，以及平滑液壓之概念，來推導研磨墊花樣對研漿流場之影響。本研究由於晶圓夾具轉速與研磨墊承座轉軸非同心，因此在晶圓工作區內之流場，由於花樣之存在變的複雜而且隨位置產生變化，故首先先將晶圓切成無數小的元素。每個元素內其流體會因溝槽區與非溝槽區的面積比例在 、 方向入口比例之不同而有不同的流量分佈。配合流量守恆及平滑液壓概念，再加上流體受粗糙度效應與顆粒效應的作用，本研究推導出一新雷諾方程式予以全數涵蓋。配合數值分析方法，便可得到在晶圓面上之液壓分佈與液動負荷。另外，晶圓與研磨墊之接觸情形，利用界面接觸現象，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，再由力之作用力與反作用力定律，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與砥粒之接觸面積半徑，再代入本文所推導之砥粒刮蝕機械移除率理論與一系列有關鈍化層生成部分的研究與奈米機械性質的實驗，驗證所建理論之正確性。

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、楊氏模數關係之奈米壓痕實驗。最後，藉由控制自動平衡點的位置，提供CMP研磨參數如研磨墊、研磨液、砥粒粒徑與背壓力等施工條件最佳化設計參數選擇之參考依據。

本論文最終獲得幾項結論：在研磨墊花樣效應方面，研磨墊含同心圓花樣溝槽較研磨墊無花樣溝槽之移除率明顯提升，而非均勻度之差別則較少，不同深度與不同寬度之同心圓花樣溝槽研磨墊，亦會造成其移除率與均勻度的變化。在微顆粒效應方面，偶合參數N值越大，流場內之耦
合黏度效應及應力偶效應偶合參數N值越大，流場內之耦合黏度效應及應力偶效應越明顯，將會使移除率降低。研磨粉體初始粒徑值越大，可能固含量濃度越高之研磨液，因而造成越大的晶圓彈塑性變形體積，故移除率升高。另外，不同的鈍化層硬度會對移除率與非均勻度產生影響，
硬度值越小，移除率越高，非均勻度值較小。利用微接觸力學之彈塑性變形理論可導出研磨過程中之接觸壓大小，再配合研磨墊彈性變形理論，力平衡，力矩平衡便可得到平衡狀態下之最小水膜厚度，攻擊角與旋轉角。

In Chemical Mechanical Polishing (CMP), the material and pattern of pad are chosen by considering for the coating of wafer. The rule that pattern of pad plays in CMP is very complicated and there are not many researches mentioned about it. Actually the pattern of pad is significant for removing rate and uniformity of wafer after CMP. The theoretic simulation for flow field due to pad pattern of concentric circle is established in this study. The method can be developed for other patterns and helpful for removing rate and uniformity of wafer after CMP. A valid method of evaluating the effect of pad pattern to CMP is presented, too.

The established model is considered for the effect of pad pattern to both of the flow field and the contact mechanism among wafer, slurry, and pad. For the analysis of flow field, the Reynolds equation considered for effects of the pad pattern, micro particle couple stress, and pad roughness is established. Numerical computing for theoretic analysis can solve the hydrodynamic pressure, liquid film thickness, and fluid velocity filed. For solid contact, the model for removing rate, which calculates deformation of pad roughness and substrate and includes abrasive and adhesive behaviors of wear, is established according to elastroplastic deformation theory.

Deriving the effect of pad pattern to flow field of slurry is according to the principle of conservation of mass and concept of smooth hydro pressure. The rotating axes of pad and wafer are not concentric, so the flow field in the working area during CMP depends on position and pattern. The flow filed is so complicated that we mesh the working area into elements. There is different flow rate in every meshed element because of the different area ratio no matter in radial or tangential direction. Computing the hydro pressure and hydrodynamic load by numerical analysis for the modified Reynolds equation. In the other hand, evaluating the true contact pressure, contact area, and deformation between pad and wafer by analysis for the interface contact phenomena. Then we obtain those among pad, abrasive, and wafer by the theorem of acting and reacting forces. Finally, modifying the contact area between abrasive and wafer by adhesion theory and deriving the theory of mechanical abrasive removing rate. The established theories are verified by experiments of research for passivation and nanomechanical properties.

About experiments, the 3-D profile meter (resolution of 10nm), Scanning Probe Microscope (resolution of 0.1nm), and Nano Indentation Test (resolution of 1nm) are used for measuring profile of wafer, hardness and Young’s modulus of passivation. We purpose a rule for choosing operation parameters, such as pad, slurry, radius of abrasive and backpressure, optimally according to the automatic equilibrium position controlling.

There are several conclusions in this study. The pad pattern of concentric circles increases removing rate more than uniformity, and depth and width of groove of concentric circles are also affecting factors. For micro particle effect, the greater coupling value, which indicates more coupling viscosity and stress coupling effects, makes removing rate smaller. The greater initial radius of slurry powder, which causes larger elastroplastic deformation volume, increases removing rate. In the other hand, the smaller hardness of passivation, the larger removing rate and uniformity. According to the elastroplastic deformation theory of micro contact mechanics, we derive the contact pressure under polishing and solve the minimum fluid film thickness, attack angle, and rotating angle in equilibrium of force and moment.

參考文獻
[1] M. A. Fury, “Chemical Mechanical Planarization of Aluminum-Based Alloys for MultilevelMetallization,“ Solid state Technology, Vol. 20,1995, pp.61.
[2] F. W. Preston, “The Theory and Design of Plate Glass Polishing Machines,” J. Soc. Glass Technology, Vol. 11,1927, pp.214-247.
[3] J.S. McFarlane and D.Tabor, Relation Between Fraction and Adhesion, Proc. Roy. Soc.,Landon , Series A, Vol. 202,1950, pp.244-253.
[4] A.C. Eringen, Theory of Micropolar Fluids, J. Math.
Mech., Vol.16, 1966, pp 1-18.
[5] A.A. Kingbury, “New Oil Testing Machine and Some of its Results,” Trans. ASME, Vol.24, 1903, pp.144-150
[6] L. M. Cook, “Chemical Process in Glass Polishing,” J. Non-Crystalline Solid, Vol.120,1990, pp.152-171.
[7] 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.
[8] 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.
[9] S. R. Runnels, L. M. Eyman, “Tribology Analysis of Chemical Mechanical Polishing,” J. Electrochem. Soc., Vol. 141, no.6, June 1994 , pp.1698-1701.
[10] 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.
[11] 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.
[12] S. P. Murauka and R. Gutmann, 1994 Annual Report Of The New York State Scoe, Semiconductor Research Corporation, Research Triangle Park, Nc (1994).
[13] 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.
[14] 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.
[15]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.
[16]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.
[17] 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.
[18] 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.
[19] 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.
[20] 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.
[21] H. Liang, F. Kaufman, R. Sevilla, S. Anjur, “Wear Phenomena in Chemical Mechanical Polishing,” Wear, Vol.211, 1997, pp.271-279.
[22] 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.
[23] M. Pourbaix, Atlas of Electrochemical Equilibria in Aqueous Solutions, NACE, Houston, TX, 1975.
[24] 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.
[25] 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.
[26] D. Zeidler, Z. Stavreva, M. Plotner, K. Drescher, “Characterization of Cu chemical mechanical polishing by electrochemical investigations,” Microelectronic Engineering 33, 1997, pp.259-265.
[27] 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.
[28] B. R. Munson, K. F. Young, and T. H. Okiishi, Fundamentals of Fluid Mechanics, John Wiley & Sons Inc.,p360-362,1994
[29] Nadir Patir, Effects of Surface roughness on Partial Film Lubrication Using an average Flow Model Based on Numerical Simulation, Doctor of Philosophy, Field of Mechanical Engineering and Astronautical Sciences, Northwestern University, 1978.
[30] Mysore.N.L. Narasimhan, “ Principles of Continuum Mechanics,” 1982,John WILEY & Sons, Inc.,New York.
[31] T. Kato, M.M. Razzzaque, “Effects of a rove on the Behavior of a Squeeze Film Between a Plain Rotating Annular Disk, ”
ASME Journal of Tribology,Vol.121,pp. 808-815,1999
[32] 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.
[33] Franklin Institute Research Lab.,”NASA Contribution to Fluid-Film Lubrication – A Survey,” NASA SP-5058.
[34] A. Gameron, Ed. Basic Lubrication Theory, Ellis Horwood Ltd., London 1981.
[35] 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.
[36] 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.
[37] N. Patir, “Effects of Surface Roughness on Partial Film Lubrication using An Average Flow Model Based on Numerical Simulation,” Northwestern University, June1978
[38] 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.
[39]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.
[40] B. Bhushan,Ph.D.,D.Sc, Handbook of Micro/Nano Tribology, CRC Press.,1986, Chap 3.
[41] M. J. Schick and A. T. Hubbard, Interfacial Forces and Fields：Theory and Applications, Marcel Dekker, New York, 1999, pp519-523.
[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]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.
[55]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.
[56]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.
[57]歐陽裕龍, “銅膜化學機械研磨碎形量測及砥粒刮蝕黏附效應對鈍化層生成與移除影響之理論建立與實驗驗證”, 碩士論文, 國立成功大學機械工程研究所, 2002.
[58] R.A. Niefer and P.N. Kaloni, “Motion of A Rigid Sphere in A Shear Field In A Micropolar Fluid,” Int. J. Engng Sci.,1981, Vol.19, pp. 959-966
[59] G.K. Batchelor, “An Introduction to Fluid Dynamics,” Cambridge University Press.,1967,Chap 4.