在現今科技日新月異的技術中對半導體的製程上，化學機械研磨(Chemical Mechanical Polishing，簡稱CMP)，能讓晶圓表面的平坦度增加是很重要的技術，通常在CMP的製程上會加入維持環(retaining ring) 來提高平坦度。為了要有效的控制材料移除率，所以本論文選擇用對電腦記憶體負擔較小的邊界元素法(BEM)來進行分析，並且可以在很短的時間內求解軸對稱問題，建立化學機械研磨之二維軸對稱的準靜態模型。以完整黏合與完整接觸兩種模態來分析，再分析化學機械研磨加入維持環的過程中，晶圓與研磨墊之間的von Mises應力分佈與材料移除率的關係。探討引起晶圓表面不均勻度(Non-Uniformity)的原因，以及增加維持環之後不均勻度降低的原因。藉由改變研磨墊的厚度與彈性係數、維持環的壓力和彈性模數與施加在晶圓背面之壓力，觀察其對於表面應力與不均勻度所受到的影響，並討論晶圓表面von Mises應力的分佈。結果顯示在沒有維持環的情況下，多層結構的晶圓與研磨墊完整黏合模式分析得到:1.晶圓表面von Mises應力與不均勻度隨著晶圓承載器背壓成正比。2.研磨墊厚度研磨墊的厚度會影響晶圓表面的變形量；當研磨墊為0.055in.時，研磨墊的不均勻度最大。3.載具膜的厚度會影響晶圓表面的變形量；載具膜的厚度越厚，von Mises應力值越大；當載具膜厚度為0.04in.時，晶圓表面von Mises應力最大。4.研磨墊的彈性模數增加，晶圓表面von Mises應力也會隨著增加，而且應力曲線的最大值都大約出現在3.5in.的地方，代表改變材料的彈性模數並不會影響晶圓表面von Mises應力分佈。由上可知，以多層結構的晶圓與研磨墊完整接觸模式分析可得到完整接觸是讓晶圓與研磨墊分開，直接分析晶圓表面，提高了精準度，所以模擬出來的結果比完整黏合模式的不均勻度還低。再增加維持環的情況下，以多層結構的晶圓與研磨墊、維持環與研磨墊的完整黏合模式得到增加維持環的確可以降低晶圓表面的不均勻度；而有維持環多層結構的完整接觸模式與完整黏合模式結果相同，且不均勻度比完整黏合模式還低。

Nowadays technology is changing rapidly the chemical mechanical polishing (CMP) is an important technique for the improvement of planarization and material removal rate in the current semiconductors manufacturing. In order to control the material removal rate, the retaining ring is always applied in the CMP to increase the planarization.The boundary element method (BEM) is used in this study due to its computing efficiency. It can solve the 2D axisymmetric problem in a very short period of time and to establish two dimensional symmetry axis of the chemical mechanical polishing quasi-static model for CMP. Two different models will be analyzed: complete glue and complete contact.The relation between von Mises stress distribution and material removal rate on the wafer and pad, and the nonuniformity of wafer caused by two different models as above mentioned will be discussed in this study. By changing the thickness and elasticity modulus of the pad, pressure and modulus of elasticity retaining ring and increase the pressure at the back of the wafer to observe the nonuniformity of the surface stress with the were affected and discuss the wafer surface von Mises stress distribution. Ignoring a retaining ring and based on a complete glue model between the multilayer structure wafer and pad, the von Mises stress on wafer surface and nonuniformity is proportional to the back pressure of the wafer; The thickness of the pad surface will affect the amount of deformation of the carrier, When the pad thickness is 0.055in., the pad nonuniformity is the maximum thickness of 0.055in.;The thickness of the carrier film surface will affect the amount of deformation of the wafer, When the carrier film thicker, von Mises stress values greater; when the carrier film thickness is 0.04in., von mises stress on the wafer surface is the maximum,when the elastic modulus of the pad increases, the wafer surface von Mises stress also increases, but the maximum stress curves are approximately in 3.5in place, which means that changes the elastic modulus of the material does not affect the wafer surface von Mises stress distribution. Otherwise, ignoring a retaining ring and based on a multi-layer structure complete contact model between the wafer and pad, the wafer separates from the pad, the wafer surface is directly and individually analyzes to improve the accuracy, the nonuniformity is lower than the glue model. Considering a retaining ring and based on a complete glue model between the multi-layer structure wafer and pad and between the retaining ring and pad, the setup of retaining ring can reduce the nonuniformity effectively. Otherwise, considering a retaining ring and based on a complete contact model between the multi-layer structure wafer and pad and between the retaining ring and pad, the effect of the retaining ring is similar to the glue model and the nonuniformity is lower than the glue model.

目錄
摘 要 ............................................................................................................II
Abstract IV
誌謝............................................................................................................ VI
目錄 .VIII
表目錄 XIV
圖目錄 XVIII
符號說明 XXV
第一章 緒論 1
1.1 前言 ……………………………………………………………………………........1
1.2 研究動機 ……………………………………….…………………………….….....2
1.3 文獻回顧 ……………………………………………………………………..….....3
第二章 化學機械研磨法 6
2.1 化學機械研磨簡介....................................................................…...…...6
2.2 化學機械研磨機構 …………………………………………………….…...……7
2.3 化學機械研磨作動原理 …………………………………………………...…...8
第三章 邊界元素法 …….11
3.1 邊界元素法概論 ……………………………………………………………......11
3.2 二維軸對稱準靜態模式建立…………………………………………….......13
3.3 基本解(Fundamental solution) ……………………..……………………...15
3.3.1 位移的微分方程式(Navier equation)………………………………....15
3.3.2 源點解(Kelvin solution)………………………………………...…….…15
3.3.3 功的互換定理(Betti’s theorem)…………………………………….…..16
3.3.4 高斯積分(Gaussian quadrature)………………………………………..17
3.4 二維軸對稱方程式 ………………………………………..…………….......18
3.4.1 軸對稱位勢方程式....................................................................................18
3.4.2 軸對稱位勢問題……………………………………………………….….19
3.4.3 軸對稱彈性方程式……………………………………………………..…20
3.4.4 邊界元素法處理接觸面方程式………………………………………..24
第四章 多層結構的晶圓與研磨墊表面應力分析……………………....27
4.1晶圓與研磨墊完整黏合………………...............................…………...….27
4.1.1 驗證模型…………………………………………………………………....30
4.1.2 晶圓與研磨墊完整黏合之晶圓表面應力與不均勻度分析……...32
4.1.2.1晶圓承載器背壓對晶圓表面von Mises應力和不均勻度的影響..................................................................................................................32
4.1.2.2 研磨墊厚度對晶圓表面von Mises應力和不均勻度的影響…33
4.1.2.3載具膜厚度對晶圓表面von Mises應力和不均勻度的影響….35
4.1.2.4研磨墊彈性模數對晶圓表面von Mises應力和不均勻度的影響36
4.2完整黏合模式下，載具膜局部與全域背壓對晶圓表面不均勻度的影響
(無維持環)............................................................................................................38
4.2.1 驗證模型..........................................................................................................39
4.2.2晶圓與研磨墊完整黏合之局部與全域載具膜壓力對晶圓表面應力與
不均勻度分析.................................................................................................40
4.2.2.1局部與全域載具膜壓力對晶圓表面von Mises應力和不均勻度的影
響.....................................................................................................................40
4.2.2.2局部與全域載具膜壓力對晶圓表面von Mises應力和不均勻度的影
響.....................................................................................................................42
4.3晶圓與研磨墊完整接觸...................................................................................45
4.3.1晶圓與研磨墊完整接觸之晶圓表面應力與不均勻度分析 ………....45
4.3.1.1晶圓承載器背壓對晶圓表面von Mises應力和不均勻度的影響..45
4.3.1.2 研磨墊厚度對晶圓表面von Mises應力和不均勻度的影響……..47
4.3.1.3 載具膜厚度對晶圓表面von Mises應力和不均勻度的影響…….48
4.3.1.4 研磨墊彈性模數對晶圓表面von Mises應力和不均勻度的影響…………………………………………………………………….……...…49
4.4晶圓與研磨墊、研磨墊與維持環完整接觸………….........…..……….52
4.4.1 驗證模型……………………………………………………………………........52
4.4.2晶圓與研磨墊、維持環與研磨墊完整接觸之晶圓表面應力與不均勻度分析………………………………………………………………………..……....53
4.4.2.1維持環-晶圓承載器負載比對晶圓表面von Mises應力和不均勻度的影響…...…..........................................................................................................53
4.4.2.2晶圓與維持環間距對晶圓表面von Mises應力和不均勻度的影響
............................................................................................................................55
4.4.2.3研磨墊厚度對晶圓表面von Mises應力和不均勻度的影響
……………………………………………………………………………........57
4.4.2.4研磨墊彈性係數對晶圓表面von Mises應力和不均勻度的影響
..………………………………………………………………………….……..58
4.4.2.5載具膜厚度對晶圓表面von Mises應力和不均勻度的影響……...60
4.5 晶圓、研磨墊、載具膜與晶圓承載器完整黏合、維持環與研磨墊完整黏合…………………………………………………………………………….....….61
4.5.1 驗證模型…………………………………………………………………….….63
4.5.2晶圓與研磨墊、維持環與研磨墊完整黏合之晶圓表面應力與不均勻度分析……………………………………………………………..……………….64
4.5.2.1維持環-晶圓承載器負載比對晶圓表面von Mises應力和不均勻度的影響……………………………………………………………………………64
4.5.2.2晶圓與維持環間距對晶圓表面von Mises應力和不均勻度的影響
…………………………………………………………………………….…….65
4.5.2.3研磨墊厚度對晶圓表面von Mises應力和不均勻度的影響……..67
4.5.2.4研磨墊彈性係數對晶圓表面von Mises應力和不均勻度的影響.68
4.5.2.5載具膜厚度對晶圓表面von Mises應力和不均勻度的影響……..70
4.6 完整黏合模式下，載具膜局部與全域背壓對晶圓表面不均勻度的影響(含維持環)…………………………………………………………………...….…71
4.6.1 驗證模型………………………………………………………………………...73
4.6.2晶圓與研磨墊、維持環與研磨墊完整黏合之局部與全域載具膜壓力對晶圓表面應力與不均勻度分析…………………………………………….74
4.6.2.1局部與全域載具膜壓力對晶圓表面von Mises應力和不均勻度的影響
………………………………………………………………………………….74
4.6.2.2局部載具膜壓力對晶圓表面von Mises應力和不均勻度的影響..75
4.7 完整黏合模式與完整接觸模式下，晶圓表面不均勻度之比較(不含維
持環)………………………………………………………………………….……77
4.8 完整黏合模式下，載具膜壓力對晶圓表面不均勻度之比較(無維持環)
..............................................................................................................81
4.9 完整黏合模式與完整接觸模式下，晶圓表面不均勻度之比較(含維持環)
……………………………………………………………………………………...85
4.10 完整黏合模式下，載具膜壓力對晶圓表面不均勻度之比較(含維持環)
…………………………………………………………………………………...84
第五章 結論與未來展望……………………………………………………….…85
參考文獻…………………………………………………………………………….….88

參考文獻
1. 羅正忠、張鼎張，「半導體製程技術導論」，歐亞書局有限公司，　　　　　　
　 pp.493. 2001。
2. 林明獻，矽晶圓半導體材料技術(修訂版)．全華圖書股份有限公　
　 司，2007。
3. C. Srinivasa-Murthy,D.W. ,S.P. Beaudoin,T. Bibby,K. Holland,T.S. 　　　
　 Cale,'' Stress distribution in chemical–mechanical polishing,'' Thin
　 Solid Films,308,pp.533–537,1997.
4.　王建榮，半導體平坦化CMP技術，全華圖書股份有限公司，1999。
5.　Preston ,F,''Optimization of computer controlled polishing'', Glass
　　Tech,pp.214–219,1927.
6.　S.R. Runnels,P.R.,''Modeling the effect of polish pad deformation on
　　wafer surface stress distributions during chemical–mechanical
　　polishing'',. Dielectr. Sci. Technol,pp.110–121,1993.
7.　S.R. Runnels,L.M.E,''Tribology analysis of chemical mechanical
　　polishing'', J. Electrochem. Soc,p.141 (6)1698–1701,1994
8.　D. Wang,J.Lee,K. Holland,T. Bibby,S. Beaudoin,T. Cale,''von Mises
　　stress in chemical–mechanical polishing processes'', J.Electrochem.
　　Soc.,pp.144 (3)1122–1127,1997.
9.　陳俊甫，化學機械研磨晶圓承載器之維持環與背壓對晶圓應力分佈之影響，國立臺灣科技大學碩士論文， 2000。
10. Y. Y. Lin and S. P. Lo, “A Study of a finite element model for chemical mechanical polishing process,” Int. J. Adv. Manuf. Technol., Vol.23, pp.644-650, 2004.
11. Y. Y. Lin and S. P. Lo, “A study on the stress and nonuniformity of the wafer surface for the chemical mechanical polishing process,” Int. J. Adv. Manuf. Technol., Vol.22, pp.401-409, 2003.
12.　Parshuram B. Zantye,A.K.,A.K. Sikder,''Chemicalmechanical　
　　　planarization for microelectronics applications'',. Materials Science
and Engineering,pp. R 45,89–220,2004.
13.　Patrick,W.J.,W. L. Guthrie,C. L. StandleyandP.M.Schiable,
Applicationof chemical-mechanical polish to the fabrication of VLSI circuitinterconnections,J.Electrochem. Soc. Vol. 138,No. 6. p. 1778-1784,1991.
14.　賴宏智，異向性材料點熱源熱應力之邊界元素法分析，逢甲大學，
2005。
15. 鄺國能，工程實用邊界單元法，中國鐵道出版社，1989。
16. 黃湧翔，撓性材質虛擬變型機制之研究─模擬含張力軟性薄膜之切割
與斷裂，朝陽科技大學工業工程與管理系研究所，2008。
17. 劉孟龍，邊界元素法分析二維矩型水槽承受水平及垂直振動之水沖激
行為，臺大造船及海洋工程學研究所，2002。
18.　A.A. Becker, The Boundary Element Method in Engineering A complete course, 1992.
19. 莊惟舜，建立邊界元素法分析化學機械研磨製程維持環對晶圓表面應力及不均勻度之影響，元智大學碩士論文，2013。
20.　JianfengLuo,Integrated modeling of chemical mechanical
planarization. CALIFORNIA, BERKELEY,2003.
21.　林有鎰、羅仕鵬、李文喜，化學機械研磨製程背壓分佈對晶圓應力
和不平坦度的影響研究，德霖技術學院，2010。