化學機械研磨研加工過程中，會將晶圓旋轉且下壓於一旋轉的研磨墊。研磨液持續地被輸送於粗糙的研磨墊上，且在晶圓和研磨墊間形成潤滑薄膜。而本研究基於一個可應用於粗糙研磨墊和考慮研磨墊壓縮性的廣義雷諾方程式下，提出一個研磨液流動模型，並採用複式網格法減少計算時間。根據力與力矩平衡方程式，將可以得到晶圓於加工過程中的傾斜角和研磨液厚度。當研磨墊表面為粗糙時，由於研磨墊的轉動，在模型裡要考慮對時間微分的擠壓項。探討負載、研磨墊轉速、晶圓轉速、研磨墊壓縮性和表面粗度花樣對於傾斜角和研磨液厚度的影響。結果顯示，於研磨墊轉動期間，非等向性粗糙表面傾斜角度的變動比等向性時顯著。當負載減少或研磨墊轉速增加或晶圓轉速減少或研磨墊壓縮性提高時晶圓中心點的研磨液厚度會較高。

During the CMP process, a wafer is rotated and pressed face down against a rotating polishing pad. Polishing slurry is delivered on the top of pad continuously and forms a thin lubricating film between the wafer and the pad. In this study, a three-dimensional slurry flow model based on a generalized Reynolds equation is developed, which can apply to a rough pad with the compressibility of the pad, and the multi-grid method is used to reduce computational time. According to the force and moment balance equations, the tilted angles and the slurry film thickness can be evaluated. When the pad surface is rough, the squeeze term differentiated by time should be considered in this model due to the rotation of the pad. The influences of applied load, pad speed, wafer speed, pad compressibility, and surface roughness pattern on the tilted angles and the slurry film thickness are investigated. Results show that the variation of the tilted angles becomes more significant for the anisotropic than that for the isotropic during the rotation of the pad. And the slurry film thickness at the center of the wafer increases as applied load decreases or pad speed increases or wafer speed decreases or the compressibility of the pad increases.

封面 I
學位論文審定書 II
謝誌 III
總目錄 IV
圖目錄 VII
表目錄 X
符號說明 XI
中文摘要 XIII
英文摘要 XIV
第一章 緒論 1
1.1 前言 1
1.2 文獻回顧 1
1.2.1 CMP的文獻回顧 1
1.2.1.1直接接觸模型 2
1.2.1.2非直接接觸模型 2
1.2.1.3半直接接觸模型 3
1.2.2 複式網格法的文獻回顧 4
1.2.3 研究方法與目的 4
第二章 理論分析 7
2.1 研磨液厚度 7
2.1.1研磨墊表面高度(h1) 7
2.1.2晶圓表面高度(h2) 8
2.2 晶圓和研磨墊介面速度分量 9
2.3 雷諾方程式(Reynolds Equation) 9
2.4 邊界條件 13
2.5 力與力矩平衡 13
第三章 數值分析 21
3.1 複式網格法 22
3.1.1 修正法則 22
3.1.2 全近似法則 25
3.1.2 全複式網格法則 26
3.2 CMP之數值解析 27
3.3 數值解流程 28
第四章 結果與討論 37
4.1 複式網格法收斂速度上的影響 37
4.2 研磨墊表面為光滑 37
4.4 研磨墊表面為粗糙 38
第五章　結論 67
5.1 結論 67
5.2 未來展望 67
參考文獻 69

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