摘 要
本研究目的為利用彈液動潤滑理論模擬化學機械研磨（CMP），進行分析流體壓力，其中整合了微觀尺度的峰端接觸與巨觀的流體壓力。使用經修正的雷諾方程式來描述流場，以及統計學觀念導出的平均接觸壓力公式，用來表示峰端固體接觸壓力，還有墊片基材彈性變形公式，進行建構CMP模型，最後進行討論各參數對流體壓力之影響。
其結果發現當轉速或負載壓力增大時，流體負壓力會越小，形成更大的峰端接觸壓力以支撐負荷，摩擦力也變大，晶圓傾斜角度也因此越大，流體壓力值與負載同一數量級，流體壓力的會明顯地改變接觸應力之分佈。出現負壓力是因為墊片基材的變形，當接觸壓力增大或傾斜角度減小時，可發現流體壓力會越小。材料移除模型假設峰端為彈性變形，接觸壓力可以依虎克定律得到，磨粒穿透晶圓表面的深度可由晶圓與墊片達力平衡時獲得，其結果顯示當磨粒粒徑增加時，移除率下降，原因可能是磨粒與被加工物表面接觸面積的減少所引起之現象。

關鍵字：彈液動潤滑、化學機械研磨

Abstract
This paper proposes a model that integrates the microscale asperity contact and macroscale elastohydrodynamic lubrication (EHL) to simulate the pressure distribution in the chemical mechanical planarization (CMP). This model involves modified Reynolds equation used to describe the status of fluid field, the equation of the average asperity contact pressure by using statistics for solid contact pressure due to asperity contact, and the equation of the elastic pad deformation in bulk. Results show that with increasing relative velocity or load, the magnitude of the sub-ambient pressure decreases, the greater asperity contact pressure is formed to support the load, and the friction force also increases to cause the greater rotation angles. The magnitude of the fluid pressure is of the same order of magnitude as the applied normal load. Therefore, the addition of this fluid pressure may significantly change the distribution of the contact stress. The reason of the sub-ambient pressure existed is the deformation of the pad. In the material removal rate model, the elastic deformation of asperities is assumed, and the contact pressure is determined by Hooke’s law. The indentation depth can be obtained from the force balance imposed on the particles by the wafer and the pad. Results show that the material removal rate decreases with increasing abrasive size, due to the increasing contact area between the abrasive and wafer.

Keywords：Elastohydrodynamic Lubrication, Chemical Mechanical Polishing

總 目 錄
總目錄 .................................................. i
圖目錄 ................................................. iv
表目錄 ................................................. ix
符號說明 ................................................ x
中文摘要 ............................................... xv
英文摘要 .............................................. xvi
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
1.3.1 固體-固體接觸的CMP模型........................... 4
1.3.2 固體-流體-固體接觸的CMP模型...................... 5
1.3.3 半固體-固體接觸的CMP模型......................... 6
1.4 研究動機............................................ 9
1.5 論文架構........................................... 10
第二章 CMP模型之建立.................................... 16
2.1 發展方向........................................... 16
2.2 理論推導過程....................................... 17
2.3 彈液動潤滑之雷諾方程式............................. 18
2.4 峰端平均接觸壓力................................... 22
2.5 墊片基材之變形量...................................................... 23
2.5.1 Winkler elastic model.......................... 23
2.5.2 平面應變........................................ 23
2.6 流體厚度方程式..................................... 25
2.7 雷諾方程式、流體厚度方程式的離散化................. 26
2.7.1 無因次化........................................ 26
2.7.2 離散化.......................................... 27
2.7.2.1 一般格點位置離散化.......................... 27
2.7.2.2 上邊界格點位置的離散化...................... 29
2.7.2.3 左下邊界格點位置的離散化.................... 30
2.7.2.4 右下邊界格點位置的離散化.................... 31
2.8 力與力矩平衡....................................... 32
2.9 數值模擬隨機表面................................... 33
2.9.1 隨機表面的概念.................................. 33
2.9.2 數學推導........................................ 33
2.10 材料移除率........................................ 35
2.10.1 有效磨粒總數................................... 36
2.10.2 單顆磨粒移除率................................. 36
第三章 結果與討論....................................... 50
3.1 CMP模型............................................ 50
3.1.1 速度對流體壓力之影響............................ 57
3.1.2 負載對流體壓力之影響............................ 61
3.1.3 黏度對流體壓力之影響............................ 65
3.2 數值模擬隨機表面................................... 69
3.2.1 高斯隨機表面.................................... 71
3.2.2 不同方向的表面粗度對流體壓力之影響.............. 80
3.2.3 負載對流體壓力之影響............................ 83
3.3 材料移除模型....................................... 88
第四章 結論............................................. 92
參考文獻................................................ 95

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