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研究生: 曾茂仁
Tzeng, Mow-Ren
論文名稱: 銅晶圓化學機械研磨研磨墊孔洞幾何結構對研漿流場以及研磨效果之理論建立
The Theoretical Analysis for the Effect of porous structure of pad on the Slurry Flows and Tribological Performances Arising at the Chemical Mechanical Polishing of Cu-Film Wafers
指導教授: 林仁輝
Lin, Jen-Fin
學位類別: 碩士
Master
系所名稱: 工學院 - 機械工程學系
Department of Mechanical Engineering
論文出版年: 2005
畢業學年度: 93
語文別: 中文
論文頁數: 146
中文關鍵詞: 研磨墊孔洞結構滲透量化學機械研磨
外文關鍵詞: CMP, permeability, porous structure, polishing pad
相關次數: 點閱:180下載:8
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  • 摘 要
      化學機械研磨(CMP)中影響研磨效果的參數相當多,而研磨墊的孔洞結構在化學機械研磨中扮演甚麼角色,由於問題十分複雜,相關論文亦只探討研磨墊變形對研磨效果的研究,至今很少人涉獵孔洞結構的研究。事實上研磨墊孔洞結構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,因此本研究針對研磨墊孔洞結構進行流場理論上的模擬,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。

      在研磨墊部份,吾人先將描述孔洞性質的參數計算出來,全部帶到最重要的參數—滲透量內。滲透量除了是材料滲透性的指標,同時也包含了各個孔洞參數的效果在內,由滲透量可看出孔徑大小的變化及分佈、碎形維度與孔隙度等影響滲透量最重要的參數。接下來將土壤力學中雨水滲透到土壤之概念,來推導研磨墊孔洞結構Laplace’s Equation,用此方程式描述研磨墊內部之流場。再利用數值方法計算出研磨墊內部之壓力分佈,與晶圓水膜之液壓分佈做結合得到新的液壓分佈。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。最後再代入砥粒刮蝕機械移除率理論,求得帶有孔洞效應之移除率。

      本論文最終獲得下列結論:考慮研磨墊孔洞結構之後,在滲透量的影響之下,會造成液壓下降,接觸壓增加,進而造成移除率提升。較未考慮研磨墊孔洞結構之模型,移除率有所提升,而非均勻度之提昇則較少。

    Abstract
     There are many parameters that effect the CMP in the process. The rule that porous structure of pad plays in CMP is very complicated and there are not many researches mentioned about it. Actually the porous structure of pad is significant for removing rate and uniformity of wafer after CMP. The theoretic simulation for flow field due to porous structure is established in this study. The method can be helpful for removing rate and uniformity of CMP. A valid method of evaluating the effect of porous structure to CMP is presented, too.

     The established model is considered for the effect of porous structure 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 porous structure 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.

     Using the Laplace Equation of Soil Mechanics to solve the hydro pressure in the field of pad. Computing the hydro pressure and hydrodynamic load by numerical analysis for the modified Reynolds equation. In the otherhand,
    evaluating the true contact pressure, contact area, and deformation between pad and wafer by analysis for the interface contact phenomena.

    There are several conclusions in this study. The porous structure increases removing rate more than uniformity. 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.

    目錄 頁次 摘要..................................................... I 英文摘要................................................. II 誌謝.................................................... III 目錄..................................................... IV 表目錄................................................... VII 圖目錄.................................................. VII 符號表.................................................. XI 第一章 緒論................................................ 1 1.1前言................................................. 1 1.2文獻回顧............................................. 2 1.3研究目的及內容....................................... 7 第二章 化學機械研磨理論模型之建立 ......................... 12 2.1化學機械研磨(CMP)混合潤滑理論之建立................. 12 2.1.1 磨潤簡介......................................... 12 2.1.2非對心式流場運動方程式之推導..................... 14 2.1.3含研磨墊之雷諾方程式............................. 19 2.2研磨墊赫茲接觸彈塑性變形理論....................... 25 2.2.1理論推導過程.................................. 25 2.2.2 研磨墊粗度峰之平均接觸壓力.................... 25 2.2.3 研磨墊底材變形理論............................ 30 2.2.4力平衡、力矩平衡求最小水膜厚度、旋轉角、攻擊角... 35 2.3研磨面上砥粒刮蝕、黏附理論......................... 37 2.3.1 刮蝕與黏附現象與理論簡介....................... 37 2.3.2砥粒刮蝕機械移除率............................. 37 2.3.3 晶圓研磨墊間相對速度........................... 39 2.3.4 研磨面上之刮蝕頻率............................. 41 2.3.5 砥粒刮蝕梯形面積法............................. 42 2.3.6 研磨方向上單一砥粒平均移除高度................. 44 2.3.7 砥粒有效接觸百分比............................. 44 2.3.8砥粒刮蝕機械移除率理論......................... 45 2.3.9 研磨面上砥粒黏附理論........................... 45 2.3.10材料係數C之求法.............................. 47 2.3.11 自動平衡點示意圖.............................. 49 2.4研磨墊孔洞結構對流場影響之分析.................... 51 2.4.1碎形維度....................................... 51 2.4.1.1 郝思多維度................................. 52 2.4.1.2 盒子維度.................................. 52 2.4.2 其他孔洞性質之計算............................. 54 2.4.2.1 孔隙度..................................... 54 2.4.2.2 空隙比..................................... 54 2.4.2.3孔洞機率函數............................... 54 2.4.2.4 扭曲度..................................... 55 2.4.2.5含水量..................................... 55 2.4.2.6飽和度..................................... 55 2.4.2.7滲透率..................................... 56 2.4.2.8 Scheidegger的毛細管模型................... 56 2.4.3壓密理論....................................... 62 2.4.3.1壓密理論的基本方程式....................... 63 2.4.3.2 Laplace equation 的邊界條件 ................ 67 第三章 結果與討論...................................... 88 3.1 CMP含研磨墊孔洞結構之分析.......................... 88 3.1.1 研磨參數確認................................... 88 3.1.2 滲透量與各孔洞性質關係之分析................... 90 3.2CMP含研磨墊孔洞結構之數值結果與分析................. 92 3.2.1 不同工作條件下研磨墊的影響..................... 92 3.2.2 移除率與非均勻度之分析......................... 93 第四章 結論與未來研究的方向.............................. 137 5.1結論............................................... 137 5.2未來研究方向....................................... 137 參考文獻................................................. 139 自述..................................................... 146 表目錄 表3.1 CMP理論數值分析參數 132 表3.2 不同滲透量 下所對應的孔洞性質,最小孔徑 、最大孔徑 、孔隙率 、碎形維度 與覆蓋數量 133 表3.3 不同滲透量 下所對應的孔洞性質,最大孔徑 、最小孔徑 、孔隙率 、碎形維度 與覆蓋數量 133 表3.4 含孔洞研磨墊在不同轉速、下壓力條件下,經力平衡與力矩平衡所得之攻擊角、旋轉角與最小膜厚 134 表3.5 含孔洞研磨墊與無含孔洞研磨墊在不同工作條件下,平均移除率MRR與不均勻度NU的理論值 134 表3.6 含孔洞研磨墊與無含孔洞研磨墊在不同工作條件下,經力平衡與力矩平衡所得之攻擊角、旋轉角與最小膜厚 135 表3.7 含孔洞研磨墊在相同工作條件不同滲透量下,平均移除率MRR與不均勻度NU的理論值 135 圖目錄 圖1.1 化學機械研磨各參數示意圖 10 圖1.3.1 化學機械研磨結構示意圖 10 圖1.3.2 NDL六吋晶圓非對心式化學機械研磨機台示意圖 11 圖2.1.1 Stribeck圖 71 圖2.1.2 微觀真實CMP示意圖 71 圖2.1.3 穩定運轉下IPEC/Westech Model 473M CMP Polisher CMP時晶圓與研磨墊幾何相對關係與座標示意圖(1) 72 圖2.1.4 穩定運轉下IPEC/Westech Model 473M CMP Polisher CMP時晶圓與研磨墊幾何相對關係與座標示意圖(2) 73 圖2.1.5 切線速度示意圖 74 圖2.1.6 切線速度示意圖 75 圖2.2.1 晶圓與研磨墊之接觸及研磨墊底材變形示意圖 76 圖2.2.2 (a) 研磨墊粗度峰與定義z方向座標軸之示意圖, (b) CMP液動潤滑示意圖(液壓使研磨墊底材變形), (c) CMP混合潤滑示意圖(液壓及接觸壓使研磨墊底材變形) 77 圖2.2.3 (a) 研磨墊上格點A之扇形區域面積, (b) 說明格點A、B之相對位置不變,其中 (c) 卡氏直角座標軸示意圖, (d) 簡化均勻壓力區域的幾何形狀。 78 圖2.2.4 (a) 所考慮的點B(x ,y)落於分佈壓力區域外部, (b) 所考慮的點B(x ,y)落於分佈壓力區域內部, (c) 典型的直角三角形區域,其中 、 79 圖2.2.5 晶圓研磨墊間力平衡示意圖 80 圖2.2.6 晶圓研磨墊間力矩平衡示意圖 80 圖2.3.1 研磨墊粗度峰、研磨面及研磨粉體之接觸情形, (a)研磨面完全與流體接觸, (b)研磨面部份與研磨墊粗度峰接觸, (c)研磨面部份與研磨墊粗度峰及研磨粉體接觸。 81 圖2.3.2 研磨粉體與研磨面之接觸情形示意圖 (a)晶圓研磨面、研磨粉體及研磨墊粗度峰三者之接觸情形, (b)晶圓研磨面、研磨粉體接觸面放大示意圖。 81 圖2.3.3 研磨墊粗糙峰與晶圓彈性接觸示意圖 AA為研磨墊巨體變形前粗糙度振幅平均高度 BB為研磨墊巨體變形後粗糙度振幅平均高度 82 圖2.3.4 研磨粉體與晶圓彈塑性接觸區域局部放大示意圖,ha為接觸間隙,cc線段為粉體分佈平均值 82 圖2.3.5 銅膜鈍化層化學生成速率曲線、砥粒刮蝕機械移除率曲線與自動平衡點的關係。 83 圖2.4.1 Scheidegger的毛細管模型 84 圖2.4.2 用彈簧機械的壓縮解釋壓密作用 84 圖2.4.3 研磨液流經的研磨墊元素 85 圖2.4.4 Laplace’s Equation利用數值方法求解所需之邊界條件 85 圖2.4.5 理論流程圖 86 圖3.1.1 X方向(正面)剖面圖 95 圖3.1.2 Y方向(正面)剖面圖 95 圖3.1.3 X方向(反面)剖面圖 96 圖3.1.4 Y方向(反面)剖面圖 96 圖3.1.5 Z方向(正面)剖面圖 97 圖3.1.6 Z方向(反面)剖面圖 97 圖3.1.7 滲透量與最小孔徑之關係圖 98 圖3.1.8 滲透量與孔隙度之關係圖 98 圖3.1.9 滲透量與碎形維度之關係圖 99 圖3.2.1(a)~ 圖3.2.1(c) 無孔洞研磨墊在不同工作條件下,晶圓面上液動壓力 (kPa)等高線分佈與立體示意圖 100~ 102 圖3.2.2(a)~ 圖3.2.2(c) 有孔洞研磨墊在不同工作條件下,晶圓面上液動壓力 (kPa)等高線分佈與立體示意圖 103~ 105 圖3.2.3(a)~ 圖3.2.3(c) 無孔洞研磨墊在不同工作條件下,晶圓研磨墊間視面積接觸壓力 (kPa)等高線分佈與立體示意圖 106~ 108 圖3.2.4(a)~ 圖3.2.4(c) 有孔洞研磨墊在不同工作條件下,晶圓研磨墊間視面積接觸壓力 (kPa)等高線分佈與立體示意圖 109~ 111 圖3.2.5(a)~ 圖3.2.5(c) 無孔洞研磨墊在不同工作條件下,研磨墊變形量 ( )等高線分佈與立體示意圖 112~ 114 圖3.2.6(a)~ 圖3.2.6(c) 有孔洞研磨墊在不同工作條件下,研磨墊變形量 ( )等高線分佈與立體示意圖 115~ 117 圖3.2.7(a)~ 圖3.2.7(c) 有孔洞研磨墊在不同工作條件下,晶圓面上液動壓力 (kPa)等高線分佈與立體示意圖 118~ 120 圖3.2.8(a)~ 圖3.2.8(c) 有孔洞研磨墊在不同工作條件下,晶圓研磨墊間視面積接觸壓力 (kPa)等高線分佈與立體示意圖 121~ 123 圖3.2.9(a)~ 圖3.2.9(c) 有孔洞研磨墊在不同工作條件下,研磨墊變形量 ( )等高線分佈與立體示意圖 124~ 126 圖3.2.10(a)~ 圖3.2.10(c) 有孔洞研磨墊不同位置晶圓面上液動壓力 (kPa)等高線分佈圖 127~ 128 圖3.2.11 含孔洞效應研磨墊不同滲透量之移除率 128 圖3.2.12 含孔洞效應研磨墊不同滲透量之移除率 129 圖3.2.13 含孔洞效應研磨墊不同滲透量之移除率 129 圖3.2.14 相同工作條件下,有孔洞研磨墊與無孔洞研磨墊 的平均移除率與不均勻度之比較 130 圖3.2.15 不同工作條件下,有孔洞研磨墊與無孔洞研磨墊的平均移除率與不均勻度之比較 130 圖3.2.16 不同工作條件下,有孔洞研磨墊與無孔洞研磨墊的平均移除率與不均勻度之比較 131 圖3.2.17 不同工作條件下,有孔洞研磨墊與無孔洞研磨墊的平均移除率與不均勻度之比較 131

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