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研究生: 吳尚倫
Wu, Shang-Lun
論文名稱: 結合有限元素分析與MATLAB計算之新型化學機械研磨製程模擬模組發展與應用
Development of a Novel Finite Element/Matlab Integration Scheme for Chemical Mechanical Polishing Applications
指導教授: 陳國聲
Chen, Kuo-Shen
學位類別: 碩士
Master
系所名稱: 工學院 - 材料科學及工程學系
Department of Materials Science and Engineering
論文出版年: 2013
畢業學年度: 101
語文別: 中文
論文頁數: 144
中文關鍵詞: 化學機械研磨平坦化接觸應力晶圓級元件級有限元素法MATLAB製程模擬
外文關鍵詞: chemical mechanical polishing, uniformity, contact stress, wafer level, device level, finite element method, MATLAB, process emulation
相關次數: 點閱:143下載:12
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  • 隨著積體電路線寬不斷縮小,晶圓表面高低起伏對微影聚焦能力影響很大,使得晶圓平坦化的要求不斷提升。化學機械研磨於半導體元件製程技術中已被公認為最有效之全面性平坦化技術,而其研磨均勻度對晶圓元件之良率有重大之影響。微觀製程所遭遇到的問題,即在CMP製程中當研磨墊研磨至SiO2介電層與銅導線時,因為兩者之間材料性質有所差異,如硬度不同,抗磨性也不同,因此在相同負載條件下,會造成銅材料的移除率較高,使得導線銅部分形成淺碟型的凹陷及應力腐蝕型缺陷,形成缺陷。過去許多人以理論分析、有限元素法或實驗經驗法則針對化學機械研磨提出許多預測研磨率或缺陷之模型。以純有限元素法或以接觸力學理論分析進行之CMP模擬因無法模擬研磨過程之形貌改變,僅能利用初始幾何做為模擬依據,因而可能產生誤差。有鑑於此,本文提出一新型製程模擬方式,作為改善CMP模擬的方向。本文利用有限元素分析結合MATLAB建立一套製程模擬工具。先以FEM建立一CMP模型,根據模型之幾何與受力狀態,由有限元素法可得此時晶圓之應力狀態,再由MATLAB作控制及計算,計算完成後更新CMP模型進行下一次研磨,依此可簡單的控制研磨次數及研磨參數(如晶圓與研磨墊之材料常數、研磨墊與晶圓相對速度、Preston’s coefficient等),從而探討研磨參數與晶圓表面形貌之關係,可依據各種情形調整所需要的參數。而模擬結果與過去研究之實驗與模擬相互比較以驗證此方法之可行性。其結果將更可提供CMP製程最佳化參考。

    Chemical mechanical polishing (CMP) has been recognized as the most effective planarization technology in wafer processing, and its plays an important role in the state of the arts integrated circuits (IC) fabrication. For CMP, the polishing uniformity of entire wafer as well as the possible dishing and erosion observed in interconnects are the most critical concerns and therefore various analytical and numerical investigations have been conducted for enhancing CMP performance. However, due to its multi-disciplinary nature, it is difficult to conduct a full scale analysis. In particular, finite element analysis (FEA) has been widely used in associated with polishing model such as Preston’s equation for predicting the mechanical stressing effect in CMP. However, in the past, due to lack of efficient geometry updating capability, FEA can only use the initial geometry for simulation, which cannot count the geometry evolution and could possibly results in error. For this reason, in this thesis, a novel chemical-mechanical polishing modeling schemes for addressing the mechanical aspect in both wafer and device levels is analyzed and realized. The method integrates finite element analysis with Matlab for controlling the simulation geometry. The method begins with a CMP finite element model and, the stress of a particular step can be determined and the corresponding MRR can be calculated by FEA. Consequently, the surface topology is then updated based on the calculated MRR distribution, using Matlab and is used for FEA at next time increment. The interaction continues until the entire process is finished. Both wafer and device level simulations are performed by the proposed method. In wafer level, it is observed that the discrepancy between the proposed method and the traditional FEA based on initial geometry is not significant for high uniformity variation tolerance. However, as the tolerance reduceds to within 10 nm, the difference in uniformity prediction becomes remarkable. On the other hand, for device level, the proposed method can successfully predict dishing and erosion phenomena and the simulation results agree with those experimental data reported in previous literatures. Finally, essential parametric studies are performed for systematically investigating various processing parameters such as pad modulus and selectivity as demonstrations for addressing the structural integrity of interconnected structures after polishing and for the possible applicability of using the proposed method for guiding future CMP process optimization.

    中文摘要 I Absbract II 致謝 III 目錄 IV 表目錄 VIII 圖目錄 IX 符號說明 XIII 第一章 緒論 1.1 前言 1 1.2 文獻回顧 8 1.3 研究動機與目標 11 1.4 研究方法 12 1.5 本文架構 13 第二章 化學機械研磨平坦化技術 2.1 介紹 15 2.2 多重內連線製程 16 2.3 平坦化方法 18 2.4 化學機械研磨機制 22 2.5 化學機械研磨移除模型 25 第三章 化學機械研磨接觸力學理論 3.1 介紹 27 3.2 化學機械研磨接觸模型 29 3.3 接觸力學理論 31 3.4 研磨墊粗度峰平均接觸壓力 37 3.5 化學機械研磨製程晶圓級平坦區定義 42 3.6 有限元素法 51 3.7 以細胞自動機理論法進行CMP模擬與其缺失 52 第四章 製程模擬方法之介紹與探討 4.1 介紹 57 4.2 有限元素-MATLAB方法介紹 58 4.3 方法驗證 59 4.4 有限元素模型建立 62 4.4.1 晶圓級模型 62 4.4.2 元件級模型 65 第五章 晶圓級化學機械研磨模擬 5.1 介紹 73 5.2 有限元素模型建立 74 5.3 CMP模型比較 76 5.4晶圓與研磨墊接觸型態與材料性質分析 77 5.4.1平坦晶圓與研磨墊材料性質分析 77 5.4.2翹曲晶圓與研磨墊材料分析 79 5.5 考慮研磨墊鈍化 82 5.6 結論 84 第六章 元件級化學機械研磨模擬 6.1 介紹 85 6.2 有限元素模型建立 87 6.3 元件級製程模擬 88 6.4 模型比較與探討 90 6.5 實驗數據比較與探討 94 6.5.1 FEM-MATLAB與Stavreva實驗比較與探討 94 6.5.2 FEM-MATLAB與Lai實驗比較與探討 96 第七章 元件級化學機械研磨製程參數模擬分析 7.1 介紹 101 7.2 製程參數對晶圓凹陷量之影響 102 7.3 製程參數對應力腐蝕缺陷之影響 105 7.4 結論 108 第八章 新型製程模擬方法結果與討論 8.1 本文歸納 109 8.2 本文製程模擬方法之討論 110 8.3 模擬結果之討論 111 8.3.1 晶圓級結果討論 111 8.3.2 元件級結果討論 112 8.4 未來工作與展望 114 第九章 結論與未來展望 9.1 本文結論 117 9.2 本文貢獻 118 9.3 未來工作 119 參考文獻 121 附錄A1 MATLAB程式碼(晶圓級) 127 附錄A2 ABAQUS程式碼(晶圓級平坦晶圓) 129 附錄B1 MATLAB程式碼(元件級) 135 附錄B2 ABAQUS程式碼(元件級) 139 表目錄 表2.1 ㄧ般常見之平坦化方法及其特徵 18 表4.1 CMP相關製程參數表 62 表4.2 製程參數表 69 圖目錄 圖1.1 銅鍍層對窗洞進行由下而上超填之分解圖 1 圖1.2 多層金屬連線結構 2 圖1.3 銅製程簡化流程圖 3 圖1.4 各種平坦化方法及平坦化範圍 4 圖1.5 化學機械研磨機台實體圖 5 圖1.6 化學機械研磨機制示意圖 5 圖1.7 銅導線之淺碟型與應力腐蝕型缺陷 6 圖1.8 元件級CMP研磨過程三階段 6 圖1.9 FEM-MATLAB模擬流程圖 12 圖1.10 本文架構 13 圖2.1 第二章架構圖 15 圖2.2 多層金屬內連線結構之示意圖 16 圖2.3 多層內連線元件表面凹凸示意圖 17 圖2.4 SOG製程完成之截面 19 圖2.5 表面平坦化程度 21 圖2.6 研磨墊(IC1000)未使用過之表面 23 圖2.7 研磨墊(IC1400)使用後經修整前後之表面 23 圖2.8 晶圓表面材料厚度變化示意圖 24 圖3.1 第三章架構圖 28 圖3.2 化學機械研磨軸對稱模型示意圖 29 圖3.3 研磨墊表面粗度、研磨顆粒與晶圓表面接觸的型態 30 圖3.4 兩個彈性球體相互接觸之幾何示意圖 31 圖3.5 剛性球體壓痕器與試片接觸之幾何示意圖 33 圖3.6 非剛性球體壓痕器與試片接觸之幾何示意圖 35 圖3.7 剛體平板壓在可變形球體示意圖 37 圖3.8 粗度峰會受壓縮發生彈性變形示意圖 38 圖3.9 晶圓與研磨墊之接觸及研磨墊底材變形示意圖 39 圖3.10 研磨墊粗度峰、研磨面及研磨粉體之接觸情況 40 圖3.11 晶圓與研磨墊接觸示意圖 42 圖3.12 Fu and Chandra之理論分析 43 圖3.13 接觸壓力非均勻度定義曲線 44 圖3.14 DOF與最小線寬之關係圖 45 圖3.15 表面均勻度定義曲線示意圖 46 圖3.16 平坦區要求大小之差異 47 圖3.17 平坦區大小與平坦度要求關係圖 47 圖3.18 不同負載於靠近晶圓邊界處之晶圓表面形貌 48 圖3.19 接觸應力與研磨時間之關係圖 50 圖3.20 研磨過程示意圖 50 圖3.21 化學機械拋光研磨之模擬流程圖 51 圖3.22 各種不同的鄰近區狀態 53 圖3.23 CA法與CMP製程技術之對應關係圖 55 圖3.24 CMP製程模擬模組研究架構 55 圖4.1 第四章架構圖 57 圖4.2 FEM-MATLAB與過去方法於晶圓級平坦晶圓之差異 59 圖4.3 翹曲晶圓接觸行為於研磨進行中之示意圖 61 圖4.4 FEM-MATLAB與過去方法在晶圓翹曲量大時之差異與應力演化 61 圖4.5 化學機械研磨模擬之局部應力分布圖 63 圖4.6 研磨分割次數與平均研磨百分比之關係圖 64 圖4.7 元件級模型簡化示意圖, 65 圖4.8 晶圓與研磨墊接觸之有限元素網格 66 圖4.9 Cutting rate選取對研磨後表面形貌之影響 67 圖4.10 CR大小對晶圓幾何之影響 67 圖4.11 局部晶圓應力與幾何圖 68 圖4.12 參數定義與模型示意圖 69 圖4.13 製程參數對FEM-MATLAB之收斂性分析 70 圖4.14 研磨墊楊氏係數與銅線寬大小與接觸行為之關係示意圖 71 圖5.3 晶圓與研磨墊之非均勻接觸壓力分佈 76 圖5.4 平坦晶圓之平坦區 78 圖5.5 翹曲晶圓與研磨墊接觸示意圖 79 圖5.6 晶圓與研磨墊之接觸應力分析 80 圖5.7 翹曲與平坦晶圓中FEM-MATLAB與過去方法之差異 81 圖5.8 實驗數據與擬合曲線[30] 83 圖5.9 有無考慮研磨墊鈍化之差異 83 圖6.1 第六章架構圖 86 圖6.2 元件級有限元素模型收斂性分析 87 圖6.3 晶圓級研磨過程演化圖 88 圖6.4 應力腐蝕型模型示意圖 89 圖6.5 Erosion模擬結果 89 圖6.6 Fu之模型與接觸型態示意圖 91 圖6.8 彎曲因子選擇之差異 92 圖6.9 FEM-MATLAB與Fu模型之比較 93 圖6.10 Stavreva實驗模型示意圖 94 圖6.11 銅結構之Dishing演化 95 圖6.12 研磨墊接觸晶圓示意圖 95 圖6.13 Lai實驗模型示意圖 96 圖7.1 第七章架構圖 101 圖7.2 Dishing定義示意圖 102 圖7.3 研磨墊楊氏係數對凹陷量之影響 103 圖7.4 研磨選擇比對凹陷量之影響 104 圖7.5 線寬對之凹陷量之影響 104 圖8.1 晶圓表面幾何修正示意圖 114 圖8.2 CMP研磨至二氧化矽時晶圓接觸面示意圖 116

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