臺灣博碩士論文加值系統

本文的目的是利用有限元素法，建立化學機械研磨(Chemical-mechanical Polishing,簡稱CMP)的二維軸對稱準靜態模式，分析化學機械研磨過程中，晶圓承載器施壓於晶圓表面與研磨墊後，晶圓表面的應力分佈趨勢與表面不均勻度的影響，進而提出新的表面不均勻度的變化關係公式，以及表面應力不均勻度R、晶圓邊緣效應的比值Rs以及晶圓邊緣磨耗的比值Rd的公式與分析，並透過改變研磨墊與載具膜的彈性係數與厚度，以及比較施加不同的研磨壓力對於晶圓研磨表層所產生的應力變化情形，了解研磨壓力與表面不均勻度之影響來觀察晶圓受力後，晶圓表面變形的變動情形，進而提出研磨參數與表面不均勻度的變化關係。
其次，考慮在晶圓鍍膜厚度越來越薄的情況，當薄膜厚度達到奈米級尺寸時，在進行化學機械研磨製程時，就必須將鍍膜層的材料性質受奈米級尺寸效應的影響，造成鍍膜材料的楊氏係數降低加以考慮。本文將討論因鍍膜厚度的減少，而使得鍍膜層的材料性質受奈米級尺寸效應的影響，造成材料的楊氏係數降低，在化學機械研磨過程中，對晶圓表面的應力分佈與表面不均勻度的變化與影響。並透過改變研磨墊的彈性係數與厚度，以及施加不同的研磨壓力。以改善因為鍍膜厚度的減少，使得鍍膜的材料性質受奈米級尺寸效應的影響，造成材料的楊氏係數降低，在化學機械研磨過程中，對晶圓表面的應力分佈與表面不均勻度的影響。
最後，考慮晶圓表面不平整時的化學機械研磨狀態，以有限元素法模擬化學機械研磨之作動情形，了解化學機械研磨過程中，不平整之晶圓表面的軸向位移的變化與最後晶圓表面變形的變動情形之關係。
在接觸問題的處理是每一步驟開始時，暫不考慮上半部整體(包含載具、載具膜、晶圓及鍍膜層)的應力與變形，先計算出研磨墊節點在接觸區的位移增量，並求得此位移增量產生的研磨墊節點負荷力增量，將負荷力增量帶入迭代程序中，研磨墊節點負荷力增量求出上半部整體(包含載具、載具膜、晶圓及鍍膜層)接觸節點的負荷力，以求解出上半部整體(包含載具、載具膜、晶圓及鍍膜層)的變形量。再求出相對應的研磨墊接觸節點補償位移增量，並將此一變形量迭加在研磨墊接觸節點增量位移上，此變形量即為研磨墊真正彈性回彈變形量，如此便可求得鍍膜層節點下壓變形量。此變形量稱為前一次的變形量，然後重複上述的程序，再次求出上半部整體(包含載具、載具膜、晶圓及鍍膜層)接觸節點下壓變形量，此變形量稱為後一次的變形量，設定誤差量5%做為比較標準，將後一次的變形量與前一次的變形量做比較，若後一次的變形量與前一次的變形量的誤差小於5%，則本文假設已達收斂條件，後一次的變形量即為薄膜層的位移增量。本文所推導的上半部整體(包含載具、載具膜、晶圓及鍍膜層)與研磨墊接觸問題的演譯準則，其主要觀念建立於薄膜層與研磨墊接觸的有限元素節點，應能在某一收斂範圍內，有相同的位移平衡與力平衡。

The paper, utilizing Finite Element Method for establishing a two-dimensional quasi-static axial symmetrical model of Chemical-Mechanical Polishing(CMP), aims at analyzing the impacts on stress distribution trend of the wafer surface and its inhomogeneous levels after a load force is applied to the wafer surface and coating pad during the process of CMP by wafer lift. In addition, the paper studies the impact of coating stress and the inhomogeneous surface distribution of the wafer, through changing elastic modulus and the thickness of coating pad and that of the carrier film and comparing with the stress changeovers generated by different coating stresses on the wafer surface, to observe the change in deformation of the wafer surface after the wafer is applied a load force; furthermore, proposes the changing relationship between the coating parameter and the inhomogeneous distribution of the wafer surface.
Secondly, considering the coating thickness of wafer is getting thinner, Young’s modulus of coating material that is reduced resulting from the impact of the size effect on the material property of coating layer shall be taken into consideration when the thickness of thin film reaches the size of nano level under the CMP process. The paper will study the changeovers and the impacts on the stress distribution of the wafer surface and its inhomogeneous distribution under the process of CMP owing to reduced Young’s modulus of material that is caused by the size effect, which affects the material property of coating layer when coating thickness is decreasing. The paper further adjusts elastic modulus and the thickness of coating pad and applies different coating stresses to improve the impacts on the stress distribution of the wafer surface and its inhomogeneous distribution during the process of CMP. Therefore, the aforementioned Young’s modulus of material decrease resulting from the size effect, which affects the material property of coating layer, when coating thickness is decreasing, can be minimized.
At last, considering the CMP over uneven wafer surface, the paper utilizes Finite Element Method for simulating the CMP operation to research the relationship between the variations of axial deformation of uneven wafer surface and changes in the final deformation of the wafer surface.
As for the contact problem resolution, the paper, without considering the stress and the deformation of the upper half integral (including carrier, carrier film, wafer and coating layer) at the beginning of each step, firstly initials the node displacement increment of coating pad at the junction area, then applies the displacement increment to generate load factor increment of coating pad, and puts the load factor increment into the Newton-Raphson iteration for coming out load power factor of the contact node the upper half integral, so that the amount of deformation of the upper half integral can be generated. Next, the paper will ask for compensating displacement increment of corresponding contact node of coating pad and use the amount of deformation, which is the amount of deformation for actual elastic rebound of coating pad, to be superimposed on the displacement increment of the contact node of coating pad to come out the downward deformation of coating layer node. The deformation is called the amount of the former deformation. Furthermore, the paper will iterate the aforementioned procedures to compute the downward deformation of the contact node of the upper half integral, again. The deformation is called the amount of the latter deformation. Assuming the standard error of statistic is set as 5%, the latter deformation shall be the displacement increment of the thin film, if the error is within the range of 5% comparing the latter deformation with the former one.

目 錄
摘要……………………………………………………………………..Ⅰ
英文摘要……………………………………………………………….. Ⅲ
誌謝…………………………………………………………………….. Ⅴ
目錄…………………………………………………………………….. Ⅵ
圖表索引……..…………………………………………………………..
第一章 緒論….……………………………………………...1
1.1 前言……….…………………………………………………………1
1. 2 研究動機….………………………………………………………...2
1. 3 文獻回顧….………………………………………………………...5
1. 4 論文架構……………………………………………………………8
第二章 化學機械研磨加工法簡介…….………………….11
2.1化學機械研磨之簡介…………….………………………………...11
2.2 化學機械研磨之研磨機構……………..…………………..……...12
2.3 化學機械研磨之作動原理.....…………..…………………………14
第三章 化學機械研磨之有限元素模式…….………….….19
3.1 有限元素法概論…………..…………….…………………………19
3.2 準靜態模式之建立…………..………….…………………………20
3.3 二維軸對稱線彈性之基本方程式………………………………...22
3.3.1 應變位移方程式…………..……………………….…………….22
3.3.2 應變應力關係…...……………………………………………….22
3.3.3 靜平衡方程式…...…………………………………………….…23
3.3.4 相容性方程式.……..…………………………………………….24
3.4 二維軸對稱之有限元素構成方程式.……………………………..25
3.4.1 最小總位能原理(虛位移原理)….………………………………25
3.4.2 二維軸對稱有限元素方程式..….………………………………27
3.4.3 二維軸對稱有限元素分析.…….……………………………….28
第四章 平整晶圓表面之應力分析….………………………33
4.1 晶圓研磨基本假設與邊界條件…..……………...……………….33
4.2 晶圓表面應力分析………………..………………………………35
4.3 研磨墊對晶圓表面應力之影響….…………….…………………39
4.3.1 研磨墊材質對晶圓表面應力之影響.……….…………….……39
4.3.2 研磨墊厚度對晶圓表面應力之影響.……….…………….……42
4.4 載具膜對晶圓表面應力之影響……………………….………….45
4.4.1 載具膜材質對晶圓表面應力之影響…………………….….….45
4.4.2 載具膜厚度對晶圓表面應力之影響…….………………….….48
4.5 下壓力對晶圓表面應力之影響…………….………..…..………51
4.6 模擬結果討論………………………………..………..………….54
第五章 不同鍍膜厚度對晶圓應力之影響……..…………56
5.1 基本假設與邊界條件…………………………………..………56
5.2 晶圓表面應力分析……………………………………………..57
5.3 改善晶圓表面應力狀態之方法…………………………………….60
5.3.1 研磨墊材質對晶圓表面應力之影響………………………..60
5.3.2 研磨墊厚度對晶圓表面應力之影響 ………..……………..64
5.3.3 載具膜厚度對晶圓表面應力之影響………………………..67
5.3.4 下壓力對晶圓表面應力之影響……………………………..70
5.4 模擬結果討論………………………………………………….74
第六章 不平整晶圓表面之應力分析………………………76
6.1 不平整表面之晶圓研磨基本假設……………………………78
6.2 接觸問題處理…………………………………………………78
6.3 接觸介面之位移分析……………………………………………….84
6.3.1 近晶圓中心處之接觸介面位移分析……………………….84
6.3.2 近晶圓邊緣處之接觸介面位移分析……………………….89
6.4 模擬結果討論與分析…………………………………………92
第七章 結論與建議…………………………………………98
7.1 結論………………………………………………………….…98
7.2 建議……………………………………………………………101
參考文獻……………………………………………………………102

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