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系統識別號 U0026-2705202009340100
論文名稱(中文) 機器學習於薄膜應力與翹曲之分析與預測
論文名稱(英文) Prediction and Analysis of Film Stress and Warpage based on Machine Learning
校院名稱 成功大學
系所名稱(中) 機械工程學系
系所名稱(英) Department of Mechanical Engineering
學年度 108
學期 2
出版年 109
研究生(中文) 吳玟君
研究生(英文) Wen-Chun Wu
學號 N16074360
學位類別 碩士
語文別 中文
論文頁數 176頁
口試委員 指導教授-陳國聲
口試委員-陳鐵城
口試委員-陳元方
口試委員-王浩偉
中文關鍵字 Stoney Equation  薄膜應力  晶圓翹曲  有限元素分析  機器學習 
英文關鍵字 Stoney equation  Film stress  Warpage  Finite element method  Machine learning 
學科別分類
中文摘要 於半導體薄膜製程中,為達成製程目標會經歷反覆的溫度變化,過程中會因上下材料性質的差異形成熱應力且變形,而過大的薄膜應力和變形狀況均有可能產生破壞、缺陷,影響後續的製程導致良率降低,因此為量測此兩種物理量,會透過光學的方式量測晶圓的翹曲或平均曲率半徑得知變形情形,再以Stoney Equation換算出薄膜應力,然而製程中必定經過複雜的變化,過程中包含多項製程參數、材料性質、幾何參數、離散薄膜等等的綜合效應,使的基本的Stoney Equation無法適用,雖有人針對特定的案例推導其對應的半解析解,但在綜合的情形下半解析解的推導亦有其極限。因此,本文將透過有限元素數值模擬建立對應的大數據,並以此數據集做為神經網路模型的訓練,訓練成功的神經網路模型能用來預測計算薄膜應力或晶圓的翹曲、曲率半徑。本研究亦提出以區域曲率半徑計算晶圓整體變形樣貌的演算法,且此演算法於連續、離散薄膜的情形下均可適用,以神經網路模型計算預測區域的曲率半徑,再透過演算法計算,即可得到整體晶圓的變形樣貌狀態。並整合神經網路模型和曲面建構演算法於使用者圖形介面,達成讓使用者輸入參數後,經由神經網路運算出所要的薄膜應力並以演算法繪製出晶圓變形狀態。綜合以上,可達到於複雜模型情形下獲取薄膜應力和製程後的晶圓變形狀況的目的,並期望本文提出之研究方法未來能擴展至其他相似案例中使用。
英文摘要 Stoney equation is widely used to estimate the film stress in semiconductor industry, however it is accurate only under particular situation. The purpose of this thesis is to predict film stress and wafer warpages while the Stoney equation could not be used, such as multilayers structure, finite deformation and discontinue films. To achieve the goal, several machine learning models are constructed based on the finite element database. The final machine learning model is chosen with the best accuracy. The final models constructed in this work could predict the film stress or the radius of curvature. To get the warpage of the deformed wafer, a topology-reconstruction algorithm is proposed and be demonstrated in two and three-dimensional with good performance. Finally, the machine learning model and the algorithm are integrated in graphical user interface.
論文目次 摘要 I
Abstract II
Extended Abstract III
致謝 XXIII
目錄 XXV
表目錄 XXXI
圖目錄 XXXII
符號表 XL
第一章 緒論 1
1.1 前言 1
1.2 文獻回顧 4
1.2.1 Stoney Equation的發展 4
1.2.2 類神經網路與有限元素模擬結合應用 5
1.3 研究動機與目的 8
1.4 研究方法 9
1.5 本文架構 11
第二章 研究背景 13
2.1 本章介紹 13
2.2 廣義薄膜製程介紹與應力生成機制 14
2.2.1 薄膜沉積製程 14
2.2.2 晶圓重組製程 16
2.2.3 選擇性雷射熔融(SLM)積層製造 18
2.2.4 殘留應力成因 20
2.3 殘留應力的量測方法 22
2.4 Stoney Equation之發展與限制 25
2.5 薄膜應力行為 28
2.5.1 多層薄膜應力 28
2.5.2 黏彈行為 32
2.5.3 大變形 36
2.6 機器學習與類神經網路介紹 39
2.6.1 類神經網路原理 40
2.6.2 神經網路訓練 41
2.7 類神經網路與有限元素結合 42
2.8 本章總結 45
第三章 整體研究概念設計 46
3.1 本章介紹 46
3.2 概念設計 47
3.3 數據集與神經網路模型建立流程 50
3.4 薄膜樣貌建構流程 52
3.5 本章總結 53
第四章 薄膜應力模擬與類神經網路介紹 54
4.1 本章介紹 54
4.2 神經網路應用概念 56
4.3 有限元素基本模型建立與驗證 57
4.4 薄膜應力行為模擬 59
4.5 類神經網路模型設計介紹 67
4.6 本章總結 72
第五章 類經網路模型建立與預測 73
5.1 本章介紹 73
5.2 神經網路的應用驗證 74
5.3 三種應力模型訓練與預測結果 78
5.4 綜合應力模型訓練與預測結果 91
5.5 討論 97
5.6 本章總結 98
第六章 離散薄膜結構翹曲分析 99
6.1 本章介紹 99
6.2 本章流程說明 101
6.3 邊界效應的影響 104
6.4 部分薄膜移除的影響 112
6.5 討論 117
6.6 曲率建構晶圓樣貌 119
6.7 本章總結 122
第七章 離散薄膜案例分析與應用 123
7.1 本章介紹 123
7.2 流程說明 124
7.3 曲面建構 125
7.3.1 有限元素模型建立與驗證 125
7.3.2 案例展示與討論 130
7.4 使用者圖形介面整合展示 143
7.5 討論 145
7.6 本章總結 146
第八章 研究結果與討論 147
8.1 全文歸納 147
8.2 研究結果討論 149
8.2.1 薄膜應力模型數據集建立 149
8.2.2 神經網路模型預測結果 150
8.2.3 以小區域曲率建構變形樣貌 151
8.3 未來展望與未來工作 153
第九章 結論與未來展望 158
9.1 本文結論 158
9.2 本文貢獻 160
9.3 未來工作 161
參考文獻 162
附錄 166

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