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研究生：	張平昇 Chang, Ping-Shine
論文名稱：	薄膜結構基材應力分析之基本模型建立以及其在半導體隔離製程上之應用 Modeling of Thin Film Induced Substrate Stress and Its Application in Semiconductor Device Isolation Process
指導教授：	陳國聲 Chen, Kuo-Shen
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：	2006
畢業學年度：	94
語文別：	中文
論文頁數：	142
中文關鍵詞：	熱彈性力學、表面力學、有限元素法、應力分析、淺溝渠隔離結構
外文關鍵詞：	Finite element analysis, Residual stress, Shallow trench isolation (STI), Isolation structure, Cerruti’s problem, Green’s function
相關次數：	點閱：129 下載：4
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近年來半導體元件越做越小，製程技術要求更加精確，在高積極度以及小線寬的要求下，元件間的干擾越來越明顯，如Cross Talk；為了避免此干擾之發生，便需要隔離製程來達到隔離效果。雖然解決了干擾之問題，但卻也引發了像高集中應力等應力問題，此等應力問題會造成如Dislocation這類的缺陷，會影響整體元件之基本電子特性，降低可靠度。因此應力之預測，於製程設計是一項重要之資訊，我們希望於設計過程中，設計出使因隔離製程所引起之應力值達到最小之程度。本論文所探討之問題便是此等應力問題。對於薄膜結構中之隔離結構，有不少應力分析方法，但在某些限制條件下，要得到全盤之應力分析資訊，有一定之困難度。故本文提出利用力學模型結合Green’s function的概念，得到一半解析解，來做為應力分析工具，似乎是一個較為可行之方法。在此我們的想法為釐清單一Stress Source對其周邊基材所造成的應力、應變和位移之關係，進而找出核心函數，再利用此函數以Green’s function的概念進行線性疊加，即可快速評估任意設計之半導體結構，如薄膜結構、隔離結構等，其整體應力行為，設計者可利用此方式迅速求得概念設計，再由後續較詳細之有限元素分析，達成設計最佳化的目的。而本文中以STI結構為例子，對所提方法做詳細說明。利用有限元素分析求出STI結構之應力關係，用此結果與力學模型之半解析解所得到的結果，進行相互之印證，經過多方面之驗證後，可發現到利用力學模型結合Green’s function的概念，在描述隔離結構應力行為時有相當好表現，故說明了本文所提方法之可行性。文中亦說明了對於其他半導體結構應力分析當中，也可以利用相同之概念，求得其他任意設計半導體結構之應力行為，設計者可以此分析結果，為設計最佳化提供初步之方向。

Isolation techniques are essential for semiconductor device for reducing interferences between devices for sub-micro and sub 100-nm fabrication process. By separating active regions with oxide isolation structures, it is possible to reduce cross-talk between elements. However, the mismatch in thermal mechanical properties between oxide and silicon create enormous stress and it results leakage current due to generation of dislocations in active zones. As a result, it is important to carefully design the isolation structures. However, at this moment, all designs are based on finite element analysis, its trial and errors and case by case nature cause difficulty for systematic understanding and design for this problem. A semi-analytical procedure is demand. In this thesis, the stress behavior of STI structure is firstly modeled and is properly reduced to a simple model. By utilizing the Cerruti’s Problem or Hu’s Formula as the kernel function. The stress distribution of STI isolation structure can be found by using Green’s function approach. By this approach, the designer can perform a rapid conceptual design and then use more detail finite element analysis for design optimization only. The overall computational cost or working time can be effectively reduced. The proposed method is then validated by finite element simulation by using a simple plane strain structure and three-dimensional model of simple surface pattern as the test and verify model. By this approach, a computer program, called I-SA, is constructed to evaluate the stress subjected to arbitrary isolation structures. The program could provide preliminary stress analysis information for conceptual design of isolation structures. The designer could improve the designs according the results of the stress analysis. And the results show that the proposed method can essentially catch the stress distribution. Using the same conception, the proposed method can also be applied to other semiconductor structure, such as multi-layer interconnection structures.

目錄
中文摘要.....................................................................I
Abstract....................................................................II
誌謝.......................................................................III
符號表......................................................................IV
目錄.........................................................................V
圖目錄......................................................................IX

第一章 緒論
1 前言......................................................................1
2 文獻回顧..................................................................4
2 研究動機與目標............................................................7
3 本文架構..................................................................9

第二章 半導體製程之薄膜結構問題
1 半導體製程技術...........................................................12
2薄膜製程所導致之基材應力問題..............................................14
2.1薄膜結構................................................................14
2.2隔離結構................................................................18
2.3 STI製程之應力預測......................................................23
2.4 小結論.................................................................25
3 Volume Inclusion所引起之問題.............................................26
4本章結論..................................................................27

第三章 基礎表面力學及熱彈性力學之介紹
1 表面力學.................................................................30
1.1 Lame´’s strain potential.............................................30
1.2 Galerkin Vector Representation.......................................32
1.3 Kelvin’s Problem....................................................34
2 Cerruti’s Problem.......................................................36
3.1 Cerruti’s Problem.....................................................37
3.2 Flamant’s Problem.....................................................39
3 熱彈性力學...............................................................40
4 Hu’s Formula............................................................42
5 Green’s Function介紹....................................................49
6 Green’s Function之應用..................................................51
7本章結論..................................................................52

第四章 隔離結構與簡化隔離結構之應力分析
1 隔離製程之應力介紹.......................................................54
2 隔離結構之模型...........................................................56
2.1 分析模型之敘述.........................................................56
2.2 分析模型之簡化.........................................................58
3 應用力學模型於隔離結構應力之分析.........................................61
3.1 以表面力學模型為核心函數...............................................61
3.2 以熱力學模型為核心函數.................................................64
4 本章結論.................................................................66

第五章 應力分析之有限元素印證
1 簡單STI結構模型..........................................................67
2 應力分佈圖之比較.........................................................70
3 解析解與有限元素分析之比較...............................................73
3.1 應力曲線圖之比較.......................................................73
3.2 其他各個stress component之比較.........................................82
3.3 其他位置(遠場) stress component 之比較.................................85
4 結果與討論...........................................................................90
5 結論.....................................................................94

第六章 應力分析程式之建構與驗證以及應用
1簡介......................................................................95
2程式之建構................................................................96
2.1 程式流程...............................................................98
2.2 程式介紹..............................................................100
3 程式之驗證-與有限元素之比較.............................................106
3.1 平面應變問題(Plane strain) .........................................106
3.2 簡單平面外形驗證 : 方形...............................................107
4 Case study-程式之應用...................................................110
4.1平面外型一 : 十字形....................................................110
4.2平面外型二 : 圓形I.....................................................113
4.3平面外型三 : 圓形II....................................................117
5 結論....................................................................120

第七章 結論與未來展望
1 本文歸納..........................................................................121
2 結論....................................................................122
3 本文貢獻................................................................124
4 未來展望................................................................124

參考文獻....................................................................126
附錄........................................................................130

                                    

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校內：2007-08-04公開
校外：2007-08-04公開

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