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研究生：	謝岳哲 Xie, Yue-Zhe
論文名稱：	以反應曲面法分析相同尺寸晶片堆疊式封裝之最佳化設計 Optimal Design on Twin Die Stacked Packages by Using Response Surface Method
指導教授：	陳榮盛 Chen, Rong-Sheng
學位類別：	碩士 Master
系所名稱：	工學院 - 工程科學系 Department of Engineering Science
論文出版年：	2008
畢業學年度：	96
語文別：	中文
論文頁數：	141
中文關鍵詞：	部分因子設計法、累積應變能密度、反應曲面法、圖形尋覓法
外文關鍵詞：	fractional factorial design method, Accumulative Strain Energy Density, Response Surface Method, pattern search algorithm
相關次數：	點閱：95 下載：3
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由於消費性電子產品之市場日益蓬勃發展及消費者對小尺寸之要求，三維堆疊封裝結構迅速地趨於流行。然矽晶片的互相堆疊，將使材料間偶合行為更趨於複雜，已成為產品可靠度最重視也最亟待
解決的課題。
本研究以ANSYS有限元素軟體分析相同尺寸晶片堆疊式封裝體於熱循環負載下之狀態。分析模型以三維條狀模型建立，並以黏塑性有限元素分析與Darveaux理論預測疊晶封裝體錫球接點之可靠度。錫球接點疲勞壽命與錫球上之累積應變能密度有顯著的關係，故建立應變能密度的平均值與差異値，作為可靠度最佳化指標，這個方法可忽略關鍵錫球的位置，而獲得有效且完整的分析。再者，以有限元素模擬分析與錫球間累積應變能密度的觀點，探討堆疊晶片封裝體之參數對可靠度影響。
在進行堆疊式封裝體可靠度最佳化之前，先以部份因子設計法篩選出顯著的控制因子，再以反應曲面法進行實驗設計，以建構出迴歸模型。其後以數值分析方法求得最佳參數解，並建構反應曲面於次區，以求得準確的最佳參數解。最後，研究結果發現較薄的下晶片、較厚的基板、較低的封裝楊氏模數與較高的基板楊氏模數可提升封裝體之錫球可靠度，亦顯示出各元件熱膨脹係數之間不匹配與疲勞壽命之間的關係，而第二次區之反應曲面其預測值較接近實際實驗値。

Along with the vigorous development of the electronic products market and the consumer's preference for products with smaller size, the structure of 3D stacked die package rapidly becomes popular. Thus the stacked behavior of the silicon dies always makes the coupling effect among materials more complicate. Such an issue has been seriously paid attention to the reliability and becomes a critical problem.
This research applies the ANSYS finite element software to analyze a twin die stacked package under a cyclic thermal loading condition. The analytical models are built up in terms of the three-dimensional slice model as well as the viscoplastic finite element analysis and the Darveaux theory are applied to predict the solder joint reliability of the stacked die package. Certainly significant relations are found between the fatigue life of the solder joint and the distribution of the accumulated strain energy density on the solder joints. Therefore the average value and the variance value of the strain energy density are set up as the optimization indicator of the reliability. With such a method, the solder joint's position can be ignored, and accordingly an efficient and complete analysis can be obtained. Furthermore, by incorporating the simulation analysis, from the viewpoints of the accumulative strain energy density among solder balls, the effects of parameters of the stacked die packages on the reliability are discussed.
Prior to the process of the optimal design on reliability of stacked die packages, the most significant factors are chosen by the fractional factorial design method and the experiment is planned by the response surface method to construct the regression model. Subsequently, the pattern search algorithm is applied to search the optimal parameter solution and response surfaces are built on the sub-region of interest to obtain the accurate optimal parameter solution. Finally, the result of study shows that thinner bottom die, thicker substrate, lower molding compound Young's modulus and higher substrate Young's modulus can enhance the reliability of the stacked die packages. It also shows the relations between the mismatch of coefficients of thermal expansion of components and the fatigue life of the solder joint. Then, the predicted value is closer to the actual experimental value in the second sub-region.

中文摘要............................................................................................I
英文摘要...........................................................................................II
誌謝..................................................................................................IV
目錄...................................................................................................V
表目錄..............................................................................................IX
圖目錄...........................................................................................XIII
符號說明......................................................................................XVII
第一章 緒論
1-1 前言.............................................................................................................1
1-2 研究動機與目的.........................................................................................2
1-3 文獻回顧.....................................................................................................3
1-4 研究方法.....................................................................................................6
1-5 章節提要.....................................................................................................7
第二章 理論基礎
2-1 亞蘭德黏塑性本構模型...........................................................................10
2-1-1亞蘭德黏塑性本構模型.................................................................10
2-1-2 決定材料參數................................................................................13
2-2 Darveaux模型............................................................................................15
2-3 反應曲面法...............................................................................................17
2-3-1 迴歸模型........................................................................................18
2-3-2 迴歸因子實驗水準配置法............................................................21
2-3-3 迴歸模型的配適性........................................................................23
2-4 圖形尋覓法(Pattern Search Method) ......................................................25
2-4-1 圖形尋覓法之理論架構................................................................26
2-4-2 以隨機選取方式產生起始基點....................................................27
2-4-3 圖形尋覓法最佳化範例................................................................27
2-5 最佳化設計方法.......................................................................................30
2-5-1 建立反應曲面之次區....................................................................30
2-5-2 將迴歸模型以圖形尋覓法進行搜尋最佳值................................31
2-5-3 最佳化設計流程............................................................................32
第三章 應變能密度平均值為指標進行參數分析
3-1 晶片堆疊式封裝體簡介...........................................................................42
3-2 建立構裝體可靠度評估指標...................................................................44
3-2-1 以應變能量密度觀點法分析疲勞壽命........................................44
3-2-2 以PCB熱膨脹係數變化之差異分析...........................................46
3-2-3 應變能密度的平均值與差異值決定疲勞壽命分析指標............46
3-3 晶片堆疊式封裝之參數因子探討...........................................................47
第四章 以反應曲面法與圖形尋覓法進行參數最佳化
4-1 以部分因子設計法篩選控制因子...........................................................77
4-1-1 各控制因子水準值之選擇............................................................78
4-1-2 零階反應曲面法之部分因子設計................................................78
4-1-3 效果與變異分析............................................................................79
4-1-4 篩選控制因子................................................................................79
4-2 反應曲面法迴歸模型建立.......................................................................81
4-2-1 Box-Behnken迴歸模型建立..........................................................81
4-2-2 決定配適模型形式........................................................................81
4-2-3 疲勞壽命指標之迴歸模型............................................................82
4-3 以圖形尋覓法求得最佳參數解...............................................................84
4-3-1 反應曲面於此次區迴歸模型之建立............................................84
4-3-2 疲勞壽命指標次區迴歸模型........................................................85
4-3-3 次區迴歸模型之最佳參數解........................................................86
4-4 第二次反應曲面於次區迴歸模型之建立...............................................87
4-4-1 疲勞壽命指標之第二次區迴歸模型............................................87
4-4-2 第二次區迴歸模型最佳參數解....................................................88
4-5 以反應曲面法探討因子間變化對可靠度之影響...................................89
4-5-1 利用反應曲面分析幾何參數與楊氏係數變化對可靠度影響....89
4-5-2 利用反應曲面分析各元件材料係數變化對可靠度之影響........92
4-5-3 利用次區反應曲面對各元件熱膨脹係數交互作用之探討........93
4-5-4 各階反應曲面於最佳値區域之差異............................................94
第五章 結論與未來研究方向
5-1 結論.........................................................................................................135
5-2 未來研究方向.........................................................................................138
參考文獻......................................................................................................139
                                    

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校內：2010-08-01公開
校外：2010-08-01公開

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