對近年電子封裝技術而言，發展大致朝向更大I/O密度、更小體積、更高效散熱與更低製造成本努力： 從電子元件連接的效率來說，早期有DIP(Dual in-line Packaging)、SOP(Small Outline Packaging )來改善SIP(Single in-line Packaging)腳位數量，後來則有BGA(Ball Grid Array)、覆晶封裝(Flip Chip, FC)與本研究所探究的晶圓級封裝(Wafer Level Packaging, WLP)等技術帶來更多接點和減少空間占比的優勢以達到市場需求。
一項合格的產品會經過一連串實驗測試以檢驗其是否可靠，其中，幾何結構的不同尺寸、各式各樣的材料特性抑或產品製造過程等皆可能導致壽命受到影響。對於晶圓級封裝，加速熱循環負載(Thermal Cycling Test)是一種可靠度測試的方法，用來確認產品上市前的穩定性。不過，實驗的缺點在於耗費時間人力，總進程往往需要遠超三個月左右，且由於是觀察平均破壞時間(Mean Time to Failure, MTTF)，得到一筆數據也需要數組實驗嘗試。不僅在材料上帶來實際損耗，更消耗大量時間成本。
為了降低研發時數，有限元素方法在可靠度分析及模擬方面扮演重要的角色。透過經實驗得出之真實壽命數值與有限元素模型進行驗證，即可利用模擬方法來縮短研發所需時間。本研究所使用的模擬程式為ANSYS^®，具體可靠度壽命取得方式為： 晶圓級封裝體在受到熱循環負載情況下，觀察其應力分布，並將錫球產生最大等效塑性應變增量代入Coffin-Manson經驗式中以進一步計算錫球之預測壽命。模擬過程中，除了注意最有可能造成失效的位置跟實驗頻繁發生破壞之區域是否一致，並固定其網格最適大小，以達到實驗結果與模擬預估值之驗證，最小化兩者間的差異。
 
除了時間成本方面以外，研究參與人在時空背景下存在差別，著重觀察的現象也不盡相同，進而導致模擬結果五花八門。面對此現象，為求不同模型間誤差得以最小，本篇論文將會引入人工智慧中機器學習之概念作為預估壽命的手段。結合有限元素模擬與機器學習，以經實驗對照後認證的模型建立資料庫，並利用機器學習訓練以消弭不穩定性。機器學習得出的模型具有能以較短的時間預測更多在各式條件下封裝體壽命的優勢，達到增進效率、節省成本的效果。
此研究之機器學習演算法選定多項式迴歸(Polynomial Regression)，探討不同數據集、模型複雜程度、以及加入聚類分析中的K-Means深究其結果。篩選適宜的條件、決定出最好的參數配置，並透過分類法檢視能否以更簡單之模型達到更準確的結果，藉以改善模擬誤差，加快總體進程，減少所耗。

　　For common packaging technology, to pursue higher density I/O, lower volume occupation, more efficient thermal dissipation, or less manufacturing cost is the main purpose in current development. To efficiency of electronic components connection, there are DIP(Dual in-line Packaging), SOP(Small Outline Packaging ) improving the number of leads for SIP(Single in-line Packaging) at early stage. Subsequently, BGA(Ball Grid Array), FC(Flip Chip), and Wafer Level Packaging, WLP, which is applied in this study bring the advantage of more leads and less space occupation to approach what markets need.
A qualified product will be tested by a series of experiments to ensure its reliability. Some reasons may affect the reliability life, such as, different parameters of geometry structures, various material properties, or the process of manufacture, etc. For WLP, TCT is the measure to validate the stability of the product before being launched. However, the disadvantage of experiment is costing time and labor. It usually takes much more than three months to complete an experiment. On the other hand, one result requires several experiments to calculate Mean Time to Failure. For physical point of view, materials are consumed. Moreover, time consumption is considerable.
In order to reduce research time, finite element method plays an important role in reliability analysis and simulation. It can shorten the whole flow by applying simulation method through real reliability life which is obtained from experiment to verify finite element model. In this study, ANSYS^® is the software selected for simulation. The specific approach how to get reliability life is as following, observing the stress distribution when the Wafer Level Packaging is under the condition of thermal cycling load and substituting the max equivalent plastic increment on the solder ball into Coffin-Manson empirical formula can calculate prediction life. During the simulation procedure, it should be check that the position which contributes the most probability occurring failure coincides the region which crack is generated. Fixing the optimal mesh size minimizes the difference between results from experiment and values from simulation to fulfill the validation.
Diversity appears not only at the time cost aspect, but also from researchers’ backgrounds, approaches, or devices. It will result in a lot of kinds of outcomes due to the phenomena that they focus on. To this, that errors between models are minimized is desired. Therefore, the concept called Machine Learning in Artificial Intelligence field will be introduced in this study as the application predicting the reliability life. Database is generated based on the models after verification, combining the technique of finite element analysis and machine learning to train a new model for eliminating instability. The model equips the property that it is able to predict reliability life under more situations with relatively shorter time. Achieving the purpose of saving cost, improving efficiency is possible.
In this study, the machine learning algorithm, Polynomial Regression, is chosen. Different datasets, model complexities, and whether the cluster analysis, K-Means, is considered are discussed. To search the most suitable conditions, to determine the best parameters combinations, and to checking if the errors become smaller with simpler model gotten by cluster method are the targets. According to these objects, there is a probability that it can make the simulation more precise. Besides, it can proceed the whole process, reduce loss.

摘要 II
Abstract IV
目錄 VI
圖目錄 X
表目錄 XIV
第一章 緒論 1
1.1 研究動機 1
1.2 文獻回顧 2
1.3 研究目標 8
第二章 基礎理論 9
2.1 有限元素分析基礎理論 9
2.1.1 材料線彈性理論 10
2.1.2 材料非線性理論 15
2.1.3 數值方法以及收斂準則 16
2.2 材料應變硬化法則 18
2.2.1 等向硬化法則(Isotropic Hardening Rule) 19
2.2.2 動態硬化法則(Kinematic Hardening Rule) 19
2.3 Chaboche模型 20
2.4 錫球外型預測 22
2.5 封裝結構可靠度之預測方法 24
2.5.1 Coffin-Manson應變法 24
2.5.2 Darveaux 能量密度法 25
2.5.3 修正型能量密度法 26
2.6 機器學習 28
2.6.1 機器學習方式(Machine Learning Methods) 30
2.6.2 前處理器(Preprocessor) 31
2.6.3 機器學習主要應用 35
2.7 多項式迴歸(Polynomial Regression, PR) 38
2.7.1 基礎理論(Basic Theory) 38
2.7.2 表現準則(Performance Criterion) 40
2.7.3 模型求解(Model Solution) 42
2.7.4 迴歸解釋 43
2.7.5 時間複雜度 44
2.8 K-Means Algorithm 44
2.8.1 基本理論 44
2.8.2 種類 45
B. MacQueen[40] 45
第三章 有限單元模擬之分析與驗證 46
3.1 有限單元模型基本假設 48
3.2 材料參數設定 49
3.3 網格劃分及元素種類 53
3.4 邊界條件之設定 55
3.5 加速熱循環負載設定 56
3.6 測試載具(Test Vehicles) 56
3.7 有限單元模型分析與驗證 62
第四章 研究結果與討論 63
4.1 訓練資料與測試資料之建立 64
4.2 演算法之輸入定義 71
4.2.1 機器學習的必要性 74
4.2.2 最適模型之評估 77
4.2.3 前處理器之選擇 78
4.2.4 K-Means之前處理器問題 83
4.3 多項式迴歸訓練結果 86
4.3.1 數據效應(Data Effect) 86
4.3.2 多項式迴歸對比其他演算法 93
4.3.3 K-Means對多項式迴歸之影響 96
4.3.4 運算時間(Computing Time) 100
4.3.5 大量數據下的影響及建議簇類數 103
第五章 結論與未來建議工作 107
參考文獻 109

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