摩爾定律為Gordon Earle Moore所提出，他認為積體電路上可容納的電晶體數目，大約每18個月就會成長為2倍，但由於已漸漸接近物理上的極限，摩爾定律不再如此適用，因此封裝技術在後摩爾時代就益顯重要。電子封裝的發展大約可分為五個大階段，分別是TO-CAN、DIP(Dual In-line Package)、PQFP(Plastic Quad Flat Pack)、PBGA(Plastic Ball Grid Array)以及本研究所使用的CSP(Chip Scale Package)。這些演進是為了提高信號的傳輸速度、儲存的容量以及追求更高的構裝密度。而封裝體最注重的就是其可靠度，不同尺寸或是製成方式都會影響其壽命，在這些封裝體上市前，必須經過測試以及實驗，來確保其可靠度。然而，繁雜的測試和實驗會浪費許多的資源以及時間成本，導致利益無法最大化。
　　有限單元分析為一種數值方法，可將大型物理系統細分為有限個更小、更簡單的元素。本研究使用ANSYS模擬晶圓級晶片尺寸封裝(WLCSP)透過熱循環負載(Thermal Cycleing Test)，再藉由經驗公式來預估錫球之壽命，同時也固定了DNP(Distance from Neutral Point)最大位置的錫球角落網格大小，使模擬更加貼近實驗結果。經過模擬與實驗數據交互驗證後，確立模型之可用性，進而節省封裝測試以及實驗所帶來龐大的時間成本。
　　然而，有限單元分析也會因為不同的研究者而有不同的結果，導致模擬之誤差產生。為了避免此因素，以及節省建構模型所花費的時間，本研究引入了人工智慧，並結合了監督式學習以及非監督式學習，來預估錫球壽命。本研究使用經過驗證後的有限單元模型，依照不同尺寸得到不同的壽命，再將得到的大量預估數據引入人工智慧演算法當中，來達到快速預估封裝體可靠度之目的。
　　本研究所使用的演算法為可運用於分類以及迴歸的K-鄰近演算法(K-Nearest Neighbors)，並使用了不同的數據量、不同的前處理方法、不同的距離定義以及不同的權重計算方式來比較其對於此演算法預估壽命的影響。此外，還結合了非監督式學習的聚類分析分析K-means，使相同性質的資料分配到各個的聚類中，進而簡化模型複雜度，節省運算時間以及提升表現。

Moore’s law was proposed by Gordon Earle Moore, who believes that the number of transistors that can be accommodated on an integrated circuit would double about every 18 months. Since it is approaching the physical limit, Moore’s law is no longer so applicable. Packaging technology becomes more important in the post Moore era. The development of electronic packaging can be roughly divided into five stages, namely TO-CAN, DIP (Dual In-line Package), PQFP (Plastic Quad Flat Pack), PBGA (Plastic Ball Grid Array) and the CSP (Chip Scale Package) used in this research. The evolutions are to improve signal transmission speed, storage capacity and the pursuit of higher packaging density. The reliability of packages is very important. Different sizes or manufacturing methods will affect their lifetime. Before these packages are put on the market, they must be tested and experimented to ensure their reliability. However, it will waste a lot of resources and time costs, resulting in less profit.
Finite element analysis is a numerical method that can subdivide a large physical system into a finite number of smaller and simpler elements. The study uses ANSYS to simulate WLCSP (Wafer Level Chip Scale Packaging) through thermal cycling test, and used empirical formulas to estimate the lifetime of solder balls. Also, the mesh size at the corner of the solder joint from the maximum DNP (Distance from Neutral Point) is fixed. Make the simulation closer to the experiment results. After the verification of simulation and experimental data, the feasibility of the model is established, thereby saving the huge time cost of packaging testing and experimentation.
However, finite element analysis will produce different results depending on the researcher. In order to avoid this factor and save the time spent in constructing the model, this research introduces artificial intelligence and combines supervised learning and unsupervised learning to estimate the solder ball lifetime. In this study, we used the verified finite element model to obtain different lifetime according to different sizes, and then introduced a large amount of data into AI algorithms to achieve the purpose of quickly predicting the reliability of the package.
The algorithm used in this study is KNN (K-Nearest Neighbors) which can be used for classification and regression, and uses different data numbers, different preprocessing methods, different distance definitions, and different weighting methods to compare the impact of the algorithm’s predictions on the lifetime of our packages. In addition, we combine unsupervised learning methods like K-means to assign data of the same characteristic into each cluster. Try to simplify the complexity of the model, save calculation time and improve the performance of KNN.

摘要 I
Abstract III
目錄 V
圖目錄 VII
表目錄 XI
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 有限單元法基礎理論 9
2.1.1 材料線彈性理論 9
2.1.2 材料非線性理論 13
2.1.3 數值方法以及收斂準則 15
2.2 材料應變硬化法則 16
2.2.1 等向硬化法則(Isotropic Hardening Rule) 17
2.2.2 動態硬化法則(Kinematic Hardening Rule) 18
2.3 Chaboche模型 18
2.4 錫球外型預測 20
2.5 封裝結構可靠度之預測方法 22
2.5.1 Coffin-Manson應變法 22
2.5.2 Darveaux 能量密度法 23
2.5.3 修正型能量密度法 23
2.6機器學習 24
2.6.1機器學習演算法 25
2.6.2資料前處理(Data Preprocessing) 27
2.6.3分類(Classification) 28
2.6.4迴歸(Regression) 29
2.6.5過擬合(Overfitting) 30
2.7 K-鄰近演算法(K-Nearest Neighbors) 32
2.7.1 K值的決定 33
2.7.2 距離定義 34
2.7.3 權重計算 36
2.7.4 KNN的分類以及迴歸 37
2.8 聚類分析 39
第三章 有限單元模擬之分析與驗證 41
3.1 有限單元模型基本假設 43
3.2 材料參數之設定 44
3.3 網格劃分及元素種類 46
3.4 邊界條件之設定 48
3.5 循環溫度負載設定 49
3.6 有限元素模型建構 50
3.7 有限單元模型分析與驗證 51
第四章 研究結果與討論 52
4.1 訓練資料與測試資料之建立 52
4.2 超參數之設定 56
4.2.1 預處理器選擇 57
4.2.2 權重計算之選擇 62
4.2.3 距離之選擇 64
4.3 經驗K值 66
4.4 建議K值 68
4.5 KNN結合K-means 70
4.5.1 前處理對於K-means的影響 70
4.5.2 K-means對於KNN表現之探討 74
4.5.3 K-means對於經驗K值之影響 76
4.6 資料量對KNN以及KNN結合K-means之影響 79
4.6.1 KNN之訓練結果 79
4.6.2 KNN結合K-means之訓練結果 80
4.6.3 KNN以及KNN結合K-means之結果比較 82
4.7 KNN與其他演算法之比較 83
第五章 結論與未來建議 86
參考資料 87

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