隨著科技進步與消費者對於電子產品的需求，電子封裝的技術朝向體積小、更輕薄、高效能的面向來發展。封裝結構從最早期的Pin-trough hole 轉變成 Surface Mount Technology如QFP（Quad Flat Package）。再從 Surface Mount Technology 轉到球閘型引腳陣列BGA（Ball Grid Array）型封裝與覆晶封裝(Flip Chip )與本研究探討的晶圓級封裝(Wafer Level Packaging, WLP)等。電子封裝產品在進入市場前，會經歷多項實驗來檢測其可靠度。加速熱循環(Thermal Cycling Test)則是其中一種檢測可靠度檢測。實驗的檢測的缺點在需花費諸多的時間與人力資本上。
為了改善研發時間，加速研發時程，有限單元模擬分析被運用於可靠度的模擬分析中。藉由已經過真實實驗驗證過的模型來模擬封裝體獲得可靠度壽命。本研究將以 ANSYS 軟體進行晶圓及封裝體的可靠度模擬。 藉由熱循環負載施加下，模擬封裝體的應力分布。其中為了計算封裝體的可靠度壽命，本研究使用Coffin-Mansion 公式來計算。 將錫球上產生的等效塑性應變帶入Coffin-Mansion 公式，計算可靠度壽命。另外對於實驗上最常失效的位置進行網格大小的控制，以獲取較為準確的模擬數值來與真實熱循環實驗進行對比。
對於有限單元模擬分析之不足之處，不同研究者所建立的模型常得到不盡相同的數值結果。其中要透過模擬分析評估封裝體的可靠度分析需要有其專業的背景知識。 為了消除模擬誤差與減低操作的困難度，本研究透過結合機器學習的應用來進行封裝體可靠度壽命預估。將由經過真實熱循環實驗驗證過的有限單元模型來建立不同尺寸與結構的資料集。並運用於高斯過程迴歸過模型來進行資料訓練，並透過訓練完成的模型來可以快速評估不同結構的封裝體可靠度壽命。
本研究將使用高斯迴歸過程模型來進行可靠度壽命的預估，將探討不同資料量對於高斯迴歸模型對於不同核函數的效應。並且將使用聚類分析K-Means來探討資料量對於高斯迴歸模型的時間複雜度的影響。

關鍵詞:晶圓級封裝、有限單元分析、熱循環負載、可靠度預估、機器學習、高斯迴歸過程

With the advancement of technology and consumers' demand for electronic products, the technology of electronic packaging is developing towards smaller sizes, lighter and thinner, and higher performance. Before entering the market, electronic packaging products will undergo a series of experiments to test the reliability. Accelerated thermal cycling (Thermal Cycling Test) is one of the reliability tests. The disadvantage of experimental detection is that it takes a lot of time and human capital. This is for today's market demand.
Finite element analysis is used in the simulation analysis of reliability to improve the development time. A model that has been verified by real experiments is used to simulate the package to obtain the reliability life. In this study, ANSYS software will be used to simulate the reliability of wafers and packages. The stress distribution of the package is simulated by the application of a thermal cycling load. The coffin-Mansionon formula will be applied to calculate the reliability life of the package. Bring the equivalent plastic strain generated on the solder ball into the Coffin-Mansion formula to calculate the reliability life. In addition, the mesh size is controlled for the most frequently failed locations in the experiment to obtain more accurate simulation values for comparison with the real thermal cycle experiment.
The finite element analysis still has its limitations. The models established by different researchers often get different results. In order to evaluate the reliability analysis of the package through simulation analysis, professional background knowledge is required. In order to eliminate simulation errors and reduce the difficulty of operation, this research combines the application of artificial intelligence and machine learning to estimate the reliability of the package body. The data sets of different sizes and structures will be established by the finite element model verified by the real thermal cycle test.
This research will apply the Gaussian process regression model for data training to predict the reliability of the Wafer Level Chip Scale Packaging (WLCSP). Initially, the simulation results will be compared with experimental results of thermal cycle loading. With the verified model, using the same modeling process, we will create a training database that generates different parameters by using FEM. This study will explore the data effect of the Gaussian regression model on different kernel functions. The study will also combine K-Means clustering with an analysis of the time complexity of the Gaussian regression model based on the amount of data.

Keywords: Wafer level packaging, Finite Element Analysis, Thermal Cycle Load, Reliability Estimation, Machine Learning, Gaussian Regression Process

摘要 I
Abstract III
目錄 IV
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 7
第二章 基礎理論 8
2.1 有限單元法基礎理論[20] 8
2.1.1 材料線彈性理論 9
2.1.2 材料非線性理論 12
2.1.3 數值收斂方法與準則 14
2.2 材料應變硬化法 15
2.2.1 等向硬化法則(Isotropic Hardening Rule) 16
2.2.2 動態硬化法則(Kinematic Hardening Rule) 16
2.3 Chaboche 模型 17
2.4 錫球外型預測 19
2.5 封裝體可靠度預測方法 21
2.5.1 Coffin-Manson應變法 21
2.5.2 Darveaux 能量密度法 22
2.5.3 修正型能量密度法 22
2.6 機器學習 23
2.6.1 機器學習演算法 24
2.6.2 資料前處理 25
2.6.3 高斯過程迴歸模型 28
2.6.4 理論推導 28
2.6.5 超參數學習 32
2.6.6 核函數 34
2.6.7 聚類分析 36
第三章 有限單元之模型模擬驗證與分析 40
3.1 有限單元模型基本假設 41
3.2 錫球外型預估 43
3.3 網格劃分與元素 46
3.4 溫度循環負載設定 48
3.5 有限單元模型建構 49
3.5.1 Test Vehicles 50
3.6 有限單元模擬分析之驗證 56
第四章 研究結果與討論 57
4.1 資料庫的建立 57
4.2 高斯過程迴歸模型超參數之設定 62
4.3 高斯過程迴歸訓練之方法 63
4.3.1 預處理的影響 65
4.4 網格搜尋法 68
4.5 資料對於核函數的影響 76
4.5.1 單核函數對於資料量的訓練結果 76
4.5.2 雙核函數 83
4.5.3 訓練結果與測試結果比較 91
4.6 K-means 預測 96
4.6.1 K-Means預測結果比較 111
4.6.2 K-Means運算時間的比較 112
4.7 高斯過程迴歸與其他演算法比較 115
結論與未來建議工作 118
參考資料 119

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