近年來，科技的蓬勃發展增長了電子產品的需求量，同時也是其功能變得更加多元。為了順應這一趨勢，電子產品產業鏈不斷地進行改變與創新，在追求高效能的同時也積極推動產品的微型化。然而，在摩爾定律(Moore's Law)也逐漸達到極限的情況下，如何在有限的空間內實現更多功能並保持穩定性與可靠性，成為了一項艱難的挑戰。因此，先進的封裝技術不斷推陳出新，以提高封裝的效率和可靠性，期望能滿足甚至超越當前市場的需求。
電子封裝需要在產品上市之前經過完整的結構測試實驗以檢測該封裝的可靠度，而其中加速溫度循環測試(Accelerated Temperature Cycling Test, ATCT)是一個被廣泛使用的測驗，藉由提升負載的強度使封裝結構提早破壞，便能在較短的測試時間得到可靠度結果。然而實驗所需要的時間與花費對於現今封裝技術的快速發展速度來說並不符合時間成本與金錢成本，因此若能以有限單元法(Finite Element Method, FEM)對封裝體進行模擬分析以得到預估壽命的目的，便可以減少進行實驗所產生的時間成本與金錢花費。
對於晶圓級封裝(Wafer-Level Packaging, WLP)而言，在加速熱循環負載下的損壞發生的原因為晶片(Chip)與基板(Substrate)之間的熱膨脹係數(Coefficient of Thermal Expansion, CTE)不匹配，使得連接兩者結構的錫球(Solder Ball)承受熱應力並累積熱應變，通常會在距離封裝中心最遠處(Maximum Distance From Neutral Point)發生疲勞破壞。為了對錫球的疲勞壽命做預測，本研究使用有限元素模擬軟體ANSYS®對WLP封裝結構進行模擬，根據五個測試載具(Test Vehicle)建立了不同的二維簡化對稱模型，然而在模擬過程之中會有許多不同的因素會影響模擬的結果。
本研究為了減小材料模型所帶來的影響，以Chaboche模型為目標曲線引入人工神經網路(Artificial Neural Network, ANN)進行曲線擬合，藉由近年來蓬勃發展的機器學習(Machine Learning)演算法得到更為精確的材料曲線以提升模擬結果的可靠度。為了進一步的驗證其可靠度，本研究也會將人工神經網路擬合所得到的材料曲線帶入上述的五個測試載具模型進行塑性分析，同時也會與潛變分析中Hyperbolic Sine模型及Anand模型的結果進行對比，以Coffin-Manson應變法及修正型能量密度法(Modified Energy Density Method)計算錫球的預估疲勞壽命。
此外，雖然使用有限元素模擬可以減少得到可靠度結果的成本與時間，但由不同研究者根據其物理觀念所建立的模型結果不一定一致，會有差異產生。為了面對此情況，透過結合模擬與機器學習將以驗證過的模型及結果作為建立預測模型的資料庫，在經過演算法計算後訓練出合適的預測模型，可以用於在短時間內評估不同結構尺寸的封裝體壽命，在降低時間成本的同時也能減少不同研究結果的差異。
訓練時間與最佳參數搜尋時間在機器學習預測模型的研究中是一個重要的課題，兩者對於機器模型訓練的效率有很大的影響。在本研究中將針對人工神經網路模型的超參數(Hyperparameter)以網格搜索法進行最佳參數組合搜尋並討論其時間，並在平行運算的架構下進行CPU運算與GPU運算訓練時間之分析。藉由引入平行運算的結構於網格搜索法進行最佳參數搜尋，可以縮減最佳參數搜尋時間，提升以機器學習進行可靠度預估的效率。

In recent years, the rapid development of technology has increased the demand for electronic products and diversified their functions. To keep up with this trend, the electronic products supply chain has been continuously innovating and evolving, striving for high performance and actively pursuing miniaturization. However, as Moore’s law approaching its limit, it becomes a significant challenge to achieve more functions within limited space while maintaining stability and reliability. Consequently, advanced packaging technologies are continually being introduced to enhance efficiency and reliability, aiming to meet or exceed current market demands.
Electronic packaging needs to go through comprehensive structural experimental testing to ensure its reliability, one of the most popular tests is Accelerated Temperature Cycling Test (ATCT). This test increases loading strength to make structure fail earlier, getting reliability result within shorter time. Nonetheless, keeping pace with the rapid progress in packaging techniques is challenging due to the time and cost constraints associated with these experiments. So, utilizing Finite Element Method (FEM) for simulation and analysis in packaging could reduce the cost of conducting an experiment.
For Wafer-Level Packaging (WLP), failure during temperature Cycling tests is attributed to the mismatch of the Coefficient of Thermal Expansion (CTE) between the chip and substrate. The solder ball is responsible for their connection taking thermal stress and leads to the accumulation of thermal strain. Failure often occurs at maximum Distance from Neutral Point (DNP). To predict failure life of solder ball, this research applies finite element simulation software ANSYS® for simulating WLP packaging structure, developing different 2-dimensional simplified symmetric model based on five test vehicles. However, multiple factors may affect the simulation results.
To minimize the impact of material model, this research employs Artificial Neural Network (ANN) to fit Chaboche material model curve. With recent advancements in machine learning algorithms, this approach achieves a more precise material model curve, enhancing the reliability of simulation result. For further validation, the material model curve derived from ANN is applied to the previously mentioned five test vehicle models for plasticity analysis. Both Coffin-Manson strain method and Modified Energy Density method are employed for predicting the component's lifetime. Additionally, the results are compared with the results from creep analysis models utilizing the Hyperbolic Sine model and Anand model.
Although using finite element analysis can reduce the time and cost of getting reliability result, different models built by different researchers based on their own physical concept may lead to different results. To reduce the difference, this research combines simulation and machine learning. using validated models and results to generate database and train probable prediction model with algorithm. After finish training, the prediction model is used to get reliability life of different structure sizes in a brief time, reducing time and also reduce the difference between different research result.
Training time and best parameter searching time are important topics of machine learning model, both have impact on training efficiency. This research focus on the hyperparameter of ANN model, utilizing grid search method on searching best parameter combination and conducting analysis on the training time of using Central Processing Unit (CPU) parallel computing structure and Graphic Processing Units (GPU) parallel computing structure. By using parallel computing structure on grid search method, the best parameter searching time is reduced and the efficiency of WLP reliability prediction using machine learning is improved.

摘要 i
Abstract iii
目錄 v
圖目錄 viii
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 9
2.1 有限元素法基礎理論 9
2.1.1 材料線彈性理論 9
2.1.2 材料非彈性理論 13
2.1.3 數值辦法與收斂準則 16
2.2 材料硬化法則 18
2.2.1 等向硬化法則 18
2.2.2 動態硬化法則 19
2.3 Chaboche 模型 20
2.4 潛變模型 21
2.4.1 Garofalo-Arrhenius(Hyperbolic Sine)模型 21
2.4.2 Anand模型 22
2.5 錫球幾何外形預估 24
2.6 封裝結構可靠度預測 25
2.6.1 Coffin-Manson 應變法 26
2.6.2 Darveaux 能量密度法 26
2.6.3 修正型能量密度法 27
2.7 機器學習 27
2.7.1 機器學習演算法 28
2.7.2 資料前處理 30
2.8 人工神經網路模型 32
2.8.1 激活函數 33
2.8.2 損失函數 35
2.8.3 學習率與優化器 36
2.8.4 反向傳播法 40
2.9 平行運算 42
2.9.1 中央處理器(Central Processing Unit, CPU) 43
2.9.2 繪圖處理器(Graphic Processing Unit, GPU) 45
第三章 有限元素模型之建立 46
3.1 基本假設 46
3.2 材料參數設定 47
3.3 錫球幾何外形設定 48
3.4 網格劃分與元素選取 49
3.5 溫度負載測試模擬設定 50
3.6 WLP 幾何尺寸與模型建構 51
3.6.1 Test Vehicle 1 (TV1) 模擬設定 52
3.6.2 Test Vehicle 2 (TV2) 模擬設定 53
3.6.3 Test Vehicle 3 (TV3) 模擬設定 54
3.6.4 Test Vehicle 4 (TV4) 模擬設定 55
3.6.5 Test Vehicle 5 (TV5) 模擬設定 56
第四章 使用ANN擬合材料曲線研究結果與討論 57
4.1 資料選取 58
4.2 模型設計與訓練 59
4.3 Chaboche模型材料曲線擬合最佳結果 68
4.4 WLP有限元素模型驗證 70
4.4.1 塑性分析與壽命預估 70
4.4.2 潛變分析與壽命預估 73
第五章 ANN最佳參數搜尋時間研究結果與討論 76
5.1 資料庫建立 76
5.2 網格搜索法(Grid Search) 79
5.3 平行運算與網格搜索法 81
第六章 結論與未來工作 88
參考資料 90

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