隨著半導體技術的進步，電子元件的使用領域變得越發廣泛，型態也更加多樣化。其中，在車用電子領域中，相較於消費性電子產品，封裝體將暴露在相對更加嚴峻的環境條件中。此外，為了增加效能而出現的小晶片（chiplet）、三維堆疊等先進封裝技術讓結構變得更加複雜，或彼此交互作用影響，可能會導致失效更容易發生，有效的防治方法是透過可靠度測試來排除潛在失效風險。其中，電路基板扮演著讓所有元件彼此溝通的重要角色，其需要長時間且穩定的品質，因此可靠度分析變得至關重要。
以往基板的設計尺寸通常被認為不會發生電遷移（electromigration）現象，如今，可能會由於導線寬度縮小、施加功率變高等原因而逐漸逼近電遷移觸發的閾值，例如在可靠度測試的加速負載條件下，在載具上所施加的負載條件與環境條件導致基板上線路電氣失效容易被誘發。
在以往的研究中，電遷移通常僅考慮為電子風力以及結構應力之間的平衡關係，但現今的研究指出，電遷移應是一多物理場（Multiphysics）問題，並且熱效應會與電流密度分布之間產生交互作用的效應。本研究為了分析線路的失效機制，以及節省設計實驗的成本，在研究中主要利用有限元素法（Finite Element Method, FEM）進行wire bonding PBGA模擬模型的建立，並且測試在模型中應用等效熱傳係數（Equivalent Thermal Conductivity）以及多點約束法（Multi-Point Constraints, MPC）兩種模型簡化方法，來縮減建模以及模型運算時間，以期透過此載具研究基板線路的數值模型建立方法。另外，模型中利用電熱耦合（Coupled Analysis）分析線路在可靠度測試條件下施加負載時，線路因電流熱效應所引發的溫度變化情形，以及局部焦耳加熱效應對系統溫度的影響，作為後續建立電熱耦合分析複雜模型時重要的參考依據。

Because of the advancement of semiconductor technology, the utilization of electronic components has become increasingly extensive with encompassing variety of forms. In the realm of automotive electronics, compare to consumer electronics, the packaging are put into more harsh environmental conditions. In addition, using emerging advanced packaging techniques for enhaninge efficiency such as chiplets and 3D stacking technology will make structures more intricate. These situations introduce interdependencies that may lead to heightened susceptibility to failures. Effective mitigation involves the identification of potential risks through reliability testing. As a pivotal role of communication components, printed circuit boards (PCBs) need long-term and stable quality, so reliability analysis assumes paramount importance.
From previous studies, PCB design dimensions were considered to be immune to electromigration effect. However, due to decreasing wire pitch and escalating applied power, the threshold for triggering electromigration is increasingly approached. For instance, circuit electrical failures on the substrate can be induced under accelerated load conditions in reliability testing.
Although prior research primarily considered electromigration in terms of electronic wind and structural stress, studies nowadays highlight it as a multiphysics issue with thermal effects interacting with current density distribution. To investigate the failure mechanisms in circuits and economize experimental design, this study constructs a numerical model of the substrate circuit of wire bonding PBGAs and analysis results by using the Finite Element Method (FEM). In the model, the electrothermal coupling (Coupled Analysis) is used to analyze the temperature change in the circuit structure caused by the current heating effect under the reliability test condition, and the influence of local joule heating effect on the system temperature. The results can be used as reference of establishing complex models for subsequent electrothermal coupled analysis.

摘要 I
Abstract II
圖目錄 VII
表目錄 XI
1. 第一章　緒論 1
1.1 簡介 1
1.2 研究動機與目標 3
1.3 文獻回顧 5
2. 第二章　基礎理論 12
2.1 熱傳理論分析 12
2.1.1 熱傳導（Thermal conduction） 12
2.1.2 熱對流（Thermal convection） 13
2.1.3 模型熱分析 13
2.1.4 等效熱傳係數 16
2.2 有限元素法基礎理論 18
2.2.1 熱傳穩態有限元分析 19
2.2.2 多點約束法 （Multi-Point Constraints, MPC） 22
2.2.3 耦合場分析 25
2.3 電遷移效應 26
2.3.1 電遷移理論 26
2.3.2 焦耳加熱效應 27
2.3.3 電流集中效應 28
2.4 電化學遷移 29
2.5 b-HAST可靠度測試 30
2.6 PCB製程 31
3. 第三章　建立有限單元測試模型 32
3.1 電熱耦合設定 32
3.2 3D結構模型 32
3.2.1 模型與材料參數設定 37
3.2.2 邊界條件與負載設定 39
4. 第四章　測試模型模擬結果分析 40
4.1 局部模型結果與分析 40
4.2 全域模型結果與分析 43
4.2.1 環境溫度對結果之影響 43
4.2.2 不同開關導線數對模型對結果之影響 45
5. 第五章　結論與未來工作 48
6. 參考資料 50

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