現今生活中，發光二極體已被廣泛應用於各式各樣室內外照明設備，包括汽車前燈照明、背光式大屏幕液晶顯示器等，發光二極體儼然成為新一代替代光源。打線接合為發光二極體結構之重要製程，用以導通發光二極體晶片內部之電訊。打線接合製程為一複雜之物理行為，大致上分為衝擊階段、超音波震動階段和打線拉伸階段，此接合方式常見的破壞模式有墊片剝落、破裂、脫層等，這些破壞都會限制發光二極體之發展，因此如何有效預估打線接合製程時的應力，對發光二極體結構破壞之改善是一相當重要之課題。本研究將聚焦於打線製程之衝擊階段，探討並建立出一強而有力之模擬方法。
現實生活之打線系統中，於衝擊階段內夾具用以擠壓自由體球，使其接合於墊片上。相對於夾具而言，自由體球之材料特性相當軟，此時自由體球會被嚴重拉扯而造成結構大變形之行為。以有限元素模型進行模擬時，大變形行為容易造成網格嚴重扭曲變形，使得數值分析結果因發散而被迫中止。為了防止這樣的問題，許多研究減少夾具之位移量作為模擬之簡化假設，或是將自由體球上之網格切割得相當細以確保數值模擬分析之品質，如此一來除了拉長計算時間外，亦將因為夾具-自由體球之接觸下壓量不足而造成模擬結果失真的情形。本研究將以商用有限軟體ANSYS®/LS-DYNA 3D分別建立內隱式時間處理法及外顯式時間處理法之有限元素模型，以這兩種模型探討大變形行為中，網格扭曲之問題。值得注意的是，建立外顯式時間處理法之有限元素模型時，吾人將提出ALE座標描述法等網格重劃分之概念，用來解決大變形行為之數值問題。
本研究最終以二階精度之ALE座標描述法，建立出一實用有效之外顯式時間處理法之有限元素模型。衝擊階段結束瞬間，比較此模型與實際製程模型之球高，僅有0.5%之差異性。且此結果所得之幾何外型亦十分接近實際製程模型。綜合而言，本研究以外顯式時間處理法所建立出之有限元素模型，不但成功地解決打線接合製程中，網格大變形所造成之發散問題，此模型更提供一有效且實用之方法，幫助日後打線模擬研究之進行。

In recent years, light emitting diode (LED), which has applied in outdoor illumination, automotive front lighting, and backlighting for large LCD display. It has become the key for the next generation illumination application. Wire bonding is one of the main processes used for connecting the signal of LED chip, it’s a multi-physic process including impact stage, ultrasonic vibration stage, and lift off stage. The failures of LED such as pad peeling, cracking, and delamination limit the development of LED and some are influenced by the wire bonding process. In a word, predicting and analyzing the failure of LED chip during wire bonding process is an important issue for decades, and this research will dedicate to constructing an effective simulation methodology on impact stage during wire bonding process.
In wire bonding system, the material property of free air ball (FAB) is much softer than that of the capillary, which compresses the FAB to land on pad. Thus, a large deformation phenomenon comes out on FAB during wire bonding process. Due to the large deformation problem, it’s easy to have element distortion issue on FAB while executing simulation work of wire bonding process. To avoid the divergent problem of finite element (FE) analysis, many researches reduce the compression distance of capillary on their contact simulation. Consequently, it is not easy to meet a good agreement with the real wire bonding process since the contact procedure of simulation is not completed. To solve the divergence problem, this research will construct FE models to discuss the element distortion issue using commercial software ANSYS®/LS-DYNA 3D with implicit and explicit method. Especially, an arbitrary lagrangian-eulerian (ALE) algorithm and the remesh concept will be proposed while utilizing the explicit method to solve the element distortion problem.
By utilizing the explicit method with 2nd level accuracy ALE algorithm, an effective simulation methodology is successfully achieved. Observing the ball height after impact stage, there’s only 0.5% discrepancy between this model and the real wire bonding sample, the geometry of bonded wire is also similar to the real one. It is concluded that the FE model established in this research not only conquer the element distortion problem, but proposed an effective methodology for simulating wire bonding process in the future as well.

摘要 I
Abstract III
目錄 V
圖目錄 VIII
表目錄 XI
第一章 緒論 1
1.1 簡介 1
1.2 研究動機 3
1.3 打線製程介紹 4
1.4 文獻回顧 6
1.5 研究目標 20
第二章 基礎理論 23
2.1 有限元素法理論 23
2.1.1 線彈性有限元素法 23
2.1.2 材料非線性有限元素法理論 27
2.1.3 數值方法與收斂準則 30
2.2 有限元素暫態分析法 32
2.2.1 外顯式時間處理法 33
2.2.2 內隱式時間處理法 36
2.2.3 零能量模式 38
2.3 有限元素法之接觸理論 39
2.3.1 拉格朗日乘子法 40
2.3.2 罰函數法 41
2.3.3 加強型拉格朗日乘子法 41
2.4 有限元素法之網格重劃分法 42
2.4.1 ALE座標描述法 43
2.4.2 手動網格重劃分法 46
2.4.3 自適應網格重劃分法 49
第三章 內隱式時間處理法之模擬分析 51
3.1 結構尺寸設計 51
3.2 有限元素模型之基本假設 54
3.3 材料參數設定及模型建立 55
3.4 初步結果與驗證 60
第四章 外顯式時間處理法之模擬分析 64
4.1 簡化模型 65
4.1.1 模型設計及材料參數之修正 65
4.1.2 模擬方法之建立 67
4.2 全模型 72
4.2.1 模型建立、基本假設及材料參數設定 73
4.2.2 模擬結果與幾何驗證 75
第五章 結論與未來工作 83
參考文獻 85

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