發光二極體是一種發光的半導體元件，在日常生活中已被廣泛的運用在不同的照明設備上，其中打線接合為發光二極體之重要製程，用以導通內部之電訊。熱超音波打線接合是最常被使用在發光二極體上的接合方式，其過程為一複雜之物理行為，大致可以分為衝擊階段、超音波震動階段和拉伸階段。在接合過程中常見的破壞模式有墊片剝落、破裂、脫層等，這些破壞都會影響發光二極體電訊的傳遞。因此如何有效預估打線接合時之應力，對其結構破壞之改善是一重要的課題。
打線過程中，衝擊階段以夾具擠壓自由球體，而球體相對夾具為相當軟的材料，球體在受擠壓拉扯後造成結構大變形，並與晶片結構區之墊片產生接觸。以有限元素模擬時，大變形行為容易造成網格嚴重扭曲變形，使得計算之精確性與收斂性出現問題，嚴重時甚至會造成數值分析計算發生終止的情形，為了防止這樣的問題發生，許多研究裡會採取減少夾具之下移量，或是在自由球體部分網格進行加密之動作以確保模擬分析之品質。然而，下移量不足可能造成模擬結果失真，加密的結果會使計算時間拉長，但其網格嚴重變形之情形依舊無法解決。
本研究將以商用有限元素軟體ANSYS®/LS-DYNA建立外顯式處理法之有限元素模型，使用二階精度之ALE座標描述法及不同的網格平滑演算法進行網格重新劃分，用以解決大變形行為時網格扭曲之問題。在研究最終，藉由使用ALE及平衡網格平滑演算法，建立出有效的外顯式處理法之有限元素模型，並在衝擊結束時，其模擬結果之幾何外型與實際製程結果外型相符，且應力集中位置與實際樣品破壞位置相同。總而言之，此模擬方法有效的解決以有限元素法模擬打線過程時，夾具下壓不足及網格嚴重變形之問題。

Light emitting diode (LED), which has widely applied in different illuminations, is a kind of luminous semiconductor devices. Wire bonding is one of the main processes used for connecting the signal of chip. Thermosonic bonding is often applied in the LED wire bonding process, and 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 might influence the power connecting of chip. In a word, predicting and analyzing the failure of LED chip during wire bonding process is an important issue.
In the impact stage of wire bonding process, the material property of free air ball (FAB) is much softer than 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 or increase mesh density. However, reducing distance would lack fidelity, and increasing mesh density would take more time in calculation. The element distortion issue still cannot be solved.
This research will construct FE models to discuss the element distortion issue using commercial software ANSYS®/LS-DYNA with explicit method and utilize 2nd level accuracy arbitrary Lagrangian-Eulerian algorithm, and ALE method with different mesh smoothing algorithms to solve the element distortion problem. In the end of research, utilizing ALE method with equilibrium mesh smoothing algorithm demonstrates better element quality with excellent geometry prediction in impact stage of bonding process. In summary, this simulation method not only conquers the element distortion problem and lack of capillary displacement problem, but proposed an effective methodology for simulating wire bonding process. It is believed the stress/strain history and contact force will give better accuracy than other mesh smoothing algorithms or non-ALE methods.

摘要 I
Abstract III
目錄 V
圖目錄 VIII
表目錄 XII
第一章 緒論 1
1.1 研究動機 2
1.2 文獻回顧 4
1.3 研究目標 22
第二章 基礎理論 24
2.1 有限元素法理論 24
2.2 有限元素暫態分析法 28
2.3 有限元素法之接觸理論 33
2.3.1 拉格朗日乘子法 34
2.3.2 罰函數法 34
2.3.3 加強型拉格朗日法 35
2.4 有限元素法之網格重新劃分法 36
2.4.1 ALE座標描述法 36
2.4.2 網格平滑演算法 40
2.5 熱傳遞分析 44
2.5.1 熱傳遞行為 44
2.5.2 強制熱對流分析 47
2.6 摩擦力理論 48
第三章 外顯式處理法之加速模擬分析 52
3.1 有限元素模型結構與尺寸 52
3.2 有限元素模型之基本假設 56
3.3 材料溫度之驗證 57
3.4 材料參數設定與模型建立 62
3.5 網格平滑演算法選用 65
3.6 夾具尺寸修正與幾何驗證 70
3.7 結果與分析 74
第四章 實際製程之模擬分析 79
4.1 夾具速度修正 79
4.2 網格平滑演算法之使用 80
4.3 模擬結果驗證與分析 83
第五章 結論與未來工作 89
參考資料 91

圖目錄
圖 1.1 發光二極體晶片在打線製程中的破壞模式(Source : Epistar) 3
圖 1.2 打線結構示意圖[3] 4
圖 1.3 打線製程循環圖[4] 5
圖 1.4 打線球型接合流程圖[3] 6
圖 1.5 自由球體微觀結構固化過程[4] 9
圖 1.6 打線接合後球體之微觀結構[4] 9
圖 1.7 Beleran等人使用之夾具結構示意圖[12] 11
圖 1.8 Degryse等人針對low-K結構模擬示意圖[14] 14
圖 1.9 Yeh等人研究之Cu low-K結構示意圖[15] 15
圖 1.10 Yeh等人針對Cu low-K結構模擬示意圖[15] 15
圖 1.11 Ikeda等人模擬矽晶片結構之模擬示意圖[17], (a)接合力量為0.245N之幾何外型和應變率分布, (b)接合力量為0.98N之幾何外型和應變率分布 19
圖 1.12 Liu等人模擬發光二極體晶片結構示意圖[22] 19
圖 1.13 Liu等人針對發光二極體結構模擬示意圖[22] 19
圖 1.14 Lin等人使用之有限元素模型[26] 23
圖 2.1 不同座標法之描述 37
圖 2.2 Simple averaging Algorithm網格移動示意圖 41
圖 2.3 Equipotential Smoothing Algorithm節點座標示意圖 42
圖 2.4 虛擬拉伸彈簧式意圖 43
圖 2.5 一般彈簧式意圖 43
圖 2.6 摩擦力示意圖 49
圖 2.7 摩擦力與平行力之關係圖 50
圖 2.8 摩擦係數與物體相對速度之關係 51
圖 3.1 發光二極體打線實際樣品 53
圖 3.2 發光二極體打線接合之結構圖 54
圖 3.3 Lin等人使用之夾具模型 55
圖 3.4 軸對稱全模型之邊界條件 56
圖 3.5 實際放電結球製程 58
圖 3.6 熱模擬有限元素模型 59
圖 3.7 有限元素模型之邊界條件 59
圖 3.8 溫度分布隨時間之變化 60
圖 3.9 自由球體內溫度分布 61
圖 3.10 自由球體溫度與時間關係 61
圖 3.11 熱超音波打線製程之熱源示意圖 62
圖 3.12 金於不同溫度下之材料性質 63
圖 3.13 軸對稱有限元素模型及夾具鈍角示意圖 65
圖 3.14 有限元素模型 66
圖 3.15 未使用網格平滑演算法下所造成之元素失真 67
圖 3.16 平均網格劃分法之模擬結果 68
圖 3.17 等勢網格平滑法之模擬結果 69
圖 3.18 平衡網格平滑演算法之模擬結果 69
圖 3.19 網格局部加密之有限元素模型 70
圖 3.20 夾具之不同內導角設計 71
圖 3.21 實際樣品之幾何 71
圖 3.22 雙導角之尺寸參數 72
圖 3.23 修正後之有限元素模型 73
圖 3.24 模擬結果與實際樣品之比對 73
圖 3.25 模擬過程中總能量和沙漏能量走勢 74
圖 3.26 夾具反力之位置 75
圖 3.27 夾具反力與球高隨時間之變化 75
圖 3.28 對於25μm打線在不同力量製程下所得到的球高 76
圖 3.29 打線過程中結構應力分布圖 77
圖 3.30 晶片結構區應力最大值分布 78
圖 3.31 文獻中使用外顯式處理法所得之等效應力分布 78
圖 4.1 打線在不同力量下與夾具最大速度之關係[46] 79
圖 4.2 使用平衡網格平滑演算法下之von-Mises stress分布情形 81
圖 4.3 使用平衡網格平滑演算法下沙漏能量發生急劇上升之情形 81
圖 4.4 網格重新劃分效果 82
圖 4.5 同時施加平衡網格及平均網格演算法之模擬結果 82
圖 4.6 模擬過程中總能量和沙漏能量走勢 83
圖 4.7 模擬結果與實際樣品之比對 84
圖 4.8 打線過程中結構應力分布圖 85
圖 4.9 夾具反力與球高隨時間之變化 85
圖 4.10 夾具速度大小與球高隨打線力量大小之趨勢[46] 86
圖 4.11 晶片區Maximum Principal stress分布 87
圖 4.12 打線實際樣品之破壞模式 88

表目錄
表 1.1 Degryse等人提出之新舊結構比較 13
表 3.1 墊片以下之幾何尺寸 54
表 3.2 夾具模型之參數 55
表 3.3 材料溫度表 63
表 3.4 材料參數表 63
表 3.5 軸對稱模型中墊片以下各材料幾何尺寸 64
表 3.6 夾具模型之參數 72

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