電子封裝在上市前必須通過數項的可靠度測試，加速溫度循環測試(Temperature Cycling Test, TCT)是其一藉短時間內升降環境溫度測試產品可靠度測試實驗。而在試驗過程中，經常因晶片與基板之間熱膨脹係數不匹配造成過高的熱應變及熱應力，導致錫球接點提早失效，無法達到法規要求。為改善此測試表現，除了封裝材料不斷的改良精進，電子封裝結構也需良好的設計來發展可靠度更高的封裝。但評估電子封裝可靠度的實驗會花費許多時間及金錢，因此若能將電子封裝準確以有限單元法分析，以模擬取代實驗，可大幅縮短產品研發之時程。
根據JEDEC標準測試規範，常用的溫度測試範圍為-40°C到125°C，因此本研究採用此範圍進行模擬分析。且因近年來為了降低可靠度測試時間，將負載設定成更嚴苛的環境，使得測試載具提前失效以達成加速測試之目的，在加速熱循環負載測試中，溫度通常都超過焊錫材料熔點絕對溫度(K)的三分之一，因此在此過程中即會發生較為顯著的潛變效應，造成潛變應變的累積。為模擬此物理行為，現今有兩種常用的潛辨理論，Anand 模型及Garofalo雙曲正弦模型。兩者在數學形式上相似，唯前者的組成較為複雜，涵蓋第一、第二與第三階段潛變行為，而Garofalo雙曲正弦模型只預估第二階段穩態潛變行為，公式較為單純且亦可精準預估錫球的潛變行為。因此為增加可用的材料庫，期望能找到將前者轉換為後者的方式，並加以驗證。
對於壽命預估的模擬來說，有限單元法模擬所使用的單元(Elelment)尺寸對模擬結果有相當程度的影響，不同大小的單元對封裝壽命的預估會有明顯的差異，而現今對此並無一統一標準，因此需要找到適合使用於不同封裝種類的單元大小以利電子封裝的模擬有更精確的分析結果。
本研究中將分析WLCSP (Wafer Level Chip Scale Packaging) 封裝在加速熱循環條件下潛變及塑性應變之相關行為，以兩種不同理論，Anand 模型以及其所轉換出以Garofalo 雙曲正弦模型搭配Chaboche動態硬化的模型，來描述潛變及非彈性應變行為，並研究是否能以單元尺寸控制的方式在兩個模型之間得到相同的壽命預估，證明將現有之Anand model 轉換為Garofalo雙曲正弦模型進行封裝熱循環模擬的可行性，用以預估錫球壽命。

Electrical packaging’s solder bump may been damaged due to the stress and strain induced by mismatch of coefficient of thermal expansion (CTE) between chip and substrate under thermal loading or Temperature Cycling Test(TCT), which is one of the reliability test that is required before enter the market.
Besides of ameliorating the material employed on packaging, electrical packaging is also in need of good structural design to develop packaging form possessing better reliability performance and longer cycling life. Considering that assessing electrical reliability is generally time and fund consuming, simulation can be a decent alternative if it is able to analyze electrical packaging accurately via finite element method. In addition, simulation benefits companies much shorter time in research, allowing product to be more competitive
Recently, the loading of TCT is controlled to be harsher, failing test specimens at a faster pace to reduce reliability test time. According to JEDEC standard, regular test temperature ranges from -40°C to 125°C is adopted in this research. During the session of accelerated temperature cycling test, temperature exceeds one third of solder’s melting temperature frequently, triggering the creep behavior to be more obvious as the creep strain is accumulated. As a result, two theories, Anand and hyperbolic sine model were developed to describe creep behavior in order to simulate this reliability test. Since these two theories are mathematically similar to one another and the composition of the former is more complex yet having more experimental data and researches. Therefore, a method is expected to convert Anand model into hyperbolic sine model and passes validation.
Element size employed in finite element method interferes simulation result significantly. It causes considerable deviation of packaging life prediction between different elements. As a result, finding the suitable element size to various packaging is important when the accurate simulation result is required.
In summary, the purpose of this research is finding the most appropriate element size fitting experiment by analyzing the response of WLCSP accelerated temperature cycling test underlying on two theories, Anand model and Garofalo hyperbolic Sine model with Chaboche Kinematic Hardening model. In addition, the feasibility of converting the Anand model into hyperbolic sine model is also evaluated by comparing thermal cycling simulations result of original Anand parameters and converted Anand parameters, which is displayed as hyperbolic sine form. All the research subjects mentioned above will serve for the purpose of predicting solder ball lifetime accurately.

摘要 1
ABSTRACT 3
目錄 5
圖目錄 8
表目錄 11
第一章 緒論 13
1.1 研究動機 13
1.2 文獻回顧 15
1.3 研究目標 21
第二章 基礎理論 22
2.1 有限單元法基礎理論 22
2.1.1 線彈性有限單元法理論 23
2.1.2 材料非線性理論 27
2.1.3 數值方法及收斂準則 31
2.2 等向硬化法則(Isotropic Hardening Rule) 33
2.3 動態硬化法則(Kinematic Hardening Rule) 34
2.4 Garofalo-Arrhenius 潛變理論 35
2.5 Anand模型 37
2.6 Chaboche 模型 41
2.7 封裝結構可靠度預測方法 43
2.7.1 Coffin-Mason 應變法 43
2.7.2 Darveaux 能量密度法 43
第三章 溫度負載實驗有限單元模型建立 45
3.1 有限單元模型基本假設 45
3.2 WLCSP溫度負載測試模擬 45
3.2.1 WLCSP幾何尺寸及有限單元模型建立 45
3.2.2 材料參數設定 58
3.2.3 邊界條件及負載設定 61
第四章 結果分析與討論 63
4.1 壽命預估公式 65
4.2 WLCSP模擬結果分析 67
4.2.1 Anand model結果 68
4.2.2 Hyperbolic Sine model 結果 71
4.2.3 其他Anand model與Hyperbolic Sine model結果 74
4.2.4 Pure Plastic 結果 78
4.3 Modified Energy-based method公式特徵壽命預估結果 79
4.3.1 Anand model 80
4.3.2 Hyperbolic Sine model 81
第五章 結論及未來工作 82
參考文獻 86

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