臺灣博碩士論文加值系統

於此研究中，共三種預先設計好、包含凱文錫球結構之銲錫凸塊被用於非破壞性觀測電遷移測試時的電阻變化。
第一種是覆晶銲錫凸塊，其凸塊電阻小於1毫歐姆、成長時呈現凹口向上之趨勢，直到凸塊電阻上升超過10毫歐姆時，會開始急遽上升而後斷路；內部對應之微結構是孔洞的成核與成長，孔洞首先生成於電流集中區然後沿著介金屬化合物與銲錫間介面成長，在測試的末期，電遷移導致的相粗化減緩了電遷移產生的破壞，且可以發現孔洞在電遷移測試末期會分成兩段；且根據實驗結果，我們計算得到一個可表達剩餘接觸面積與凸塊電阻的關係式。
第二種試片則是六微米高的微凸塊，其微凸塊電阻呈現凹口向下之行為，從15毫歐姆開始急遽增加，然後在測試400小時後達到一個定值，早期急劇增加的幅度約5毫歐姆，這與有限元素分析法所得之結果相符；在電遷移測試中，陰極金屬墊層會與銲錫反應並將整個微凸塊轉變為Ni3Sn4，Ni3Sn4具有較銲錫佳之抗電遷移特性，所以導致凸塊電阻維持一個定值；在不同角度的凸塊電阻指出了電流集中效應雖然沒有發生在銲錫中，依舊發生在金屬墊層裡，對於微凸塊來說，完整的電壓降應該是由0度所量到的值，而這個值比180度所得到的值高了7倍，也就是說，其實微凸塊所造成的容／阻延遲相當的大；而為了要簡化描述微凸塊電阻、電流集中比與凸塊尺寸的關係，一個數值分析模型在此被提出，根據此模型，微凸塊電阻與電流集中的關係可以被表達為簡單的關係式。
最後一種試片則是十微米高的微凸塊，其電阻開始時呈現凹口向下，然後轉變為凹口向上，原因在於，其銲錫的量太多，而無法被中介板端的金屬墊層消耗完；開始時，凹口向下的反應行為與矮的微凸塊相當接近，不過因為銲錫的量太多，所以在電子流向上（由中介板端流向晶片端）之微凸塊中，2微米厚之鎳層會受電遷移影響而融入銲錫中，當這些鎳用完以後，孔洞就會產生在這些金屬墊層本來的位置上，且造成電阻曲線又轉變成凹口向上。
根據這些結果，由凱文錫球結構所獲得凸塊電阻的曲線行為經由有限元素模型的幫助，可以在測試中用來檢視其微結構的變化，有限元素模型可以很清楚的表現出不同電遷移階段電流密度的演進，因此可以幫助預測電遷移破壞的機制；此外，凱文錫球結構與過去最常用於分析墊遷移之雛菊花環結構完全的相容，兩個值可以在同時量測取得，此一點是凱文錫球結構之一大優勢。

In this study, three types of solder bump samples with Kelvin bump structures were employed to monitor non-destructively the evolution of resistance during electromigration (EM) testing.
The first type of sample was flip-chip bumps. The bump resistance was found to be less than 1 mΩ and increase as a concave-up curve. After the bump resistance increased to more than 10 times its initial value, it started to grow rapidly and then failure. The corresponding microstructure showed void nucleation and propagation. The void first formed near the current crowding spot and then grew along the interface between the intermetallic compound (IMC) and the solder. At the end stage of EM testing, phase coarsening caused by EM retarded the failure, and the void split into two parts. The relation between the remaining contact area and the bump resistance was calculated.
The second type of sample was 6-μm microbumps. The microbump resistance curve was concave-down. It started around 15 mΩ, increased rapidly in the beginning, and then reached a constant value after 400 hr of testing. The increase in the early stage of testing was around 5 mΩ, which was reasonable when compared with the results of finite-element models (FEMs). During EM testing, the cathode-side under-bump-metallization (UBM) reacted with the solder and transformed the entire microbump into Ni3Sn4. Ni3Sn4 has better EM resistance than the solder and caused the bump resistance to remain at a constant value. The bump resistances at different angles indicated that current crowding still took place, but in the Cu UBM and not in the solder. The complete voltage drop across the microbump was the value obtained at 0°. However, the bump resistance obtained at 0° was 7 times larger than that measured at 180°. That is, the RC delay caused by microbump is actually very large. For simplicity of description on the relation between microbump resistances, crowding ratio, and structural dimensions, a numerical model was built. The expressions of microbump resistance and the crowding ratio were also obtained.
The last type of sample was the 10-μm microbumps. The resistance behaved first concave-down and then concave-up because the solder was too much for the interposer-side UBM to consume. The concave-down curve was first observed for the same reason as that of the low-bump-height case. However, the height of the solder was around 10 μm, which was too high for the interposer-sider UBM to react with. When the electrons flow upward (from interposer to chip), the interposer-side UBM, 2-μm Ni, was the cathode side. Driven by EM, the-2μm Ni quickly dissolved into the solder. After the 2-μm Ni ran out, the void was formed, causing the bump resistance curve to become concave-up again.
The solder height affected the failure mechanism. When the solder height was 25 μm, void propagation was the main failure mechanism. When the solder height decreased to 10 μm, the mechanism became the combination of void propagation and IMC growth. When it was 6 μm, the failure mechanism changed to IMC growth only. The FEM described clearly the evolution of current density distribution at various stages of EM and therefore helped predict accurately the failure mechanism. Moreover, the Kelvin bump structure is compatible with the generally used daisy chain structure. Both bump resistance and daisy chain resistance could be obtained at the same time.

摘要 i
Abstract iii
致謝 v
Contents vi
Figure Captions ix
List of Tables xiv
Chapter 1. Introduction 1
1.1. Flip-Chip Technology 1
1.2. Microbump Technology 4
1.3. Electromigration 7
1.4. Current Crowding Effect 11
1.5. Failure Mechanisms of Solder Joints under Electromigration 15
1.6. Interfacial Reaction 21
1.7. Kelvin Sensing 22
1.8. Finite-Element Method 25
1.9. Motivation 26
Chapter 2. Experimental 29
2.1. Flip-Chip Solder Bumps 29
2.1.1. Sample Structure 29
2.1.2. Kelvin Bump Structures and Experimental Procedures 32
2.2. Six-Micro-Meter Microbumps 36
2.2.1. Sample Structure 36
2.2.2. Kelvin Bump Structures and Experimental Procedures 39
2.3. Ten-Micro-Meter Microbumps 42
2.3.1. Sample Structure 42
2.3.2. Kelvin Bump Structures and Electromigration Stressing Conditions 44
2.4. Procedures of Finite-Element Modeling 44
2.4.1. Element Type and Materials Properties 45
2.4.2. Model Construction and Meshization 48
2.4.3. Boundary Conditions and Solution 49
2.4.4. Post-processing 51
2.5. Models 51
2.5.1. Model of Flip-Chip bumps 51
2.5.2. Model of Microbumps 54
2.5.3. Model of Scallop Intermetallic Compounds 57
2.6. Numerical Modeling of Current Crowding Effect 59
Chapter 3. Results 63
3.1. Electromigration Test Results of Flip-Chip Bumps 63
3.1.1. Bump Resistance of Flip-Chip Bumps 63
3.1.2. Microstructure Evolution in Flip-Chip Bumps 66
3.1.3. Void Growth Rate in Flip-Chip Bumps 71
3.2. Electromigration Test Results of Six-Micro-Meter Microbumps 73
3.2.1. Bump Resistance of Six-Micro-Meter Microbumps 73
3.2.2. Microstructure Evolution in Six-Micro-Meter Microbumps 77
3.2.3. Bump Resistance at Different angles in Six-Micro-Meter Microbumps 83
3.3. Electromigration Test Results of Ten-Micro-Meter Microbumps 85
3.3.1. Resistance of Ten-Micro-Meter Microbumps 85
3.3.2. Microstructure Evolution in TenMicro-Meter Microbumps 88
3.4. Results of Finite-Element Analysis 92
3.4.1. Finite-Element Analysis of Scallop Intermetallic Compounds 92
3.4.2. Finite-Element Analysis of Flip-Chip Bumps 95
3.4.3. Finite-Element Analysis of Six-Micro-Meter Microbumps 98
3.4.4. Finite-Element Analysis of Ten-Micro-Meter Microbumps 102
Chapter 4. Discussion 104
4.1. Bump Resistance of Flip-Chip Bumps 104
4.2. Secondary Void Formation near End Stage of Electromigration Testing 109
4.3. Bump Resistance of Six-Micro-Meter Microbumps 113
4.4. Relation between Bump Resistance Behavior and Microstructure Evolution 116
4.5. Effect of Solder Height on Microstructure Evolution 117
4.6. Effect of Magnitude of Applied Current on Microstructure Evolution 119
4.7. Integration between Kelvin Bump structures and Daisy Chain Structure 119
Chapter 5. Conclusions 121
Chapter 6. References (MLA format) 124
Chapter 7. Publication List 133

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