本文所研究的分析種類是利用 ANSYS 有限元素軟體模擬分析，探討 FC-PBGA 在溫度循環負載下，分析錫球的應力-應變行為，再分別代入三 種疲勞壽命預測模型，並且將分析結果作以下結論:
1. 對 FC-PBGA 的分析結果中，可以發現錫球在第三週次中最大等效潛變 應變範圍發生在離對稱軸之第6 顆錫球左上角位置 (Node 1454)，因此 預測此位置為錫球在熱衝擊測試中最先破壞的位置。
2. 以 CFD-FSI 熱傳/結構分析方法在熱衝擊第三週次溫度循環中高溫停留 開始的第ㄧ秒 (t=1301 秒)，構裝體附近的流體開始有-22.51 到 125℃之 溫度梯度變化；在熱衝擊第三週次溫度循環中低溫停留開始的第ㄧ秒 (t=1621 秒)，構裝體附近的流體從一開始全是-55℃的狀態，到第一秒有 -55 到 92.64℃之溫度梯度變化。
3. 構裝體在熱衝擊第三週次溫度循環中高溫停留開始的第ㄧ秒 (t=1301 秒)，以 CFD-FSI 熱傳/結構分析方法此時的構裝體溫度從-27.01 到 36.5℃，構裝體內的溫差約達 63.51℃；以非等溫熱傳/結構分析方法此 時的構裝體溫度幾乎已達穩定，只有基板部分有溫度變化，溫度從 112.14 到 125℃，溫差約在 12.86℃，但比較接近真實測試情況的 CFD-FSI 熱傳/結構分析方法結果得知此時的構裝體溫差還是很大。低溫停留開 始的第ㄧ秒之構裝體也有相同的趨勢。
4. 構裝體在熱衝擊第三週次溫度循環中高溫停留結束 (t=1600 秒)，以非等 溫熱傳/結構分析方法此時構裝體內的溫度已達穩定的 125℃，而 CFD-FSI 熱傳/結構分析方法此時構裝體內的最高溫度只達 106.75℃，溫 差還有2.06℃。低溫停留結束之構裝體也有相同的趨勢。
5. 以 CFD-FSI 熱傳/結構分析方法分析，構裝體錫球最可能先破壞位置的 溫度曲線於第二和第三週次高溫停留結束和低溫停留結束的溫度就趨 於穩定，高溫停留結束為104℃左右，低溫停留結束為-34℃左右，在高 溫停留期和低溫停留期初始的溫度變化劇烈，後來呈緩慢地升溫或降溫 到停留結束，且錫球三個週次的溫度曲線都於熱衝擊測試溫度曲線內。
6. 使用 CFD-FSI 熱傳/結構分析方法在溫度循環測試中均未進塑性區，所 以錫球無塑性應變。
7. 在 TST 測試分析中，錫球的遲滯曲線在第二週次溫度循環後有逐漸穩 定收斂的趨勢。
8. 不管以黏彈性或線彈性底膠材料性質從事分析，對於錫球幾乎沒影響，
但對於銲錫凸塊就會產生影響。
9. 用同一種分析方式以不同疲勞壽命預測作計算 (Case1~Case3)，從疲勞 壽命結果可看出以 Shi 預測模型最大，Coffin-Mason 預測模型其次，
Creep-Fatigue 預測模型最小，但 (Case13~Case15 和 Case16~Case18) 有 不同趨勢，Coffin-Mason 預測模型最大，Shi 預測模型其次，Creep-Fatigue 預測模型最小。
10. 由表 4-1~表 4-4 不同的參考變數對疲勞壽命之結果得知，以不同的熱傳 /結構分析方法和底膠材料性質對錫球疲勞壽命影響不大，以不同的錫 球應變率之應力-應變曲線和錫球潛變模式對錫球疲勞壽命影響較大。
11. 本研究利用 ANSYS 有限元素軟體把流-熱-機分析作整合，以往相關之 研究通常是以不同軟體去模擬分析，先以流體分析軟體作流分析再把結 果資料代入熱-機分析軟體作分析，期間由於經過不同軟體分析可能會 有資料轉檔或資料處理等誤差，而本研究避免這方面之誤差。
12. 針對 ANSYS 輸出結果，以 Borland C++ Builder 6 程式撰寫疲勞壽命預 測理論從事計算，利用程式作計算減少人為計算上之誤差。
參 考 文 獻
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表1-1 標準型式和討論型式之分析參考變數
型式 Case 熱傳/結構分析方法 Strain Rate Creep Equation Underfill Material Fatigue Life Model 標準型式 Case 1 CFD-FSI 10-4 Double Power Law Model Viscoelastic Shi
Case 2 CFD-FSI 10-4 Double Power Law Model Viscoelastic Coffin-Mason Case 3 CFD-FSI 10-4 Double Power Law Model Viscoelastic Creep-Fatigue Case 4 Anisothermal 10-4 Double Power Law Model Viscoelastic Shi Case 5 Anisothermal 10-4 Double Power Law Model Viscoelastic Coffin-Mason Case 6 Anisothermal 10-4 Double Power Law Model Viscoelastic Creep-Fatigue Case 7 Isothermal 10-4 Double Power Law Model Viscoelastic Shi Case 8 Isothermal 10-4 Double Power Law Model Viscoelastic Coffin-Mason Case 9 Isothermal 10-4 Double Power Law Model Viscoelastic Creep-Fatigue Case 10 CFD-FSI 10-5 Double Power Law Model Viscoelastic Shi Case 11 CFD-FSI 10-5 Double Power Law Model Viscoelastic Coffin-Mason Case 12 CFD-FSI 10-5 Double Power Law Model Viscoelastic Creep-Fatigue Case 13 CFD-FSI 10-4 Hyperbolic Sine Law Model Viscoelastic Shi Case 14 CFD-FSI 10-4 Hyperbolic Sine Law Model Viscoelastic Coffin-Mason
Case 15 CFD-FSI 10-4 Hyperbolic Sine Law Model Viscoelastic Creep-Fatigue
Case 16 CFD-FSI 10-4 Norton’s Model Viscoelastic Shi
Case 17 CFD-FSI 10-4 Norton’s Model Viscoelastic Coffin-Mason Case 18 CFD-FSI 10-4 Norton’s Model Viscoelastic Creep-Fatigue Case 19 CFD-FSI 10-4 Double Power Law Model Elastic Shi
Case 20 CFD-FSI 10-4 Double Power Law Model Elastic Coffin-Mason 討論型式
Case 21 CFD-FSI 10-4 Double Power Law Model Elastic Creep-Fatigue
47
表3-1 FC-PBGA 各組成元件之熱傳和流體性質 [2]
Material Density
(Kg/m3 )
Specific Heat (J/Kg-℃)
Thermal Conduction (W/m-℃)
Die Silicon 2235 700 120
Underfill Epoxy 1500 1500 0.55
Solder Bump and Solder Ball
63Sn/37Pb 8420 176 51.8
Organic Substrate BT 1500 1800 53.7( X , Z ) 0.27( Y )
Solder Pad Copper 8954 384 398
PCB FR-4 1800 150 14
Air Air 1.1614 1005 0.0261
Liquid Galden 1770 962 0.07
48
Material Elastic Modulus
×103 (MPa)
CTE
×10-6 (1/℃)
Shear Modulus
×103 (MPa) Poisson Ratio Temperature (℃) -40 25 75 125 -40 25 75 125 -40 25 75 125 －
Die
(Silicon) 130.23 129.62 129.14 128.66 2.66 2.81 2.93 3.05 Isotropic 0.28 Underfill
(Epoxy) 6.9 6.9 6.9 6.9 29 29 29 29 Isotropic 0.3
Solder Bump and Solder Ball
(63Sn/37Pb)
Stress-Strain Curve 25 25 25 25 Isotropic 0.35
15.67
(X,Z) 14.9
(X,Z) 14.31
(X,Z) 13.71
(X,Z) 12.82
(X,Z) 12.82
(X,Z) 12.82
(X,Z) 12.82
(X,Z) 8.06
(XZ) 8.06
(XZ) 8.06
(XZ) 8.06
(XZ) 0.11 (XZ) Organic Substrate
(BT) 6.84 (Y)
6.5 (Y)
6.24 (Y)
5.98 (Y)
57 (Y)
57 (Y)
57 (Y)
57 (Y)
2.82 (XY,YZ)
2.82 (XY,YZ)
2.82 (XY,YZ)
2.82 (XY,YZ)
0.39 (XY,YZ) Solder Pad
(Copper) 131.62 128.75 126.54 124.33 16.6 16.86 17.07 17.27 Isotropic 0.35 19.15
(X,Z)
17.69 (X,Z)
16.56 (X,Z)
15.43 (X,Z)
17.6 (X,Z)
17.6 (X,Z)
17.6 (X,Z)
17.6 (X,Z)
8.71 (XZ)
7.62 (XZ)
6.79 (XZ)
5.95 (XZ)
0.11 (XZ) PCB
(FR-4) 8.33
(Y) 7.71
(Y) 7.23
(Y) 6.75
(Y) 64.1
(Y) 64.1
(Y) 64.1
(Y) 64.1
(Y) 3.8
(XY,YZ) 3.32
(XY,YZ) 2.96
(XY,YZ) 2.59
(XY,YZ) 0.39 (XY,YZ) 表 3-2 FC-PBGA 各組成元件之機械性質 [29]
49
表 3-3 Double Power Law Model 參數 [3]
Par. C1 C2 C3 C4 C5 C6 σ T
ε
&Unit s-1 - K s-1 - K MPa K s-1
Value 0.4 2 5400 21 7 9500 - - -
表 3-4 Hyperbolic Sine Law Model 參數 [4]
Par. C1 C2 C3 C4 Unit s-1 - MPa-1 K Value 131.9 3.11 0.118 6360
50
表 3-5 Viscoelastic Underfill Model 參數 [3]
0
H R (K)
E
0(MPa)
E
∞C
1τ
1C
2τ
2C
3τ
315644 5630 1300 0.264 0.198 0.200 451 0.536 30435
51
表4-1 不同的熱傳/結構分析方法下疲勞壽命結果比較
Case 1 Case 4 Case 7
熱傳/結構分析方法 CFD-FSI 非等溫 等溫
Lifetime 3580 3218 3097 Factor 1 0.9 0.87
表 4-2 不同的錫球應變率之應力-應變曲線下疲勞壽命結果比較
Case 1 Case 10
應變率 10-4 10-5
Lifetime 3580 5033 Factor 1 1.41
52
表4-3 不同的錫球潛變模式下疲勞壽命結果比較
Case 1 Case 13 Case 16 潛變模式 Double Power
Law Model
Hyperbolic Sine
Law Model Norton’s Model
Lifetime 3580 2229 1418 Factor 1 0.62 0.4
表4-4 不同的底膠材料性質下疲勞壽命結果比較
Case 1 Case 19
底膠材料 黏彈性 線彈性
Lifetime 3580 3215 Factor 1 0.9
53
型式 Case 熱傳/結構分析方法 Strain Rate Creep Equation Underfill Material Fatigue Life Model Lifetime 標準型式 Case 1 CFD-FSI 10-4 Double Power Law Model Viscoelastic Shi 3580
Case 2 CFD-FSI 10-4 Double Power Law Model Viscoelastic Coffin-Mason 1962 Case 3 CFD-FSI 10-4 Double Power Law Model Viscoelastic Creep-Fatigue 181 Case 4 Anisothermal 10-4 Double Power Law Model Viscoelastic Shi 3218 Case 5 Anisothermal 10-4 Double Power Law Model Viscoelastic Coffin-Mason 1131 Case 6 Anisothermal 10-4 Double Power Law Model Viscoelastic Creep-Fatigue 153 Case 7 Isothermal 10-4 Double Power Law Model Viscoelastic Shi 3097 Case 8 Isothermal 10-4 Double Power Law Model Viscoelastic Coffin-Mason 1131 Case 9 Isothermal 10-4 Double Power Law Model Viscoelastic Creep-Fatigue 158 Case 10 CFD-FSI 10-5 Double Power Law Model Viscoelastic Shi 5033 Case 11 CFD-FSI 10-5 Double Power Law Model Viscoelastic Coffin-Mason 3746 Case 12 CFD-FSI 10-5 Double Power Law Model Viscoelastic Creep-Fatigue 253 Case 13 CFD-FSI 10-4 Hyperbolic Sine Law Model Viscoelastic Shi 2229 Case 14 CFD-FSI 10-4 Hyperbolic Sine Law Model Viscoelastic Coffin-Mason 2939
Case 15 CFD-FSI 10-4 Hyperbolic Sine Law Model Viscoelastic Creep-Fatigue 223
Case 16 CFD-FSI 10-4 Norton’s Model Viscoelastic Shi 1418
Case 17 CFD-FSI 10-4 Norton’s Model Viscoelastic Coffin-Mason 1514 Case 18 CFD-FSI 10-4 Norton’s Model Viscoelastic Creep-Fatigue 159 Case 19 CFD-FSI 10-4 Double Power Law Model Elastic Shi 3215 Case 20 CFD-FSI 10-4 Double Power Law Model Elastic Coffin-Mason 1990 討論型式
Case 21 CFD-FSI 10-4 Double Power Law Model Elastic Creep-Fatigue 183 表 4-5 疲勞壽命預測結果
54
圖1-1 TST 之 Liquid-to-Liquid 型式測試示意圖
Liquid 125℃
Liquid
-55℃
0 400 800 1200 1600 2000
Time (Sec)
-80 -40 0 40 80 120 160
T e m p er at u re (
OC)
圖1-2 TST 測試分析溫度曲線圖 A
B C
D E F
圖1-3 熱傳/結構分析方法程序
圖3-1 二維 FC-PBGA 剖面結構示意圖 X
Y
● Z
58
圖 3-2 FC-PBGA 銲錫凸塊配置圖
59
圖3-3 FC-PBGA 之對角線剖面分析方式
60
圖3-4 FC-PBGA 有限元素網格化之基本模型
● X
Y
Z
61
圖3-5 CFD-FSI 熱傳/結構分析方法流程
62
圖3-6 CFD-FSI 熱傳分析之有限元素模型及尺寸示意圖 a
b
4b
40a
63
○
1○
2○
3○
4密 疏
● X
Y
Z
64
圖 3-8 非等溫熱傳/結構分析方法流程
65
均勻溫度 (與測試曲線一致)
前處理
求解處理
後處理
負載
結果
計算錫球
疲勞壽命 結構分析
圖3-9 等溫熱傳/結構分析方法流程
66
0 0.002 0.004 0.006 0.008
Strain (mm/mm)
0 10 20 30 40 50
St re s s ( M Pa )
TST Stress-Strain Cu rve -40OC
20 OC 100 OC 125 OC
0 0.002 0.004 0.006 0.008
Strain (mm/mm)
0 10 20 30 40 50
St re ss ( M Pa )
T CT Stress -Stra in Cu rve -40OC
20 OC 100 OC 125 OC
(a) (b)
圖 3-10 (a)應變率 10-4 (TST) 錫球應力-應變曲線；(b)應變率 10-5 (TCT) 錫球應力-應變曲線
67
圖 4-1 FC-PBGA 最大等效潛變發生之錫球位置 Critical node 1454
68
(a)
(b)
圖4-2 熱衝擊第三週次溫度循環之高溫開始第一秒(t=1301 秒)溫度分佈 (a)CFD-FSI 熱傳分析方法流體的整體溫度分佈
(b)CFD-FSI 熱傳分析方法流體的局部溫度分佈
0 400 800 1200 1600 2000
Time (Sec) -80
-40 0 40 80 120 160
Temperature (OC)
0 400 800 1200 1600 2000
Time (Sec) -80
-40 0 40 80 120 160
Temperature (OC)
(a)
(b)
圖4-3 FC-PBGA 在熱衝擊第三週次溫度循環中溫度分佈 (a)CFD-FSI 熱傳分析方法高溫開始第一秒 (t=1301 秒) (b)非等溫熱傳分析方法高溫開始第一秒 (t=1301 秒)
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Temperature (OC)
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Temperature (OC)
(a)
(b)
圖4-4 FC-PBGA 在熱衝擊第三週次溫度循環中溫度分佈 (a)CFD-FSI 熱傳分析方法高溫結束 (t=1600 秒) (b)非等溫熱傳分析方法高溫結束 (t=1600 秒)
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Temperature (OC)
(a)
(b)
圖4-5 熱衝擊第三週次溫度循環之低溫開始第一秒(t=1621 秒)溫度分佈 (a)CFD-FSI 熱傳分析方法流體的整體溫度分佈
(b)CFD-FSI 熱傳分析方法流體的局部溫度分佈
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Temperature (OC)
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Temperature (OC)
(a)
(b)
圖4-6 FC-PBGA 在熱衝擊第三週次溫度循環中溫度分佈 (a)CFD-FSI 熱傳分析方法低溫開始第一秒 (t=1621 秒) (b)非等溫熱傳分析方法低溫開始第一秒 (t=1621 秒)
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Temperature (OC)
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Temperature (OC)
(a)
(b)
圖4-7 FC-PBGA 在熱衝擊第三週次溫度循環中溫度分佈 (a)CFD-FSI 熱傳分析方法低溫結束 (t=1920 秒) (b)非等溫熱傳分析方法低溫結束 (t=1920 秒)
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Temperature (OC)
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Temperature (OC)