第四章 有限元素分析
4.8 封裝效應：類型二
本部分探討構裝體對於電晶體(類型二)之影響，首先比較電晶 體製程部分二維與三維模型之結果，在三維模型部分取兩個切面作為 比較，圖4-39 為兩切面之示意圖，圖 4-40、4-41 為 X 方向之應力比 較，圖 4-42、4-43 為 Y 方向之應力比較。比較兩切面之結果，可發 現切面二之應力梯度分布較近似於二維模型，因切面二位於正中央其 受外圍處材料改變之影響較小。
圖 4-39 切面示意圖
1
SIGE_TRANSISTOR OF SUB LEVEL FOUR ELEMENTS
MAT NUM
1
SIGE_TRANSISTOR OF SUB LEVEL FOUR ELEMENTS
MAT NUM
切面一 切面二
2D model 3D model cut plane 1
1
MX MN
SIGE_TRANSISTOR OF SUB LEVEL FOUR -2000
-1600 -1200
-800 -400
0 400
8001000 NODAL SOLUTION
STEP=8 SUB =6 TIME=8 SX (AVG) RSYS=0 DMX =.132E-04 SMN =-4952 SMX =1047
1
MNMX
SIGE_TRANSISTOR
-2000 -1600
-1200 -800
-400 0
400 800 NODAL SOLUTION
STEP=8 SUB =6 TIME=8
SMX =1060 SX (AVG) RSYS=0 DMX =.160E-04 SMN =-4917
1000
圖4-41 X 方向應力分布 (切面二)
圖4-42 Y 方向應力分布 (切面一)
圖4-43 Y 方向應力分布 (切面二)
1
MX MN
SIGE_TRANSISTOR OF SUB LEVEL FOUR -2000
-1600 -1200
-800 -400
0 400
800 1000 NODAL SOLUTION
STEP=8 SUB =6 TIME=8 SX (AVG) RSYS=0 DMX =.
SMN =-SMX =9
132E-04 4952 25.62
1
MNMX
SIGE_TRANSISTOR -2000
-1600 -1200
-800 -400
0 400
800 1000 NODAL SOLUTION
STEP=8 SUB =6 TIME=8
SMX =1060
2D model 3D model cut plane 2
3D model cut plane 1 2D model
SX (AVG) RSYS=0 DMX =.160E-04 SMN =-4917
1
MX MN
SIGE_TRANSISTOR -2000
-1600 -1200
-800 -400
0 400
800 1000 NODAL SOLUTION
STEP=8 SUB =6 TIME=8 SY (AVG) RSYS=0 DMX =.160E-04 SMN =-3084 SMX =1620 1
MN MX
SIGE_TRANSISTOR OF SUB LEVEL FOUR -2000
-1600 -1200
-800 -400
0
400 1000
800 NODAL SOLUTION
STEP=8 SUB =6 TIME=8 SY (AVG) RSYS=0 DMX =.132E-04 SMN =-2423 SMX =2073
3D model cut plane 2 2D model
1
MX MN
SIGE_TRANSISTOR -2000
-1600 -1200
-800 -400
0 400
800 1000 NODAL SOLUTION
STEP=8 SUB =6 TIME=8 SY (AVG) RSYS=0 DMX =.160E-04 SMN =-3084 SMX =1620 1
MN MX
SIGE_TRANSISTOR OF SUB LEVEL FOUR -2000
-1600 -1200
-800 -400
0 400
800 1000 NODAL SOLUTION
STEP=8 SUB =6 TIME=8 SY (AVG) RSYS=0 DMX =.132E-04 SMN =-2423 SMX =1627
接著考慮構裝體之封裝效應，依據前一章所述之構裝體全域模
圖 4-44 構裝體全域模型應力分布
型及各階層之次模型，將構裝體之效應加到電晶體上，兩效應相加的 部分則使用初始應力法，圖4-44 所示為構裝體全域模型三方向與 von Mises 之應力分布，圖 4-45~4-51 所示為第一層至第四層次模型三方 向與von Mises 之應力分布。
1 1
MN
MX X Y
Z
-129.664-105.045-80.427 -55.808-31.189
-6.571 18.048 42.667 67.286
91.904 NODAL SOLUTION
STEP=2 SUB =1 TIME=2 SX (AVG) RSYS=0 DMX =.279979 SMN =-129.664 SMX =91.904
NODAL SOLUTION STEP=2 SUB =1 TIME=2 SY (AVG) RSYS=0 DMX =.279979 SMN =-36.42 SMX =34.969
MN
MX X
Y Z
-36.42-28.488-20.556 -12.624-4.692
3.24 11.172 19.104 27.037
34.969
1
MN MX
X Y
Z
-129.033-104.438 -79.842
-55.246 -30.651
-6.055 18.541
43.137 67.732
92.328 NODAL SOLUTION
STEP=2 SUB =1 TIME=2 SZ (AVG) RSYS=0 DMX =.279979 SMN =-129.033 SMX =92.328
1
MN X MX Y
Z
.58098614.735 28.89
43.044 57.198
71.353 85.507
99.661 113.816 NODAL SOLUTION
STEP=2 SUB =1 TIME=2 SEQV (AVG) DMX =.279979 SMN =.580986 SMX =127.97
Sxx Syy
Szz von Mises stress
127.97
1
MN MX
-720.558-592.41 -464.261
-336.113 -207.964
-79.816 48.333
240.556 NODAL SOLUTION
STEP=2 SUB =1 TIME=2 SX (AVG) RSYS=0 DMX =.079084 SMN =-720.558 SMX =240.556
1
圖4-45 第一層次模型應力分布 (I)
圖4-46 第一層次模型應力分布 (II)
MN MX
-1819 -1515 -1210
-905.788 -601.279
-296.769 7.74
464.504 NODAL SOLUTION
STEP=2 SUB =1 TIME=2 SY (AVG) RSYS=0 DMX =.079084 SMN =-1819 SMX =464.504
1
-720.558-592.41 -464.261
-336.113 -207.964
-79.816 48.333 NODAL SOLUTION
STEP=2 SUB =1 TIME=2 SX (AVG) RSYS=0 DMX =.079084 SMN =-720.558 SMX =240.556
240.556
Sxx
1
-1819 -1515 -1210
-905.788 -601.279
-296.769 7.74 NODAL SOLUTION
STEP=2 SUB =1 TIME=2 SY (AVG) RSYS=0 DMX =.079084 SMN =-1819 SMX =464.504
464.504
Syy
1
MXMN
-717.516 -584.664
-451.811 -318.958
-186.105 -53.253
79.6 278.879 NODAL SOLUTION
STEP=2
DMX =.079084 SMN =-717.516 SMX =278.879 SUB =1 TIME=2 SZ (AVG) RSYS=0
1
MN MX
2.945 195.93
388.915 581.9
774.885 967.869
1161 1354
1450 NODAL SOLUTION
STEP=2 SUB =1 TIME=2 SEQV (AVG) DMX =.079084 SMN =2.945 SMX =1450
1
-717.516 -584.664
-451.811 -318.958
-186.105 -53.253
79.6 NODAL SOLUTION
STEP=2 SUB =1 TIME=2 SZ (AVG) RSYS=0 DMX =.079084 SMN =-717.516 SMX =278.879
278.879
Szz
von Mises stress
1
MX
2.945 195.93
388.915 581.9
774.885 967.869
1161 1354 NODAL SOLUTION
STEP=2 SUB =1 TIME=2 SEQV (AVG) DMX =.079084 SMN =2.945 SMX =1450
1450
圖 4-47 第二層次模型應力分布(I)
圖4-48 第二層次模型應力分布(II)
1
MN MX
-134.814-88.642 -42.47
3.701 49.873
96.045 142.217
211.474 NODAL SOLUTION
STEP=2 SUB =1 TIME=2 SX (AVG) RSYS=0 DMX =.078047 SMN =-134.814 SMX =211.474
1
MX MN
-17.577-12.371 -7.166
-1.96 3.246
8.452 13.658
21.466 NODAL SOLUTION
STEP=2 SUB =1 TIME=2 SY (AVG) RSYS=0 DMX =.078047 SMN =-17.577 SMX =21.466
1
MN
-134.814-88.642 -42.47
3.701 49.873
96.045 142.217
211.474 NODAL SOLUTION
STEP=2 SUB =1 TIME=2 SX (AVG) RSYS=0 DMX =.078047 SMN =-134.814 SMX =211.474
1
-17.577-12.371 -7.166
-1.96 3.246
8.452 13.658
21.466 NODAL SOLUTION
STEP=2 SUB =1 TIME=2 SY (AVG) RSYS=0 DMX =.078047 SMN =-17.577 SMX =21.466
Sxx
Syy
1 1
NODAL SOLUTION STEP=2 SUB =1
NODAL SOLUTION STEP=2 SUB =1 TIME=2
SZ (AVG) RSYS=0 DMX =.078047 SMN =-134.412 SMX =211.57
TIME=2 SZ (AVG) RSYS=0 DMX =.078047 SMN =-134.412 SMX =211.57
MN MX
-134.412 -88.281
-42.15 3.981
50.112 96.243
142.374 211.57
1
MN
MX
13.838 36.797
59.756 82.715
105.674 128.633
151.591 186.03 NODAL SOLUTION
STEP=2 SUB =1 TIME=2 SEQV (AVG) DMX =.078047 SMN =13.838 SMX =186.03
-134.412 -88.281
-42.15 3.981
50.112 96.243
142.374 211.57
1
13.838 36.797
59.756 82.715
105.674 128.633
151.591 NODAL SOLUTION
STEP=2 SUB =1 TIME=2 SEQV (AVG) DMX =.078047 SMN =13.838 SMX =186.03
Szz
von Mises stress
186.03
1
MN MX
-143.399 -102.882
-62.365 -21.847
18.67 59.187
99.704 160.48 NODAL SOLUTION
STEP=2 SUB =1 TIME=2 SX (AVG) RSYS=0 DMX =.077742 SMN =-143.399 SMX =160.48
1
MN
MX
-14.099 -13.062
-12.025 -10.989
-9.952 -8.915
-7.878 -6.322 NODAL SOLUTION
STEP=2 SUB =1 TIME=2 SY (AVG) RSYS=0 DMX =.077742 SMN =-14.099 SMX =-6.322
1
MN MX
-142.997 -102.563
-62.13 -21.696
18.738 59.171
99.605 160.255 NODAL SOLUTION
STEP=2 SUB =1 TIME=2 SZ (AVG) RSYS=0 DMX =.077742 SMN =-142.997 SMX =160.255
1
MN
MX
1.592 23.845
46.097 68.349
90.601 112.853
135.106 168.484 NODAL SOLUTION
STEP=2 SUB =1 TIME=2 SEQV (AVG) DMX =.077742 SMN =1.592 SMX =168.484
Sxx Syy
von Mises stress Szz
圖4-49 第三層次模型應力分布
1
MX MN
SIGE_TRANSISTOR OF SUB LEVEL FOUR -769.614
-658.567 -547.52
-436.473 -325.426
-214.378 -103.331
63.239 NODAL SOLUTION
STEP=2 SUB =6 TIME=2 SX (AVG) RSYS=0 DMX =.07767 SMN =-769.614 SMX =63.239
1
MN MX
SIGE_TRANSISTOR OF SUB LEVEL FOUR -749.403
-634.403 -519.403
-404.404 -289.404
-174.404 -59.404
113.095 NODAL SOLUTION
STEP=2 SUB =6 TIME=2 SY (AVG) RSYS=0 DMX =.07767 SMN =-749.403 SMX =113.095
1
MN MX
SIGE_TRANSISTOR OF SUB LEVEL FOUR -1052
-906.785 -762.033
-617.281 -472.529
-327.777 -183.026
34.102 NODAL SOLUTION
STEP=2 SUB =6 TIME=2 SZ (AVG) RSYS=0 DMX =.07767 SMN =-1052 SMX =34.102
1
MN
MX
SIGE_TRANSISTOR OF SUB LEVEL FOUR 1.112
88.516 175.92
263.324 350.727
438.131 525.535
656.641 NODAL SOLUTION
STEP=2 SUB =6 TIME=2 SEQV (AVG) DMX =.07767 SMN =1.112 SMX =656.641
Sxx Syy
von Mises stress Szz
圖4-50 第四層次模型應力分布 (切面一)
1
MN MX
SIGE_TRANSISTOR OF SUB LEVEL FOUR -768.909
-660.408 -551.907
-443.407 -334.906
-226.405 -117.905
44.846 NODAL SOLUTION
STEP=2 SUB =6 TIME=2 SX (AVG) RSYS=0 DMX =.07767 SMN =-768.909 SMX =44.846
1
MN MX
SIGE_TRANSISTOR OF SUB LEVEL FOUR -749.403
-634.146 -518.889
-403.632 -288.375
-173.118 -57.861
115.024 NODAL SOLUTION
STEP=2 SUB =6 TIME=2 SY (AVG) RSYS=0 DMX =.07767 SMN =-749.403 SMX =115.024
1
MN MX
SIGE_TRANSISTOR OF SUB LEVEL FOUR -1052
-904.457 -757.377
-610.297 -463.217
-316.137 -169.057
51.563 NODAL SOLUTION
STEP=2 SUB =6 TIME=2 SZ (AVG) RSYS=0 DMX =.07767 SMN =-1052 SMX =51.563
1
MN
MX
SIGE_TRANSISTOR OF SUB LEVEL FOUR 1.289
83.53 165.772
248.013 330.254
412.496 494.737
618.099 NODAL SOLUTION
STEP=2 SUB =6 TIME=2 SEQV (AVG) DMX =.07767 SMN =1.289 SMX =618.099
Sxx Syy
von Mises stress Szz
圖4 )
向約為 39.6%，在 Z 方向約為 128%，因此可知封裝效應對於電晶體 -51 第四層次模型應力分布 (切面二
兩效應合併之結果分別顯示於圖 4-52、4-53，最後取電晶體 Z 方向的通道應力值與二維模型比較，圖 4-54 為所取通道應力位置與 電晶體之 Z 方向示意圖。如圖 4-55 所示為製程所產生之應力比較，
圖4-56 所示為封裝效應所產生之應力比較，圖 4-57 所示為兩效應合 併之應力比較，圖4-58~4-60 所示為三方向之兩效應合併前後之應力 比較。由圖4-56 發現封裝效應在 X 以及 Z 方向對電晶體之通道應力 影響約為150MPa，Y 方向之影響約為~20MPa；觀察圖 4-58~4-60 中 可看出兩效應合併前後影響的程度，在 X 方向約為 50.8%，在 Y 方
1
MX MN
PACKAGE STRESS ZOOM IN SIGE S/D MOSFET -2000
-1600 -1200
-800 -400
0 400
8001000 NODAL SOLUTION
STEP=2 SUB =6 TIME=2 SX (AVG) RSYS=0 DMX =.07767 SMN =-4502 SMX =987.845
1
MN
MX
PACKAGE STRESS ZOOM IN SIGE S/D MOSFET -2000
-1600 -1200
-800 -400
0 400
8001000 NODAL SOLUTION
STEP=2 SUB =6 TIME=2 SY (AVG) RSYS=0 DMX =.07767 SMN =-2656 SMX =1990
1
MN MX
PACKAGE STRESS ZOOM IN SIGE S/D MOSFET -2000
-1600 -1200
-800 -400
0 400
8001000 NODAL SOLUTION
STEP=2 SUB =6 TIME=2 SZ (AVG) RSYS=0 DMX =.07767 SMN =-2838 SMX =661.933
1
MN
MX
PACKAGE STRESS ZOOM IN SIGE S/D MOSFET -2000
-1600 -1200
-800 -400
0 400
8001000 NODAL SOLUTION
STEP=2 SUB =6 TIME=2 SEQV (AVG) DMX =.07767 SMN =1.113 SMX =3851
Syy Sxx
Szz von Mises stress
圖4-52 兩效應合併之應力分布 (切面一)
1
MX MN
PACKAGE STRESS ZOOM IN SIGE S/D MOSFET -2000
-1600 -1200 -800 -400
0 400
8001000 NODAL SOLUTION
STEP=2 SUB =6 TIME=2 SX (AVG) RSYS=0 DMX =.07767 SMN =-4569 SMX =876.368
1
MX MN
PACKAGE STRESS ZOOM IN SIGE S/D MOSFET -2000
-1600 -1200
-800 -400
0 400
8001000 NODAL SOLUTION
STEP=2 SUB =6 TIME=2 SY (AVG) RSYS=0 DMX =.07767 SMN =-2656 SMX =1728
1
MN MX
PACKAGE STRESS ZOOM IN SIGE S/D MOSFET -2000
-1600 -1200
-800 -400
0 400
800 1000 NODAL SOLUTION
STEP=2 SUB =6 TIME=2 SZ (AVG) RSYS=0 DMX =.07767 SMN =-2938 SMX =1376
1
MN
MX
PACKAGE STRESS ZOOM IN SIGE S/D MOSFET -2000
-1600 -1200
-800 -400
0 400
800 1000 NODAL SOLUTION
STEP=2 SUB =6 TIME=2 SEQV (AVG) DMX =.07767 SMN =1.289 SMX =3939
Sxx Syy
Szz von Mises stress
圖4-53 兩效應合併之應力分布 (切面二)
圖 4-54 通道應力位置示意圖
圖4-55 製程所產生之應力比較(2D&3D)
0 100 200 300 400 500 600 700 800 900 1000 Z (nm)
-400 -200 0 200 300 400 600 80
-300 -100 100 500 700 0
St ress ( MP a)
3D Cha nel_stress Sxx n 3D Channel_stress Syy 3D Channel_stress Szz 2D Channel_stress Sxx 2D Channel_stress Syy
1
z y
x
SIGE_TRANSISTOR
Channel Stress：along the direction Z
-200 -150 -100 -50 0 50 100
圖4-56 封裝效應所產生之應力比較
圖4-57 兩效應合併之應力比較
3D Channel_stress Sxx 3D Channel_stress Syy 3D Channel_stress Szz
)a re ss (MP St
0 100 200 300 400 500 600 700 800 900 1000 Z (nm)
0 100 200 300 400 500 600 700 800 900 1000 Z (nm)
-500 -400 -300 -200 -100 100 200 300 400 500 600
700 3D Channel_stress Sxx
3D Channel_stress Syy 3D Channel_stress Szz
)a
re ss ( M P St 0
圖4-58 比較
圖
兩效應合併前後之 X 方向應力
4-59 兩效應合併前後之 Y 方向應力比較
~ 50.8%
0 100 200 300 400 500 600 700 800 900 1000 Z (nm)
-500 -400 -300 -200 -100 0 100
200 Process Channel_stress Sxx
Sum Channel_stress Sxx
) St ress (MP a
-300 -200 -100 0 100 200 300
400 Process Channel_stress Syy
Sum Channel_stress Syy
)
0 100 200 300 400 500 600 700 800 900 1000 Z (nm)
St ress (MP a
~ 39.6%
-400 -300 -200 -100 0 100 200 300 400 500 600 700 800
圖4-60 兩效應合併前後之 Z 方向應力比較