FR4
Si die
Cu plate
encapsulation
current flow i
i
i
Solder joint A
140 μm
Underfill
Al
PCB
Cu
Solder
Silicon Die
100
μm
Ni UBM
Fig. 8.7 Cross section of the test module and solder joints (Ye et al. 2003a)
Table 8.1 Time to failure
Current density (Amp/cm
2
)
Experiment
Time to failure (h)
Finite element simulations
Time to failure (h)
0.6 Â 10
4
1058.7
1098.2
0.8 Â 10
4
446.6
435.33
1.0 Â 10
4
228.7
222.41
Table 8.2 Material properties for SAC405
Property
Unit
SAC405
Vacancy relaxation time (T s )
seconds
1.80 Â 10
À03
Effective charge number (Z
*
)
N/A
10
Resistivity (R)
u m
3
s
À3
A
À2 kg
R T
ð Þ ¼ 1:52 Â 10
11
þ3:50 Â 10
8 T K
ð Þ
Atomic volume (Ω)
u m
À3
2.71 Â 10
À11
Vacancy concentration at stress-free state (C v0 ) um
À3
1.107E+06
Young’s modulus (E)
GPa
E(T ) ¼ 57.7 À 0.056T(K )
Poisson’s ratio
N/A
0.33
Initial yield stress (σ y0 )
MPa
σ y T
ð Þ ¼ 79:98 þ 95=
ffiffiffi
d
p
À0:2133T K
ð Þ
Coefficient of thermal expansion (CTE)
K
À1
18.9 Â 10
À06
Linear kinematic hardening cons (c 1 )
k gsu m
À1
9.63 Â 10
3
Nonlinear kinematic hardening cons (c 2 )
k gsK
À1 um
À1
7.25 Â 10
2
Saturation isotropic hardening (R 1 )
k g s u m
À1
0
Isotropic hardening rate (c)
N/A
383.3
Dimensionless constant (A)
N/A
7.60 Â 10
9
Burger vector (B)
um
3.18 Â 10
À04
Initial average grain size
um
2.45
Grain size exponent
N/A
3.34
Stress exponent
N/A
6.65
(continued)
422
8 Unified Mechanics of Metals under High Electrical Current Density:. . .
Si die
Cu plate
encapsulation
current flow i
i
i
Solder joint A
140 μm
Underfill
Al
PCB
Cu
Solder
Silicon Die
100
μm
Ni UBM
Fig. 8.7 Cross section of the test module and solder joints (Ye et al. 2003a)
Table 8.1 Time to failure
Current density (Amp/cm
2
)
Experiment
Time to failure (h)
Finite element simulations
Time to failure (h)
0.6 Â 10
4
1058.7
1098.2
0.8 Â 10
4
446.6
435.33
1.0 Â 10
4
228.7
222.41
Table 8.2 Material properties for SAC405
Property
Unit
SAC405
Vacancy relaxation time (T s )
seconds
1.80 Â 10
À03
Effective charge number (Z
*
)
N/A
10
Resistivity (R)
u m
3
s
À3
A
À2 kg
R T
ð Þ ¼ 1:52 Â 10
11
þ3:50 Â 10
8 T K
ð Þ
Atomic volume (Ω)
u m
À3
2.71 Â 10
À11
Vacancy concentration at stress-free state (C v0 ) um
À3
1.107E+06
Young’s modulus (E)
GPa
E(T ) ¼ 57.7 À 0.056T(K )
Poisson’s ratio
N/A
0.33
Initial yield stress (σ y0 )
MPa
σ y T
ð Þ ¼ 79:98 þ 95=
ffiffiffi
d
p
À0:2133T K
ð Þ
Coefficient of thermal expansion (CTE)
K
À1
18.9 Â 10
À06
Linear kinematic hardening cons (c 1 )
k gsu m
À1
9.63 Â 10
3
Nonlinear kinematic hardening cons (c 2 )
k gsK
À1 um
À1
7.25 Â 10
2
Saturation isotropic hardening (R 1 )
k g s u m
À1
0
Isotropic hardening rate (c)
N/A
383.3
Dimensionless constant (A)
N/A
7.60 Â 10
9
Burger vector (B)
um
3.18 Â 10
À04
Initial average grain size
um
2.45
Grain size exponent
N/A
3.34
Stress exponent
N/A
6.65
(continued)
422
8 Unified Mechanics of Metals under High Electrical Current Density:. . .