Compression Deformation Response
of 95.5Sn-3.9Ag-0.6Cu Solder*
P. Vianco
J. Rejent
Sandia National Laboratories
Albuquerque, NM
*Sanida is a multiprogram laboratory operated by Sandia Corporation, a Lockheed-Martin
Company for the United States Dept. of Energy, under Contract DE-AC04-94AL85000.
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Hot
Cold
Failure Probability
Empirical, accelerated aging programs are fast becoming
impractical for developing long-term reliability databases
Number of Cycles
Weibull Distribution/Plot
•A vast array of currently-used electronic packages
•Rapid development of new electronic packaging technologies
•Shift from OEM “circuit board technology” …
… to CMS “circuit board assembly”
• ...and now -- Pb-free solders
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Computational modeling will be heavily relied upon to
predict the reliability of Pb-free solder interconnects
Compile materials properties data
for model input parameters.
Material
Material Properties
Properties
Develop the computational model:
model
•Constitutive equation
•Finite element code (mesh)
•Optimization routines
Computational
Computational Model
Model
Model validation using limited
accelerated aging experiments.
Model
Model Validation
Validation
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A Unified Creep-Plasticity (UCP) constitutive equation
provides the basis for a computational model
[
]
dε11/dt = fo exp(-Q/RT) sinhp |σ11 - B11| sgn (σ11-B11)
βD
“A Visoplastic Theory for Braze Alloys,” … Neilsen, Burchett, Stone, and Stephens (1996)
dε11/dt ….. the inelastic strain rate (creep + plasticity)
σ11 ...……... applied stress
T …………. temperature
B11 ……….. back stress
D …………. isotropic strength (plasticity)
β …………. constant (plasticity)
fo …………. constant (creep)
Q …………. apparent activation energy (creep)
p …………. “sinh law” exponent (creep)
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Finite element analysis provides the spatial “locator” of
stress and strain rate within the solder joint geometry
Finite
Finite element
element mesh
mesh (x,
(x, y,
y, z)
z)
ddε
ε11
/dt = ƒ {σ(x, y, z); T; t}
11/dt = ƒ {σ(x, y, z); T; t}
(x, y, z)
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Objective
Develop a unified creep-plasticity constitutive model to predict
the reliability of 95.5Sn-3.9Ag-0.6Cu soldered interconnects.
•Step 1 … Materials properties database
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Experimental procedures
Compression testing (ASTM E9-89A):
95.5Sn-3.9Ag-0.6Cu
10 mm
Chill-cast
(modified bullet mold)
Machined
19 mm
10 mm
Specimen
Specimen geometry
geometry
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Experimental procedures
Test Temperatures:
Upper platen
Upper temperature
control platen
-25°C, 25°C, 75°C, 125°C, 160°C
Strain rates (stress-strain):
Temperature
control
lines
4.2 x 10-5 s-1, 8.3 x 10-4 s-1
Sample
Lower temperature
control platen
Lower platen
Mechanical Testing
Creep stress (percent of σy):
Upper temperature
control platen
20%, 40%, 60%, 80%
(2.7 - 35 MPa)
Sample
Samples test conditions:
•as-fabricated
•post - 125°C, 24 hour heat treat
Lower temperature
control platen
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((-25°C)
-25°C)
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Experimental procedures
•Dynamic elastic modulus meausurements:
•
-50°C to 200°C
•
Temperature dependence of density, ρ:
Rx
Sample
Tx
Furnace
25°C
+ 4.0 x 10-4 g/cm3-C°
- 4.0 x 10-4 g/cm3-C°
7.30 g/cm3
•Thermal expansion coefficient measurements:
•
•
-50°C to 200°C
LVDT
Convert the expansion data to a
coefficent of thermal expansion (CTE).
Furnace
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Sample
9
Microstructure of the as-cast Sn-Ag-Cu solder
Dendritic microstructure was prevalent near the cylinder walls.
D
C B A
E
Untested
100 µm
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Microstructure of the as-cast Sn-Ag-Cu solder
Equiaxed microstructure was observed near the cylinder interior.
D
C B A
E
Untested
100 µm
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Microstructure of the as-cast Sn-Ag-Cu solder
Effect of the 125°C, 24 hour aging treatment
on the Sn-Ag-Cu solder microstructure:
The dendritic morphology near the cyclinder walls
became slightly more equiaxed in appearance.
There was no noticeable change to the microstructure
that was interior to the cylinder sample geometry.
D
C B A
E
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Stress/strain response of the Sn-Ag-Cu solder
60
-25°C
True Stress (MPa)
50
40
25°C
30
20
75°C
10
0
5 s--1
4.2
4.2 xx 10
10--5
s1
0
0.02
0.04
0.06
0.08
0.1
0.12
True Strain
• “Roll-up” to linear-elastic deformation for tests at -25°C and 75°C.
• Transition from linear-elastic to plastic deformation for tests at 25°C.
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Stress/strain response of the Sn-Ag-Cu solder
20
Aged ... 8.3 x 10
-4
s
Aged ... 4.2 x 10
-5
s
-1
-1
-5
As-cast ... 4.2 x 10
15
True Stress (MPa)
-4
As-cast ... 8.3 x 10
-1
s
-1
s
10
5
125°C
125°C
0
0
0.02
0.04
0.06
0.08
0.1
0.12
True Strain
Plastic deformation appears to reflect two simultaneous processes:
work hardening ? dynamic recovery.
recovery
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Stress/strain response of the Sn-Ag-Cu solder
Plastic deformation at 125°C:
work hardening ? dynamic recovery
Thermal aging:
WORK HARDENING > dynamic recovery.
Faster strain rate:
WORK HARDENING > dynamic recovery.
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Stress/strain response of the Sn-Ag-Cu solder
16
-4
As-cast ... 8.3 x 10
14
Aged ... 8.3 x 10
-4
s
Aged ... 4.2 x 10
-5
s
True Stress (MPa)
12
10
As-cast ... 4.2 x 10
s
-1
-1
-1
-5
s
-1
8
6
4
160°C
160°C
2
0
0
0.02
0.04
0.06
0.08
0.1
0.12
True Strain
Plastic deformation appears to reflect two simultaneous processes:
work hardening ? dynamic recrystallization
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Stress/strain response of the Sn-Ag-Cu solder
Plastic deformation at 160°C:
work hardening ? dynamic recrystallization
Thermal aging:
WORK HARDENING > dynamic recrystallization.
Faster strain rate:
WORK HARDENING > dynamic recrystallization.
Work hardening, dynamic recovery and dynamic recrystallization are
not adequately understood to develop quantitative state variables.
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Deformation microstructure of Sn-Ag-Cu solder
D
C B A
E
As-cast
160°C
8.3 x 10-4 s-1
100 µm
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Yield stress versus temperature (ASTM E9-89)
50
As-cast condition
Aged: 125°C, 24 hours
Yield Stress (MPa)
40
5 s--1
4.2
4.2 xx 10
10--5
s1
30
20
10
0
-50
0
50
100
150
200
Test Temperature (°C)
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Yield stress versus temperature (ASTM E9-89)
50
As-cast condition
Aged: 125°C, 24 hours
40
Yield Stress (MPa)
4 s--1
8.3
8.3 xx 10
10--4
s1
30
20
10
0
-50
0
50
100
150
200
Test Temperature (°C)
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Static elastic modulus versus temperature (ASTM E111-82)
6000
Elastic Modulus (MPa)
5000
4000
3000
2000
As-cast condition
1000
Aged: 125°C, 24 hours
5 s--1
4.2
4.2 xx 10
10--5
s1
0
-50
0
50
100
150
200
Test Temperature (°C)
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Dynamic (acoustic) elastic modulus versus temperature
60
As-cast sample #1
As-cast sample #2
Aged sample #1
Elastic (Young's) Modulus (GPa)
55
50
45
40
35
30
-50
0
50
100
150
200
Test Temperature (°C)
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Differential expansion versus temperature
Differential Expansion (mm)
100 10 -3
75 10 -3
50 10 -3
25 10 -3
As
-cast
As-cast
0 10 0
-50
-25
0
25
50
75
100
125
150
175
200
Temperature (°C)
There was no indication of solid-state phase transitions.
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Coefficient of thermal expansion versus temperature
Coefficient of Thermal Expansion (°C
-1
)
30 10 -6
25 10 -6
20 10 -6
As-cast #1
As-cast #2
15 10 -6
Aged #1
Aged #2
10 10 -6
-50
-25
0
25
50
75
100
125
150
175
200
Temperature (°C)
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Analysis of the creep test data
dε/dtmin = fo exp(-Q/RT) sinhp (ασ)
5 10 -7
0.03
Stress:
Stress: 10.2
10.2 MPa
MPa
Temp:
75°C
Temp: 75°C
As-cast
As-cast condition
condition
Hyperbolic Sine Creep Law
0.03
0.02
Strain
3 10 -7
Independent variables:
•
•
•
•
•
•
ln(fo ),
-Q/R,
p
2 10 -7
0.01
ln(dε/dtmin),
(1/T),
ln[sinh (ασ)]
Coefficients:
0.02
1 10 -7
0.01
0
0
2 10 5
4 10 5
6 10 5
8 10 5
0
1 10 6
Time (s)
Independent parameter
Reported
Reported data
data will
will be
be for
for
the
-CAST condition.
the AS
AS-CAST
condition.
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Strain Rate (1/s)
Multivariable
Multivariable Linear
Linear Regression
Regression Analysis
Analysis
4 10 -7
Analysis of the creep test data
5 10 -7
0.03
Stress:
Stress: 10.2
10.2 MPa
MPa
Temp:
75°C
Temp: 75°C
As-cast
As-cast condition
condition
0.02
2 10 -7
0.01
1 10 -7
0.01
0
0
2 10 5
4 10 5
6 10 5
8 10 5
0
1 10 6
Stress:
Stress: 10.2
10.2 MPa
MPa
Temp:
75°C
Temp: 75°C
As-cast
As-cast condition
condition
0.1
8 10 -7
0.08
6 10 -7
0.06
4 10 -7
0.04
2 10 -7
0.02
Time (s)
0
0
2 10 5
4 10 5
6 10 5
8 10 5
0
1 10 6
Time (s)
A large degree of sample-to-sample variability was
observed for specimens tested in the as-cast condition.
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Strain Rate (1/s)
Strain
3 10
-7
Strain Rate (1/s)
0.02
1 10 -6
0.12
4 10 -7
Strain
0.03
Analysis of the creep test data
10-4
True Strain Rate (/s) -25C
True Strain Rate (/s) 25C
True Strain Rate (/s) 75C
True Strain Rate (/s) 125C
True Strain Rate (/s) 160C
True Strain Rate (s
-1
)
10-5
10-6
10-7
10-8
10-9
0
5
10
15
20
25
30
35
True Stress (MPa)
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Analysis of the creep test data
-10
-12
75°C
ln[(d ε/dt)
min
] (dε/dt
min
-1
, s )
160°C
125°C
25°C
-14
-16
-25°C
-18
-20
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
ln[sinh(ασ)] (σ, MPa)
dε/dtmin = 34856 exp(-43? 13 (kJ/mol)/RT) sinh4? 3 (0.005σ)
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Summary
1. A Unified Creep Plasticity (UCP) model is being developed to
describe inelastic deformation in 95.5Sn-3.9Ag-0.6Cu (wt.%) solder.
solder
for the conditions:
As-fabricated
Aged: 125°C … 24 hours
2. Yield stress, elastic (Young’s) modulus, bulk modulus, Poisson’s
ratio, and coefficient of thermal expansion were determined for:
-25°C to 160°C
3. The creep data as-cast samples were fit to a hyperbolic sine law:
dε/dtmin = 34856 exp(-43? 13 (kJ/mol)/RT) sinh4? 3 (0.005σ)
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A final note ….. the back stress, B11
[
]
dε11/dt = fo exp(-Q/RT) sinhp |σ11 - B11| sgn (σ11 - B11)
βD
•The impact of the back stress, B11,
or Bauschinger effect, on the
fatigue response of solder
is not well defined.
A scenario in which B11 = 0 can be hypothesized
when recovery processes occur very rapidly
after load reversal
Stress
σy
tension
Strain
•The back stress, B11, is difficult
to measure experimentally.
Experimental techniques almost certainly
require load reversal procedures.
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σy
compression
σσyy >> σσyy
30