A Finite Element Study of Strain
Energy Density Distribution
Near A Triple Grain Junction and
Its Implication on Whisker Growth
Third iNEMI Sn Whisker Workshop
May 30, 2006
Peng Su and Min Ding
Technology Solutions Organization
Freescale Semiconductor Inc.
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Outline
• Experimental
• Test Condition
• -55ºC to 85ºC, 2000 cycles
• Components:
• Sn-plated component strips (Assembly site 1)
• Singulated 64LQFPs (Assembly site 1)
• Singulated 100TQFPs (Assembly site 2)
• Materials:
• Matte Sn, 10 µm nominal
• CDA194 leadframe
• Microstructure observations after test
• Hypothesis and assumptions for the growth process
• Establishment of the finite element model
• Strain energy density (SED) distribution at grain-junctions
• First attempt at a predictive model for whisker growth
Slide 2
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Microstructure Observations-1
• Component strips: Overview after AATC
“Beach
pattern” and
recessed
grains near
whiskers
“Beach
pattern” and
recessed
grains near
whiskers
Slide 3
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Peng Su, Ph.D. ([email protected])
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or service names are the property of their respective owners. © Freescale Semiconductor, Inc. 2005.
Microstructure Observations-2
• 64LQFP: Overview after AATC
“Beach
pattern” and
recessed
grains near
whiskers
“Beach
pattern” and
recessed
grains near
whiskers
Slide 4
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or service names are the property of their respective owners. © Freescale Semiconductor, Inc. 2005.
Microstructure Observations-3
• 100TQFP: Overview after AATC
“Beach
pattern” and
recessed
grains near
whiskers
“Beach
pattern” and
recessed
grains near
whiskers
Slide 5
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Peng Su, Ph.D. ([email protected])
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or service names are the property of their respective owners. © Freescale Semiconductor, Inc. 2005.
Microstructure Observations-4
• Magnified view of consumed grains near whiskers #1
Recessed
grains
Strain / stress
concentration
points?
Slide 6
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Microstructure Observations-5
• Magnified view of consumed grains near whiskers #2
“Beach”
patterns
Whisker
Slide 7
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Microstructure Observations-6
• Magnified view of consumed grains near whiskers #3
“Beach
Patterns”
Slide 8
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Microstructure Observations-7
• Magnified view of consumed grains near whiskers #4
Recessed
grains
Whiskers
Slide 9
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Microstructure Observations-8
1. Fracture
lines of an
as-plated
grain near
the root of
the whisker.
2. More
ductile
behavior of
another
grain next to
the root of
the whisker.
Slide 10
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So How Are Whiskers Formed?
(h1k1l1)
(h2k2l2)
(h1k1l1)
Step 1
• Thermal strain / stress creates
concentration points at grain
boundaries or multi-grain
junctions. The gradient of strain
energy is higher if the one of the
grains is very rigid.
(h1k1l1)
(h2k2l2)
Step 2
• High strain energy induces
damage (fracture) to the weaker
grain. The damage is worse at
higher temperatures because Sn
is more brittle.
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(h2k2l2)
Step 3
• Recovery and nucleation occur
at these sites and forms whisker
grains. Whisker grains may not
have any orientation correlation
with as-plated grains.
(h1k1l1)
(h2k2l2)
Step 4
• Surface diffusivity of the recessed grains is very high. Sn atoms travel
along the surface (almost like sand) to the base of whiskers to support
their continuous growth.
• Certain grains in short distances may also diffuse to the growth site.
Slide 11
(h1k1l1)
(h2k2l2)
Step 5
• The original as-plated grain
may be completely consumed at
long test durations. Whisker’s
growth may slowly saturate or
stop.
Hypothesis and Assumptions
• The significance of grain orientations
• Whiskers only nucleate and grow near certain grains. While these grains can be consumed very quickly by
the growth of whiskers, some of the immediate neighboring grains often do not experience any damage.
• Grain orientations are the most probable caused that induces such differences.
• Sn is very anisotropic. Mechanical properties along different planes and directions can be very different.
• A growth model does not necessarily need to address long-range damage and diffusion activities.
Groups or pairs of Sn grains can be treated as discrete samples and analyzed separately.
• Assumptions for the finite element model
• The goal of the model is to answer the question: Which grain boundary or grain junctions is mostly likely to
whisker?
• We only need to identify the strain energy distribution prior to the actual damage / whisker growth occurs.
Thus plasticity does not need to be calculated.
• It is assumed that higher strain energy density will correlate to high possibility of whisker growth.
• Grain orientations are assigned based on XRD analysis.
• Grains are horizontally rotated along the surface and strain energy is calculated for each rotation.
Slide 12
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Geometry of the Model
Grains simulated in this model
The focus is to investigate the effects of
rotation on strain energy levels
As-plated
Sn grain
structure
(after FIB)
(h1k1l1)
Grain
structure
in finite
element
model
(h2k2l2)
(h3k3l3)
Slide 13
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Material Properties
• Basic properties
• Sn thickness is 10µm, Cu thickness is 50 µm.
• Published stiffness matrix is used for Sn. Cu is assumed to be
mechanically isotropic.
• Elements are pure elastic.
• Two sides of the Sn+Cu stack are fixed. The other two sides are
coupled to ensure equivalent displacements.
• Top and bottom surfaces are both free.
• Grain orientations
• The horizontal plane systems of as-plated Sn finish can be determined with X-ray diffraction. (*)
• Three arbitrary orientations are selected for the model.
(220)
(211)
(321)
(431)
20
30
40
50
Slide 14
TM
60
70
2 Theta
80
90
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100
110
120
Why Not Compare Stresses?
• Stress distribution (arbitrary grain orientation, all 6 stress components)
σx
σy
σz
τ xy
τ yz
τ xz
Slide 15
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The Convenience of Using Energy
• Total strain energy density (SED) of a generalized stress state
1
U = (σ xε x+σ yε y + σ z ε z+τ xyγ xy + τ yzγ yz + τ xzγ xz )
2
ε
xx
=
ε
yy
=
ε
zz
=
γ
xy
=
τxy
γ
yz
=
x
γ
zx
=
y
x
δ
y
γxy
Slide 16
TM
[
zz
)
]
[
xx
)
]
[
yy
)
]
1
σ xx − ν ( σ yy + σ
E
1
σ yy − ν ( σ zz + σ
E
1
σ zz − ν ( σ xx + σ
E
2 (1 + ν )
σ xy
E
2 (1 + ν )
σ yz
E
2 (1 + ν )
σ zx
E
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Steps of Simulation
• We will individually rotate the 3 grains and calculate the SED levels in the 3-grain system.
• The three horizontal plane systems are arbitrarily chosen as (112), (321), and (220)
• Each grain is individually rotated in 20º steps. After each rotation, the SED of the entire system and the
junction of the grains (circled below) are compared.
(112)
(220)
SED
Z
Z
Y
X
Y
-55ºC to 85ºC
X
Z
Y
(321)
X
Slide 17
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Effects of Rotation on Total and Center SED
0.50
SED (Arbitrary Unit)
• For the selected grain orientation configuration,
horizontal rotation of the grains does not have a
significant impact on the total SED of the system (blue
lines).
• However the triple-grain junction is significantly affected
by the rotation angles (purple lines).
• The rotation of the (220) grains has the highest impact
on the grain junction.
• The rotation of the (112) grain also has an obvious
effect on the total and center SED.
• The rotation of the (321) grain has very non-symmetrical
impact on the total and central SED.
0.40
0.30
Total SED
Center SED
Rotation of (220)
0.20
0
50
100
150
200
250
Rotation Angles
300
350
400
300
350
400
0.50
0.50
Rotation of (321)
Rotation of (112)
SED (Arbitrary Unit)
SED (Arbitrary Unit)
0.40
0.40
0.30
0.30
0.20
Total SED
Total SED
Center SED
Center SED
0.20
0.10
0
50
100
150
200
250
Rotation Angles
Slide 18
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300
350
400
0
50
100
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150
200
250
Rotation Angles
SED Gradient of Each Rotation
• A parameter Alpha is defined as
Alpha =
SED center
SED Total
• Clearly when the (220) grain is rotated to certain angles, it induces a high SED in the triple-grain junction.
1.5
Alpha
1.0
0.5
(112) Alpha
(321) Alpha
(220) Alpha
0.0
0
50
Slide 19
TM
100
150
200
250
Rotation Angles
300
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350
400
The Effects of Rotation on Each Individual Grain
3.0E-06
2.5E-06
SED (Arbitrary Unit)
• Here we plot the SED in each of the 3 grains at each of
the rotation angles.
• Again the (220) grain has the most significant
modulating effect on the neighboring grains. Each
rotation of the (220) grain induces strong reaction in
itself and the other 2 grains.
• The rotation of (112) grain has certain effect on the
other 2 grains.
• The rotation of (321) grain does not have a strong
effect on either itself or the neighboring grains.
2.0E-06
1.5E-06
1.0E-06
(220) SED Total
5.0E-07
(112) SED Total
0.0E+00
3.0E-06
3.0E-06
2.5E-06
2.5E-06
SED (Arbitrary Unit)
SED (Arbitrary Unit)
0
2.0E-06
1.5E-06
1.0E-06
(220) SED Total
5.0E-07
(112) SED Total
50
100
150
200
250
Rotation Angles
300
350
400
2.0E-06
1.5E-06
1.0E-06
(220) SED Total
(112) SED Total
5.0E-07
Rotation of (112)
Rotation of (220)
(321) SED Total
(321) SED Total
(321) SED Total
Rotation of (321)
0.0E+00
0.0E+00
0
50
100
150
200
250
Rotation Angles
Slide 20
TM
300
350
400
0
50
100
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150
200
250
Rotation Angles
300
350
400
Using SED to Predict Whisker Growth
(Density and Growth)
• The SED gradient
• Experimental observations and modeling results suggest
that the orientation relationship among grains are very
important for whisker nucleation and growth
• For a simplified predictive model, SED gradient at a 2grain boundary may be sufficient.
Sn Grain 1
(h1k1l1)
Sn Grain 2
(h2k2l2)
ε
Cu Substrate
• Whisker density
• Assume that within a 2-grain system, whiskers will nucleate if the SED level reaches certain threshold
level (SED1,th)(*) for the weaker grain (here we assume it is grain #1). The possibility for whisker nucleation
can be estimated with
Wgrain1, grain 2 = f ( g ( SED1,θ , SED2,γ ))
where Θ is the horizontal rotation angle of grain 1, and γ is the horizontal angle of grain 2,
g(x) is the SED concentration in the weaker grain (grain 1) when it is coupled with grain 2,
f(x)=1 if g(SED1,Θ,SED2,γ) ≥ SED1,th, and f(x)=0 if g(SED1,Θ,SED2,γ) < SED1,th.
• Whisker growth
• Assuming greater SED gradient correlates to greater growth, the overall whisker growth for this pair of
grains, at the specific rotation angles, can then be estimated with a Whisker Growth Index (WGI),
WGI grain1, grain 2 = Wgrain1, grain 2 ⋅ [ g ( SED1,θ , SED2,γ ) − SED1,th ]
Slide 21
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Whisker Growth Propensity of a 2-Grain System
• Calculating the average whisker growth rate
360 360
Wi =
∫ ∫ f ( g (SED θ − SED γ )) ⋅ dθ ⋅ dγ
1,
2,
Rotation of Grain 2 only
2.0E-06
SED (Arbitrary Unit)
• SED in a 2-grain system of any orientation can be
readily calculated with the finite element model.
• The W and WGI of a specific pairing configuration can
be estimated with ( i denotes this particular pairing)
2.5E-06
1.5E-06
1.0E-06
θ =0 γ =0
360 360
WGI i =
∫ ∫ W ⋅ (SED θ − SED
θ γ
i
1,
1,th
Grain 1
5.0E-07
Grain 2
Grain Pair
Example #1
0.0E+00
) ⋅ dθ ⋅ dγ
0
100
200
Rotation Angles
300
400
2.5E-06
5.0E-06
2.0E-06
4.0E-06
SED (Arbitrary Unit)
SED (Arbitrary Unit)
=0 =0
1.5E-06
1.0E-06
Grain 1
5.0E-07
Grain 2
Grain Pair
Example #2
Rotation of Grain 2 only
3.0E-06
2.0E-06
Grain 1
1.0E-06
0.0E+00
Grain 2
Grain Pair
Example #3
0.0E+00
0
100
200
Rotation Angles
Slide 22
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300
400
0
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100
200
Rotation Angles
300
400
Calculate Pairing Possibilities
• Calculation of pair combinations
• If we have a macro-view of the orientation information, we can calculate the pairing possibilities.
%
AN EXAMPLE
15%
3.5%
If the orientation mix
looks like this
30%
20.0%
8.5%
13%
15.0%
Slide 23
TM
The pair mix looks
like this (MonteCarlo method)
30%
10.0%
5.0%
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(312)-(312)
(411)-(312)
(411)-(411)
(321)-(321)
(321)-(312)
(321)-(411)
(112)-(321)
(112)-(112)
(112)-(312)
(112)-(411)
(211)-(321)
(211)-(112)
(211)-(211)
(211)-(312)
(211)-(411)
(220)-(321)
(220)-(112)
(220)-(211)
0.0%
(220)-(220)
30.644
32.018
43.871
44.902
55.33
62.538
63.783
64.576
72.414
73.195
79.47
89.409
95.163
95.562
96.695
97.414
103.271
104.864
111.659
112.096
113.343
114.126
120.594
(220)-(312)
2 Theta
2.915
2.793
2.062
2.017
1.659
1.484
1.458
1.442
1.304
1.292
1.205
1.095
1.0434
1.0401
1.0309
1.0252
0.9824
0.9718
0.931
0.9286
0.9219
0.9178
0.8868
(220)-(411)
d
( 2 0 0)
( 1 0 1)
( 2 2 0)
( 2 1 1)
( 3 0 1)
( 1 1 2)
( 4 0 0)
( 3 2 1)
( 4 2 0)
( 4 1 1)
( 3 1 2)
( 4 3 1)
( 1 0 3)
( 3 3 2)
( 4 4 0)
( 5 2 1)
( 2 1 3)
( 6 0 0)
( 3 0 3)
( 5 1 2)
( 6 2 0)
( 6 1 1)
( 3 2 3)
pair %
( h k l)
Whisker Growth Propensity of the Entire System
• Whisker density
• We have calculated the average possibility of whisker nucleation, Wi, for a specific paring configuration.
• We also calculated the percentage of each pair of the total paring possibilities.
• The density of whiskers can then be estimated with
n
W total = ∑ (W i ⋅ p i )
i =1
where pi is the probability of the specific pairing i, n is the total number of possible pairing.
• Whisker growth rate
• Similarly, we have estimates the growth rate for each specific paring, WGIi.
• Utilize the probability of each pairing pi, the total WGI of the system is then
n
WGI total = ∑ (WGI i ⋅ pi )
i =1
• Verification of W and WGI
• Initial success: Freescale data, published data
• More detailed microstructure information, particularly near whiskers, will help to improve the accuracy of
the predictive models.
• Whisker testing needs to be done with non-formed components strips.
• Forming process introduces mechanical damage and stress into Cu and Sn layers.
• Complete whisker population data after test (more than just longest whisker) is also necessary.
Slide 24
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Summary and Further Work
• Experimental observations
• During the AATC test, whisker growth appears to be strongly associated with neighboring grains that have
specific crystallographic orientations.
• These grains are likely under higher strain / stress compared with the rest of the Sn finish, due to Sn’s
mechanical anisotropy.
• These grains also have very high surface diffusivity, which further assists the growth of whiskers.
• Finite element modeling
• Investigation of additional grain orientation mixes and SED
distribution characterization is planned.
• Effects of other material variations such as thickness (on-going),
substrate, and grain geometries needs to be investigated.
• Effects of other stressing situations, such as vertical indentation
and stress from IMC growth will be studied.
Whisker Growth on SnPb Finish
2-phase whiskers, recessed grains
• First attempt at a predictive model
• The WGI parameter has provided initial success in correlating
microstructure to whisker growth.
• Further experimental and simulation work will help improve the
precision of such predictive model. Orientation measurement
with techniques such as EBSD will be beneficial.
• With certain modifications, such model can also be used at
situations with different stress origins.
Slide 25
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or service names are the property of their respective owners. © Freescale Semiconductor, Inc. 2005.
TM
Freescale™ and the Freescale logo are trademarks of Freescale Semiconductor, Inc. All other product
or service names are the property of their respective owners. © Freescale Semiconductor, Inc. 2005.