A Numerical Approach Towards the Correlation Between Ball Impact Test and Drop Reliability
Chang-Lin Yeh*, Yi-Shao Lai
Stress-Reliability Lab, Advanced Semiconductor Engineering, Inc.
26 Chin 3rd Rd., Nantze Export Processing Zone, 811 Nantze, Kaohsiung, Taiwan
*Email: [email protected]
1-4244-0665-X/06/$20.00 ©2006 IEEE
2. Board-level Drop Test
We consider a 10×10×0.8 mm3 thin-profile fine-pitch ball
grid array (TFBGA) chip-scale package interconnected to a
132×77×1 mm3 standard 8-layer JEDEC drop test board. The
package contains a 5.5×5.5×0.25 mm3 silicon die and a 0.26
mm thick substrate. The diameter and standoff of a solder
joint are 0.35 mm and 0.21 mm, respectively. Openings of a
solder joint on the package side and the test board side are
0.26 mm and 0.28 mm, respectively. The pitch between
adjacent solder joints is 0.5 mm. The mounting scheme of
packages on the test board is shown in Fig. 1, following
JESD22-B111 [16]. The figure also depicts the quarter
symmetry modeling region for the finite element analysis. We
consider the layout for which only the package at the center of
the test board, U8, is implemented.
132 mm
Fixed end
U11
U12
U13
U14
U15
U6
U7
U8
U9
U10
U1
U2
U3
U4
U5
77 mm
1. Introduction
The adoption of stiffer and more brittle lead-free solder
alloys [1] along with the prevalence of mobile electronic
devices brings the need of characterizing solder joint
reliability under dynamic loads. The common way to
characterize the reliability of solder joints is through boardlevel tests. For board-level test vehicles subjected to
mechanical loads of reasonably high strain rates, it is
frequently observed that fracturing occurs around the interface
between the solder joint and its bonding pads, where
intermetallic compounds (IMCs) develop [2-8]. Therefore,
characterization of the strength of IMC is crucial to the
assessment of reliability of solder joints under a dynamic
loading condition. However, each solder joint in a board-level
test vehicle connects to two bonding pads on the package side
as well as the test board side. Quite often geometric
configurations and surface finishes of the two pads are distinct
[7]. It is therefore fairly difficult to specify a loading condition
that allows fracturing to occur dominantly around a preferred
pad, at which the IMC strength is to be examined. Considering
the high cost and long duration a board-level test takes, direct
testing on a package-level solder joint that involves only a
single pad meets the demand more efficiently and
economically.
For a single package-level solder joint, the ball shear test
that shears off the solder joint along the direction parallel to
the pad is generally employed in the industry to evaluate the
strength of the solder joint. This test is simple and convenient
to implement. However, from both experiments and numerical
analyses, it has been noted that a conventional low-strain- rate
ball shear test with a crosshead speed slower than 0.1 mm/s
seldom leads to fracturing of IMC [9]. The same situation also
occurs when a number of solder joints on a board-level test
vehicle are sheared off simultaneously [10]. Since a
conventional ball shear test with a low shearing velocity is
unable to reproduce the typical IMC fracturing failure mode
encountered in a board-level drop test, it can be expected that
there is hardly a chance for ball shear testing results to be
correlated with the drop reliability.
Apparently, if a test equipment capable of evaluating the
IMC strength is to be developed based on the configuration of
the ball shear test, the shearing velocity must be greatly
enhanced [1,11-14]. Meanwhile, the test apparatus must be
carefully designed to suppress structural resonance in order to
obtain reliable force or acceleration measurements [15]. A
high sampling rate data acquisition system is also a necessity.
Efforts have been devoted to the empirical correlation
between board-level drop reliability and characteristics of the
impact force profile from the ball impact test (BIT) [14]. In
this paper, both board-level drop test and package-level BIT
are examined numerically. We consider different Sn-Ag-Cu
solder joint compositions, namely, Sn-4Ag-0.5Cu (SAC405),
Sn-3Ag-0.5Cu (SAC305), Sn-2.6Ag-0.6Cu (SAC266), Sn1Ag-0.5Cu (SAC105), and Sn-Ag-Cu solder alloys dopped
with trace elements: Sn-Ag-Cu-Sb (SACSb), SACXY1,
SACXY2, SACXY3, and SACXY4. Through numerical
solutions, insights into the analytical correlation between the
drop reliability and characteristics of the impact force profile
are provided.
71 mm
Abstract
The ball impact test is developed as a package-level
measure for the board-level drop reliability of solder joints in
the sense that it leads to fracturing of solder joints around the
intermetallics, similar to that from a board-level drop test. In
this paper, both board-level drop test and package-level ball
impact test are examined numerically for solder joints of nine
Sn-Ag-Cu solder compositions. Correlations between the drop
reliability and characteristics of the impact force profile are
sought.
Modeling
region
105 mm
Fig. 1: Schematic of test board and modeling region
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2006 Electronics Packaging Technology Conference
Fig. 2 shows the finite element model of the board-level
test vehicle around the package. The finite element model
contains 50,127 linear hexahedral solid elements and 180,909
degrees of freedom. The structure of the solder joint is
simplified in the way such that the two bonding pads are both
neglected. The test vehicle is dropped with the package facing
downward under JEDEC drop test condition B [16], for which
a half-sine impact acceleration pulse with a peak acceleration
of 1500 G and a pulse duration of 0.5 ms is prescribed. The
transient analysis, which follows the support excitation
scheme [17,18] and incorporates with the implicit time
integration, is performed using ANSYS v. 10.0.
solder alloys dopped with trace elements, namely, SACSb,
SACXY1, SACXY2, SACXY3, and SACXY4. Fig. 3 shows
stress-strain curves for these solder alloys, obtained from
quasi-static uniaxial tensile tests on 10×60×3 mm3 dog-bone
specimens at a strain rate of approximately 2×10-4 s-1. We
construct trilinear elastoplastic constitutive relationships for
the solder alloys based on these curves. For all solder alloys, ν
is 0.36 and ρ is 7.44 g/cm3. Isotropic hardening is presumed.
40
35
Stress (MPa)
30
Compound
Die
Substrate
25
20
15
10
SAC105
SAC266
SACXY1
SACXY3
Solder joint
5
Test board
0
0.0
0.5
1.0
1.5
2.0
2.5
SAC305
SACSb
SACXY2
SACXY4
3.0
SAC405
3.5
4.0
4.5
5.0
Strain (%)
Fig. 2: Finite element mesh around the package
Elastic properties of constituent components except for the
solder alloy are presented in Table 1. Transversely isotropic
material properties are assigned for the test board and the
substrate, Table 2. In these tables, E is the Young’s modulus,
ν the Poisson’s ratio, ρ the mass density, and G the shear
modulus. Note that z denotes the out-of-plane direction while
x and y refer to in-plane directions. Mass-weighted damping
and stiffness-weighted damping of the test vehicle are
assumed 0.08 and 0.0013, respectively.
Table 1: Elastic properties of constituents
Component
Substrate
Die
Compound
Test board
E (GPa)
ν
Transversely
isotropic
131
28
Transversely
isotropic
Transversely
isotropic
0.23
0.35
Transversely
isotropic
ρ (g/cm3)
1.91
2.33
1.89
1.91
Fig. 3: Stress-strain curves for solder alloys
In reality, material properties of the solder alloy depend
greatly on the process, test methodology, and specimen size.
In this regard, the actual mechanical response of the solder
joint is quite difficult to obtain. The strain rate effect is
ignored in this study since it is particularly difficult to identify
without proper experimental measurements. Moreover, as of
now, there are no suitable rate-dependent constitutive
relationships for lead-free solder alloys that suit JEDEC drop
test conditions, for which the strain rate is up to around 102 s-1
[5].
We denote normal stress, shear stress, and equivalent
plastic strain as σn, σs, and εp, respectively. Here σn stands for
the normal component whereas σs the squared-root sum of the
two shear components of the surface traction. Fig. 4 shows the
most critical solder joint and the locations where maximum σn,
σs, and εp occur during the course of the drop impact.
y
z
Table 2: Trnasversely isotropic properties for test board
and substrate
Ex, Ey (GPa)
Gxz, Gyz (GPa)
νxz, νyz
Ex, Ey (GPa)
Gxz, Gyz (GPa)
νxz, νyz
Test board
15.1
Ez (GPa)
6.82
Gxy (GPa)
0.39
νxy
Substrate
16.8
Ez (GPa)
7.59
Gxy (GPa)
0.39
νxy
B
Package side
6.65
2.98
0.11
A
x
C
Test board side
x
7.40
3.31
0.11
Maximum σn
D
Maximum σs
Maximum εp
In this study, we compare Sn-Ag-Cu solder alloys, namely,
SAC405, SAC305, SAC266, and SAC105, and Sn-Ag-Cu
Fig. 4: Locations of maximum σn, σs, and εp
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2006 Electronics Packaging Technology Conference
Table 3 summarizes maximum σn, σs, and εp experienced
on the package side of the most critical solder joint during the
course of the drop impact.
Table 3: Maximum σn, σs, and εp
Solder alloy
SAC405
SAC305
SAC266
SAC105
SACXY1
SACXY2
SACXY3
SACXY4
SACSb
σn (MPa)
σs (MPa)
εp (%)
107.6
102.0
93.45
76.34
100.1
92.25
102.5
96.44
105.9
44.16
44.44
33.67
28.53
37.51
40.90
45.27
43.15
39.62
6.831
7.577
8.265
11.075
7.530
8.860
7.570
8.360
6.675
experiences force concentration around the contact region
with the pin, incurring large deformations. To avoid
hourglassing, a numerically instable feature particularly for
linear hexahedral solid elements subjected to a concentrated
force, linear tetrahedral elements are applied on the regions
depicted in Fig. 7. We neglect IMC in the numerical model
since it is too thin to be implemented [24]. The transient
analysis is performed using ANSYS/LS-DYNA v. 970.
300
240
Vi = 1.4 m/s
240
Solder
Pin
Fig. 5 shows stress loci of σn-σs for different solder joint
compositions at Point A, where maximum σn occurs on the
package side of the critical solder joint, from the onset of the
drop impact to when the peak σn occurs. Apparently, during
the course of the drop impact, σn is about 5.25 times greater
than σs at Point A.
Soldermask
Pad
Soldermask
18
15
220
Substrate
240
400
800
16
Fig. 6: Physical model for BIT (unit: µm, not to the scale)
12
5.25
σs (MPa)
1
8
SAC405
SAC305
SAC266
SAC105
SACXY1
SACXY2
SACXY3
SACXY4
SACSb
4
0
-4
-20
0
20
40
60
80
σn (MPa)
Fig. 5: Stress loci of σn-σs at Point A during drop impact
3. Ball Impact Test
The numerical methodology that deals with transient
fracturing of a package-level solder joint subjected to a
displacement-controlled impact load has been developed by
Yeh and coworkers [19-25]. In this study, we follow the same
methodology to examine transient impact force responses of
the solder joints with different solder compositions.
The physical model for BIT is shown in Fig. 6. A rigid pin
moves horizontally from left to right and strikes on the
package-level solder joint with a constant impact velocity, Vi.
In this study, we assume Vi = 1.4 m/s. It has been realized that
when the IMC strength is not great enough, different Vi do not
bring significantly different impact force responses [24].
Fig. 7 shows the three-dimensional symmetric finite
element model for the test vehicle. For components other than
the solder joint, linear hexahedral solid elements are applied.
Since the solder joint is spherical, at the onset of impact, it
Fig. 7: Symmetric finite element model
Fracturing of the test vehicle can be categorized into two
different types: fracturing within the solder alloy and
interfacial fracturing between solder alloy and pad, at which
IMC develops. Adequate fracturing mechanisms and
corresponding failure criteria are therefore required to
characterize the path of fracture propagation subjected to an
impact load. Considering that fracturing within the solder
alloy is a failure mode secondary to IMC fracturing during
drop impacts [5-8], in this study, we focus on interfacial IMC
fracturing of the package-level solder joint only.
Interfacial IMC fracturing is modeled using the tiebreak
nodes-to-surface contact [24], which links adjacent meshes
and confines the movements of nodes until the bond breaks.
The bond failure is characterized by
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2006 Electronics Packaging Technology Conference
Cn
 fs 

+
S 
 s 
Cs
≥1
(1)
where the subscripts n and s denote normal and shear,
respectively, and f and S the weld force and the ultimate force
when the bond breaks, respectively. In this study, an elliptical
failure envelope, Cn = Cs = 2, is adopted. Moreover, the shear
strength of IMC is assumed to be two times greater than the
normal strength of IMC. That is, Ss = 2 Sn = 2 σ0 × Ae, in
which Ae is the equivalent area of the contact element while σ0
the tensile IMC strength in terms of the stress. Note that this
merely represents an assumption and requires further
experimental work to justify.
Characteristics of the impact force profile can be defined
according to Fig. 8. Since the post-failure structural behavior
of the solder joint is extremely complicated and hardly
reproducible, we consider only the ascending part of the
primary peak of the impact force profile, which stands for the
structural behavior of the solder joint from the initiation of the
impact load till fracturing starts.
impact process, we have S r ≅ Vi × K r , where Kr stands
for the equivalent stiffness of the solder joint.
Figs. 9, 10, and 11 show Fmax, Er, and dr with respect to σ0,
respectively, for different solder alloys.
300
250
200
σ0 (MPa)
 fn 


S 
 n 
150
SAC405
SAC305
SAC266
SAC105
SACXY1
SACXY2
SACXY3
SACXY4
SACSb
100
50
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Fmax (N)
Fig. 9: Fmax with respect to σ0
300
Fmax
0.5Fmax
250
Sr
200
σ0 (MPa)
Force
1
Ar
150
SAC405
SAC305
SAC266
SAC105
SACXY1
SACXY2
SACXY3
SACXY4
SACSb
100
0.1Fmax
τr
50
Time
0
0
15
30
45
Fig. 8: Typical impact force profile
75
90
Fig. 10: Er with with respect to σ0
Characteristics of the typical impact force profile depicted
in Fig. 8 and those derived from these characteristics are
described in the following:
1. Fmax: The maximum impact force, or the impact resistance,
which relates to the IMC strength.
2. τr: The duration of the ascending part of the impact force
profile, which stands for the ductility, dr, of the solder
joint. If Vi varies insignificantly during the entire impact
process, we have d r ≅ Vi × τ r , which also stands for the
stroke from the onset of the impact till fracturing starts.
3. Ar: The area below the ascending part of the impact force
profile, which represents the toughness of the solder joint.
This quantity is proportional to the impact energy exerted
during the ascending part, Er. If Vi varies insignificantly
during the entire impact process, we have Ei ≅ Vi × Ar .
4.
60
Er (µJ)
300
SAC405
SAC305
SAC266
SAC105
SACXY1
SACXY2
SACXY3
SACXY4
SACSb
250
σ0 (MPa)
200
150
100
50
0
0
10
20
30
40
50
dr (µm)
Sr: The slope of the ascending part of the impact force
profile. If Vi varies insignificantly during the entire
Fig. 11: dr with respect to σ0
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2006 Electronics Packaging Technology Conference
Fig. 12 shows stress loci of fn-fs at Point A for different
solder joint compositions during BIT. It is clear that the slope
is approximately 1.23 and is nearly independent of solder
compositions.
the figures that Fmax, Er, and dr are not particularly good BIT
indices to correlate with the drop reliability index P because
the correlations are not universal; they vary according to
different solder compositions.
25
3.0
SAC405
SAC305
SAC266
SAC105
SACXY1
SACXY2
SACXY3
SACXY4
SACSb
15
2.5
2.0
P
fs (mN)
20
1.5
SAC405
SAC305
SAC266
SAC105
SACXY1
SACXY2
SACXY3
SACXY4
SACSb
1
10
1.0
1.23
5
0.5
0
0
5
10
15
20
0.0
25
0
fn (mN)
1
Fig. 12: Stress loci of fn-fs at Point A during BIT
3
4
Fig. 13: P versus Fmax
Comparing between stress loci at Point A induced by the
board-level drop test, Fig. 5, and those induced by BIT, Fig.
12, we note that σn plays a more significant role in the failure
mechanism of a board-level drop test rather than that of BIT.
Also noted is that these slopes are different from those
obtained in our previous numerical studies [24,26] because of
different constitutive relationships for the solder alloys.
3.0
2.5
P
2.0
4. Reliability Indices
Interfacial IMC fracturing is the primary failure mode of
solder joints under drop impacts, in particular for lead-free
solder joints [5-8]. From the previous analysis, σn is also
found to be several times greater than σs. We therefore assume
that the mean value of the drop count to failure, Nf, is
proportional to σ0 while inversely proportional to the
maximum σn in a power-law formulation such that
σ 
N f = a 0 
σn 
2
Fmax (N)
1.5
SAC405
SAC305
SAC266
SAC105
SACXY1
SACXY2
SACXY3
SACXY4
SACSb
1.0
0.5
0.0
0
20
40
60
80
Er (µJ)
Fig. 14: P versus Er
b
(2)
3.0
where a and b are universal constants independent of
structures, materials, and assembly processes. We define
2.0
(3)
P
σ
P= 0
σn
SAC405
SAC305
SAC266
SAC105
SACXY1
SACXY2
SACXY3
SACXY4
SACSb
2.5
1.5
1.0
as the drop reliability index. A larger P indicates a better drop
reliability. Note that, ideally, σn is obtained from the transient
analysis for the board-level drop test while σ0 is identified by
correlating transient analysis for BIT with the measured
impact force profile. In this study, however, due to the lack of
BIT measurements, σ0 is a prescribed magnitude.
Following this concept, we plot P with respect to Fmax, Er,
and dr in Figs. 13, 14, and 15, respectively. It is apparent from
0.5
0.0
0
10
20
30
40
50
dr (µm)
Fig. 15: P versus dr
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2006 Electronics Packaging Technology Conference
From Figs. 13 through 15, we note that curves for solder
joints of different compositions are close when Er is small.
This indicates that, compared to Fmax or dr, under the
circumstance that P is small, Er or a physical term related to
the impact energy serves as a good indicator of drop reliability
of board-level solder joints regardless of their compositions.
This particular feature has been reported by Wong et al. [1]
and Yeh et al. [14] from experimental observations. However,
when σ0 of the solder joint increases, plasticity develops
around the location where fracturing initiates [25], and hence
the curves vary significantly according to different solder
compositions. Consequently, the correlations between P and
these BIT characteristics become non-universal.
To obtain universal correlations between P and these BIT
characteristics, here we propose to multiply Fmax, Er, and dr by
constant multipliers, fa, fb, and fc, respectively. Magnitudes of
these multipliers are listed in Table 4 for different solder
alloys. Note that these magnitudes are empirically selected
without a theoretical background.
3.0
2.5
P
2.0
0.5
0.0
0
fb
1.00
1.10
0.55
0.60
0.65
1.00
1.15
1.10
0.70
SAC405
SAC305
SAC266
SAC105
SACXY1
SACXY2
SACXY3
SACXY4
SACSb
0.0
1.0
1.5
2.0
2.5
fa Fmax (N)
Fig. 16: P versus fa×Fmax
3.0
3.5
P
60
70
80
90
3.0
1.5
SAC405
SAC305
SAC266
SAC105
SACXY1
SACXY2
SACXY3
SACXY4
SACSb
0.5
2.0
0.5
50
1.0
2.5
0.0
40
2.0
3.0
0.5
30
2.5
Correlations between P and fa×Fmax, fb×Er, and fc×dr are
plotted in Figs. 16, 17, and 18, respectively. With the
empirical multipliers, the modified correlations appear to be
universal, i.e., independent of solder compositions. However,
physical meanings of these multipliers certainly require
further investigations.
1.0
20
Fig. 17: P versus fb×Er
fc
1.00
1.00
0.70
0.60
0.80
0.85
1.00
0.95
0.85
1.5
10
fb Er (µJ)
P
fa
1.00
1.10
0.90
1.10
0.90
1.10
1.10
1.15
0.90
SAC405
SAC305
SAC266
SAC105
SACXY1
SACXY2
SACXY3
SACXY4
SACSb
1.0
Table 4: Multipliers for different solder alloys
Solder alloy
SAC405
SAC305
SAC266
SAC105
SACXY1
SACXY2
SACXY3
SACXY4
SACSb
1.5
4.0
0.0
0
10
20
30
40
50
fc Dr (µm)
Fig. 18: P versus fc×dr
5. Conclusion
Board-level drop test and package-level BIT are examined
numerically in this paper. Different Sn-Ag-Cu solder joint
compositions, namely, SAC405, SAC305, SAC266, and
SAC105, and Sn-Ag-Cu solder alloys dopped with trace
elements, namely, SACSb, SACXY1, SACXY2, SACXY3,
and SACXY4, are considered. Through numerical solutions,
insights into the analytical correlation between the drop
reliability and characteristics of the impact force profile are
provided.
We note that Fmax and dr are not particularly good BIT
indices to correlate with board-level drop reliability because
their correlations are not universal, varying according to
different compositions of the solder joints. Nevertheless, Er
can be a reasonably good indicator as long as P is small.
Although the correlations become universal by introducing
constant multipliers to these indices, physical meanings of
these empirically chosen multipliers certainly require further
investigations. Besides, numerical solutions presented in this
paper follow rate-independent constitutive relationships for
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2006 Electronics Packaging Technology Conference
the solder alloys. For these dynamic problems, rate-dependent
constitutive relationships are in serious need.
Acknowledgment
Solder samples examined in this study were provided by
Accurus Scientific Co., Ltd. (Tainan, Taiwan), a joint
development partener with ASE Group on solder alloys and
soldering technologies.
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2006 Electronics Packaging Technology Conference