COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE
EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China
©2006 Tsinghua University Press & Springer
Application of Computational Mechanics to Reliability Studies of
Electronic Packaging
N. Miyazaki *, T. Ikeda
Department of Mechanical Engineering and Science, Kyoto University, Kyoto, 606-8501 Japan
Email: miyazaki@mech.kyoto-u.ac.jp
Abstract Computational mechanics approaches, especially computational fracture mechanics, have been utilized as a
powerful tool for reliability studies of large-sized structures such as air crafts, pressure vessels, piping and so on.
Electronic packages are considered as small-sized structures to protect electrical integrity of electronic devices. So the
computational mechanics can be successfully applied to the reliability studies of electronic packaging. In the
electronic packages, there exist a lot of interfaces between different materials, so that the interface fracture mechanics
is very useful for such studies. In the first part of the present paper, we summarize the interface fracture mechanics,
and then we provide two examples of the application of computational mechanics to the reliability studies of electronic
packaging. One example is the strength evaluation of a plastic package during solder reflow process, and another is the
delamination evaluation of anisotropic conductive adhesive films under moisture/reflow sensitivity tests.
Key words: interface fracture mechanics, stress intensity factors, electronic package, plastic package, anisotropic
conductive films, moisture absorption
INTRODUCTION
Computational mechanics approaches, especially computational fracture mechanics, have been utilized as a powerful
tool for reliability studies of structural components. The fracture mechanics parameters such as the stress intensity
factor and J-integral calculated using the computational mechanics have been successfully utilized in assessing the
structural integrity of large-sized structures such as air crafts, pressure vessels, piping and so on. Electronic devices are
incorporated not only into electric appliances but also into various kinds of mechanical systems. For example, they are
used to control the ignition of the engines in automobiles. In such a case, the failure of the electronic devices may
induce the safety problems of the automobile. So the reliability of electronic devices is one of key issues of the safety of
automobiles. The protection of electronic devices from the external environment and the electric connection between
the electronic devices and substrate are generally called as electronic packaging. Electronic packages are considered as
small-sized structures to protect electrical integrity of electronic devices. So the computational fracture mechanics can
be successfully applied to the reliability studies of electronic packaging. In the electronic packages, there exist a lot of
interfaces between different materials, so that the interface fracture mechanics is very useful for such studies. In the
first part of the present paper, we summarize the interface fracture mechanics. Then we provide two examples of the
application of computational mechanics to the reliability studies of electronic packaging to show the effectiveness of
the fracture mechanics to the reliability studies of electric packaging. One is the strength evaluation of plastic packages
during solder reflow process. Another is the delamination evaluation of anisotropic conductive adhesive films under
moisture/reflow sensitivity tests.
INTERFACE FRACTURE MECHANICS
Here we summarize the interface fracture mechanics useful to the reliability studies of electronic packaging.
1. Asymptotic solution in the vicinity of a corner of jointed dissimilar materials Chen and Nishitani [1] derived
the asymptotic solution in the vicinity of a corner of jointed dissimilar materials whose geometry is shown in Fig.1.
— 112 —
Figure 1: A coordinate system around a corner of jointed dissimilar materials
The orders of stress singularity for the mode I and mode II deformations 1 − λ1 and 1 − λ2 are obtained from the
following characteristic equations:
D1 (α,β,γ,λ) = (α – β) 2 λ 2 (1 – cos 2γ) + 2λ(α – β)sin γ{sin λγ + sin λ(2π – γ)}
+ 2λ(α – β)βsin γ{sin λ(2π – γ) – sin λγ } + (1 – α 2 ) – (1 – β 2 )cos 2λπ
+ (α 2 – β 2 )cos {2λ(γ – π)} = 0
(1)
D2 (α,β,γ,λ) = (α – β) 2 λ 2 (1 – cos 2γ) – 2λ(α – β)sin γ{sin λγ + sin λ(2π – γ)}
– 2λ(α – β)βsin γ{sin λ(2π – γ) – sin λγ } + (1 – α 2 ) – (1 – β 2)cos 2λπ
+ (α 2 – β 2 )cos {2λ(γ – π)} = 0
(2)
where α and β are Dunders parameters. They are defined as
G1 (κ 2 + 1) − G2 (κ1 + 1)
G (κ −1) − G2 (κ1 −1)
, β= 1 2
G1 (κ 2 + 1) + G2 (κ1 + 1)
G1(κ 2 + 1) + G2 (κ1 + 1)
(3)
κ i = (3 − ν i ) /(1+ ν i ) for plane stress, 3 − 4ν i for plane strain
(4)
α=
where (G1,G2 ) and (ν1,ν 2 ) are shear moduli and Poisson’s ratios for materials 1 and 2, respectively. A unique real
solution for λ2 can be obtained from Eq.(2) for all ranges of the combinations of materials. If the combination is
selected as
β (α − β ) > 0
(5)
a unique real solution for λ1 also can be obtained from Eq. (1).
The stress field in the vicinity of the corner of jointed dissimilar materials selected as in Eq.(5) is shown as
σ kl .i =
K I ,λ1
1− λ1
K II ,λ2
1− λ2
f klII,i (θ )
(6)
r
where σ kl ,i (kl = xx, yy, xy) represent the stresses in the region of material i, K I ,λ1 and K II ,λ2 represent the stress
I
II
intensity factors of the corner for Mode I and Mode II deformations, respectively, and f kl.i
(θ ) and f kl.i
(θ ) are the
coefficient functions of θ . The displacements around the corner are described by the stress intensity factors K I ,λ1 and
K II ,λ2 as
ui =
r
f klI ,i (θ ) +
r λ1 K I ,λ1
2 2π G1
g1,iI (θ ) +
r λ2 K II ,λ2
2 2π G1
g1,iII (θ )
vi =
,
r λ1 K I ,λ1
2 2π G1
I
g2,i
(θ ) +
r λ2 K II ,λ2
2 2π G1
II
g2,i
(θ )
(7)
where ui and v i are components of the displacement in the x and y directions within the region of the materials I, and
I
II
g1,iI (θ ) , g1,iII (θ ) , g2,i
(θ ) and g2,i
(θ ) are the coefficient functions of θ .
— 113 —
The stress intensity factors K I ,λ1 and K II ,λ2 are calculated from Eq. (7) using the displacement extrapolation method.
2. Stress intensity factors of an interface crack between dissimilar materials If a coordinate system around an
interface crack is defined as shown in Fig. 2, the asymptotic solution of the stress components along the x-axis in the
vicinity of an interface crack tip is expressed as [2]
iε
K I + iK II ⎛ r ⎞
(σ yy + iσ xy )θ = 0 = 2πr ⎜⎝ l ⎟⎠
k
(8)
where K I and K II represent the stress intensity factors of an interface crack for the mode I and mode II deformations
respectively, lk is the characteristic length, which can be taken as an arbitrary constant, and ε is the bimaterial
constant defined as
ε=
1 ⎡⎛ κ1 1 ⎞ ⎛ κ 2 1 ⎞⎤
ln⎢⎜ + ⎟ ⎜ + ⎟⎥
2π ⎣⎝ G1 G2 ⎠ ⎝ G2 G1 ⎠⎦
(9)
Figure 2: A coordinate system around an interface crack
The value of characteristic length lk should be fixed at a certain value. It is difficult to decide the most suitable value
of lk , but it is expected to be close to the size of a fracture process zone [3]. For convenience, we use lk =10 μm in this
study. When the value of lk is changed to lk' , K I and K II are transformed into K I' and K II' , as follows [4]:
⎛ K I′ ⎞ ⎡cosQ −sinQ⎤⎛K I ⎞
⎜ ′ ⎟=⎢
⎥⎜ ⎟
⎝K II ⎠ ⎣ sinQ cos Q ⎦⎝K II ⎠
(10)
⎛l′ ⎞
Q = ε ln⎜ k ⎟
⎝ lk ⎠
(11)
We need to consider the sign of K II for the interface crack, because the deformation mode of the interface crack
between dissimilar materials depends on the direction of shear stress around a crack tip. When the interface crack is
located on the left side, and the material indices denoted by 1 and 2 belong to y ≥ 0 and y<0, respectively, as shown in
Fig. 2, we accept the sign of K II in the case of ε <0, but use the reverse sign of K II in the case of ε >0.
The stress intensity factors can be calculated from the modified virtual crack extension method in conjunction with the
finite element method [5].
APPLICATIONS OF FRACTURE MECHNICS
1. Strength evaluation of plastic packages during solder reflow process Plastic packaging is the most popular
technique to protect electronic devices from the external environment because of low cost and ease of manufacture.
Plastic packages, however, sometimes fail due to cracks in the molding resin during the solder reflow process, when
they absorb moisture. Such failure is called popcorn cracking. Here we deal with the popcorn cracking. It occurs at a
corner of molding resin. So we applied the stress intensity factors of a V-notch defined by Eq. (6).
1) Fracture toughness of a V-notched molding resin: We measured the fracture toughness of a V-notch cut with the
open angle of 90˚ in the molding resin at the temperatures of 20˚C, 100˚C and 240˚C, using three-point bending test
specimens. In the present case, the orders of stress singularity 1 − λ1 and 1 − λ2 are obtained as 0.456 and 0.091 by
solving Eqs.(1) and (2), and the mode II stress intensity factor K II ,λ2 in Eq. (6) is always equal to zero because of the
— 114 —
symmetric loading condition for the three-point bending tests. The fracture toughness or the stress intensity factor of
the V-notch for the molding resin at the onset of failure K I ,λ1 ,C was calculated from the fracture load obtained by the
three-point bending test. Fig. 3 shows the temperature variation of fracture toughness of the V-notched molding resin.
The fracture toughness decreases drastically at the glass transition temperature of the molding resin 150˚C and it is
0.54MPa•m0.456 at the temperature of 240˚C.
Figure 3: Temperature variation of fracture toughness of the V-notched molding resin
Figure 4: A 100-pin quadrangle flat package (QFP)
2) Estimation of the critical vapor pressure of crack occurrence: In the present paper, we deal with a 100-pin
quadrangle flat package (QFP) illustrated in Fig. 4. Complete delamination between the die pad and the molding resin
at both the lower and side surfaces of the die pad was observed prior to the crack occurrence at the corner of the
molding resin or the popcorn cracking. Vapor is generated from moisture absorbed in the molding resin during the
solder reflow process where the temperature of the molding resin rises up to 240˚C. Considering these facts, we can
assume that the diving force of the popcorn cracking is the vapor pressure exerting in the cavity between the die pad
and the molding resin. The critical vapor pressure of the popcorn cracking was estimated for the QFP.
We performed the three-dimensional stress analysis to obtain the stress intensity factors of the V-notch corner per unit
vapor pressure at the temperature of 240˚C. Figure 5 shows a three-dimensional quarter-model of the QFP. Although
there exists the mode II stress intensity factor, it can be neglected in the present study because of the small level of the
shear stress around the corner in the QFP. The distributions of the mode I stress intensity factor along the short and
long corner fronts of the package are shown in Fig.6. As shown in Fig.6, we can predict that a crack occurs from the
center of the long corner front. The critical vapor pressure for the crack occurrence PVC is predicted using the
maximum mode I stress intensity factor per unit vapor pressure K I ,λ1 ,max /PV and the fracture toughness of the
V-notched molding resin at the temperature of 240˚C K I ,λ1 ,C as
PVC =
K I ,λ1 ,C
(12)
K I ,λ1 ,max /PV
— 115 —
where PV denotes vapor pressure. Substituting K I ,λ1 ,max /PV = 0.53 m0.456 and K I ,λ1 ,C =0.54MPa•m0.456 into Eq. (12),
we predict the critical vapor pressure PVC =1.02MPa for the QFP.
Figure 5: A three-dimensional symmetrical quarter-model of the QFP
Figure 6: Stress intensity factor of a V-notch corner per unit vapor pressure
along the short and long corner fronts
3) Measurement of the diffusion coefficient and the Henry’s law coefficient of the molding resin: We determined the
diffusion coefficient and the Henry’s law coefficient of the molding resin, using the experimental data of the moisture
absorption tests for the molding resin. Such tests were performed at the conditions of 30˚C/80%RH (RH: relative
humidity), 85˚C/85%RH and 121˚C/100%RH, and the weight of absorbed moisture versus time curves were obtained
experimentally. The size of each test specimen with a rectangular shape is 20mm × 10mm × 4mm for 30˚C/80%RH
test, and 80mm × 10mm × 4mm for 85˚C/85%RH and 121˚C/100%RH tests. The moister weight concentration in the
molding resin C is obtained by solving the following equation:
D∇2C =
∂C
∂t
(13)
where D is the diffusion coefficient and t is the time. This equation can be solved using the finite element method
under the initial condition and the boundary conditions. Because of a low concentration of moisture in the resin, the
Henry’s law approximates the boundary condition on the surface.
C(surface, t) = HρPS
(14)
where H is the Henry’s law coefficient, ρ the relative humidity of atmosphere, and PS the saturated vapor pressure.
The diffusion coefficient and the Henry’s law coefficient were found out using a trial and error method by comparing
the weight of absorbed moisture versus time curves obtained from the experiments with those calculated from the
solution of Eq. (13). The Arrhenius expressions are used as the temperature dependence of D and H.
⎛ −E ⎞
⎛ −E ⎞
D = D0 exp⎜ D ⎟ , D = H 0 exp⎜ H ⎟
⎝ RT ⎠
⎝ RT ⎠
(15)
— 116 —
where T (K) is the temperature, D0 (mm2/hr) and H 0 (mg/mm3MPa) the frequency factors, E D (J/mol) and E H
(J/mol) the activation energies, and R (= 8.314J/mol•K) the universal gas constant. The frequency factors and
activation energies for the molding resin were determined as follows:
D0 = 6.6 × 10 4 mm2/hr, E D = 4.7 × 10 4 J/mol, H 0 = 3.1 × 10−7 mg/mm3MPa, E H = −3.9 × 10 4 J/mol.
4) Estimation of the vapor pressure during solder reflow process: The two-dimensional finite element analysis was
performed to solve Eq. (13) for the QFP. The boundary conditions used in the analysis are shown in Fig. 7. Fig. 8
shows the variations of the moisture concentration at the points A and B under the die pad with the absorption time.
The result of the one-dimensional diffusion equation for the point A is given by the sold line in Fig. 8. The solution of
the one-dimensional diffusion equation is given as follows:
⎧⎪ 4
C( x, t) = Ns ⎨1−
⎪⎩ π
∞
⎛
k=1
⎝
+1)
∑ 2k1+1 exp⎜− (2k 4L
2
2
π2
⎞ (2k + 1) πx ⎪⎫
Dt ⎟sin
⎬
2L ⎪⎭
⎠
(16)
where the coordinate x is taken, as shown in Fig.7. It is found from Fig.8 that the one-dimensional solution agrees well
with the two-dimensional finite element solution.
Figure 7: Boundary conditions for the two-dimensional moisture absorption analysis
Figure 8: Variations of the moisture concentration at the points A and B
under the die pad with the absorption time
We estimated the vapor pressure during the solder reflow process using the moisture concentration under the die pad
predicted by Eq. (16). For simplicity we assumed the Henry’s law relationship between the vapor pressure and the
moisture concentration under the die pad. Then the vapor pressure during the solder reflow process is predicted as
follows
PV = PS
when C ( L, t ) ≥ H (Tr )× PS (Tr )⎫⎪⎪
⎬
PV = C ( L, t ) H (Tr ) when C ( L, t ) < H (Tr )× PS (Tr )⎪⎪⎭
(17)
where C(L,t) is the moisture concentration under the die pad after the moisture absorption, Tr the temperature under
the die pad, H(Tr ) and PS (Tr ) the Henry’s law coefficient and the saturated vapor pressure at the temperature Tr ,
respectively, and PV is the estimated vapor pressure under the die pad. The estimated vapor pressures in the QFP after
— 117 —
moisture absorption at the atmosphere condition of 85˚C/85%RH are shown in Fig. 9 for several assumed temperatures
during the reflow process. The critical vapor pressure of crack occurrence or popcorn cracking of the QFP is indicated
in Fig. 9 with the broken line. The critical moisture absorption time, which causes a crack in the molding resin during
the solder reflow process, can be predicted at the crosspoint of the broken line and solid line in Fig. 9. If the
temperature under the die pad during the solder reflow process is assumed to be 240˚C, the critical moisture absorption
time under the atmosphere condition of 85˚C/85%RH is approximately 35 hours.
Figure 9: Estimated vapor pressure for several assumed temperature under the die pad
5) Solder reflow tests of the QFP after moisture absorption and comparison between test result and theoretical
prediction: The solder reflow tests of the QFPs were performed using the QFP test samples after the QFPs absorbed
moisture for 6, 12, 24, 48 and 96 hours under the condition of 85˚C/85%RH. The moisture-absorbed QFP test samples
were then heated up and were maintained at approximated 240˚C for six seconds to simulate the solder reflow process.
After that, the failure mode of the QFP was observed. The results of the observation are as follows:
(1) Partial delaminations around the corner were observed for the QFP samples with 6-hour absorption time,
(2) Whole delaminations under the die pad were observed for the QFP samples with 12-hour, 24-hour and 48-hour
absorption times, and
(3) Cracks from the corners of the die pads into the molding resin or popcorn cracks were observed in the almost all
samples with 96-hour absorption time. These cracks occurred near the corners of the long corner fronts.
According to these results, it is found that the critical moisture absorption time in the 85˚C/85%RH atmosphere is
between 48 hours and 96 hours. The place where the crack occurred corresponds with the predicted location. The
estimated critical moisture absorption time 35 hours is, however, shorter than the actual time. One of the possible
reasons for the disagreement is the delay of mass transfer of the moisture from the molding resin into the delamination
cavity. We assumed immediate mass transfer to get into cavity space as well as the instantaneous steady state
conditions, which can be approximated using the Henry’s law. Moisture transfer is actually delayed as the moisture
diffuses through the molding resin. Conclusively, the estimation method proposed here provides a reasonably safety
estimation of the critical absorption time of the popcorn failure.
2. Delamination Strength of Anisotropic Conductive Adhesive Films during Solder Reflow Process An
anisotropic conductive adhesive film (ACF) is a thermoset adhesive containing conductive particles that supply
electrical connections. The ACF has been used for electronic assemblies such as the connection between a liquid
crystal display (LCD) panel and a flexible print circuit board (FPC). Compared with traditional solder interconnection
technology, ACF connections have several advantages, including fine pitch, flexibility, low temperature processing,
etc. The ACF is expected to be one of the key technologies for flip chip packaging, system in packaging and chip size
packaging. Delamination initiated from the interface between a chip and the ACF, a substrate and the ACF, or a pattern
and the ACF, is one of the main causes of failure in electronic packaging using the ACF connection. An evaluation
methodology for the delamination of the ACF connections is herein proposed. In the present study, we deal with the
delamination of the ACF absorbing moisture during the solder reflow process.
1) Estimation of delamination strength: Three types of specimens, that is, the system A of Si chip (or Al)-ACF
(A)-substrate, the system B of Si chip (or Al)-ACF (B)-substrate, and the system C of Si chip (or Al)-ACF
(C)-substrate, were used in this study. The material properties are summarized in Table 1. The ACF(C) has two layers,
the chip-side layer and the substrate-side layer, as shown in Table 1.
— 118 —
Table 1 Material properties at room temperature
Material
E
ν
(GPa)
Tg
CTE(10-6/˚C)
(˚C)
<Tg
>Tg
ACF (A)
1.84
0.38
126
100
800
ACF (B)
2.52
0.38
160
100
400
ACF(C)-Chip
2.78
0.38
155
80
300
ACF(C)-Sub.
2.65
0.38
126
90
600
Substrate
16.5
0.20
156
11.6
1.4
Si chip
170
0.30
3
Al
68.9
0.355
23
E: Young’s modulus, ν: Poisson’s ratio, Tg: glass transition temperature, CTE: coefficient of thermal expansion,
ACF (C)-Chip: chip side of the ACF (C), ACF (C)-Sub.: substrate side of the ACF (C).
Delamination toughness expressed by the stress intensity factors was calculated from the load at the onset of
delamination, using the modified virtual crack extension method in conjunction with the finite element method [4, 5].
The total stress intensity factor defined by the following equation is utilized as the delamination toughness.
K i = K I2 + K II2
(18)
The variations of delamination toughness with temperature are shown in Fig.10 for the system B. The delamination
toughness decreases with temperature. Table 2 shows the delamination toughness at 240℃ for the respective systems.
The delamination toughness of the system B is higher than those of the systems A and C. The delamination toughness
of the system C strongly depends on the side, on which initial delamination is introduced, because the two-layered
adhesive film has different Young’s moduli and different coefficients of linear expansion for the respective layers.
Figure 10: Temperature variations of total stress intensity factor at the onset of delamination
(fracture toughness) for the system B
Table 2 Delamination toughness at 240℃
Kic
(MPa m )
Interface
System A
System B
Si chip side
Sub side
Al side
0.0160
0.0143
0.0077
0.0297
0.0260
0.0130
System C
0.0422
0.0116
0.0230
Si chip side: a crack between Si chip and ACF, Sub side: a crack between substrate and ACF,
Al side: a crack between Al and ACF
— 119 —
2) Moisture/reflow sensitivity tests of flip chip using ACF: Several tests were carried out to estimate failure of the
flip chip using the ACF during solder reflow process after moisture absorption, which is called moisture/reflow
sensitivity test hereafter. At first we baked the specimens for 24 hours at 125˚C. Subsequently, the flip chip was
exposed to an atmosphere of 85˚C/85%RH for 168 hours, and then heated at 240˚C for 40 seconds to simulate the
solder reflow process. After heating process, the conductive resistance of the daisy-chain circuit on the flip chip was
measured to detect any disconnection of the ACF connections. Fig. 11 shows a schematic of a flip chip used for the
moisture/reflow sensitivity test in this study. Table 3 shows the number of disconnected flip chips after the
moisture/reflow sensitivity tests. Obviously, the system B shows the highest durability against the moisture/reflow
sensitivity. The flip chip that does not fail during the first heating process also does not fail in the second and third
heating processes. We suppose that the vapor pressure during the solder reflow process causes the disconnection of the
ACF connection. The specimen is dried during the first heating process, and the vapor pressure during the second and
the third heating processes is supposed to be less than that during the first heating process.
3) Measurement of the diffusion coefficients and the Henry’s law coefficients of the ACFs and the substrates: We
determined the diffusion coefficients and the Henry’s law coefficients of the ACFs and the substrate to use diffusion
analysis of the moisture absorption of the flip chip, the results of which were utilized to calculate the vapor pressure in
the flip chip during the solder reflow process. Rectangular thin specimens of the ACF and the substrate were baked for
24 hours at 125˚C. The size of each specimen is 12mm×12mm×0.1mm for the ACFs and 28mm×28mm×0.8mm
for the substrate. Subsequently, the specimens were exposed to an atmosphere of 30˚C/80%RH (in case of substrate:
40˚C/80%RH), 85˚C/85%RH and 120˚C/100%RH until the specimens were saturated. The moisture concentration in
the test specimen is approximated by the solution of the one-dimensional diffusion equation, Eq. (16), because of thin
thickness of the specimen, compared with other dimensions. In Eq. (16), L and x denote the thickness of the specimen
and the distance of one-dimensional diffusion direction.
Figure 11: Schematic of a flip chip used in this study
Table 3: Number of disconnected flip chips after the moisture/reflow sensitivity tests
System
System A Disconnected chips
System B Disconnected chips
System C Disconnected chips
RF1
RF2
RF3
10/10
2/10
7/10
2/10
7/10
2/10
7/10
Disconnected chips: number of test specimens,
RF1, RF2, RF3: first, second and third reflow
As shown in the first application, the diffusion coefficient D and the Henry’s law coefficient H were found out using a
trial and error method by comparing the weight of absorbed moisture versus time curves obtained from the
experiments with those calculated from the solution of Eq. (16). The Arrhenius expressions shown in Eq. (15) were
used as the temperature dependence of D and H. The frequency factors D0 and H0 and activation energies ED and EH
were determined for the ACFs and the substrate, and they are given in Table 4.
Table 4: The frequency factors D0 and H0 and activation energies ED and EH for the ACFs and the substrate
D0 (103mm3/hr)
ED (104J/mol)
H0 (106mg/mm3/MPa)
EH (104J/mol)
ACF(A)
ACF(B)
ACF(C)
Substrate
2.47
3.257
20.68
−3.019
1.42
3.228
16.92
−3.167
3.80
3.429
19.89
−3.036
12.7
4.304
0.67
−3.792
— 120 —
4) Estimation of the vapor pressure during solder reflow process: The three-dimensional diffusion analysis of the flip
chip was performed by the finite element method using the diffusion coefficients and the Henry’s coefficients of the
ACFs and the substrate shown in Table 4 in order to obtain the moisture concentration in a flip chip. The temperature
and the relative humidity around the flip chip were 85˚C and 85%RH, respectively. The weight gain with moisture
absorption time obtained by the three-dimensional diffusion analysis corresponds well with that obtained from
moisture absorption test, as shown in Fig. 12. According to the three-dimensional diffusion analysis of the flip chip,
the moisture concentration is highest in the ACF around the gold bump and Cu (Cu/Ni/Au) terminal located at the chip
corner. It is therefore concluded that the vapor pressure is the highest there.
Figure 12: The weight gain with moisture absorption time
The vapor pressure is estimated from the moisture concentration in the ACF around the gold bump and the Cu terminal
during the solder reflow process. A small gap caused by delamination is assumed to exist at the interface between the
ACF and gold bump and at the interface between the ACF and Cu terminal. We also assume that equilibrium condition
holds between the vapor pressure in the gap and the moisture concentration in the ACF. Therefore, the Henry’s law
can be applied to the calculation of vapor pressure at the interface between the gold bump and the ACF and at the
interface between the Cu terminal and the ACF during reflow process. As shown previously, such vapor pressure is
predicted by Eq. (17), using the calculated value of the moisture concentration in the ACF. Fig. 13 shows the predicted
vapor pressure on a surface of the gold bump and the Cu terminal located at the chip corner, at which the moisture
concentration becomes maximum in the diffusion analysis.
(a) Interface between Au bump and ACF
(b) Interface between Cu terminal and ACF
Figure 13: Predicted vapor pressure in a flip chip during reflow process
— 121 —
Figure 14: Assumption of a penny shaped crack
Figure 15: A penny shaped crack between dissimilar materials
5) Estimation of delamination of flip chip: At the solder reflow temperature of about 240˚C, small compressive stress
or tensile stress is expected to act on the ACF layer between the gold bump and Cu terminal due to expansion of the
ACF. It is also reasonable to assume that the interface between the ACF and bump (or terminal) is delaminated by
vapor pressure at the reflow temperature, because adhesion strength between the epoxy resin, that is, matrix resin of
the ACF, and the gold used as bumps and plated on the Cu terminals is very small. Accordingly, we assumed that the
interface between the ACF and the gold bump or Cu/Ni/Au terminal is delaminated when estimating the delamination
of the flip chip under solder reflow process. The vapor pressure acts on the gap generated by the delamination between
the ACF and the bump or the terminal during solder reflow process. We considered a penny shaped crack with the
same size of gold bump (or Cu terminal) at interface between the ACF and Si chip (or Al pattern or substrate), as
shown in Fig. 14, for the evaluation based on the fracture mechanics. Furthermore, to predict crack propagation caused
by vapor pressure, we used the stress intensity factors of a penny shaped crack between dissimilar materials subjected
to uniform tension applied to its crack surface, as shown in Fig. 15. The stress intensity factors are given by Kassir [6],
as follows:
K I + iK II = 2 pa a
Γ(2 + γ )
(19)
Γ (0.5 + γ )
where p is the uniform tension applied to crack surface, and a is the radius of a penny shaped crack, Γ(x) is the gamma
function, and i = −1 . The bielastic constant γ is given in terms of shear moduli ( G1, G2 ), and Poisson’s ratios
( ν1, ν 2 ) of materials by
γ=
1 ⎛⎜ G2 + G1 (3 − 4ν 2 )⎞⎟
⎟⎟
ln ⎜
2πi ⎝⎜⎜ G1 + G2 (3 − 4ν1 ) ⎠⎟
(20)
We calculated the stress intensity factors of the penny shaped crack of the interface between the ACF and a Si chip (or
an Al pattern or a substrate) from Eqs. (19) and (20) when vapor pressure applies to crack surface. In this case, the
penny shaped crack is the same size (a=50μm) as the radius of the gold bump and Cu (Cu/Ni/Au) terminal. Fig. 16
shows the comparison between the total stress intensity factor KiV caused by the predicted vapor pressure during
reflow process and delamination toughness Kic measured by delamination test at the 240˚C.
As the results of the system A, the stress intensity factors of the interface crack between the ACF and Si chip and
between the ACF and substrate caused by the vapor pressure during reflow process are lower than the delamination
toughness at the 240˚C. On the other hand, the total stress intensity factor of the interface crack between the ACF and
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the Al pattern caused by the vapor pressure are slightly higher than the delamination toughness at 240˚C.
Consequently, the delamination in the flip chip connected by the ACF (A) is expected to propagate along the interface
between the ACF and the Al pattern from the bottom of gold bump due to vapor pressure during reflow process after
moisture absorption. Once the interface between the ACF and the Al pattern is delaminated, the delamination
propagates along the interface between the ACF and the Si chip until vapor pressure is released from the flip chip.
(a) System A
(b) System B
(c) System C
Figure16: Comparison between delamination toughness and stress intensity factors of respective
interfaces during reflow process after moisture absorption test (KiV; total stress intensity factors
caused by vapor pressure in penny shaped crack, Kic; delamination toughness measured by
delamination test at 240˚C)
In case of the system B and system C connected by the ACF(B) and ACF(C) respectively, the values of delamination
toughness for all jointed interfaces are higher than the total stress intensity factors caused by the vapor pressure during
reflow process. So, the system B and system C are expected not to be delaminated. If we assume that the system B has
a penny shaped crack with the radius of 120μm at the interface between the ACF and the Al pattern, the total stress
intensity factor due to the vapor pressure are almost the same as the delamination toughness of an interface crack
between the ACF and the Al pattern. Therefore, we could presume that disconnected flip chips of the system B shown
in Table 4 have a delamination or void equivalent to a penny shaped crack with the radius of 120μm at the interface
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between the ACF and the Al pattern. Similarly, we could presume that the system C has a penny shaped crack with the
radius of 100μm at the interface between the ACF and a substrate.
Conclusively, the occurrence of the delamination of ACF in a flip chip during solder reflow process after moisture
absorption can be estimated by comparing the delamination toughness with the stress intensity factor caused by the
vapor pressure.
CONCLUDING REMARKS
We dealt with the reliability studies of electronic packaging, that is, the strength evaluation of plastic packages during
solder reflow process, and the delamination evaluation of anisotropic conductive adhesive films during solder reflow
process. In both studies, computational mechanic approaches can be applied as a powerful tool for obtaining moisture
concentration in the resin and the stress intensity factors of a V-notch and an interface crack. It can be concluded that
computational mechanics approaches are key technologies for the reliability studies of electronic packaging
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