Moisture-induced delamination failure in a semiconductor package

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Investigation of moisture-induced delamination failure in a semiconductor package via multi-
scale mechanics
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2011 J. Phys. D: Appl. Phys. 44 034007
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IOP P
UBLISHING
J
OURNAL OF
P
HYSICS
D:A
PPLIED
P
HYSICS
J.Phys.D:Appl.Phys.44 (2011) 034007 (10pp)
doi:10.1088/0022-3727/44/3/034007
Investigation of moisture-induced
delamination failure in a semiconductor
package via multi-scale mechanics
Hak-Sung Kim
1
,Jeehyang Huh
2
and Jongeun Ryu
3
1
Department of Mechanical Engineering,Hanyang University,Seoul,Republic of Korea
2
Department of Mechanical Engineering,Korea Advanced Institute of Science and Technology,
Daejeon,Republic of Korea
3
Mechanical and Aerospace Engineering Department,University of California,Los Angeles,CA 90095,
USA
E-mail:kima@hanyang.ac.kr
Received 24 May 2010,in final form28 August 2010
Published 22 December 2010
Online at
stacks.iop.org/JPhysD/44/034007
Abstract
In this work,moisture-induced interfacial delamination in a semiconductor package was
investigated by experiment and multi-scale numerical analysis.The interfacial adhesion
strength between a silicon wafer and an epoxy adhesive layer was characterized by a die-shear
test with respect to moisture concentration and temperature.Molecular dynamics simulation
was performed to study the effect of moisture and temperature on the interfacial adhesion
energy and strength at the Si/epoxy adhesive interface.Based on the molecular dynamics
predicted interfacial adhesion strength,a numerical stress analysis was performed considering
hygro-swelling stress and the thermo-mechanical stress during a solder reflow process to
predict the moisture-induced delamination failure of the semiconductor package.The
multi-scale simulation result was compared with the actual reliability test result.Fromthis
study,it was concluded that the proposed multi-scale simulation technique can be used
successfully for the prediction of moisture-induced package failure.
(Some figures in this article are in colour only in the electronic version)
1.Introduction
Moisture-induced package failures such as interfacial delami-
nation and pop-corn cracking are common failure phenomena
during a solder reflow process in the semiconductor indus-
try [1].The factors governing the moisture-induced package
failure are mainly moisture content and adhesion strength of
the interface at the elevated temperature during a solder reflow
process [1,2].Therefore,it is important to understand and pre-
dict the interfacial adhesion strength as a function of levels of
moisture content and temperature to improve the reliability of
the package products.Recently,many researchers have inves-
tigatedthephysical phenomenarelatedtothemoisture-induced
delaminationproblem,suchas moisturediffusion,hygroscopic
swelling and vapour pressure generation.Kim and Song
investigated the characteristics of constituent package materi-
als such as interfacial strength,hygro-swelling properties and
vapour pressure experimentally [1].Yoon et al measured the
hygro-swelling properties of an anisotropic conductive film
and printed circuit board (PCB).Based on the experimen-
tal result,they investigated the stress distribution of a solder
ball array during a solder reflow process using finite element
analysis [2].Wong et al,Wang et al and Tee and Ng anal-
ysed the hygro-swelling characteristics,in particular vapour
pressure generation,at the interface in IC package materials
based on several assumptions,such as Wong,Kitano and Bhat-
tacharyya’s assumptions [3–5].
Several researchers investigated moisture diffusion at the
interface using molecular dynamics simulation.Molecular
dynamics and mechanics are numerical solution methods for
a general n-body system of atoms,in which the interaction
physics among neighbouring atoms are approximated using
a pre-defined force field or a potential energy expression.It
has been proved to be useful to understand and predict the
0022-3727/11/034007+10$33.00
1
©2011 IOP Publishing Ltd Printed in the UK &the USA
J.Phys.D:Appl.Phys.44 (2011) 034007 H-S Kimet al
Table 1.Material properties of the package materials [1].
Thermo-mechanical properties Hygroscopic coefficients
Materials Elastic modulus (GPa) CTE (ppm

C
−1
) D
0
(m
2
s
−1
) E
D
(J K
−1
mol
−1
) B (%/%) β (ε%/C%)
EMC 23.5 (at 25

C) 23.5 (at 25

C) 2.38e
−6
40487 0.0188 0.51
1.5 (at 260

C) 35 (at 260

C)
PCB 27.5 (at 25

C) 13.7 (at 25

C) 4.41e
−10
9980 0.0047 0.2
Adhesive 2.5 (at 25

C) 120 (at 25

C) 4.60e
−10
8487 0.01 0.4
0.07 (at 260

C) 150 (at 260

C)
Silicon 160 2.8 — — — —
behaviour and dynamics of amorphous membrane polymers
and the interface of two distinct materials [6,7].Also,it
has been considered to be an effective tool for monitoring
microscopic physical quantities,such as atomic positions,
velocities and forces,as well as macroscopic physical
properties,such as deformation profile [7].
Hoffman et al studied the moisture effect on the interfacial
adhesion at the interface between a polymer and a zeolite by
running a molecular dynamics simulation [6].Edward et al
investigated interfacial adhesion energy between copper and
anepoxymouldingcompound(EMC) under different moisture
levels experimentally.They studied the effect of moisture
on the interfacial bonding energy by running a molecular
dynamics simulation [8].
However,although several researchers have investigated
the moisture-induced interfacial adhesion failure numerically
using several simulation techniques,most research results
are focused on atomic or molecular level characterization
of the interface,and few studies deal with multi-scale
mechanics simulation which covers macroscopic prediction
of the delamination phenomena as well as microscopic
characterization of the interface.
In this work,a moisture-induced interfacial delamination
in a semiconductor package was investigated by both
experiment and multi-scale numerical analysis technique.The
interfacial adhesion strength between a silicon wafer and an
epoxy adhesive layer was characterized by a die-shear test with
respect to moisture concentration and temperature.Molecular
dynamics simulation was performed to study the effect of
moisture and temperature on the interfacial adhesion energy
and strength at the Si/epoxy adhesive interface in a molecular
level.Then,the molecular dynamics simulation result was
compared with the die-shear test result and discussed.Based
on the molecular dynamics predicted interfacial strength,
a finite element stress analysis for the moisture-induced
semiconductor package failure was performed by applying a
cohesive element modelling technique,in which a quadratic
traction damage initiation law was used,considering hygro-
swelling stress and the thermo-mechanical stress during a
solder reflowprocess.Finally,the multi-scale simulationresult
was compared with the actual package failure behaviour.
2.Experimental details
2.1.Hygroscopic characteristic of the package material
In our previous work,the hygroscopic properties such as
diffusivity,saturated moisture concentration and swelling
coefficient of the package materials were measured and
characterizedexperimentally[1].The diffusioncoefficient can
be expressed as the following equation [9]:
D = D
0
exp
￿
E
D
RT
￿
,(1)
where D
0
,E
D
,T and R are the diffusion constant,
the activation energy,temperature (K) and gas constant
(8.314 J K
−1
mol
−1
),respectively.The determined diffusion
constant and activation energy of the package materials are
summarized in table 1 [1].
When a polymer material has a weak chemical interaction
with water molecules,the saturated concentration C
sat
at the
boundary of the polymer can be described by Henry’s law
[10] as
C
sat
= S ×P
VP
,(2)
where P
VP
is the ambient vapour pressure (Pa).Using the
definition of relative humidity (RH,the ratio of the vapour
pressure to the saturated vapour pressure P
sat
),equation (2)
can be rewritten as
C
sat
= S ×P
sat
×RH.(3)
The saturated vapour pressure and solubility can be expressed
by the Arrhenius relationship as
P
sat
= P
0
exp
￿

E
VP
RT
￿
,(4)
S = S
0
exp
￿
E
S
RT
￿
,(5)
where P
0
and S
0
are the constants and E
VP
and E
S
are the
activation energies for the vapour pressure and solubility,
respectively,and R is the gas constant 8.3145 J K
−1
mol
−1
.
The value of P
0
and E
VP
can be determined by fitting the
pressure–temperature curve of the steam table [11];P
0
=
6.07 × 10
10
Pa and E
VP
= 0.44 eV = 42455 J mol
−1
.
Combining equations (4) and (5),the saturated concentration
can be written as
C
sat
=
￿
S
0
×P
0
exp
￿
E
S
−E
VP
RT
￿￿
×RH.(6)
Wong and Rajoo [12] first reported that the magnitudes of
E
S
for the packaging materials range from0.44 to 0.46 eVand
thus S×P
sat
is virtually independent of temperature.Also,E
S
and E
VP
are independent of the relative humidity.Therefore,it
2
J.Phys.D:Appl.Phys.44 (2011) 034007 H-S Kimet al
Figure 1.Die-shear test between silicon chip and adhesive:(a) schematics;(b) photograph.
is evident that the saturated moisture concentration and relative
humidity can be expressed as the following linear equation:
C
sat
= B ×RH,(7)
where,C
sat
,B and RH are the saturated moisture
concentration,the material constant and the relative humidity,
respectively.
Thedeterminedmaterial constant Bis alsolistedintable1.
Using table 1,equations (1) and (2),the diffusion coefficient
and saturated moisture concentration of the package materials
can be obtained under any arbitrary temperature and relative
humidity.Swelling coefficient (β) of the packaging materials
was measured using a combined thermo-mechanical analyzer
(TMA) and thermo-gravity analyzer (TGA) measurement [1].
The measured swelling coefficients β of the package materials
are shown in table 1.The hygroscopic material data were used
in the moisture diffusion and stress analysis using the finite
element method.
2.2.Interfacial adhesion strength measurement
The interfacial adhesion strength of the Si/epoxy interface was
tested with respect to moisture concentration and temperature
by the die-shear test.3 mm ×3 mm diced silicon chips were
attached on a silicon wafer using EPON828 epoxy adhesives
and cured at 175

C for 2 h,(figure 1(a)).For the experiment,
a die-shear tester of DAGE 4000 (DAGE,USA) was used and
the test speed was 20 µmmin
−1
.Moisture concentration of
the adhesive layers was varied by placing them in a humidity
chamber (85

C,85% RH) for a different time duration.
Die-shear tests were performed varying the temperature from
25 to 260

C (maximum temperature of the solder reflow
process).Inthis work,it was assumedthat moisture desorption
during the die-shear test was negligible as only around 20 s
were required to increase the temperature of the specimens to
260

C due to the high thermal conductivity (149 Wm
−1
K
−1
)
and the low heat capacity (757.7 J Kg
−1
K
−1
) of the silicon
chip.Also,the silicon/epoxy joint has a little exposure area
(10 µmthickness,four sides areas of the adhesive layer) to air
(figure 1).During the experiment,shear force was acquired
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
0 50 100 150 200 250 300
0.0 % water
0.2 % water
0.6 % water
1.0 % water
1.5 % water
Interfacial strength (MPa)
Tem
p
erature
(
ºC
)
Figure 2.Adhesion strengths between silicon wafer and adhesive
versus moisture concentration and temperature.
by the load cell in the equipment.Average interfacial shear
strength can be calculated by the following equation:
S
13
= S
23
=
F
A
,(8)
where,S
13
and S
23
are the average interfacial shear strength at
the Si/epoxy adhesive interface.F and A are the failure load
and adhesion area,respectively.
As shown in figure 2,the interfacial adhesion
strength decreased as the temperature increased and/or
moisture concentration increased.It was found that the
adhesion strength decreased significantly when the moisture
concentration in the adhesive is higher than 1.0%,which might
be the critical moisture concentration value for the interfacial
delamination generation.Also,it was found that the failure
mode of the silicon/epoxy joint changed from the cohesive
failure mode of the adhesive layer itself tothe interfacial failure
mode between the adhesive layer and the silicon substrate
as the moisture concentration increased above 1% (figure 3).
This phenomenon might be because the adhesion energy at
the Si/epoxy interface decreased considerably with the critical
moisture concentration.Further theoretical investigation was
carriedout usingthefollowingmolecular dynamics simulation.
3
J.Phys.D:Appl.Phys.44 (2011) 034007 H-S Kimet al
(
a
) (
b
)
C o h e s i v e f a i l e d
a d h e s i v e l a y e r
I n t e r f a c i a l f a i l u r e
( L i t t l e a d h e s i v e r e m a i n e d )
F i g u r e 3.F a i l e d s u r f a c e o f s i l i c o n/e p o x y i n t e r f a c e:(a) c o h e s i v e f a i l u r e m o d e o f t h e a d h e s i v e l a y e r a t 1 7 5

C w i t h o u t m o i s t u r e;
(b) i n t e r f a c i a l f a i l u r e m o d e b e t w e e n s i l i c o n a n d a d h e s i v e a t 1 7 5

C w i t h 1.0 % o f m o i s t u r e c o n c e n t r a t i o n.
3.M o l e c u l a r d y n a m i c s a n a l y s i s o n t h e i n t e r f a c i a l
a d h e s i o n s t r e n g t h
T h e m o l e c u l a r l e v e l a d h e s i o n c h a r a c t e r i s t i c s b e t w e e n t h e
s i l i c o n a n d e p o x y c o n s t i t u e n t s w e r e e v a l u a t e d u s i n g m o l e c u l a r
d y n a m i c s s i m u l a t i o n s.I n t h i s a n a l y s i s,c o m m e r c i a l l y a v a i l a b l e
m o l e c u l a r d y n a m i c s s i m u l a t i o n s o f t w a r e ( M a t e r i a l s S t u d i o,
A c c e l r y s I n c.) w i t h C o n d e n s e d - p h a s e O p t i m i z e d M o l e c u l a r
P o t e n t i a l s f o r A t o m i s t i c S i m u l a t i o n S t u d i e s ( C O M P A S S ) f o r c e
fi e l d w a s u s e d.I n C O M P A S S f o r c e fi e l d,t h e g e n e r a l
r e l a t i o n s h i p b e t w e e n a n y t w o a t o m s i n t h e s i m u l a t i o n c a n b e
d e fi n e d b y t h e f o l l o w i n g f u n c t i o n a l f o r m o f t h e p o t e n t i a l e n e r g y
e x p r e s s i o n,a l i n e a r c o m b i n a t i o n o f a l l p o s s i b l e b o n d e d ( B ),
c r o s s - t e r m ( C T ) a n d n o n - b o n d e d ( N B ) i n t e r a c t i o n s [1 3]:
U
t o t a l
= U
B
+ U
CT
+ U
NB
.(9)
The non-bonded interaction energy component consists of
electrostatic (Coulombic) energy and van der Waals potential
energy as in equation (10).Here,Lennard-Jones potential
function was used to express the van der Waals interaction
term.Inequation(10),r
ij
is the spatial positionvector between
the two atoms,q
i
and q
j
are the atomic charges,and A
ij
,B
ij
and χ are material-dependent constants.
U
NB
(r
ij
) =
q
i
q
j
χ|r
ij
|
+
￿
A
ij
r
9
ij

B
ij
r
6
ij
￿
.(10)
To calculate the interfacial adhesion energy,silicon and
epoxy layers were constructed according to the methodology
as follows.First,a silicon substrate layer having a size of
30.720 678,30.720 678 and 31.226 525 Åwas constructed and
minimizedusingaconjugategradient method.Then,theepoxy
adhesive material,a blend of epoxy resin (EPON828) and
the cross-linking agent 4,4

-Methylenedianiline (MDA) in a
molar ratio of 2:1,was constructed.EPON 828 is a mixture
of linear epoxies based on diglycidyl ether of bisphenol A
(DEGBA) whose n is 0.2,corresponding to 4:1 molar ratio
of DEGBA (n = 0) and DEGBA (n = 1).The chemical
structure of DEGBA and MDA are shown in figure 4.The
final mixture has 32 DEGBA (n = 0),8 DEGBA (n = 1)
and 20 MDA molecules.These molecules were assembled
in an amorphous cell with the lattice parameters matching
that of the silicon substrate.After creating both the epoxy
adhesive layer and the silicon substrate,the Si/epoxy interface
was constructed by placing the two layers together.Then,
the epoxy was cured following the method suggested by
Wu and Xu [14].Figure 5 shows the molecular modelling
of the Si/epoxy interface before and after curing without
a water molecule.After creating the interface between
the silicon substrate and the fully cured epoxy,0/5/10/15
molecules of water,corresponding to 0/0.45/1.0/1.5 wt% of
moisture,were added randomly between each layer and
minimized (figure 6).According to Fan et al [15],the
moisture diffusion coefficients at the EMC/Cu interface are
larger (almost one order of magnitude) than those in the bulk
EMC material.Therefore,seepage along the interface is the
dominant mechanismfor moisture diffusion into the EMC/Cu
interface in plastic packages,while moisture diffusion via the
bulk EMC material is only a secondary moisture penetration
path to the interface.Therefore,in this work,all the water
molecules were located at the Si/epoxy interface.Each
system was equilibrated at 25

C/130

C/220

C/260

C using
molecular dynamics simulation under NVT (canonical,i.e.
the number of particles N,the volume V and the temperature
T of the system are kept constant) ensemble.The total time
step of each simulation was 100 ps with the time increment
of 1 fs.After equilibrium,interaction energy and work of
adhesion of the interface between the silicon substrate and the
epoxy with moisture were calculated by equations (11) and
(12),respectively:
E
int
= E
total
−(E
surface
+ E
epoxy+water
),(11)
W
ad
= −
E
int
A
s
,A
s
:interfacial area.(12)
4
J.Phys.D:Appl.Phys.44 (2011) 034007 H-S Kimet al
Figure 4.Chemical structure of the epoxy adhesive (EPON828):(a) epoxy resin (DEGBA);(b) cross linker molecule (MDA);(c) chemical
reaction involved in the curing of a DEGBA with a MDA molecule.
Figure 5.Molecular modelling of the Si/epoxy interface (a) before and (b) after curing without a water molecule.
The calculated work of adhesion is plotted in figure 7 with
respect to the moisture concentration and temperature.The
work of adhesion at the interface decreased as the temperature
increased,showing similar trends to the die-shear test results
in figure 2.Also,the work of adhesion showed a slight
increase below 1% of moisture concentration,and it started
to decrease rapidly as the moisture level increased afterwards.
However,the die-shear test results in figure 2 indicate that
the interfacial strength decreased when the moisture level
was below 1%,which is different from the MD simulation,
and above 1% moisture level,the interfacial strength started
to decrease significantly as in the MD calculation result.
Although Chan et al [16] argued that the interfacial energy
slightly increases up to a certain point of moisture content,
then decreases as the moisture level increases through MD
calculation of interfacial energy at the copper–epoxy interface,
most researchers observed degradation of interfacial strength
by humidity [17–19].Due to computational limitation,the
water–epoxy system that we modelled was relatively small
having only 5/10/15 water molecules and its periodically
repeating replicas.The limitation of the modelling might
result incalculationerrors,suchas overestimationof interfacial
5
J.Phys.D:Appl.Phys.44 (2011) 034007 H-S Kimet al
Figure 6.Molecular modelling of the Si/epoxy interface with water molecules:(a) 0 wt%,(b) 0.45 wt%;(c) 1.0 wt%;(d) 1.5 wt%.
0.00
0.05
0.10
0.15
0.20
0.25
0 50 100 150 200 250 300
0 % water
0.45 % water
1.0 % water
1.5 % water
Work of adhesion (J/m
2)
Tem
p
erature (ºC)
Figure 7.MD predicted work of adhesion of the interfaces with respect to moisture and temperature.
strength under 0.45% of moisture concentration.Further
research will be carried out on this in our future work.
For the interfacial strength calculation,the work of
adhesion of the interface was calculated while varying the
interfacial separation distance.Interfacial stress was then
evaluated as follows using a first-order central difference
method:
σ
IJ
=
F
int
J
A
I
=
−[E
int
],
J
A
I
= [{W
ad
}
I
],
J
,
σ
33
=
d[W
ad

33
)]

33
,(13)
where A
I
is the area normal to Ith direction and δ
33
is the gap
distance in the z-direction.
Figure 8 shows the interfacial tensile stress versus the
separationdistance without moisture at 25

C.It was foundthat
the interfacial stress is highlycompressive at a small separation
distance (about 0.1 Å).This behaviour is a consequence of the
repulsive component of the Leonard-Jones potential energy
(the first term in brackets in equation (10)),which dominates
non-bonded interactions at small atomic separation distances.
Figures 9(a) and (b) show the interfacial tensile stress
versus separation gap with different moisture concentrations
(0 wt%,0.45 wt%,1.0 wt%and 1.5 wt%) at 25

C and 260

C,
respectively.It was found that the maximum interfacial
stress was almost the same as the case without moisture
when the moisture concentration was 0.45%.However,
when the moisture concentration was higher than 1.0%,the
maximum interfacial stress level decreased significantly.The
interfacial tensile strengths for all cases were determined
from the maximum point on the respective stress-separation
curve (figure 9) and are plotted in figure 10.The trend of
interfacial tensile strength from the molecular dynamics is
similar to the experimental die-shear test results in figure 2.
In both cases,1 wt% moisture concentration was the critical
moisture content,which induces the dramatic degradation of
the interfacial adhesion strength of the Si/epoxy interface.The
adhesionstrengthdegradationbythemoisturecontent might be
the main reason for the failure mode change fromthe cohesive
mode to the interfacial mode as shown in figure 3.It is
noteworthy that the experimental adhesion strength decreased
above the glass transition temperature of the epoxy adhesive
(about 145

C) as shown in figure 2.However,the molecular
dynamics predicted interfacial strength did not degrade as
much as the experimental results above the glass transition
temperature.This difference might be because of the failure
mode differences between the molecular dynamics simulation
and the die-shear test.The experimentally obtained adhesion
strength is the mixed mode failure strength with a cohesive
failure mode and interfacial failure mode while the molecular
dynamics predicted interfacial strength is the pure interfacial
failure mode strength.Therefore,the experimental strength
value,which includes the cohesive failure mode,is mainly
6
J.Phys.D:Appl.Phys.44 (2011) 034007 H-S Kimet al
Figure 8.MD predicted interfacial tensile stress at the Si/epoxy interface at 25

C without moisture.
Figure 9.Interfacial tensile stress at Si/epoxy interface with
different moisture concentrations:(a) at 25

C;(b) at 260

C.
based on the adhesive material’s property itself,which is
affected much by its glass transition temperature,while the
molecular dynamics case is not.Another possible reason is
that the experimentally obtained adhesion strength generally
tends to be underestimated due to the unrelated damage modes
which arise as a consequence of the test configuration or the
stress concentration generated by local bending phenomena
by loading configuration.Further research on this difference
is also being considered in the author’s current research.
The molecular dynamics predicted interfacial strengths with
respect to the temperature and moisture concentration were
used in the macroscopic delamination prediction analysis of
the package product using the finite element method.
4.Prediction of interfacial delamination
4.1.Moisture diffusion analysis
Based on the hygroscopic material properties in table 1,the
moisture diffusion analysis of the semiconductor package
was performed using a finite element method.The diffusion
phenomenoncanbe describedbythe diffusionequation(Fick’s
law):
∂C
∂t
= D
￿

2
C
∂x
2
+

2
C
∂y
2
+

2
C
∂z
2
￿
,(14)
where C is the local moisture concentration,Dis the isotropic
moisture diffusivity and t is the time.In the analysis,a
commercial software Abaqus 6.7 (Dassault Syst
`
emes,USA)
was used.A quarter analysis model of the total package was
used in the analysis considering the symmetry of the model
(figure 11(a)).Amass diffusion element DC3D8 was used and
thetotal number of elements andnodes were24 132and39 082,
respectively.The outer surface of the package was defined as
the saturatedconcentrationunder 85

C/85%RHconditionand
the moisture concentration inside the package was calculated
as a function of time.The change in the moisture distribution
in the package with time is shown in figure 11(b),where the
moisture diffused through the EMC and the PCB substrate.
The moisture distribution in the adhesive layer between the
silicon chip and the PCB preconditioned at 85

C/85%RHfor
3 h,(i.e.JEDEC level 1 moisture sensitivity specification) is
shown in figure 11(c).As shown in figure 11(c),the moisture
concentration at the edges of the adhesive layer was saturated
to be about 1.6%while that of the centre part of the adhesive
layer was 1.2%.Note that the moisture concentrations in
the total adhesive layer were higher than its critical moisture
concentration value,1.0%,for the delamination generation.
The resulting moisture distribution was used in the following
delamination prediction analysis using Abaqus 6.7.
4.2.Stress and delamination prediction analysis
The stress analysis and delamination prediction of the package
during a reflowprocess were performed considering the hygro-
swelling stress and thermo-mechanical stress.The integrated
strain was calculated as follows:
ε
tot
= ε
th
+ ε
sw
= α ×T + β ×C,(15)
where ε
tot

th
and ε
sw
are the total strain,thermal strain and
hygro-swelling strain,respectively.
The hygro-swelling stress was calculated combined
with the moisture diffusion analysis result of the package
preconditioned at 85

C/85% for 3 h.According to Tee and
Zhong [20],the diffusivity of packaging materials at the
7
J.Phys.D:Appl.Phys.44 (2011) 034007 H-S Kimet al
0.00
5.00
10.00
15.00
20.00
25.00
30.00
0 50 100 150 200 250 300
Interfacial strength (MPa)
0 % water
0.45 % water
1.0 % water
1.5 % water
Temperature (ºC)
Figure 10.MD predicted interfacial tensile strength with respect to temperature and moisture concentration.
Figure 11.Moisture diffusion analysis of the package product:(a) a quarter analysis model of total package;(b) moisture distribution in the
package with time;(c) moisture distribution in the total adhesive layer at 85

C/85%for 3 h.
maximum temperature (260

C) during a reflow process is a
few orders higher than the case at room temperature.They
found that the external package surface loses a significant
amount of moisture due tohighmoisture desorptionrate during
the 5 min solder reflow.However,the moisture distribution at
the critical locations for delamination generation (i.e.at the
interface between silicon and the EMC) remains relatively
almost unchanged as the solder reflow process is generally
done in a fewminutes.Therefore,in this work,it was assumed
that the moisture distributiondoes not change duringthe reflow
process.The hygro-swelling stress was calculated considering
the moisture distribution of the package (figure 11) by
equation (15).The thermo-mechanical stress was calculated
with the assumption that the temperature increased from
175

C (the EMC moulding temperature of the package
product) to 260

C (the maximum reflow temperature).In
the stress analysis,a 3D continuum element C3D8 was used
and the interfacial layers between silicon and the adhesive
were modelled using a cohesive element COH3D8.The
total number of elements and nodes were 26 328 and 37 424,
respectively.In order to predict the delamination in the
package,a cohesive element modelling technique,which
is commonly applied for predicting interfacial failure,was
adopted as shown figure 12(a).In this work,the damage is
assumed to be initiated when a quadratic interaction function
(f:damage index) involving the nominal stress ratio reaches
a value of 1 as follows:
f =
￿

σ
33

S
33
￿
2
+
￿

σ
13

S
13
￿
2
+
￿

σ
23

S
23
￿
2
,(16)
where σ
33

13
and σ
23
indicate the normal stress in the
33 direction,the shear stresses in the 13 and 23 directions,
respectively.S
33
,S
13
and S
23
mean the normal strength
in the 33 direction,the shear strengths in the 13 and 23
directions,respectively.The symbol   used in the criterion
represents the Macaulay bracket which is used to signify
that a pure compressive stress state does not initiate damage.
In this work,the quadratic stress interaction criterion was
chosen because it has been used by many researchers as it
can consider the interaction between the normal and shear
tractions and the effect of the compressive normal stress on the
delamination initiation [21–24].Furthermore,in the quadratic
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J.Phys.D:Appl.Phys.44 (2011) 034007 H-S Kimet al
Figure 12.Stress analysis:(a) cohesive layer model;(b) stress distribution in the cohesive layer (unit:MPa).
stress interaction criteria,the strength value obtained fromthe
molecular dynamics can be directly used,which is appropriate
for multi-scale simulation in this work.In this delamination
analysis,the interfacial normal (S
33
) strength acquired from
the molecular dynamics was used as a function of moisture
concentration and temperature (figure 10).According to
Kinloch,the value of the interfacial shear strength (S
13
,S
23
)
was almost the same as the interfacial normal strength (S
33
)
and it is decreased as the absorbed moisture weight and
temperature increase similarly to the case of the interfacial
normal strength (S
33
) [25].Therefore,in this work,the
interfacial shear strengths (S
13
,S
23
) were assumed to be
the same as the interfacial normal strength predicted from
the molecular dynamics.Figure 12(b) shows the interlaminar
stress distribution at the interface of the Si/epoxy adhesive.It
was found that the tensile normal stress was generated in the
middle part of the adhesive layer,while the highly compressive
normal stress was generated at the edge.The compressive
normal stress didnot contribute tothe delaminationgeneration,
which was considered using the Macaulay bracket   in the
delaminationfailurecriteria(equation(16)).Also,it was found
that the high interlaminar shear stresses were generated in the
middle part of the adhesive layer which is also the main factor
for the delamination failure (figure 12(b)).
The damage index f defined in equation (11) at the
interfaces is calculated and illustrated in figure 13(a).As
shown in figure 13,the present multi-scale model predicts that
the initiation point of the interfacial delamination is located
slightly inside the chip rather than at the edge,which is because
the high compressive normal stress (σ
33
) along the edge of
the chip prohibited the delamination as shown in figure 12(b).
Once the delamination begins,it propagates towards the centre
of the chip (figure 13(a)).The weak region of the adhesion
interface predicted by the current multi-scale mechanics model
agrees well with the result of the physical failure phenomenon
as shown in figure 13(b) [1].The SAT image of the failed
package in figure 13(b) shows that the delamination lies inside
the chip which is similar to the current multi-scale prediction
model.Considering all the analytical and experimental results,
it was concluded that the moisture-induced failure of the
package resulted mainly from a rapid decrease in the work of
interfacial adhesion between the silicon chip and the adhesive
due to the higher moisture absorption than the critical value
(about 1.0%).
5.Conclusions
In this work,moisture-induced interfacial delamination in
a semiconductor package was investigated by experiment
and the multi-scale numerical analysis technique.The
molecular dynamics simulation could predict that 1 wt% of
moisture concentration was the critical moisture weight for
the interfacial delamination phenomenon,which is similar to
the experimental die-shear test result.Using the molecular
dynamics predicted interfacial strength,the stress analysis
and delamination prediction of the package during a reflow
process were performed considering the hygro-swelling stress
and thermo-mechanical stress.From the study,it was found
that the weak region of the adhesion interface predicted by
the current multi-scale mechanics model agrees well with the
result of the physical failure phenomenon.
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J.Phys.D:Appl.Phys.44 (2011) 034007 H-S Kimet al
Figure 13.Multi-scale interfacial delamination prediction results;(a) delamination propagation at Si/adhesive interface (red:delaminated
region;blue:intact adhesively bonded region);(b) physical package failure phenomena (C-scanned image) [1].
Acknowledgment
This work was supported by the research fund of Hanyang
University (HY-2010-N) and is highly appreciated.
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