H. Kristiansen, Z. L. Zhang and J.
Liu, Characterization of mechanical properties of
metal-coated polymer spheres for anisotropic
conductive adhesive, Proceedings of 10th Int.
Symposium on Advanced Packaging Materials:
Processes, Properties and Interfaces, 2005, p
209-213
Characterization of Mechanical Properties of Metalcoated Polymer Spheres for Anisotropic Conductive
Adhesive
H. Kristiansen1, Z. L. Zhang2 and J. Liu3
1: Conpart A.S, ,
N-2027 Kjeller, Norway, E-mail: helge@conpart.no
2: Faculty of Engineering Science and Technology, Norwegian University of Science and Technology,
N-7491 Trondheim, Norway
3: Sino-Swedish Microsystem Integration Technology (SMIT) Center, Shanghai University, Shanghai China /
Department of Microtechnology and Nanoscience (MC2), Chalmers University of Technology, Se 412 96, Göteborg, Sweden
Abstract- Metal coated small (micron sized) polymer particles
are used in developing anisotropic conductive adhesives (ACA).
The mechanical properties of polymer particles are of crucial
importance both to assembly process and the reliability of ACA. In
this paper we present a method to determine the mechanical
properties of polymer sphere particles by using inverse indentation
test – soft elastic sphere against rigid flat. Finite element analyses
have been carried out to study the large deformation contact
between the sphere particle and a rigid flat. The classical Hertz
solution works only for small sphere deformation. A modification
has been made to the Hertz contact force-displacement solution and
an approximate equation is presented. A capacitance based
experimental setup for particle indentation has been built. The
proposed method has been applied to determine the elastic
properties of typical polymer particles used for conductive
adhesives. For the metal plated polymer particles tested, it has been
found that a linear elastic model seems to hold for a large range of
deformation.
Chip
Substrate
Fig. 1. Schematic plot of flip-chip connection using anisotropic conductive
adhesives.
I. INTRODUCTION
Anisotropic conductive adhesives are an enabling technology for a
growing number of electronic packaging applications, in particular in
flip chip packaging applications. Fig. 1 illustrates the the principal of
flip-chip connections using ACA [1]. In general, ACA materials are
prepared by dispensing electrically conductive particles in an adhesive
matrix. These particles can be pure metals such as gold, silver or nickel,
or metal-coated particles typically with polymer cores. The volume
fraction of particles is well below the percolation threshold (typically
between 5 and 10 %), and the particles mostly range from 3 to 10 Pm in
diameter. Due to the low volume fraction, there are no continuous
conductive paths among the particles in the x-y plane of the film. The
adhesive therefore conducts electricity in only z direction - anisotropic
conductive adhesives.
The reliability of ACA assembly strongly depends on the thermomechanical properties of the conductive particles. A detailed
knowledge of the mechanical properties and failure mechanisms is
required in order to ensure good process yield and reliable products,
and provide accurate inputs to finite element simulations of package
performance. Due to temperature and mechanical induced loading,
various failure mechanisms such as deformation, delamination,
cracking and fracture, thermal fatigue, creep can occur during
production and service. Fig. 2 shows different failure mechanisms
which are observed in compression tests [2].
Because of small size scale nature (particle diameter under 10Pm),
there is no well established method to characterize the mechanical
behaviour of conductive particles. One of the feasible approaches to
determine the mechanical properties of single particles is to perform
inverse indentation test, Fig. 3 by using nanoindenter. To distinguish
with the common sense indentation where a rigid sphere is pressed
against a deformable half space, here the inverse indentation is meant
the opposite – contact of rigid flats against a deformable sphere. This
method is still under development. Similar methods for contact test of
larger scale spheres (about 300 Pm) can be found in [3].
It should be noted that significant amount of research has been carried
out recently in the research community on the indentation problem of a
half space by a rigid sphere or sharp tip. However, the inverse
indentation of a soft sphere with a rigid flat is different to the common
indentation problem. In the common indentation the indenter tip radius
remains constant while the curvature of the deformable sphere in the
inverse indentation is changing.
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II.
CLASSICAL HERTZ SOLUTION
Hertz’s solution considers the contact of two elastic spheres with
radii R1 and R2 in the absence of adhesion and friction. Define the
contact curvature 1/RC and elastic contact modulus KC as
1
1
1
(1)
R C R1 R 2
and
4 ª 1 Q12 1 Q 22 º
«
»
3 ¬« E1
E 2 ¼»
KC
Fig. 2. Different particle failure modes observed; a) cracking and delamination
of metal layer, b) fracture in polymer particle and c) complete disintegration.
The initial diameter of these particles are about 10µm. [Ref]
The paper is organized as follows. Section 2 describes the classical
Hertz solution. The finite element analysis and the new explicit large
contact deformation equation are reported in section 3. In section 3,
both spheres made of single material and two materials have been
studied. The inverse indentation test setup, application of the proposed
large deformation contact equation and elastic properties of the tested
polymer spheres are presented in section 4. The paper is concluded with
discussions and summary.
F
1
(2)
where E1 , Q1 and E 2 , Q 2 are the Young’s modulus and Poisson’s
ratio of sphere 1 and 2, respectively. By assuming that the contact area
is much smaller than the size of the spheres, Hertz theory provides the
following relation between the contact deformation h C h1 h 2 and
the contact force F,
1.5
F K C R 0.5
(3)
C hC
The Hertz’s solution states that the contact force is proportional to the
power 1.5 of the sphere deformation. For an elastic sphere and rigid flat
contact problem considered in this paper, Fig. 3, the contact modulus,
contact radius of curvature and contact deformation can be written as
4 E
KC K
and R C R , respectively.
3 1 Q2
Denote h C h1 h . Substitute these into (3), the Hertz contact
equation for the inverse indentation problem becomes
KR 0.5 h1.5
F
(4)
Equation (4) can be re-written as
3
F
SR 2
K § h ·2
S ¨© R ¸¹
(5)
or
VS
K
h
F
1
HS 1,5
S
(6)
where VS and HS are defined as sphere contact stress and strain.
It can be observed from (6) that Hertz theory states that the contact
stress in an elastic sphere is proportional to the power of 1.5 of the
sphere contact strain.
A number of modifications have been made to extend the Hertz
theory to large deformations. Yoffe [4] modified Hertz solution with a
first-order correction for the errors which are introduced when relatively
large contact areas are present. Later, by invoking a non-linear elastic
response Tatara [5] presented a large deformation formulation for
predicting the compressive behaviour of elastomeric spheres up to a
value of 60% deformation. However, Tatara’s theory is complicated
and does not present explicit solutions.
Fig. 3. Schematic plot of the large deformation contact problem between an
elastic sphere and rigid flat
0-7803-9085-7/05/$20.00 ©2005 IEEE
III.
FINITE ELEMENT ANALYSIS
The success of Hertz theory has been well established. However, the
limitation of the Hertz theory to the inverse indentation is not clearly
understood. In the following large deformation finite element analyses
has been carried out to study the mechanical behaviour of single
polymer particles. Sphere made of a single material is studied. The
effect of elastic coating properties on the indentation curve has also
studied by using a bi-material sphere model. ABAQUS was used to
study the inverse indentation problem. The finite element mesh used in
the analyses is shown in Fig. 4. ¼ of the sphere has been modelled. The
model consists of about 3700 4-node axisymmetric elements and 4000
nodes. A convergence study has been performed to ensure that the
mesh applied is sufficiently accurate. Very fine mesh was used in the
contact region. The mesh has also been deigned in such a way that the
same model can be applied to study the coating effect. The minimum
element size in the model is about 0.1% of the initial sphere radius.
VS
K
1
HS 1,519
2, 6
(7)
for sphere strain HS ” 10%. It can be seen from (7) that for large
deformation contact the contact force is proportional to the power of
about 1.52 of the sphere strain. Note that this is on the similar form as
the Hertz equation.
For even larger contact deformation (10% < HS ” 35%), the above
equation is not accurate and following equation can be used to describe
the contact force and sphere strain relation:
VS
K
0.0667HS 0.5105HS2 0.5724HS3
(8)
Once an experimental inverse indentation curve is obtained, (7)-(8)
can be applied to determine the contact modulus K by dividing the
contact stress by the power equation or the polynomial equation.
0,0003
FEM
Hertz
Shpere stress/K
A. Sphere of homogenous material
Fig. 5a compares the finite element results with the Hertz solution.
The contact stress has been normalized by the contact modulus K. Fig.
5a shows a very good agreement between the finite element results and
the Hertz solution when the sphere strain is small. Depending on the
accuracy requirement apparent deviation from the Hertz solution occurs
when the sphere deformation is larger than, for example 1%. It can be
seen from Fig. 5b that the Hertz solution underestimates the sphere
contact stress more than 40% when the sphere strain has reached 35%.
It must be noted that the finite element solution presented in Fig. 5b
is universal as long as the material behaves linear elastically. The finite
element solution can be fitted by the following power law equation
0,0002
0,0001
0,0000
0
0,002
0,004
0,006
0,008
0,01
Sphere strain
0,12
FEM
Shpere stress/K
0,10
Hertz
0,08
0,06
0,04
0,02
0,00
0
0,05
0,1
0,15
0,2
0,25
0,3
0,35
Sphere strain
Fig. 4 Finite element mesh (1/4 model) used for the analyses. The model consists of
about 4000 nodes and 3700 elements.
Fig. 5 Comparison of the Hertz solution and the finite element solution for small and
larger deformation. Respectively.
0-7803-9085-7/05/$20.00 ©2005 IEEE
EXPERIMENTAL STUDIES
An experimental setup has been developed [7] to perform the
inverse indentation test, Fig. 6. Two double side polished silicon
chips were taken as the rigid flat. One side of the opposing chips
was coated with aluminium, while the other side was oxidised.
The distance between the two silicon chips was measured by
measuring the capacitance between them by an LCR meter. The
use of silicon as sample holders was beneficial for several
reasons. The chips were cut from a low resistivity wafer, which
means that the electrical impedance through the chip is
controlled by the resistivity at the test frequency of 100 kHz.
The silicon oxide layer on the other hand which is of the order
of 0.5 mm thick electrically insulates the particles from the
electrodes. The polished silicon surface is very flat, and makes a
near ideal surface for the small spheres. The high E-modulus
and hardness means that the surface undergoes only negligible
deformations compared to the polymer particles during the test.
A controlled compressive force is obtained by mounting the
lower chip onto an electromagnetic device, where a current was
used to control the force. A number of particles with a truly
uniform size distribution are tested in parallel. The force per particle
was obtained by didiving the total force by the number of particles.
Two types of metal-coated polymer particles, A and B have been
tested. Both particles have same diameter 10 Pm but differ in elastic
properties. Particle A has been tested to about 7% deformation while
particle B was tested up to about 20% deformation. Fig. 7 compares the
experimental sphere stress versus strain results with the finite element
solution Eq. (7) using an average effective contact modulus. It is
interesting to note that the obtained contact modulus appears to
be independent of the sphere deformation up to 7%. The average
measured contact modulus is 1175 MPa.
10
EXP
8
Sphere stress [MPa]
IV
Eq.(7)
6
4
2
0
0,00
0,02
0,04
0,06
0,08
Sphe re s train
Fig. 7 Mechanical properties of particle type A: a) indentation curves
The results of large deformation contact of particle B are
shown in Fig. 8. The deformation range of particle B is about
three times that of particle A. The minimum contact modulus,
1380 MPa appeared at a sphere deformation about 3% while the
maximum contact modulus, 1948 MPa occurred at 15%
deformation. The average contact modulus is 1731 MPa.
V
DISCUSSIONS AND CONCLUDING REMARKS
Mechanical properties of conductive particles are an important
part of the ACA technology. In order to provide reliable data for
design and reliability assessment of packaging it is essential to
develop complete understanding of their failure mechanisms and
methodology to characterize their mechanical behavior. In this
study a so-called inverse indentation method has been
introduced to characterize the elastic properties of micron sized
polymer particles.
70
Sphere stress [MPa]
60
Exp
(8)
Eq. (9)
50
40
C
30
20
10
0
0,00
0,05
0,10
0,15
Sphere strain
0,20
0,25
Fig. 6. Experimental setup for testing the mechanical properties of polymer particles.
Fig. 8. Indentation curves showing mechanical properties of particle type B
0-7803-9085-7/05/$20.00 ©2005 IEEE
Finite element analysis of large deformation contact shows
Hertz solution works only in a small deformation range (less
1%). An approximate but universal sphere stress versus sphere
strain equation has been proposed. With the proposed sphere
stress-strain relation, the elastic contact modulus can be
estimated from the experimental inverse indentation results. It is
an open question whether linear elasticity exists in large
deformation contact of polymer spheres. The present
investigation indicates that estimated elastic contact modulus is
relatively constant.
The experimental work has shown clear indications of
hysteresis during loading and de-loading of the particles. It is at
the moment not clear whether this is cased by material
properties or interfacial forces. The experimental work will also
include new measurements with more advanced instruments.
Further FEM work will include adhesion forces between particle
and indenter as well as non elastic material properties.
REFERENCES
[1] Kristiansen, H, et al, “Electrical and Mechanical Properties
of Metal-coated Polymer Spheres for Anisotropic
Conductive Adhesive”, Proc, PEP 99; Gothenburg Oct.
99, pp 63 – 71
[2] Kristiansen, H, et al, “Characterisation of Electrical and
Mechanical Properties of Metal-coated Polymer Spheres
for Anisotropic Conductive Adhesive”, Proc, IMAPS
Nordic 04; Helsingør Oct. 99, pp 63 – 71
[3] K K Liu et al, “The large deformation of a single microelastiomeric sphere”, 1998 J. Phys. D: Appl. Phys. 31 294303.
[4] E. H. Yoffe, “Modified hertz theory for spherical
indentation”, Philosophical Magazine A: Physics of
Condensed Matter, Defects and Mechanical Properties, 50,
n 6, Dec, 1984, p 813-828.
[5] Y. Tatara , S. Shima and J. C. Lucero, J. Engng Mater
Tech. ASME 1991, 113, 292-295.
[6] H. D. Espinosa, B. C. Prorok, Size effects on the
mechanical behaviour of gold thin films, Journal of
Materials Science 38 (2003) 4125 – 4128.
[7] Kristiansen, H, Liu, J, “Behaviour and Properties of
Conductive Particles in Anisotropic Conductive
Adhesive”, High Density Electronics Packaging 2002,
Shanghai, July 2002
0-7803-9085-7/05/$20.00 ©2005 IEEE