assessing central cracks and interconnect reliability in ... · pdf filelinear elastic...

International Journal of Engineering & Technology IJET-IJENS Vol:14 No:02 24

142502-6868-IJET-IJENS © April 2014 IJENS I J E N S

Abstract— one of the most common forms of failures

observed in brittle thin films subjected to stress is cracking. The

crack growth rate depends on intrinsic film properties, stress and

some environmental factors. we investigate central crack on

different material planes. The planes are made from silicon,

copper, aluminum, polyamide and silicon nitride. Each plane is

1.0m x 0.4m and has a crack length of 0.04m. Because of

symmetry only 0.5m and o.2m of the plate is used. They are

subjected to a normal stress of 100MPa. A two dimensional (2D)

Finite Element Analysis (FEA) model is developed and ANSYS

software is used to calculate the MODE I Stress Intensity Factor

(SIF) on each material plane. Silicon had a SIF of 21.562,

aluminum 23.838, copper 23.383, polyamide 24.948 and silicon

nitride 22.371. From the results, silicon had the lowest MODE I

SIF while polyamide had the highest.

Index Term— ANSYS, Flipchip, Interconnect, Stress

Intensity Factor (SIF)

I. INTRODUCTION

Multi silicon dies stack is required for higher performance,

greater package miniaturization and more functionality

electronic device. Silicon passivation cracking and

interconnect metal thin film cracking are organic packaging

failure modes which occur due to global thermal expansion

mismatch between the package and the silicon and also local

thermal expansion mismatch among interconnect metals and

passivation materials .Experimental data have shown that

some properties have to be considered before designing an IC

to minimize the risks encountered due to thermal mismatch.

Some of these properties include: the size of the chip, the

(Interlayer Dielectric) ILD material and also the number of die

layers. We used ANSYS 14.0 to analyze MODE I SIF on the

different materials used.

II. LINEAR ELASTIC STRESS ANALYSIS OF 2D CRACKS

Homogeneous and isotropic materials with cracks have

stress surrounding the crack tip analyzed assuming linear

elastic material behavior. Linear Elastic Fracture Mechanics

(LEFM) method assumes the plastic region near crack tip is

much smaller than the dimensions of the crack and the

structural member. This is a very important concept, scientists

and engineers call it small-scale yielding [1], since it

simplifies stress analysis near the tip. Assuming the geometry

has very small displacement and the material is elastic,

homogeneous and isotropic. The governing equations for

linear elastic analysis in 2-D are:

The strain-displacement relationships:

(1)

(2)

*

+

(3)

The stress-strain relationships:

For plane strain, where

( )( )[( ) ]

(4)

( )( )[( ) ] (5)

(6)

( )

(7)

For plane stress, where

[ ]

(8)

[ ]

(9)

(10)

( )

(11)

Assessing Central Cracks and Interconnect

Reliability in Flipchips

Juma Mary Atieno, Zhang Xuliang



The equilibrium equations:

(12)

(13)

The compatibility equation:

*

+ ( )

(14)

The Airy stress function, Φ, can satisfy all the governing

equations and is used to derive the stress field near the crack

tip.

√ ⁄ (

)

(15)

(16)

Solving Eq. (16) yields the stress fields for Mode I as:

√

*

+

(17)

√

*

+

(18)

√

(19)

( )

(20)

(21)

The displacement fields are:

√

*

+

(22)

√

*

+

(23)

(24)

The coordinates (r, θ) for the stress components are shown

in Fig. 1.

Fig. 1 Coordinate systems for the stress components [1].

III. CALCULATION OF STRESS INTENSITY FACTORS (SIF)

USING THE FINITE ELEMENT METHOD

Several publications have discussed the stress intensity

factor and methods involved in its calculation. Enough

literature exists addressing the analysis procedure for

structures made of composites [2]. In unidirectional fiber

composites, the behavior of cracks aligned along the fiber is

well characterized by the SIF [3]. Different experimental

techniques have been used in the past to determine the SIF for

cracks in composites by various researchers. Singular stress

field in the neighborhood of the periphery of an annular crack

was studied by Gdoutos et al. [4]. The case of fiber debonding

originating from the annular crack was also considered. In the

study, they calculated KI and KII stress intensity factors and

energy release rates. The energy release rate was derived by

Liu and Kagawa [5] for an interfacial debonding of a crack in

a ceramic-matrix composite and they used the Lame solution

for an axisymmetric cylindrical fiber/matrix model. A

numerical solution was carried out for the problem of interface

crack by Aslantas and Tasgetiren [6]. Variations in the stress

intensity factors KI and KII, with load position were obtained

for various cases such as different combinations of material of

coating layer and substrate, changes in the coefficient of

friction on the surface. Xia et al. [7] analyzed fatigue crack

initiation in SiC fiber (SCS-6) reinforced titanium on the basis

of a finite element model. Their results showed that the

formation of matrix crack largely depends on the applied

stress and reaction layer thickness. A new method that obtains

the complex stress intensity factor was presented by Bjerken

and Persson, [8] for an interface crack in a bimaterial using a

minimum number of computations. Dirikolu and Aktas [9]

carried out a comparative study regarding the determination of

stress intensity factors for nonstandard thin composite plates.

Carbon-epoxy composite plates were also considered for the

study.

Various methods have been used for the determination of

stress intensity factors [10], [11], [12], [13] and [14].One of

these methods is a numerical method like Green's function,

weight functions, boundary collocation, alternating method,

integral transforms, continuous dislocations and finite



elements methods. In this paper, we used the finite elements

method to calculate the KI of five different materials used in

flipchip packaging.

TABLE 1

MATERIALS PROPERTIES

Material Young Modulus

(GPa)

Poisson’s Ratio

Silicon 150 0.17

Aluminum 70 0.33

Copper 110 0.33

Silicon nitride 166 0.23

Polyamide 2.1 0.4

IV. RESULTS AND DISCUSSION

Based on the above materials properties, we give the

simulation results and discussions obtained from ANSYS

GUI.

Silicon elements distribution along the cracks on silicon plate

Fig. 2 Silicon elements

Elements, nodes, keypoints and areas used in cracked silicon plate simulation

Fig. 3 Silicon output window

MODE I, II and III SIFs values along the crack on silicon plate

Fig. 4 Stress intensity factor in silicon

Aluminum elements distribution along the cracks on aluminum plate

Fig. 5 Aluminum elements

Elements, nodes, keypoints and areas used in cracked aluminum plate

simulation

Fig. 6 Aluminum output window

MODE I, II and III SIFs values along the crack on aluminum plate



Fig. 7 Mode I SIF of Aluminum

Elements number and distribution on cracked polyamide plate

Fig. 8 Elements in polyamide

Number of elements, nodes, lines and areas used in the cracked polyamide simulation

Fig. 9 Output window for polyamide

MODE I, II and III SIFs values along the crack on polyamide plate

Fig. 10 Mode I SIF for polyamide

Elements number and distribution on cracked copper plate

Fig. 11 Elements in copper crack region

Number of elements, nodes, lines and areas used in the cracked copper

simulation

Fig. 12 Output window of cracked copper

MODE I, II and III SIFs values along the crack on copper plate



Fig. 13 Mode I SIF of copper

Elements number and distribution on cracked silicon nitride

Fig. 14 Elements in cracked silicon nitride

Number of elements, nodes, lines and areas used in the simulation

Fig. 15 Output window of cracked silicon nitride

MODE I, II and III SIFs values along the crack on silicon nitride plate

Fig. 16 Mode I SIF of cracked silicon nitride

The results and discussions of each material type we used in

the simulation of the central holes in silicon, copper,

aluminum, polyamide and silicon nitride are discussed in

details.

The output windows were of real relevance to us since they

showed the specifications we put in the system for the analysis

to take place. In this paper, we used 94 elements, 95 nodes, 5

keypoints, 5 lines and 1 area. We only used a single area

which was rectangular and because of symmetry, we used

only half of the area for simulation. The numbers of nodes

used as shown by the output windows for each material are the

same. This is because we used the same plate size with the

same crack position and length.

We used KCALC command to get the mode I SIFs of each

material used. Only one specific value of SIF for each material

is given. Since our focus for this paper was mode I SIF, the

mode II and III SIFs for each material used is noted to be zero.

This is clearly shown by the KCALC diagrams for each

material used. Silicon material had the lowest MODE I SIF of

21.562 while polyamide which is a dielectric material had the

highest MODE I SIF of 24.948. We noted that copper and

aluminum had the same values of MODE I SIF of 23.838

each. Silicon nitride had a MODE I SIF of 22.371. In general,

the MODE I SIFs of the materials we used ranged from 21 to

25.

V. CONCLUSION AND RECOMMENDATIONS

In this project, we investigated cracks in flipchip package

using different materials namely silicon, aluminum, copper,

polyamide and silicon nitride using ANSYS release 14 and 2D

FEA model. The first step involved the design of the

rectangular plate with a central crack on each material plate.

We used material plates of sizes 1.0m by 0.4m. The crack

length on each plate was 0.04m. Because of symmetry, only

half the plate was relevant for simulation. GUI then did the

simulation of the different plate materials based on the

materials properties such as Poisson’s ratio and young’s

modulus. The output window showed the total number of

nodes used in the simulation. In this paper, a total of 95 nodes

were used on each material to mesh 94 elements. It is evident

that the nodes number is higher than the elements number

because the nodes are the ones which join to give the elements

so the elements number cannot be higher than that of nodes.



We performed the elastic stress analysis using the KCALC

command. We observed that different materials used had

different MODE I SIFs. Silicon material had the lowest

MODE I SIF of 21.562 while polyamide which is a dielectric

material had the highest MODE I SIF of 24.948. We noted

that copper and aluminum had the same values of MODE I

SIF of 23.838 each. In general, the MODE I SIFs of the

materials used ranged from 21 to 25. The table below

summarizes the MODE I SIFs of the five materials we used in

this project.

TABLE II

Summary of results for all the materials used in the project

Material Young’s Modulus (GPa)

Poisson’s ratio MODE I SIF

Silicon 150 0.17 21.562

Aluminum 70 0.33 23.838

Copper 110 0.33 23.838

Polyamide 2.1 0.4 24.948

Silicon nitride 166 0.23 22.371

The recommendations we made on this project include:

Copper and aluminum can be used interchangeably

where mechanical strength is concerned since they have

the same MODE I SIF.

Silicon is the best material as per this project to be used

as a chip in flipchip ball grid arrays since it has the

lowest SIF.

When dielectric materials are selected for use, Silicon

nitride should be considered more than polyamide since

it has a lower MODE I SIF.

MODE I SIF can be used to categorize materials

according to their mechanical strength. Those with

lower SIFs can be considered stronger than those with

higher SIFs.

With more material properties integrated, more precise

results will be achieved and other parameters apart from

stress and deformations. These approaches will help

curb cracking problem in chips therefore making

electronic devices more reliable in the market. The

electronic devices can also be used for a longer period

of time and the problem of repair will be solved.

APPENDIX

List of symbols

E = Modulus of Elasticity (GPa)

v = Poisson’s Ratio (-)

ε = Strain (-)

u = Displacement (mm)

σ = Normal Stress (GPa)

τ = Shear Stress (GPa)

G = Shear Modulus (GPa)

Φ = Airy Stress Function (kN)

K = Stress Intensity Factor (GPa √ )

a = crack length (mm)

P = geometrical parameter depends on structural member and

crack

@ = at

Step by step inputs in cracked polyamide plate simulation

Fig. 17. ANSYS central crack Input File for polyamide

Step by step inputs in cracked silicon nitride plate simulation

Fig. 18. ANSYS central crack Input File for silicon nitride



Step by step inputs in cracked silicon plate simulation

Fig. 19. ANSYS Silicon central hole input file

Step by step inputs in cracked aluminum plate simulation

Fig. 20. ANSYS Aluminum central hole input file

Step by step inputs in cracked copper plate simulation

Fig. 21. ANSYS Copper central hole input file

ACKNOWLEDGMENT

These lines I want to dedicate for giving my thanks to all

people without who this paper would have not been possible. I

want to thank my advisor, doctor Zhang Xuliang, first for

believing in me and for giving me the opportunity to work

with him on this paper, and then for being a great help during

my work, with his constant patience, useful advices and

suggestions. I am especially grateful to him for his great

personality regarding giving me professionally honest and

timely feedback to the very last day of my work. I will always

remember him .My regards also go to other lecturers in our lab

since they were of great help too by giving their contributions

towards the work. My thanks also go to my friends especially

those in the same lab who, during the rough moments like

software installation, cheered me up and gave me the strength

to go on.

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Control in Structures: Application of Fracture Mechanics, Philadelphia, 1999.

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Performance of Fiber Composites. John Wiley and Sons. New

Jersey.

[3] Anderson, T. L. 1995. Fracture Mechanics-Fundamentals and Applications. CRC Press. Boca Ralton.

[4] Gdoutos, E.E., Giannakopoulou, A., Zacharopoulos, D.A., 1999.

Stress and failure analysis of brittle matrix composites. Part II: Failure analysis. International Journal of Fracture 98. 279-291.

[5] Liu, Y.F., Kagawa, Y., 2000. The energy release rate for an

interfacial debond crack in a fiber pull-out model. Composites Science and Technology 60 (2). 167–171.

[6] Aslantas_, K., Tas_getiren, S., 2002. Debonding between coating

and substrate due to rolling sliding contact. Materials and Design 43. 871–876.

[7] Xia, Z.H., Peters, P.W.M., Dudek, H.J., 2000. Finite element

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titanium alloys. Composites Part A: Applied Science and

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stress intensity factors for interface cracks in bimaterials.

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[14] Majid Mirzaei, Fracture Mechanics: Theory and Applications. Dept. of Mechanical Eng.. TMU.

http://www.modares.ac.ir/eng/mmirzaei.

http://www.modares.ac.ir/eng/mmirzaei.

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