EFFECT OF INTEGRATED CIRCUIT CHIP GEOMETRY ANGLE ON
THERMAL STRESSES IN A PRINTED CIRCUIT BOARD
by
Amir Roomi
B.S.M.E., University of Engineering at BaghdadIraq, 1985
A.A.S., Red Rocks Community College at LakewoodColorado, 1997
A thesis submitted to the
University of Colorado at Denver
in partial fulfillment
of the requirements for the degree of
Master of Science
Mechanical Engineering
This thesis for the Master of Science
Degree by
Amir Roomi
has been approved
by
James C. Gerdeen
Date
Roomi, Amir (M.S., Mechanical Engineering)
Effect of Integrated Circuit Chip Geometry Angle on Thermal Stresses in
a Printed Circuit Board
Thesis directed by Professor James C. Gerdeen
ABSTRACT
This masters thesis contains preliminary studies of stress analysis in a
model that simulates an integrated circuit (IC) chip mounted onto a
printed circuit board (PCB). These studies are particularly useful for
considering the thermal stress effects in establishing design criteria of an
electronic circuit board and the meaning of these criteria to the
performance of the electronic circuit board.
The objective of this problem is to determine the change in temperature
(AT) that causes the proposed structures to shear off and the potential
impact of the strip geometry angle on inducing stresses at the strip
corners. In addition, to predict the maximum shear stresses of these
structures while they are subjected to a temperature increase and to
study the mechanical behavior of each strip structure. This study thereby
provides the ability to ameliorate the stress concentration and singularity
problem in the electronic circuit board design and manufacturing
industry.
in
The proposed model that simulates this problem consists of two strips, the
bottom strip is made from high carbon air hardening steel A2 and the top
strip is made from aluminum 6061. These two strips are bonded together
using a high thermal expansion epoxy. The following methods are used to
the achieve the objective of this study:
1. ClosedForm Approach.
2. Experimental Approach.
3. Finite Element Analysis using ProMechanica Structure Software
Approach.
The results of this study show the effect of the integrated circuit (IC) chip
geometry on the stress concentration of the printed circuit board (PCB)
due to the singularities at the chip corners.
The temperature difference between the integrated circuit (IC) chip and
the printed circuit board needs to be held below a certain threshold in
order to reduce the stresses and strains on the solder joint between the
chip and the board.
This abstract accurately represents the content of the candidates thesis. I
recommend its publication.
Signed _____
James C. Gerdeen
IV
DEDICATION
I dedicate this masters thesis to my mother for her unlimited love,
understanding support, and prayers during this long journey.
ACKNOWLEDGEMENT
I wish to thank the faculty of the Mechanical Engineering Department at
the University of Colorado at Denver for their patience, understanding,
and contributions that made this thesis possible. Special thanks are to go
to my advisor, Professor James C. Gerdeen for his contribution, directing,
advising, and technical support as I am so grateful for his knowledge and
offering encouragement to ensure this masters thesis is accomplished
accurately.
I would like to thank Professor John Trapp and Associate Professor
Samuel Welch for their contributions, advising and comments to achieve
this thesis.
Also I would like to thank Paul Miller for his effort in manufacturing the
required samples needed for the experimental approach of this study.
In addition, I would like to thank GAMBRO BCT for allowing me to use
their lab equipment and test devises in order to achieve the objective of
this study and for their support and ongoing encouragement to pursue a
graduate degree.
CONTENTS
Figures..........................................................x
Tables.........................................................xiv
Introduction....................................................xv
Chapter
1. Surface Mount Circuit Board Technology and Design............1
1.1 Explanation of Surface Mount Technology (SMT)................1
1.2 Active Surface Mount Components Integrated Circuit (IC)....1
1.3 Leaded Integrated Circuits Package Design....................1
1.4 Printed Circuit Board SMT Design Guidelines..................3
1.5 Substrate Materials..........................................4
2. Thermal Stresses in Printed Circuit Board  Previous Research.6
2.1 Objectives of Thermal Design.................................6
2.2 Factors Controlling Stress in a Chip Mounted on a Substrate...9
2.3 Modeling Stresses in a Chip Mounted on a Substrate...........9
2.4 Modeling Delamination in a Chip Mounted on a Substrate.....10
vii
2.5 Stress Modeling
11
2.6 Delamination Modeling......................................12
3. Mechanical Behavior of Strip Structure Made From Aluminum
and Steel..................................................14
3.1 Problem Description........................................14
3.2 Predicting the Mechanical Behavior of Metal Strip Structure
With Dissimilar Coefficient of Thermal Expansion...........14
3.3 Problem Approaches....................................... 18
3.3.1 Theoretical Approach Closed Form Solution..............18
3.3.2 Experimental Approach Thermal Cycling Solution.........29
3.3.3 Finite Element Approach Pro/Mechanica Solution.........32
4. Results and Discussion.....................................41
4.1 Theoretical Approach Closed Form Solution................41
4.2 Experimental Approach Thermal Cycling Solution...........42
4.3 Finite Element Approach Pro/Mechanica Solution...........46
viii
5. Summary and Conclusions
77
6. Recommendations
79
6.1 Mathematical Model.......................................79
6.2 Metal Structure Materials................................79
6.3 Metal Structure Design................................. 79
6.4 Thermal Epoxy Layer.................................... 79
Appendix.....................................................81
A. Metal Structures Engineering Drawings....................81
B. Finite Element Analysis Pro/Mechanica Software Results.95
Glossary....................................................119
References.....................................................121
IX
FIGURES
Figure
1.1 Manufacturable Package and Lead Design for SMDs [3].........2
1.2 Insufficient Joint Compliancy During Power Cycling Causing
Joint Cracking Between the Device and Epoxy Substrate [3]..4
2.1 Side View of Integrated Circuit Chip Assembly [4]...........10
2.2 32Node Three Dimensional Crack Tip Element [4].............10
2.3 Computed Displacements in Xdirection as a Function of the
Distance From the Package Centerline [4]...................11
2.4 Computed Displacements in Ydirection as a Function of the
Distance From the Package Centerline [4]...................12
2.5 Mixed Mode Stress Intensity Factors for a= 2.54 mm Crack [4] ...13
2.6 cjyy Stress Distribution and Deformed Configuration [4].....13
3.1 Physical Metal Structures Modeled: Aluminum 6061 on High
Carbon Air Hardened Steel A2...............................15
3.2 Thermal Expansions of Super Conducting Ceramics [1].........16
3.3 BiMetal Model With Two Layers..............................19
3.4 Normal and Shear Stresses in a BiMetal Model...............20
3.5 Distribution of Stresses [5]................................20
3.6 Instron Test Specimen.......................................25
3.7 Instron Tester.............................................26
3.8 Total Load Determined Using Instron Tester..............27
3.9 BiMetal Structures........................................30
3.10 Optical Measurement Inspection System.....................32
3.11 Constraints of BiMetal Structure With 30 Geometry Angle... .35
3.12 Constraints of BiMetal Structure With 45 Geometry Angle.36
3.13 Constraints of BiMetal Structure With 90 Geometry Angle.37
3.14 Constraints of Instron Specimen Structure.................40
4.1 Stress Crack at the Aluminum Upper Strip Corner for 30
Geometry Angle Occurred at 130 F......................43
4.2 Stress Crack at the Aluminum Upper Strip Corner for 45
Geometry Angle Occurred at 160 F.........................44
4.3 Stress Crack at the Aluminum Upper Strip Corner for 90
Geometry Angle Occurred at 130 F......................45
4.4 Fringe Plot for 30 Geometry Angle Showing the Maximum
Shear Stress............................................ 48
4.5 Contour Plot for 30 Geometry Angle Showing the Maximum
Shear Stress..............................................49
4.6 Fringe Plot for 45 Geometry Angle Showing the Maximum
Shear Stress..............................................51
4.7 Contour Plot for 45 Geometry Angle Showing the Maximum
Shear Stress..............................................52
XI
4.8 Fringe Plot for 90 Geometry Angle Showing the Maximum
Shear Stress...........................................53
4.9 Contour Plot for 90 Geometry Angle Showing the Maximum
Shear Stress...........................................54
4.10 Fringe Plot for Instron Metal Structure Showing the
Maximum Shear Stress..................................55
4.11 Contour Plot for Instron Metal Structure Showing the
Maximum Shear Stress..................................56
4.12 Maximum Shear Stress at the Curve Arc Length for 30
Geometry Angle Metal Structure........................58
4.13 Maximum Shear Stress at the Curve Arc Length for 45
Geometry Angle Metal Structure........................59
4.14 Maximum Shear Stress at the Curve Arc Length for 90
Geometry Angle Metal Structure........................60
4.15 Maximum Shear Stress at the Curve Arc Length for Instron
Metal Structure.......................................61
4.16 Maximum Stress xy Versus the P Loop Pass for 30 Geometry
Angle Metal Structure.................................63
4.17 Maximum Stress xy Versus the P Loop Pass for 45 Geometry
Angle Metal Structure.................................64
4.18 Maximum Stress xy Versus the P Loop Pass for 90 Geometry
Angle Metal Structure.................................65
4.19 Maximum Stress xy Versus the P Loop Pass for Instron Metal
Structure.............................................66
xii
4.20 Maximum Stress yz Versus the P Loop Pass for 30 Geometry
Angle Metal Structure...................................68
4.21 Maximum Stress yz Versus the P Loop Pass for 45 Geometry
Angle Metal Structure...................................69
4.22 Maximum Stress yz Versus the P Loop Pass for 90 Geometry
Angle Metal Structure...................................70
4.23 Maximum Stress yz Versus the P Loop Pass for Instron Metal
Structure...............................................71
4.24 Strain Energy Versus the P Loop Pass for 30 Geometry Angle
Metal Structure.........................................73
4.25 Strain Energy Versus the P Loop Pass for 45 Geometry Angle
Metal Structure.........................................74
4.26 Strain Energy Versus the P Loop Pass for 90 Geometry Angle
Metal Structure........................................ 75
4.27 Strain Energy Versus the P Loop Pass for Instron Metal
Structure...............................................76
xiii
TABLES
Table
1.1 Various Substrate Materials and Their Physical
Characteristics [3] .........................................5
3.1 Material Properties of Aluminum and Steel....................17
4.1 Theoretical Approach Results.................................41
4.2 Experimental Approach Results................................42
4.3 Finite Element Approach Results..............................46
XIV
INTRODUCTION
Recently, surface mount technology (SMT) has become the most favored
technology in the electronic packaging industry. Reasons for preferring
the use of this technology over the use of the throughhole technology are
that surface mount technology allows the use of smaller components
soldered directly to the pads on the printed wiring board (PWB). Also, the
components can be mounted on both sides of the board due to the lack of
the holes on the board.
The thermal stresses are considered vital for electronic packaging designs
and analyses. Most of the materials expand when they are subjected to a
temperature increase and contract when they are subjected to a
temperature drop. The deformation caused by expansion or contraction
due to temperature change in the absence of mechanical loads is called
thermal strain. For a small temperature change, the strain has a
proportional relationship with the temperature change. This
proportionality is expressed by the coefficient of thermal expansion (CTE),
which is defined as the change in length, per unit of length per one degree
of Fahrenheit change in temperature.
A structure made of more than one material and uniformly heated with no
external constraints will experience thermal stresses due to the different
coefficients of thermal expansion and mechanical properties for its
materials.
XV
The electronic package assembly is a typical example of a structure that
consists of different materials and is subjected to thermal loading. Due to
the electronic component, i.e integrated circuit (IC) chip geometry angle,
material mechanical properties, and thermal expansion mismatch,
thermal stresses can be induced inside the electronic package during the
manufacturing process and while it is being used in the field.
The determination of thermal stresses in electronic packaging is not an
easy task.
A closedform solution of a simple structure that has simple geometry
with a temperature loading is very useful for research purposes, but is
very limited in applications and difficult to obtain. A finite element
solution is one of the most accurate methods for obtaining approximate
results for the thermal stresses and strains in electronic packages.
In this study, the thermomechanical stresses are mainly caused by a
large coefficient of thermal expansion (CTE) mismatch between the upper
strip of the study model that represent the integrated circuit (IC) chip and
the lower strip that represent.the substrate in the electronic package.
The delamination of the underfill and solder joint cracking are considered
one of the most typical failures in the electronic packaging industry.
The objective of this study is to examine the interrelationship between the
various geometry angles of an integrated circuit (IC) chip mounted, on a
printed wiring board (PWB) and predict the geometry angles potential
impact on the underfill and the solder joint crack due to the induced
stresses and singularities at the integrated circuit (IC) chip corners. In
XVI
addition, this study serves to determine where these stresses are
concentrated using three different methods of prediction.
XVII
1. Surface Mount Circuit Board Technology
and Design
1.1 Explanation of Surface Mount Technology
(SMT)
Circuit board assemblies manufactured using the surface mount
technology are those that are built with surface mount components. These
components are defined as any devices, leaded or unleaded mounted on
one or both sides of a substrate and interconnected to the substrate via a
lap solder joint.
1.2 Active Surface Mount Components 
Integrated Circuit (IC)
Surface mount integrated circuit (IC) chip components are described as an
active devices come in a variety of electronic package designs, materials in
two different configurations, leaded or unleaded. The selection of a
specific electronic package design can significantly affect the reliability of
the assembly.
1.3 Leaded Integrated Circuits Package
Design
The construction of integrated circuit (IC) chip lead design is considered
one of the major concerns in the electronic package design. As the
package size or lead count increases, the compliance of the package must
also increase in order for it to overcome CTE mismatch, wrap and twist of
the substrate, and vibration stresses. A lead design which has worked
1
well for both the component and assembly manufacturer is illustrated in
Figure 1.1.
Upon review of this lead design, the length from the lead of the body to
the first lead bond I 0.053 in. This allows for added compliancy and an
adequate clearance for lead forming.
Figure 1.1 Manufacturable Package and Lead Design for SMDs [3]
In this case, the dimension 0.076 in. body height from the substrate
surface allows a lid clearance of 0.026 in., which is considered a maximum
to a 0.015 in. clearance, which is the minimum. This is based on
cleanliness and vibration concerns.
That is, a body surface closer than 0.015 in to the substrate surface would
impose cleaning difficulties, and a body surface greater than 0.026 in.
would impose vibration and lead damage concerns. The leads foot length
of 0.050 in. provides sufficient length for reflow tooling, leadtopad
pattern recognition, and a strong lap joint (Carmen Capilo, Surface
Mount Technology, Material, Processes and Equipment, April 01, 2003,
2
This material is reproduced with permission of the McGraw Hill
companies).
The lead angle of 11 is required for stress concentration and singularity
reduction at the solder joint
1.4 Printed Circuit Board SMT Design
Guidelines
Leads are acting as the compliant member for the leaded type of surface
mount devices (SMDs) since they allow expansion differences between
the component and the substrate. These differences are caused by
variations in the coefficient of thermal expansion (CTE) and in the
temperature due to the energy dissipation occurs within the device.
In case of using unleaded surface mount devices (SMDs), the device is
directly soldered to the substrate surface and therefore, the solder joint
here is considered the compliant member.
This solder joint receives the stresses resulting from the differential
movement of the devices body and the substrate material. The solder joint
may receive stresses that are sufficient to result in a joint stress crack due
to the mechanical properties of the solder used in the soldering operation.
This type of solder joint stress crack induced by power cycling of the
electronic package assembly as shown in Figure 1.2.
This solder joint crack will not be discovered until field usage of the
electronic package assembly for a period of time and when the solder joint
starts to be weakened to the point where the crack forms, leading to
fatigue and failure.
The component surface area is considered one of the most important
factors in this subject. Stresses due to the component and substrate
3
I
I
Figure 1.2 Insufficient Joint Compliancy During Power Cycling Causing Joint
Cracking Between the Device and Epoxy Substrate [3]
coefficient of thermal expansion (CTE) differences are small if the
components surface area is small. This fact explains why small surface
mounts on epoxy substrate do not result in enough stresses for solder
joints to crack.
1.5 Substrate Materials
Due to the large differences between the coefficient of thermal expansion
(CTE) of the integrated circuit chip and the substrate that is mounted on,
solder joint cracking would easily occur under thermal conditions. In
order to overcome this reliability issue when mounting the chip onto
epoxy laminates, suitable substrate materials selection have been
developed and evaluated as shown in table 1.1.
4
Substrate material Glass transi tion temper ature TC Coeffi cient of thermal expan sion (CTE), ppmTC Lateral thermal conductiv ity, Btu/h ft F XY tensile mod ules, psi x 106 Mois ture absorp tion, % by weight
G10 epoxy fiber glass 125 1418 0.2 2.5 0.10
G30 polyimide fiberglass 250 1216 0.2 2.8 0.35
Epoxy Kevlar 125 68 0.13 4.4 0.85
Polyimide Kevlar 250 58 4.0 1.50
99.5% BeO 57 120 44.0 '
Table 1.1 Various Substrate Materials and Their Physical Characteristics [3]
5
2. Thermal Stresses in Printed Circuit Board 
Previous Research
2.1 Objectives of Thermal Design
The criteria for thermal design of electronic equipment are given in
terms of the upper bound for the junction temperature. (Tj) and that for
the variation of junction temperature in the equipment (ATj).
There have been widely held notions about what these indexes mean to
the reliability and performance of the equipment. They are enumerated as
follows, together with cautionary comments.
1. As Tj is lowered, corrosive reactions of impurity elements that attack
electronic devices and wires on the chip are deterred. Namely, the cooler
the equipment is held, the longer the equipment survives.
Based on this notion, Tj is defined at low levels for expensive large
systems, for instance, in a 55 to 60 C range for mainframe computers.
For consumer electronic equipment the junction temperature of a round
100C is often allowed.
We need a large volume of failure data to establish the design criteria. As
a matter of fact, the introduction of new products has been outpacing the
accumulation of temperaturerelated failure data. There are few concrete
data bases that justify the setting of Tj at particular levels. The prevailing
idea is stick to the criteria which have worked well by now.
2. The characteristics of electronic devices are affected by the
temperature. Hence, the variation of junction temperatures increases the
probability of timing mismatch between devices, thereby slowing down
6
the signal; processing. In principle, this is true. However, due to
complexity of signal flows, and also due to the effects of other factors such
as the dimensional tolerance in fabrication of devices on device
characteristics, there is little ground on which a concrete value is assigned
to ATj. Again, the followingtheprecedence idea prevails, and ATj is
usually set in a range 10 to 15 C.
The comments made in (1) and (2) do not necessarily propose to abolish
the presently prevailing design criteria. Instead, they are stated not only
to raise caution about the pitfalls but also to point out the multiple
aspects of thermal management.
1. The existing criteria a lone may not be sufficient to guarantee the
reliability of new generations of electronic equipment. As increasingly
finer structural features are involved in the packaging, additional criteria
may have to be defined to guarantee the structural integrity of
components and systems. For instance, the temperature difference
between the module and the wiring board needs to be held below certain
threshold in order to reduce stress and strain on the solder joints between
the module and the board.
2. Since the criterion for Tj itself is hazy to a certain extent, it is not
justifiable to attempt to meet the criterion with unduly high accuracy. If
more tolerance for Tj, say, 5 K higher, means substantial reduction of
manufacturing cost, it is worth pursuing alternative designs allowed
under a modified Tj. This does not mean to recommend lax design
practice, but comes out of the very nature of electronic packaging design.
7
That is, the packaging design is an art of synthesizing the results of
analysis, experiment, prototype testing, and cost evaluation.
The thermal criteria need to be defined from a view point that extends
over whole aspects of packaging design.
3. As electronic devices find their ways into diverse applications, some of
them operate in a hightemperature environment. In hightemperature
applications, the environment temperature already exceeds the
traditional Tj of 50 to 100 C. if conventional criteria are adopted, we need
refrigeration systems, which are often not affordable due to required
space and cost. The temperature acceleration test normally conducted to
find correlation between Tj and the failure rate is not feasible, because it
is likely to cause failure mechanisms of totally different nature, such as
melt down of solder joints. The only way left for the packaging design of
hightemperature devices is the identification of possible failure
mechanisms on the basis of laboratory experiment and analysis, and the
development of countermeasures to failure through materials selection,
heatflow management, and structural design. The socalled Physicsof
Failure is universally important for the packaging design of all electronic
equipment; however, more time and resources are needed to develop it
into a standard practice in the electronics industry. (John Lau, C.P.
Wong, John L. Prince and Wataru Nakayama, Electronic Packaging,
Design, Process and Reliability, April 28, 2003, This material is
reproduced with permission of the McGrawHill companies).
8
2.2 Factors Controlling Stress in a Chip
Mounted on a Substrate
The chip mounted on a laminate is under a complex state of stresses as a
result of a large difference in thermal expansion between the chip, and the
board (substrate) upon cooling during the thermal cycling.
The difference in coefficient of thermal expansion (CTE) between the chip
and the substrate induces cyclic stresses during a temperature drop.
A model can be used to determine the principal and shearing stresses in a
two layer structure such as a chip and a substrate The magnitude of the
stresses is a function of the mechanical properties of the materials used in
the model and the temperature difference from the stress free state as
well.
It is very important to note that the chip geometry angle will increase the
stresses at the corners due to the stress singularities at these corners.
2.3 Modeling Stresses in a Chip Mounted on
a Substrate
The finite element modeling (FEM) technique is considered the most
accurate technique that can be used to determine the residual stresses in
a chip mounted on a substrate.
The chip itself consist of a silicone die mounted on a substrate and
encapsulated with underfill material. The purpose of using the underfill
is to bond the chip to the substrate that is mounted on and to form the
fillet structure on the boundary of the chip as shown in Figure 2.1 (IEEE,
Advanced Packaging Materials Processes, Properties, and Interfaces,
This material is reproduced with permission of the International
Microelectronics And Packaging Society IMAPS).
9
The finite element model provides approximate results for the principal
and shear stresses at the neighborhood of the junction between the chip
corner and the underfill layer.
Figure 2.1 Side View of Integrated Circuit Chip Assembly [4]
2.4 Modeling Delamination in a Chip
Mounted on a Substrate
To determine the driving forces that are responsible for causing the
interface crack problems for. a chip mounted on a substrate, a finite
element formulation can be utilized.
The 32noded three dimensional crack tip element shown in Figure 2.2,
with four nodes located at the crack front [4]. This element can be used in
a finite element analysis for this case.
Figure 2.2 32Node Three Dimensional Crack Tip Element [4]
10
2.5 Stress Modeling
The residual stresses in a chip mounted on a substrate are found by
assuming a uniform temperature change from the service temperature
down to the room temperature.
This residual stresses development model, assumes that prior to cooling
the entire assembly is stress free and during the cooling process the
stresses start to reside.
Figures 2.3 and 2.4 are plots of the computed displacements in the
silicone die as a function of distance from the package centerline
calculated for a 140 C change in temperature (AT). These results were
generated for a commercial underfill resin. [4].
............................. _,jÂ£Â£vg
.vwJyA'iw;
[]::JHH 4? ; )'
%
Figure 2.3 Computed Displacements in Xdirection as a Function of the
Distance From the Package Centerline [4]
Upon cooling, the silicone chip contracts in Xdirection as shown in Figure
2.3 and deflects in Ydirection as shown in Figure 2.4 [4].
11
Figure 2.4 Computed Displacements in Ydirection as a Function of the
Distance From the Package Centerline [4]
2.6 Delamination Modeling
The 3D finite element modeling results of the thermal cycling problem
are shown in Figure 2.5. A center crack of length a = 2.54 mm is
considered. The mixed mode stress intensity factors are plotted along the
crack front for a temperature change of +1 C. A total of 1516 3D finite
elements are used, with 5 layers through the thickness in Z direction.
Figure 2.6 shows the corresponding deformed configuration of the package
and (Jyy stress distribution under the specified thermal loading. Note that
Z = 3b/4, where b is the thickness of the package in the Zdirection.
Mode I stress intensity factor is negative, reflecting crack surface contact.
This can also be seen in Figure 2.6.
12
Figure 2.5 Mixed Mode Stress Intensity Factors for a = 2.54 mm Crack [4]
The other interesting result is that, ModeIll stress intensity factor
increases considerably near the free surface and in this region its
magnitude is highest compared to the others stress intensity factor
components. [4].
<*
z
Figure 2.6 csyy Stress Distribution and Deformed Configuration [4]
13
3. Mechanical Behavior of Strip Structure
Made From Aluminum and Steel
3.1 Problem Description
Thermal stresses, caused by the thermal expansion and contraction of a
material, can often be the cause of unexpected part failure. When two
materials with greatly dissimilar coefficients of thermal expansion are
combined in the circuit board assembly, thermal stress is of the greatest
concern. Differences in the thermal movement of the materials may cause
problems in stress concentration and singularity when the geometry plays
a big role in this design.
A typical example of this problem is an integrated circuit (IC) chip
mounted on a surface mount circuit board. It is well known that the life of
a chip mounted on a surface mount circuit board assembly can he
improved by reducing the stresses induced as a result of the chip
geometry angle.
This study focuses on determining the proper chip geometry angle that
minimizes the stress singularity at the chip corners.
3.2 Predicting the Mechanical Behavior of
Metal Strip Structure With Dissimilar
Coefficient of Thermal Expansion
The metal structures under consideration are shown in Figure 3.1a
through c, where their dimensions are also specified on the engineering
drawings, see Appendix A. This strip structure consists of top conductor
made from aluminum 6061 and bottom ground plane made from high
14
carbon air hardening steel A2. Figure 3a is strip structure with 30
geometry angle, Figure 3b with 45 geometry angle and Figure 3c is
manufactured with 90 geometry angle. The boundaryvalue problem is to
calculate the thermal shear stresses of these three structures while they
are subjected to a temperature drop from service temperature to room
temperature and to locate the maximum stress on the structure.
0.270
0.500
]
30 Angle
(a)
45 Angle
(b)
90 Angle
(c)
Figure 3.1 Physical Metal Structures Modeled :Aluminum 6061 on High
Carbon Air Hardened Steel A2
The coefficients of thermal expansion of the super conducting ceramics
used in manufacturing of the printed circuit board (PCB) are compiled
and summarized in Figure 3.2.
15
Figure 3.2 Thermal Expansions of Super Conducting Ceramics [1]
Youngs Modulus and Poissons Ratios of these materials are given in
Table 3.1. It can be seen that Poissons Ratios of these materials are
basically the same, but Youngs Modulus varies dramatically (e.g, Youngs
Modulus of steel is more than two times that of aluminum). As the
temperature drops from the service temperature to room temperature,
these metal structures are subjected to a very complex stress state due to
the large thermal expansion mismatch and stiffness differences between
the aluminum and steel.
16
Youngs
Modulus
Thermal Coefficient
Material
(psi) x 106
Poissons
Ratio
of Linear
Expansion
(10_6/F)
Aluminum 6061 10.5
0.334
13.0
Steel A2
28.0
0.295
5.96
Table 3.1 Material Properties of Aluminum and Steel
Furthermore, because of the geometry angle of the metal structures, the
determination of the stresses in them is very difficult. For this reason, the
finite element method was chosen. Three dimensional model type
elements for only one half of the structure have been used for the
construction of these models.
17
3.3 Problem Approaches
3.3.1 Theoretical Approach Closed Form
Solution
In this approach, the temperature change within the proposed model will
be determined in order to be used in the finite element structure approach
as a thermal global load for the strip structure under analysis.
Assumptions:
1. 1D analysis for each layer, the aluminum strip and the steel base.
2. Bending will be neglected, and only average axial normal
stresses and shear stresses will be accounted for.
3. The model consists of two layers that have the same length L as
shown in Figure 3.3.
4. Consider the thickness of layer 1 is ti and of layer 2 is t2.
5. The edges at x= 0 and x= L are stress free.
6. The average normal stress has a maximum aon at x= L/2 as shown in
Figure 3.4.
7. In order to satisfy the boundary conditions at x= 0 and x= L,
and the symmetry condition, assume the distribution of stresses as
shown in Figure 3.5.
8. u= u(x), i.e y 1 such that aon Ton => so that u results from a
only.
9. Change in temperature AT in both layers is constant.
18
Layer 1 ' ti
Layer 2 i . t2
L
Figure 3.3 BiMetal Model With Two Layers
Analysis:
Let us look at the stresses in an individual layer n of the model, as shown
in Figure 3.4 For equilibrium, the shear stresses on the top and bottom
faces change sign and oppose.each other. Approximate the stresses as sine
functions as follows:
2nx
On Oon Sill
L
2nx
Tn Ton Sill
For axial equilibrium of forces (Figure 3.4), we must have:
L/2 L/2
Oontn J Tndx jVn \dx
0 0
L/2 f f2^c L/\ f27DC]
(Jontn I Ton Sill ax 1 Ton 1 sml ,
J 0 l L \ J ^L)
dx
Oontn Ton
( 270} 2 ( 27Tx\
 cos Ton 1  cos r
L v L )\ 0 L V L J]
L, \
Oontn \Ton Ton 1 j
n
(3.1a)
(3.1b)
19
X
Max. Normal
Stresses
X=L/2
Tn
Figure 3.4 Normal and Shear Stresses in a BiMetal Model
Figure 3.5 Distribution of Stresses [5]
Now derive the displacement (u) equation
The model consists of two layers:
1. Layer 1 is the aluminum 6061.
2. Layer 2 is the steel (high carbon) A2.
Assume u= u(x) only
Assume: y 1 such that Gan r => u results from a only
The total strain e is the sum of the strain due to stress and the strain due
to a change in temperature AT=>
du G
== + aAT
dx E
Un = \~dx + CbATnL
" En
0
fGon
Un = ICPC + CbATnL
En
Gem L
Un = () + CtnATnL
Sjti Z
Plug equation (3.2) in equation (3.3)
(Ton Ton l') / t
JttnK 7 I L
Un =
En
2)
+ OnATnL
(3.3)
L L , ,
Un =*[Ton Ton l) + CbATnL
2 En JTtn
Consider:
2 En Jtin
and cbiL Bn
Rewrite equation (3.4) =>
Un Ani^Ton Ton l) + BnATn
This equation is called the Difference Equation.
Assume: un = un\ = u\ = m=....= u = constant = average exp ansion
Ano\ + BiATi = Ai{ To\) + B2AT2
AiToi + A2T01 = B2AT2 B\AT\
(3.4)
(3.5)
21
Toi(Ai + At) = B2AT2 BiATl
(3.6)
But:
Ai + A2 =
Zf E2t2 + Eiti
Ai + A2 = 
2n E\t\E2t2
Consider:
E2t2 + E\t\ 1
E\t\E2t2 E
(37)
But:
B2AT2 B1AT1 = L{gc2AT2 aiAT 1)
(3.8)
Plug equations (3.7) & (3.8) in equation (3.6) =>
Now apply equation (3.9) to calculate the stress:
L = 1.0 in.
To determine E:
1 E2t2 +E\t\
E EitiE2t2
E\t\E2t2
E2t2 + E\t\
\2tcE)
Toil? = 2nEl\a.2AT2 a\AT\)
To1 = {(X2AT2a\AT\)
Jj
t = ((X2AT2 a\AT\)
(3.9)
22
Ea\ = E1 = 10.5 x 106 psi (For tension or compression)
Est = E2 = 28.0 x 106 psi (For tension or compression)
tAi = t\ = 0.120 in.
tst = ti = 0.090 in.
(103 x 106)(0.120)(28.0 x 106)(0.090)
(28.0 x 106)(0.090) + (l 0.5 x 106)(0.120)
3.1752 x 1012
3780000
.. E = 840000
OAi = a\ = 13.0 pin / in. F = 13.0 x 106 in/in. F
ast = a2 = 5.96 juin / in. F = 5.96 x 106 in/ in. F
In order to determine the shear stress for the epoxy used in bonding both
strip structures in the model, a specimen was designed and
manufactured. This Specimen consists of two pieces 3x0.5x0.125 of
high carbon steel A2 and 1 piece 5x0.5x0.125 of aluminum 6061 bonded
together using high thermal expansion epoxy (max. service temperature
300 F) as shown in Figure 3.6.
The specimen was tested on the Instron Test Devise at GAMBRO BCT as
shown in Figure 3.7 in order to determine the total load required to
calculate the shear stresses in the model. From this test it was found that
the total load required to shear off the proposed specimen is 470 lb. as
shown in Figure 3.8.
P
23
r =
Pjl
P = 470lb From Instron Test Results (see Figure 3.8)
A = 1 x Oi = 0 5in2
470/2
0.5
.\ r = 470psi This shear stress represents the average stress within the
proposed model.
1.890
3.000,:
1.250
0.250
0.500 *
Figure 3.6 Instron Test Specimen
25
Figure 3.7 Instron Tester
26
K)
Figure 3.8 Total Load Determined Using Instron Tester
Consider: AT\ = ATi = AT
470 = 24840000) (596AT 13Ar) x 10e
470 = 37.15AT"
AT = 12.65 F
This change in temperature (AT) represents the minimum temperature
that is required to induce the shear stresses in the proposed model that
will affect the properties of the structure and causes the crack at the
upper strip corners.
28
3.3.2 Experimental Approach Thermal
Cycling Solution
3.3.2.1 Modeling Material Behavior
The purpose of this experimental study is to examine the
interrelationships between the various material mechanical properties
and predict their impact on the proposed model subjected to change in
temperature (AT) which simulates the potential effect of the integrated
circuit (IC) chip geometry angle on inducing stresses into the printed
circuit board (PCB) assembly.
3.3.2.2 Materials
The three proposed metal structures under consideration that will be used
in achieving the experimental approach are shown in Figure 3.9. This
strip structure consists of the top strip made from aluminum 6061 in
three different geometry angles 30, 45 and 90 and the bottom ground
plane made from air hardening high carbon steel A2. This high carbon
steel A2 was purchased from MSC. A high thermal epoxy (max. service
temperature 300 F) was obtained from Hardman Epoxies (part no.
Yellow 04002) and used as a metal bonding glue.
29
! Figure 3.9 BiMetal Structures
I
j
3.3.2.3 Structure Specimen Preparation
The three proposed Bimetal structures described in the materials section
were prepared for thermal stresses and crack testing. The upper
aluminum strip and the bottom steel ground plane were fabricated with
the dimensions specified on the engineering drawings, see Appendix A.
The bottom surface of the upper strip and the top surface of the ground
plane were machined with 64 RMS surface finish using the EDM machine
in order to ensure the adequate surface adherence between both
materials. This surface finish grain direction was made perpendicular to
the normal stress.
! The structure surfaces were cleaned with isopropyl alcohol in order to
remove any contaminants from these surfaces which will improve the
bonding quality.
The epoxy was perfectly mixed with the supplied accelerator provided
with this epoxy following the manufacturer instructions. A thin layer of
the prepared epoxy was uniformly applied to the surfaces under bonding.
i
30
The specimens were cured at 20 psi constant clamping pressure at room
temperature and humidity for 24 hours.
3.3.2.4 Temperature Cycling Test
A temperature cycling test was performed on all three specimens in order
to, monitor the epoxy crack at the upper strip corners due to the
singularity as a result of the geometry angle.
The three specimens were placed inside the oven and the temperature
was increased by 10 F every hour. This thermal cycling time was
determined by monitoring the temperature within the structure body
using a digital thermal probe in order to ensure that the temperature was
uniformly distributed within the structure prior to removing the structure
from the oven and scanning the crack.
3.3.2.5 Computerized Scanning Microscopy
The fractured surface of the epoxy at the aluminum upper strip corners
were examined for all three specimens every 10 F thermal cycle using the
Optical Measurement Inspection System (OMIS) at GAMBRO BCT
provided with a camera to. scan and track the crack as shown in Figure
3.10.
31
3.3.3 Finite Element Approach 
Pro/Mechanica Solution
3.3.3.1 Modeling Thermal Stresses
The finite element analysis technique was used in this approach in order
to determine the residual stresses in the proposed model that simulates
an integrated circuit (IC) chip mounted on a surface mount printed circuit
board (PCB) assembly. The chip itself consists of a silicone die mounted
on a substrate and encapsulated with an underfill. The following
describes the data applied to the finite element design study and entered
into the Pro/Mechanica software for the three BiMetal structures and
Instron structure.
32
3.3.3.1.1 Model Type BiMetal Structure
3D model type was applied to the proposed model.
3.3.3.1.2 Material
The aluminum 6061 was assigned to the upper strip and the steel A2 was
assigned to the ground plane.
3.3.3.1.3 Load
Thermal load was applied to the entire structure assembly with global
temperature distribution as follows:
Model Temp. = 160 F
Reference Temp. = 70 F
3.3.3.1.4 Constraints
Left surface for the upper strip and the ground plane were:
Translation: Fixed in X direction and free in Y and Z direction.
Rotation: Free in X, Y and Z direction.
Two corner points on the upper strip were:
Translation: Fixed in Y direction and free in X and Z direction.
Rotation: Free in X, Y and Z direction.
Right edge on the ground plane was:
Translation: Fixed in Z direction and free in X and Y direction.
Rotation: Free in X, Y and Z direction as shown in Figures 3.11, 3.12 and
3.13.
33
3.3.3.1.5 Analysis
Type: static
Multi pass Multi adaptive
Polynomial order: Min.= 1 and Max.= 9
Limits: Percent Convergence = 10%
Converge on: Local displacement, local strain energy, and global RMS
stress.
34
OJ
U\
Point 2
, \ j' Hi ^*Â£jf
'>wArf
i' v'1'r
! Hi 
Left Surface
m
Point 1
Jiipi
m 1 f*\a%s
jpff
mmf
fS^f r
.iwip
Figure 3.11 Constraints of BiMetal Structure With 30 Geometry Angle
U)
On
Point 2
Figure 3.12 Constraints of BiMetal Structure With 45 Geometry Angle
4
Point 2 ,
Left Surface
Figure 3.13 Constraints of BiMetal Structure With 90 Geometry Angle
3.3.3.1.6 Model Type Instron Structure
3D model type was applied to the proposed model.
3.3.3.1.7 Material
The aluminum 6061 was assigned to the middle strip and the steel A2
was assigned to the upper and lower plane.
3.3.3.1.8 Load
Uniform total load 470.0 lb calculated using the Instron tester was
applied to the middle aluminum strip in Xdirection.
3.3.3.1.9 Constraints
Right surface for the upper and lower plane were:
Translation: Fixed in X direction and free in Y and Z direction.
Rotation: Free in X, Y and Z direction.
Two corner points on the upper plane were:
Translation: Fixed in Y direction and free in X and Z direction.
Rotation: Free in X, Y and Z direction.
Right edge on the upper and lower plane was:
Translation: Fixed in Z direction and free in X and Y direction.
Rotation: Free in X, Y and Z direction as shown in Figure 3.14.
3.3.3.1.10 Analysis
Type: static
Multi pass Multi adaptive
Polynomial order: Min.= 1 and Max.= 9
38
Limits: Percent Convergence = 10%
Converge on: Local displacement, local strain energy, and global RMS
stress.
39
Point 2
Figure 3.14 Constraints of Instron Specimen Structure
Left Surface
4. Results and Discussion
The metal structures that simulate the effect of an integrated circuit (IC)
chip geometry angle on inducing stresses into the surface mount printed
circuit board (PCB) are shown in Figure 3.9. In this chapter, the results
obtained from using the three approaches described in chapter 3 are
summarized and discussed.
4.1 Theoretical Approach Closed Form
Solution
In this approach, the shear stress equation was derived and applied on
the proposed model in order to be able to predict the change in
temperature that causes the structure to shear off. Table 4.1 summarizes
these results:
Load P (lb) Shear Stress x (psi) Change in Temp. AT (F)
470.0 470.0 12.65
Table 4.1 Theoretical Approach Results
The shear stresses calculated using this approach represents the average
stresses induced into the proposed model.
The change in temperature (AT) represents the minimum temperature
that is required to induce these stresses into the model and causes the
41
crack at the upper strip corners however, this temperature doesnt reflect
the actual temperature that, causes the crack.
4.2 Experimental Approach Thermal
Cycling Solution
In this approach, it was found that the structures designed with 30 and
90 geometry angles were cracked at the aluminum upper strip corner
when the temperature of the structure reached 130 F while the other
structure designed with 45 was cracked at 160 F. The shear stresses are
calculated for these structures using the equation derived in the
theoretical approach. Table 4.2. summarizes these results:
Geometry Angle 30 45 90
Change in Temp.AT (F) 60 90 60
Calculated Shear Stress (Average) t (psi) 2229.0 3334.5 2229.0
Table 4.2 Experimental Approach Results
/
The fractured surface of the epoxy at the aluminum upper strip corners
for all three structures were examined and scanned using a computerized
microscopy with a camera to track the crack as shown in Figures 4.1, 4.2
and 4.3. These figures show that the crack had started at the corners then
expanded along the strip edge.
42
Figure 4.1 Stress Crack at the Aluminum Upper Strip Corner for 30 Geometry
Angle Occurred at 130 F
43
i
i
i
Figure 4.2 Stress Crack at the Aluminum Upper Strip Corner for 45 Geometry
Angle Occurred at 160 F
I
44
Figure 4.3 Stress Crack at the Aluminum Upper Strip Corner for 90 Geometry
Angle Occurred at 130 F
45
4.3 Finite Element Approach Pro/Mechanica
Solution
In this approach, the residual stresses were determined by applying a
uniform thermal load with temperature change (AT) 160 F. Table 4.3
summarizes the output data for this approach obtained from running the
Pro/Mechanica software for all metal structures including the Instron
structure. In addition the run data files for the detailed report is attached
to this study, see Appendix B.
Structure Geometry Angle Max. Shear Stress (psi) Displacement Magnitude (in.) Strain XY (psi) Strain YZ (psi) Strain Energy Stress VM (psi)
30 8071 0.00074 0.00026 0.00088 0.023 66068
45 4685 0.00074 0.00026 0.00018 0.024 38631
90 8889 0.00075 0.00037 0.00024 0.025 72888
Instron 3151 0.00030 0.00014 0.00013 0.738 23647
Table 4.3 Finite Element Approach Results
46
Figures 4.4 and 4.5 show the fringe and contour plot respectively for the
30 geometry angle metal structure with maximum shear stress of 8071
psi at the aluminum upper strip far corner.
47
Stress Max Shear (Maximum)
Original Model
.LoadSell
Principal Units:
Inch Pound Second (IPS)
B.071e+03
IJSWSW.
A
3
2
2
2
1
1
a
4
t> l +fj'4
21'2e + 04
011e+04
4 1 Oet04
009e+04
609c+Q4
2000+04
07le+03
063e+03
4iS3ei 01
V
. .1*
^ Fringe Plot Max. Shear Stress 5Q_Degree Angle
Figure 4.4 Fringe Plot for 30 Geometry Angle Showing the Maximum Shear Stress
Figures 4.6 and 4.7 show the fringe and contour plot respectively for the
45 geometry angle metal structure with maximum shear stress of 4685
psi at the aluminum upper strip far corner.
Figures 4.8 and 4.9 show the fringe and contour plot respectively for the
90 geometry angle metal structure with maximum shear stress of 8889
psi at the aluminum upper strip corner.
Figures 4.10 and 4.11 show the fringe and contour plot respectively for
the Instron metal structure with maximum shear stress of 3151 psi at the
aluminum upper strip far corner.
50
"Stress Max Shear (Maximum) Original Model LoadSetl Principal Units.* 1 rich Pound second (IPS) 4 . & i. i)91e+04\' kku: 1.859e+Q4 S 1.627e+04 1.395e+04 1 1 164e+04
3 .320e+03 T7.002e+03 4.6B5e+03 ; 2.368e+03
t. . 5.0G7el01
i' i ' f ; * " 'r f; t 'it, : v.  X ;
. Â£* L Fringe Plot Max. Shear Stress 45 .Degree Angle 4
Figure 4.6 Fringe Plot for 45 Geometry Angle Showing the Maximum Shear Stress
'Stress Max Sheaf
/'Original' Model
LoadSetl
Principal Units*
Inch Pound Second
heat (Maximum!
( IPS!
B.HHSp+03
Fringe Plot .Mq&. Shear. Stress 9Q : Pogreo Apgje
S.631e101
Figure 4.8 Fringe Plot for 90 Geometry Angle Showing the Maximum Shear Stress
FStress Max Shear (Maximum)
Original Model
LoadSetl
Principal Units:
Inch Pound Second (IPS)
;S. lSle+03
Y
J
Fringe Plot Max. Shear Stress, l.nstron
i 4 .Me+04
1 180e+04
1.036e+04
, 8.919e+03
! H 7.477e+03
6. 035e+03
4 . 5S3e+03 .
3. lSle+03
1 . 709e+03
*7 G~3e+00
Figure 4.10 Fringe Plot for Instron Metal Structure Showing the Maximum Shear Stress
(Stress Max. Shear (Maximum)
Averaged Values
Original Model
.LoadSetl
Principal Units:
Inch Pound Second (IPS)
i_ bi 3 ^ Ou
v
Contour Plot Max. Shear Stress Instrori
Figure 4.11 Contour Plot for Instron Metal Structure Showing the Maximum Shear Stress
br> l534e + 03:
B 5.188~fQ.
 C 4.405e+0
iTj in
Figure 4.12 shows the distribution of the maximum shear stress along the
curve arc length 0.25. This curve represents the bonded surface for both
materials of the structure with 30 geometry angle. Note that the shear
stress reached its maximum value at the curve end. When this plot is
compared with the plots shown in Figures 4.13 and 4.14 for the 45 and
90 geometry angle metal structures respectively, it is clear that the shear
stress for the 45 structure almost behaves like the 90 angle structure
while the 30 angle structure plot behaves slightly different than these
two structures.
Figure 4.15 shows the maximum shear stress distribution along the curve
length that represents the bonding surface of the aluminum strip and the
steel base used for Instron test specimen. Obviously, the shear stress
reached its maximum value at the external edge of the steel base.
57
oc
Stress Mox Sheor (Maximum)
Curves
LoodSetl
Principal UnitSi
Inch Pound Second
b
C
cn
X
O
i/)
a>
(/)
Curve Arc Length (Maximum)
Max. Shear Stress 30 Degree Angle
Figure 4.12 Maximum Shear Stress at the Curve Arc Length for 30 Geometry Angle Metal Structure
Stress Mox Sheor (Top)
Curves
LoodSetl
Principol Units* Inch Pound Second (IPS) 9.
ro O + LiJ X 8.
0 0) & 1 7 /
(/) V)
5.
0.0( ) o.o; D ' o!lC oils 0.2C ) ' 0.25
Curve Arc Length (Top)
Mox. Sheor Stress 45 Dearee Anale
Figure 4.13 Maximum Shear Stress at the Curve Arc Length for 45 Geometry Angle Metal Structure
Stress Mox Sheor (Top)
Curves
Curve Arc Length (Top)
Mox. Sheor Stress 90 Degree Angle
Figure 4.14 Maximum Shear Stress at the Curve Arc Length for 90 Geometry Angle Metal Structure
Stress Mox Sheor (Top)
Curves
Mox. Sheor Stress Instron
Figure 4.15 Maximum Shear Stress at the Curve Arc Length for Instron Metal Structure
Figure 4.16 shows the distribution of the maximum stress in xy plane
versus the P loop pass for the structure with 30 geometry angle. Note
that the stress reached its maximum value at 7000 psi and converged at
pass 8. When this plot is compared with the plots shown in Figures 4.17
and 4.18 for the 45 and 90 geometry angle metal structures respectively,
it is clear that the maximum stresses in xy plane is the highest for the 45
geometry angle structure than the other two structures.
Figure 4.19 shows the maximum stress in xy plane distribution for
Instron test specimen. Obviously, the stress reached its maximum value
at 12000 psi and converged at pass 6.
62
mox stress xy
PPoss
P Loop Poss Mox. Stress xy 30 Degree Angle
Figure 4.16 Maximum Stress xy Versus the P Loop Pass for 30 Geometry Angle Metal Structure
mox stress xy
PPoss
LoadSetl 12
Principal Unitst
Inch Pound Second (IPS)
ro
O
+
yj
x
x
8
in
tn
tn
x
o
0
4
8
: /
;/
/
1 ' 2 3 4 5 g 7 8
P Loop Pass
P Loop Pass Mox. Stress xy 45 Degree Angle
Figure 4.17 Maximum Stress xy Versus the P Loop Pass for 45 Geometry Angle Metal Structure
mox stress xy
PPoss
LoodSetl 12
Principol Units:
Inch Pound Second (IPS)
8
ro
O
+
UJ
X
>
x
U)
Q>
X
O
E
A
0
A
8
\ \ \ \ \ \ \
1 2 3 A ' 5 G 7 00.
P Loop Poss
P Loop Poss Max. Stress xy 90 Degree Angle
Figure 4.18 Maximum Stress xy Versus the P Loop Pass for 90 Geometry Angle Metal Structure
max stress xy
PPoss
LoodSetl 12
Principol Units*
Inch Pound Second (IPS)
10
ro
O
+
yj
x
>*
x
(/>
in
t/>
8
6
4
2
/
/
/
/
1 ' 2 3 A 5 6
P Loop Poss
P Loop Poss Mox. Stress xy Instron
Figure 4.19 Maximum Stress xy Versus the P Loop Pass for Instron Metal Structure
Figure 4.20 shows the distribution of the maximum stress in yz plane
versus the P loop pass for the structure with 30 geometry angle. Note
that the stress reached its maximum value at 5000 psi and converged at
pass 1. When this plot is compared with the plots shown in Figures 4.21
and 4.22 for the 45 and 90 geometry angle metal structures respectively,
it is clear that the maximum, stress in yz plane is the highest .for the 45
geometry angle structure than the other two structures. In addition, the
stress plot for the 45 geometry angle metal structure almost behaves in a
similar way for the 90 geometry angle metal structure while the 30
angle metal structure behaves differently.
Figure 4.23 shows the maximum stress in xy plane distribution for
Instron test specimen. Obviously, the stress reached its maximum value
at 2200 psi and converged at pass 6.
67
o
mox stress yz
PPoss
P Loop Poss Mox. Stress yz 30 Degree Angle
Figure 4.20 Maximum Stress yz Versus the P Loop Pass for 30 Geometry Angle Metal Structure
mox stress yz
PPoss
P Loop Poss Mox. Stress yz 45 Degree Angle
Figure 4.21 Maximum Stress yz Versus the P Loop Pass for 45 Geometry Angle Metal Structure
mox stress yz
PPoss
P Loop Poss Mox. Stress yz 90 Degree Angle
Figure 4.22 Maximum Stress yz Versus the P Loop Pass for 90 Geometry Angle Metal Structure
mox stress yz
PPoss
P Loop Poss Mox. Stress yz Instron
Figure 4.23 Maximum Stress yz Versus the P Loop Pass for Instron Metal Structure
Figure 4.24 shows the distribution of the strain energy versus the P loop
pass for the structure with 30 geometry angle. Note that the curve
converged at pass 8 like the other two structures, 45 and 90 geometry as
shown in Figures 4.25 and 4.26 respectively.
Figure 4.27 shows the distribution of the strain energy for Instron test
specimen. Obviously, the curve converged at pass 6. The strain energy
plot exhibit an almost identical behavior for all four structures.
72
stroin energy
PPoss
P Loop Poss Stroin Energy 30 Degree Angle
Figure 4.24 Strain Energy Versus the P Loop Pass for 30 Geometry Angle Metal Structure
stroin energy
PPoss
LoodSell
Principal Units* u.uo
Inch Pound Second (IPS)
0.07
>.
o
C
a>
c
'6
to
0.06
0.05
0.04
0.03
0.02
\
\
r 2 3 ' 5 6 7 ' 8
P Loop Pass
P Loop Pass Slroin Energy 45 Degree Angle
Figure 4.25 Strain Energy Versus the P Loop Pass for 45 Geometry Angle Metal Structure
stroin energy
PPoss
P Loop Poss Stroin Energy 90 Degree Angle
Figure 4.26 Strain Energy Versus the P Loop Pass for 90 Geometry Angle Metal Struct
strain energy
PPass
LoadSell
P Loop Pass Strain Energy Instron
Figure 4.27 Strain Energy Versus the P Loop Pass for Instron Metal Structure
5. Summary and Conclusions
It is apparent from the thermal shear stress equation used in this study
that change in temperature (AT) predicts failure when large mismatch
between the coefficient of thermal expansion (CTE) for the two materials
used in the proposed models in this study is chosen These stresses
represent the average shear stresses which are much smaller than the
maximum stresses predicted in the finite elements analysis approach.
Since the experimental approach predicts the actual average shear
stresses for the models with 30 and 90 geometry angle, a conclusion can
be established that these failures occurred sooner due to the stress
concentration and singularities at the upper strip corners. For the three
cases considered, the strip with 45 geometry angle is structurally the
best substrate match, while the 30 and 90 geometry angle structures are
the worst.
Since the thermal stresses induced into the printed circuit board (PCB)
assembly are dependent on the integrated circuit (IC) chip geometry
angle, it is important to note that the results of this study can be
improved if structures with more angles are analyzed given as a function
of this angle. For example, when using the experimental and finite
element analysis approach, structures with at least structures with 10
different angles are needed to be used in the shear stress failure
prediction.
The mechanical and fracture behavior of a model consists of two different
materials with large coefficient of thermal expansion (CTE) mismatch as
77
a function of the upper strip geometry angle has been analyzed. These
models predict failure at the corners due to the singularities.
The finite element analysis reveals that shear stresses developed at the
corners due to the mismatch in the coefficient of thermal expansion (CTE)
between the substrate and the silicone die.
The results in this study were obtained using three different approaches
linked together in order to achieve the objective of this study, and
therefore the analyses developed, especially the finite elements analysis,
are beneficial to many mechanical engineers working in the electronic
components design field. It was found that the finite elements analysis
technique is the most accurate since an automatic iteration to solve the
huge number of equations up to the 9border were used to achieve the
required convergence.
78
6. Recommendations
6.1 Mathematical Model
The evaluation of the mathematical model includes the effect of the
integrated circuit (IC) chip geometry angle is recommended. There is no
such mathematical model that include a relation between the stresses as
a function of the geometry angle.
6.2 Metal Structure Materials
Metal structures simulate the problem using the same materials as used
in a circuit board assembly are recommended to be used in more similar
studies for the stress analysis making reasonable for the present need of
accurate results. Thought the use of these materials, complemented with
experimental studies, it may be possible to predict more accurate results.
6.3 Metal Structure Design
The use of a structure that has a similar geometry and dimensions of an
integrated circuit (IC) chip mounted on a substrate is recommended in
order to simulate the exact amount of stresses induced into the assembly.
6.4 Thermal Epoxy Layer
The use of high expansion thermal epoxy that has known physical and
mechanical properties is recommended. The availability of these
properties will allow adding this epoxy layer to the models used in the
79
finite element analysis approach in order to conduct more accurate results
for the maximum stresses.
80
APPENDIX A
Metal Structures Engineering Drawings
81
I 000
r" ^ ~^?35. 00 \
\
t ae> 250
I I
Scale 2:1
Amir Roomi Me c h. Eng. University of Colorado
STRIP 1
1 1 / 0 7 / 0 2 Aluminum 6061
1 1
I 000
500
h
.090
Scale 2:1
Amir Roomi Mec h. Eng. University of Colorado
BASE 1
1 1 / 0 7 / 02 Steel A2
!
