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CHARACTERIZATION OF MICROSTRUCTURAL EVOLUTION
OF CREPT, AGED AND THERMOMECHANICALLY FATIGUED
EUTECTIC Sn-Ag SOLDER JOINTS USING ORIENTATION
IMAGING MICROSCOPY

By

Adwait U. Telang

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
' for the degree of

MASTER OF SCIENCE
Department of Chemical Engineering and Materials Science

2002

ABSTRACT

CHARACTERIZATION OF MICROSTRUCTURAL EVOLUTION OF CREPT,
AGED AND THERMOMECHANICALLY FATIGUED EUTECTIC Sn-Ag
SOLDER JOINTS USING ORIENTATION IMAGING MICROSCOPY

By

Adwait U. Telang
Single shear lap eutectic Sn—Ag solder joints with copper substrate were subjected to
isothermal aging, creep at room and elevated temperature, and thermomechanical fatigue
(TMF). Orientation Imaging Microscopy (OIM) studies reveal how the crystallographic
orientations are correlated with microstructural features in the solder joints. Certain
misorientations appear to be energetically favored during solidification, which have twin
and Z boundary type relationships. Changes in the crystallographic orientations, grain
size and misorientation angles between grains, occurring due to subsequent heating
and/or deformation were documented and analyzed. The gross texture components
remained unchanged after creep and aging. High temperature processes caused some
grain boundary motion and modest grain growth. Observations made in three different
regions of a specimen that underwent 150 and 370 TMF cycles indicate that no
significant changes occurred, though grain boundaries moved, resulting in slight grain
growth. This study shows that the lead-free solder joints are multi-crystals, so that
deformation is very heterogeneous and sensitive to crystal orientation, strain and the

temperature history.

Cepyfight by
ADWAIT U TELANG

2002

ACKNOWLEDGMENTS

I would like to convey my deepest thanks to my advisor, Dr.T.R.Bieler whose
constant support and encouragement provided the driving force for this research project.
I would also like to thank Dr.K.N.Subramanian for his excellent tutelage and support
during the course of my Master’s Program. Observing and learning from the unique
ways in which both these professors approach problems has been a rewarding experience
of my graduate studies for which I am extremely grateful.

I also extend my thanks to Dr.D.Liu for being a member on my committee. Many
thanks to Dr.J.P.Lucas and Dr.M.A.Crimp for generously sharing their facilities for such
studies to transpire.

I would like to express my appreciation to my colleagues Mr.J.G.Lee, Mr.H.Rhee,
Mr.B.Simkin, Mr.B.C.Ng, Mr.P.Sonje, Dr.F.Guo and Dr.S.Choi for their support and
camaraderie.

Finally, my deepest gratitude to my family who have always stood by me,

providing me the much needed perspective and strength and the inspiration to keep going.

iv

TABLE OF CONTENTS

LIST OF TABLES ................................................................................. vii
LIST OF FIGURES .............................................................................. viii
CHAPTER 1
INTRODUCTION .................................................................................. 1
1.1 BACKGROUND FOR TEXTURE AND OIM ....................................... 7
Electron Back-scatter Diffraction Pattern (EBSP) ................................... 14
Microtexture Data Collection ........................................................... 16
Sample Preparation and Mounting ...................................................... 18
Pattern Recognition ...................................................................... 19
1.2 LITERATURE REVIEW ............................................................... 21
A) Thermal and Mechanical Processes Experienced by a Solder Joint in Service..21
Aging ....................................................................................... 21
Creep ........................................................................................ 22
Thermomechanical Fatigue (TMF) ..................................................... 26
B) Eutectic Tin-Silver Solder ............................................................... 31
Crystal Structure and Directional Properties ......................................... 31
Microstructure of Eutectic Tin-Silver ................................................. 35
C) Lead-based Solders ....................................................................... 38
Microstructure of Lead-based Solders ................................................ 38
Evolution of Sn-Pb Microstructure .................................................... 42
Effect of Eutectic Sn-Pb Microstructure on the Mechanical Properties
of Solder Joints ........................................................................... 43
1.3 AIM ........................................................................................ 50
1.4 REFERENCES ........................................................................... 51

CHAPTER 2

EXPERIMENTAL PROCEDURES .......................................................... 57
2.1 SOLDER JOINT PREPARATION .................................................. 57
2.2 THERMAL AND MECHANICAL TESTING ...................................... 64
2.3 CRYSTALLOGRAPHIC DATA COLLECTION AND
TEXTURE MEASUREMENT ......................................................... 69
2.4 REFERENCES ........................................................................... 73
CHAPTER 3
RESULTS AND DISCUSSION ................................................................. 74
3.1 CREEP ..................................................................................... 75
Room Temperature Creep of Eutectic Sn-Ag Solder Joints ......................... 75
High Temperature Creep of Eutectic Sn-Ag Solder Joints .......................... 95
3.2 AGING
Isothermal Aging of Eutectic Tin-Silver Solder .................................... 115
3.3 THERMOMECHANICAL FATIGUE
TMF of Eutectic Sn-Ag Solder Joints ................................................ 126
3.4 REFERENCES .......................... ’ ................................................. 153
CHAPTER 4
SUMMARY ........................................................................................ 154
CHAPTER 5
APPENDIX ......................................................................................... 157

vi

LIST OF TABLES

Table 1. Composition and melting temperature of various solders ............................. 3
Table II. Possible slip and twin systems in B-Sn ................................................ 32
Table III. Constants for various solder joint constituents ...................................... 34
Table IV. Solder joint specimens used to characterize microstructural evolution ......... 65

Table V. Angle/ axis pairs as seen in MODF for the eutectic Sn-Ag
as-fabricated specimen (Figure 18) ............................................................... 81

Table VI. Comparison of Microtextural Features for the Three Regions
after Several TMF Cycles ........................................................................ 150

Table VII. Comparison of Misorientation Angles for the Three Regions
after Several TMF Cycles. ....................................................................... 151

Table VIII. Comparison of Grain Size for the Three regions after
Several TMF Cycles .............................................................................. 152

vii

LIST OF FIGURES

Figure 1. An illustration of the relationship between (a) micro and
(b) mesotexture. Macrotexture shows 14 grains oriented with respect
to the specimen X, Y and Z. (a) Microtexture correlates specific grains
and their crystal orientations; three different grain orientations have
three different c-axis poles (shown by red, blue and green colored
grains)23 in Figure 1(c). (b) Mesotexture shows grain boundary
relationships (shown by dotted and black thick lines) which help
reveal grain boundary character that is statistically described in
Figures 1(d) misorientation distribution function (MODF) and
Figure 1(e) histograms of misorientation angle ..................................... 10

Figure 1(c). Pole figure with point plots and a Gaussian distribution that

shows the macrotexture .............................................................. 11
Figure 1(d). Misorientation distribution functions (MODF) ................................... 12

Figure 1(e). Histograms of misorientation angle ................................................ 13

Figure 2. Kikuchi pattern of tin crystal. (a) Pattern showing Kikuchi bands and
(b) after indexing ........................................................................ 15

Figure 3. Typical setup for EBSP ................................................................. 17

Figure 4. Typical creep curve showing the three stages of creep.
Curve A is constant-load test; curve B, constant-stress test36 ...................... 23

Figure 5. Typical fatigue stress cycles. (a) Repeated reversed sinusoidal stress
curve with complete reversal of stresses, (b) repeated stress reversals on
the positive (tensile) side, (c) random fatigue cycle and (d) cyclic
deformation with hold times ............................................................ 27

Figure 6. B-Sn unit cell (lattice parameters, a=b= 5.8197 A and c=3. 175 A 48) ............ 31

viii

Figure 7. SEM micrographs revealing microstructure of eutectic Sn-Ag solder.
(a) Solder joint showing equiaxed Sn-cells surrounded by Ag3Sn
intermetallic, (b) same joint revealing dendritic Sn-cells in some other
region and (c,d,e and f) higher magnification micrographs of particular
regions of the same joint. These features are common to all solder
joints depending on the maximum temperature reached during soldering
and the cooling rate ...................................................................... 36

Figure 8. Effect of cooling rate on the microstructure of eutectic Sn-Pb
solder. (a) Furnace cooling, (b) air cooling and (c) quenching
(from Ref. 14) ............................................................................ 41

Figure 9. Schematic illustrating the creep properties of fine-grained eutectic
Pb-Sn solder from Ref. 68 ............................................................. 45

' Figure 10 (a) Solder joint configuration. (b) Fixture for manufacturing solder

joints used in this study. Copper dog bones were about

500m in thickness, while the glass plate was ground to about

600m thickness, which facilitates making lOOum thick solder joints. . . . .....59

Figure 11. Jig used for polishing specimens showing a specimen with copper
pieces used as backing to avoid bending and twisting of the joint.
Middle piece is not moved because it supports the solder joint
during polishing ........................................................................ 62

Figure 12. Setup for dead weight loading miniature creep testing frame ................... 66

Figure 13. Temperature profile for thermomechanical fatigue cycling (-15°C to
150°C)7 .................................................................................. 68

Figure 14. Inverse pole figure color key for an inverse pole figure orientation maps
in the [010] direction with sample crystal orientations for grains
having a particular color .............................................................. 72

Figure 15. SEM micrographs of as-fabricated eutectic Sn-Ag solder joint.
Figure 15(b) is 170um to right of Figure 15(a) used for

ix

Figure 16.

Figure 17.

Figure 18.

room temperature creep study ........................................................ 78

OIM maps of as-fabricated eutectic Sn-Ag solder. Figure 15(b) is

170 pm to the right of Figure 15(b). White boundaries 55-65°,

are twin boundaries; thin and thick black lines correspond to 3-5°

and 5-15° misorientations respectively .............................................. 79

[O O 1] and [O l 0] equal area pole figures of as-fabricated
Sn-Ag eutectic specimens. 17(a and b) correspond to Figures

16(a and b) respectively ............................................................... 82
Misorientation distribution function for as-fabricated specimen
with 2.5° bin size. .................................................................... 83

Figure 19(a). Misorientation profile for as-fabricated and room

temperature crept specimens corresponding to Figure 16(a) ............... 85

Figure 19(b). Misorientation profile for as-fabricated and room

Figure 20.

Figure 21.

Figure 22.

Figure 23.

Figure 24.

temperature crept specimens corresponding to Figure 16(b) ................. 86

Grain size distribution for as-fabricated and room
temperature crept specimens .......................................................... 87

SEM micrographs of as-fabricated eutectic Sn-Ag solder joint

after a global shear creep strain of 0.32. (a) Center and (b) Right

of the joint. The scratch in Figure 21(a) was intentionally put on

the specimen to assist in the measurement of the amount

of creep the specimen had undergone and is not a result of deformation ...... 91

OIM scans of eutectic Sn-Ag solder after room temperature
creep of 0.32 global shear strain ....................................................... 92

[0 O 1] and [O 1 0] equal area pole figures of Sn-Ag eutectic
specimens after room temperature global creep to 0.32 shear strain.
Figures 23(a and b) correspond to Figures 22(a and b) respectively ........... 93

Misorientation distribution function with 2.5° bin size for

specimen after global creep to 0.32 shear strain ................................... 94
Figure 25. SEM micrographs of as-fabricated eutectic Sn-Ag solder joint
used for 85° creep study ............................................................... 97

Figure 26. OIM maps of as-fabricated eutectic Sn-Ag solder joint
used for 85° creep study. Figure 25(b) is 324m to the
left of Figure 25(a) ...................................................................... 98

Figure 27. [O 0 1] and [l 0 0] pole figures of as-fabricated Sn-Ag solder
joint specimen used for 85° creep study ............................................. 99

Figure 28. Misorientation distribution before high temperature creep ...................... 100

Figure 29(a). Misorientation profile for as-fabricated and high
temperature crept specimen corresponding to Figure 26(a) ................. 101

Figure 29(b). Misorientation profile for as-fabricated and high
temperature crept specimen corresponding to Figure 26(b) ................ 102

Figure 30. Grain size distribution for as-fabricated and high
temperature crept specimen ......................................................... 103

Figure 31. SEM micrographs of the same regions as shown in
Figure 25(a and b), after global creep of 0.37 shear strain at 85°C ............ 109

Figure 32. OIM scans of eutectic Sn-Ag solder joint after high
temperature creep with a global shear strain of 0.37 ............................. 110

Figure 33. Pole figures of eutectic Sn-Ag solder joint after high
temperature creep with a global shear strain of 0.37. Figures 33(a and b)
correspond to Figures 32(a and b) respectively .................................. 111

Figure 34. Misorientation distribution after high temperature creep with
a global shear strain of 0.37 ......................................................... 112

xi

Figure 35.

Figure 36.

Figure 37.

Figure 38.

Figure 39.

Figure 40.

Figure 41.

Lattice orientations for as-fabricated specimen. The lattice show
orientations corresponding to Figure 26(a) before the crack
development seen after high temperature creep .................................. 113

Lattice orientations corresponding to various colors on either side

of crack in Figure 32(a) that developed after high temperature creep.

The lattice are taken from the same region as in Figure 35. Lattice
orientations corresponding to various colors in Figure 32(a) after high
temperature creep ..................................................................... 114

Effect of isothermal aging on as-fabricated eutectic Sn-Ag joint made
from paste solder. (a) As-fabricated condition and with overlay of OIM
map on SEM micrograph and (b) corresponding pole figures to (a),

(c) aged condition with overlay of OIM map on SEM micrograph

and ((1) corresponding pole figures to (0). Small highly misoriented
grains with a white boundary disappeared (near [110], marked with

a “+” on the pole figure in (b), is diminished in (d)). Point plots of

the pole figures of both specimens are inserted in-between (b and d)
with as-fabricated orientations shown in black and the aged orientations
in gray (each point represents one or more pixels of the scan). The
aged orientations in the (001) pole figure show 3 or 4 clusters of
orientations ............................................................................ 120

Misorientation angle histograms before and after isothermal aging.
The fraction of misorientations at 43, 60 and 70° decrease after aging,
and the number of misorientations in the 6-10° range increased .............. 121

Misorientation distribution function for as-fabricated specimen
showing 43° misorientations rotated about a [101] crystal direction
and 60° misorientations rotated about a [101] crystal direction ............... 122

Misorientation distribution function after aging showing decrease
in the intensity of the 43° misorientations and an increase in the (25°
misorientations ........................................................................ 123

Grain size distribution for as-fabricated and aged specimen
corresponding to the OIM maps in Figure 37. Aging causes an increase
in the size of the smaller grains ..................................................... 124

xii

Figure 42.

Figure 43.

Figure 44.

Figure 45.

Figure 46.

Effect of isothermal aging on relative misorientations starting

from the bottom to the top of the red line shown in

Figure 37(a,b). Aged specimens had a misorientation of about

10° from the as-fabricated orientation using the orientation at

the bottom as a reference orientation .............................................. 125

SEM micrographs after 370 TMF cycles. (a) Region 1 is near the
center of the joint, (b) region 2 is 362nm to the left of (a), (c) region 3
is 229m to the right of (a) and ((1) joint configuration .......................... 129

Effect of TMF on as-fabricated eutectic Sn-Ag joint made from

paste solder from region 1 in Figure 42(a). (a) OIM map of as-fabricated
condition (b) OIM map of same region after 150 TMF cycles,

and (c) OIM map of same region after 370 TMF cycles ........................ 130

(a) Pole figures corresponding to OIM map of as-fabricated

specimen in Figure 43(a), (b) pole figure after 150 TMF cycles,

and (c) after 370 TMF cycles. The dominant orientation has persisted

after 370 cycles, which is evident on comparison of the (001)

pole figures ............................................................................ 131

Misorientation angle histogram corresponding to region 1 in
degrees for as-fabricated, 150 and 370 TMF cycled specimen.

The fraction of misorientations at 43, 60, 70 and >75° diminish
after 370 TMF cycles and there is an increase in the number of <10°

misorientations and no change in the 20° misorientations after
370 TMF cycles ....................................................................... 133

Figure 47 (a). Misorientation distribution function for as-fabricated specimen

showing 60° misorientations rotated about a [100] crystal
direction. Misorientations >75° are rotated about an axis
close to a [313] crystal direction ................................................ 134

Figure 47(b). Misorientation distribution function after 150 TMF cycles showing

decrease in the >75° misorientations and a slight increase in the <15°
misorientations as compared to Figure 46(a) ................................. 135

Figure 47(c). Misorientation distribution function after 370 TMF cycles showing

an increase in the intensity of <15° misorientations ......................... 136

xiii

Figure 48. Grain size distribution corresponding to region 1 for as-fabricated,
150 and 370 TMF cycled specimen and OIM maps shown in Figure 43.
TMF caused an increase in the grain size from 10pm to 20pm and a
decrease in 2pm grains .............................................................. 137

Figure 49. Effect of TMF on as-fabricated eutectic Sn-Ag joint made from
paste solder from region 2 in Figure 42(b). (a) OIM map of
as-fabricated condition (b) OIM map of same region after 150
TMF cycles, and (c) OIM map of same region after 370 TMF cycles ........ 140

Figure 50. (a) Pole figures corresponding to OIM map of as-fabricated
specimen in Figure 48(a), (b) pole figure after 150 TMF cycles, and
(c) after 370 TMF cycles . The dominant orientation has persisted
after 370 cycles, which is evident on comparison of the (001)
pole figures ............................................................................ 141

Figure 51. Misorientation angle histogram corresponding to region 2 in degrees
for as-fabricated, 150 and 370 TMF cycled specimen.
The fraction of misorientations at 43, 70, 75 and 80° diminish after
370 TMF cycles and there is an increase in the number of <10
and 60° misorientations after 370 TMF cycles .................................... 142

Figure 52. Grain size distribution corresponding to region 2 for as-fabricated,
150, and 370 TMF cycled specimen and OIM maps shown
in Figure 48. TMF caused an increase in the grain size from 10 to
20pm) and decrease in the 2pm grains ............................................ 143

Figure 53. Effect of TMF on as-fabricated eutectic Sn-Ag joint made
from paste solder from region 3 in Figure 42(c). (a) OIM map of
as-fabricated condition (b) OIM map of same region after 150
TMF cycles, and (c) OIM map of same region after 370 TMF
cycles. The primary orientation in the as-fabricated specimen
was consumed by the secondary orientation after 370 TMF cycles ........... 144

Figure 54. (a) Pole figures corresponding to OIM map of as-fabricated
specimen in Figure 52(a), (b) pole figure after 150 TMF cycles
and (c) after 370 TMF cycles. The dominant orientation switched
places after 370 cycles, which is evident on comparison of the
(001) pole figures ......................................................................... 145

xiv

Figure 55. Misorientation angle histogram corresponding to region 3 in
degrees for as-fabricated, 150, and 370 TMF cycled specimen.
The fraction of misorientations <10° and at 43° diminish after
370 TMF cycles and there is an increase in the number of 60,70
and 75° misorientations after 370 TMF cycles ..................................... 146

Figure 56. Grain size distribution corresponding to region 3 for as-fabricated,
150, and 370 TMF cycled specimen and OIM maps
shown in Figure 52. TMF caused an increase in the grain size

from 10 to 20pm grains and a decrease in the 2pm grains ...................... 147

Images in this thesis are presented in color

XV

INTRODUCTION

Soldering is a joining technique being used since ancient times (2000 to 3000
years‘). Soldering, like welding joins two materials on heating them to a temperature
with a filler material whose liquidus does not exceed 450°C. In the past several decades
solder joints have made valuable connections in automobiles, aircrafts, spacecrafts,
computers, televisions and electronics.

Soldering has emerged as an integral part of the electronic assembles where it
helps in connecting several devices on to printed circuit boards (PCB). Several new
packaging technologies like surface mount technology (SMT), ball-grid array (BGA),
plated through-hole (PTH) and multi-chip modules (MCM), have made it possible to
reduce the size of the electronic packages. Miniaturization of electronic components has
led to smaller electronic packages and an increase in the interconnection density.
However, the higher package density and the reduction of joint dimensions has
compelled the solder joints to perform better.

So far, no other technique has been developed to replace solder as an interconnect
to the same level of performance. Individual components such as chips, resistors,
capacitors, etc. are mounted via SMT or PTH type assemblies on PCBs with the solder as
the only interconnect in most cases (except when larger components need to be mounted
and then screws and straps are used). These solder joints not only serve as mechanical
supports, which physically incorporate such components onto the PCB, but also as
electrical connections for linking the components to the electronic circuitry. Smaller
electronic packaging puts forth several constraints on the solder interconnect and

necessitates better inherent properties in the solder to resist failure during operation.

About 70% of failure in most electronic circuitry is solder related, which makes it
important to understand their deformation behavior and modes of failure.

Lead-based solders have been used for several decades as solder interconnect
material. Table I shows some of the lead-based solders along with their melting
temperatures. However, since lead is toxic, environmental concerns and international
trade restrictions have warranted the eradication of lead from all electronic based
components 2'5. Several alternatives have been sought in this regard to replace lead-based
solders, some of which are given in Table I. Eutectic tin-silver (96.5Sn-3.5Ag by wt.%)
based solders have gained particular interest in recent years due to their higher melting
temperatures (221°C) as compared to lead-tin (37Pb-63Sn wt.%) solders (183°C). There
is sufficient data on mechanical properties and microstructural details of lead-based
solders, however much less is known about tin-based solders, which has different
characteristic properties than Sn-Pb solders. Therefore the selection of the right material
to replace Sn-Pb solders is still in the embryonic stages because deformation
characteristics and failure modes for eutectic Sn-Ag have not been fully characterized.
Different damage accumulation processes occur in service, at different times during the
life cycle that can lead to the ultimate failure of a solder joint. Hence there is need to

study Sn-based solders to ascertain their usefulness as good solder interconnects.

Table 1. Composition and melting temperature of various solders.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Alloy Melting Range Bulk Tensile Brinell
(wt.%) (”0 Strength Hardness
Liquidus Solidus (MP3) (BI-IN)
Sn-based
9OSn-10Ag 221 295 61.5 12.9
9SSn-5Ag 221 245 - -
96.5Sn-3.5Ag 221 221 61.5 12.9
9SSn-5Sb 233 240 43.9 1 1.4
808n-202n7 200 270
508n-501n7 1 17 125
42Sn-58Bi 138 138
9SSn-3.5Ag-1Cd-O.58b8 218 221
99.38.1070:2 227 227
95.58n-4Cu-05Ag2 - 216 216
Pb-based
90Pb-lOSn 3 225 300
80Pb-20Sn 183 277 - -
70Pb-30Sn 183 257 41.9 8.7
50Pb-508n 183 216 — -
37Pb-638n 183 183
97.5Pb-lSn-1.5Ag 309 310
93.5Pb—58n-1.5Ag7 296 301
52Pb-30Sn-18Cd7 145 145
32Pb-16Sn-52Cd8 96 96
50Pb-501n7 180 209

 

 

 

 

 

 

* All data can be found in Ref.6, exceptions are the ones with specific reference numbers.

 

Deformation is inherent in any material put in service over a period of time. One
of the most important deformation processes is TMF, wherein the solder material goes
through several cycles of repeated reversed stress states and relaxation as a consequence
of temperature variations. The stresses can be induced by mechanical means, but during
service it is most often due to the coefficient of thermal expansion (CTE) mismatches
between solder/substrate/component. Anisotropic behavior of Sn plays an important role
9 at stress levels possible in a joint. Bulk tin expands much more (along the c-axis) on
heating as compared to the copper substrate, leading to various stress states within the
joint depending on the relative orientation of crystals. Lee et.al.9 have made an attempt to
look at the stresses that can arise within a solder joint as a consequence of different
crystallographic orientations of the Sn grains over a 165° range of temperature.

Another important factor which needs consideration during deformation is that
eutectic Sn-Ag solder does not have a soft phase like Pb in Sn-Pb solder which can
accommodate the stresses resulting from the anisotropic deformation of Sn, hence
retained stress in the solder joint leads to extensive stress accumulation during the large
temperature excursions (which can range from sub-zero to 150°C) in typical automotive
under-the—hood type of situations. This stress is not completely relaxed even after long
periods of time”, resulting in nucleation of micro cracks that progress with time and
combine to cause failure of the jointn'lz. Most solder joints tend to fail in regions close
to the interphase boundary in the solder matrix due to the solder being relatively soft as
compared to the hard interphase intermetallic layer formed between the solder and the

substrate.

Other prominent processes occurring during service, are aging and creep. Solder
joints can experience high homologous temperatures during service. Under normal
operating conditions temperatures of around 150°C (423°K) are common. This
temperature is greater than 0.5Tm for Tin-silver solder (where Tm=221°C, i.e. 494°K) and
hence there is recrystallization, recovery and grain growth occurring simultaneously in
the solder joint. Solder joints not only serve as electrical connections but are also
mechanical supports to the surface mount components and hence need to have good creep
properties which are of great concern at such high homologous temperatures.

There is a strong correlation between the microstructure and the properties
exhibited by the solder materia12’13'”. There is also a direct correlation between
microstructure and the crystallographic orientations that go with the microstructure. Such
crystallographic orientations can affect fracture behavior and mechanics, corrosion
resistance, precipitation and recrystallization. Texture studies have been carried out for
several years using X-rays and the technique has allowed theories to be developed that
describe how preferred crystallographic arrangement in the material evolves during
service conditions. Orientation Imaging Microscopy (OIM) using Electron Backscattered
Diffraction Pattern (EBSP) is the latest development in the texture arena, and it enables
us to visualize the direct correlations between texture and the microstructure.

Humphreys15 in his overview paper discusses how EBSP is used to investigate
phase distributions, grain and subgrains and grain boundary characteristics in Al alloys.

Randle et.al.16

discuss how grain boundary misorientations and texture affect anomalous
grain growth in the nickel-based alloy Nimonic PE16 for particular heat treatment

conditions. Tai et.al.l7 in their paper have used the EBSP technique to study the

 

crystallographic orientations of PZT ceramics and their average and local preferred

orientations. Hasegawa et.al.18

discuss how EBSP technique was used to study the
mechanisms of microstructure development caused by static and dynamic
recrystallization in pure nickel. Hong et.al.19 showed that the magnetic property of grain
orientation in electrical steels is strongly dependent on the texture orientation of the
secondary recrystallized grains. Herein the grain size and texture during primary
recrystallization influence the evolution of secondary recrystallization and hence the
magnetic properties of grain oriented electrical 3% Si steels. Bieler and Serniatin20 used
EBSP to examine heterogeneous deformation mechanisms in hot working of Ti-6Al-4V.
The investigations illustrated above indicate that EBSP was effective to study
how changes in the microstructure cause changes in the properties. There is need to
know how properties change during service in Sn-based solders to predict reliability.
Thus EBSP may help identify mechanisms of change that affect properties of solder
joints. Since no prior studies with respect to crystallographic orientations and texture

have been carried out in Sn-based solders, EBSP has a broad scope with the ability to

explore a variety of issues of concern in solder material.

1.1 BACKGROUND FOR TEXTURE AND OIM

Texture is defined as a collective distribution of crystallographic orientations in a
polycrystalline aggregate”. Gaining control of texture gives enhanced ability to optimize
properties at the production level and hence reduce costs. X-ray diffraction has been the
most commonly used technique to determine texture of materials (macro texture).
However, X-rays provide no better spatial resolution than the area illuminated by the
beam, which can be quite small when a synchrotron source is used22 (which is a high
intensity parallel and focused X-ray beam). Hence a technique based on X-rays is
usually only good for macrotexture determination, where no information about
misorientations between grains can be obtained.

The transmission electron microscope (TEM) and scanning electron microscope
(SEM) using electrons as their primary source can also be used for microtexture
determination. Microtexture is defined as a population of individual crystallographic
orientations, which are usually related to one or more features in the microstructure.
TEM can be used where precise measurements of grain and subgrain orientation or
misorientations are desired. However, the TEM process is quite tedious because
multistage specimen preparation is time consuming. Since only a small electron
transparent region in the foil is obtained, the orientation of only a small fraction of the
total volume of the thin foil is obtainable, and hence it is difficult to have statistical
certainty that observations correlate to the bulk changes and texture in the specimen.
Also, TEM needs off-line diffraction pattern indexing, though recently on-line techniques

are commercially available (hkl Channel Acquisition software version 4.2 by HKL

Technology, Inc., Blaakildevej, 17k, Hobro, DK-9500, Denmark and OIM data collection
software version 3.5 by TSL Laboratories, Draper, UT).

Grain orientations can be measured in the SEM with two techniques, namely
Selected Area Channeling (SAC) and Electron Back-scatter Diffraction Pattern (EBSP).
In SAC one measures the orientation of individual grains, but the limited angular range
(15°) and spatial resolution of ~15um are some of the drawbacks along with the lack of
automation. Thus, it is tedious to measure the entire set of local orientations to correlate
with the microstructure of the specimen. One can obtain a “mesotexture” for the larger
grains, which provides us information about particular grains and their orientation
relationships with neighbors. (See Figure 1).

On the other hand, EBSP has a better spatial resolution (100-300nm) and angular
range (up to about 80°), possibly easier specimen preparation and on-line acquisition of
data and analysis, which allow large regions of the specimen to be analyzed quickly with
reasonably good accuracy. Hence it has gained popularity in a very short time. The
texture one obtains with EBSP is called microtexture where crystallographic information
of individual crystals / grains and the grain boundaries is delineated in the form of a two-
dimensional map, where every pixel corresponds to the spot from where it was taken on
the specimen during the scan. This map is called an Orientation Imaging micrograph and
this technique is called Orientation Imaging Microscopy (OIM). These maps correlate
very well with the microstructural features and give an insight into the crystallographic
orientations, which is invaluable for comprehensively studying any material and material

behavior. Solder joints are often about 100m thick; hence conventional X-rays are

impracticable. SAC is time consuming and hence the EBSP technique is a favorable

technique to analyze texture of solder joint specimens rapidly.

Macrotexture

w‘yg

 

 

 

   

Microtexture / Mesotexture
‘ ’ \‘ .
L é
n
(b)

 

Figure 1. An illustration of the relationship between (a) micro and (b) mesotexture.
Macrotexture shows 14 grains oriented with respect to the specimen X, Y and Z. (a)
Microtexture correlates specific grains and their crystal orientations; three different grain
orientations have three different c-axis poles (shown by red, blue and green colored
grains)23 in Figure 1(c). (b) Mesotexture shows grain boundary relationships (shown by
dotted and black thick lines) which help reveal grain boundary character that is
statistically described in Figures 1(d) misorientation distribution function (MODF) and
Figure 1(e) histograms of misorientation angle.

Max = 100

010

 

 

 

 

001 "0

 

 

 

(C)

Figure 1(c). Pole figure with point plots and a Gaussian distribution that shows the
macrotexture.

ll

10° 110 2 40° 110

  
  

0° ’10 33° 110

100 001 100 001 ":0 001

  
  
  

50° 110 60° '10 70° 110 80° 110

  

100 001 100 00l

00° '10 . .
:8
.64
‘ raga,
Pnln‘ODO

100 001 100
((1)

90" 110 1

Figure 1(d). Misorientation distribution functions (MODF).

Misorientation

 

Frequency

 

 

 

 

Distance B Misorientation, deg

(e)

Figure 1(e). Histograms of misorientation angle.

13

1) Electron Back-scatter Diffraction Pattern (EBSP): Incoherent scattering of
elastically scattered electrons in a thick specimen gives rise to Kikuchi patterns. These
electrons are sometimes called diffusely scattered electrons. Elastic scattering takes place
due to deflection of the electrons by the positive charge of the nucleus, taking into
account the negative charge of the revolving electrons and near collision with electrons.
The interaction volume‘ in the solid specimen gives rise to the effect of back-scattering.
Most of these electrons are deviated by about 90° from the incident direction during back-
scattering. These electrons then undergo both elastic and inelastic scattering in the
interaction volume before they re-enter the unit hemisphere of solid angle from which
they enteredz“. The diffracted beam will be in the form of cones which when projected
onto a screen in 2-dimension appears to look like parabolas. These parabolas appear as
two parallel lines (called Kikuchi lines) if one is to view them near the optic axis. These
Kikuchi lines are fixed (both angular and spatial) for a particular crystal structure and
they are the projections of the geometry of the lattice planes in a crystal”. The angles
between the Kikuchi lines (or Kikuchi bands as they are sometimes called) along with the
stereographic projection are used to index the Electron Back-scatter Diffraction pattern

(EBSP) or Kikuchi pattern. (Figure 2)

 

Interaction volume is the volume inside the specimen in which interactions between the incident electrons
and those from the specimen take place. This volume depends on 1) the atomic number of the material of
the specimen; higher atomic number implies more electron absorbance and hence a smaller interaction
volume, 2) the accelerating voltage; higher voltages implies more penetration and generation of a larger
interaction volume and 3) the angle of incidence for the electron beam; the greater the angle (further from
normal) the smaller the interaction volume.

14

 

(b)

Figure 2. Kikuchi pattern of tin crystal. (a) Pattern showing Kikuchi bands and (b) after
indexing.

2) Microtexture Data Collection: Automated EBSP (Electron Backscattered Pattern) is
the most preferred technique to study micro and meso textures. The essential components
for this method of data collection are an SEM with a stage tilt control, a phosphor screen
viewed with a CCD video camera and a TV, all interfaced with a computer for on-line
data analysis. Figure 3 is a simple sketch illustrating EBSP formation and data
collection. The specimen is mounted in a holder and tilted to an angle of 70°. The
electron beam trajectory strikes the surface of the specimen emitting backscattered
electrons, which hit the phosphor screen and are converted into optical light pulses
transmitted through optical fiber cable, which are then reconverted into an electronic
signal and displayed on a TV screen. The computer captures the screen image (which is
typically averaged to improve resolution) and indexes the pattern in real time to give a
crystal orientation recorded in terms of “Euler” angles. The beam then moves to the next

spot and the procedure is repeated.

16

Phosphor screen
Electron beam

 

Backscattered electrons

TV Monitor

 

Kikuchi pattern

Figure 3. Typical setup for EBSP.

3) Sample Preparation and Mounting: The sample preparation for EBSP is relatively
straightforward. The surface need not be absolutely flat, though it needs to be free from
any oxide layer, impurities and contamination since the penetration depth for back-scatter
electrons is approximately 20nm. This can be easily accomplished by ultrasonic
cleaning, plasma cleaning (incases where high temperatures is not a problem since
surface temperature of 300°C are reached) followed by storing the specimen under a non-
oxidizing environmentzs. Surface deformation can cause difficulty in indexing the EBSP
pattern (which may get distorted or become less distinct) and there are various levels of
deformation, which can be tolerated for indexing. Since the angular relationships
between bands remains unchanged, it might be possible to index the EBSP, however the
confidence in indexing depends on the extent of deformation, as the intensity of the
Kikuchi bands decreases with increase in deformation. It is believed that the usual
metallographically prepared specimens are not suitable for EBSP and additional steps are
required. As a general rule it is proposed that all specimens undergoing EBSP analysis
be chemically etched, electro polished or metallographically polished with 20nm silica

particles in an alkali suspension26

. Once the specimen is ready, it needs to be mounted
onto the sample holder taking care that there is no surface damage or contamination
during mounting.

The specimen is mounted in a specimen holder, which is designed so that the
surface of the specimen makes an angle of about 70° 23 with the horizontal axis. Precise
tilt is an integral part of the calibration setup. Calibration is achieved using a Silicon

single crystal with [001] as the surface normal. The geometrical aspects and procedure

for calibration can be found in Ref 23.

18

Spatial resolution is dependent on the acceleration voltage, probe current, working
distance and tilt angle. Higher acceleration voltage is preferred to increase the size and
depth of the interaction volume, however 20—25kV seems to be an optimum value. Probe
currents of the order of about 5mA or higher are considered optimal. Shorter working

distances are preferred to minimize focusing problems. A decrease in the angle from 75°

to 60° results in the increase in spatial resolution, with a loss in the proportion of

backscatter electrons to absorbed electronszms.

Hence a 70° angle is considered most
favorable29 in majority of cases, though in a particular system one can obtain better
conditions by tweaking one of these parameters with a trial and error approach.
4) Pattern Recognition: The EBSP pattern can be used to identify crystal structure. The
EBSP pattern first obtained is studied for rotation angles and mirror planes which can be
easily accomplished by looking at the intersecting Kikuchi bands. Further, calculations
of angles between various bands on the EBSP and the spacing between parallel bands can
be determined. Further information on crystallographic details that can be obtained from
an EBSP are found in referenceszs'w”.
Once all the above steps are completed and a region of interest is located, the
beam is rastered over a chosen area of specimen. The scan coils of the SEM are turned
off (i.e. the spot mode), and the beam interacts with only a small volume of the specimen
to display an image of the EBSP on a low-light TV monitor. The computer program
indexes the zone axes and Kikuchi bands and measures the inter-axial and inter-planer

angles. The orientation is determined in real time and a pixel of orientation data is stored

before the beam is automatically positioned to the next spot and the process repeated.

19

Being an automated process, several such areas can be scanned one after the other. The
dataset is subsequently post-processed to generate maps and plots.

OIM (orientation imaging microscopy) assigns a color to particular crystal
orientation, so that a given crystal orientation has the same color. Misorientations
between grains can be visualized by the degree of color difference. Thus microstructure
and crystal orientation are simultaneously displayed on a map. Figure 1 shown earlier
reveals the different ways information obtained from an OIM scan can be processed for
better understanding of the data. Figure 7 shows crystal orientations being expressed
using color-coded maps and inverse pole figures. Grain size, shape, distribution, etc., are
available and can be deduced with the software. The distribution of grain boundary
misorientations (i.e. high, low, twin, special boundaries) are expressed as misorientation
distribution functions (MODF) or histograms of rrrisorientation angle.

The fast and relatively easy automated setup, along with simple sample
preparation and user friendliness, EBSP allows researchers to explore topics such as
recrystallization, grain size, grain growth and microstructural evolution. The software
allows us to represent texture in terms of pole figures or OIM maps. The grain boundary
distribution can be studied with the help of misorientation distribution functions (MODF)
and histograms of rrrisorientation angles. The plots along with the OIM maps serve as
effective tools to understand grain boundary formation and changes. Hence OIM is an
indispensable tool for better understanding and characterization of the highly dynamic

microstructure of solder in a joint configuration.

20

1.2 LITERATURE REVIEW

A) Thermal and Mechanical Processes Experienced by a Solder Joint in

Service:

1) Aging:

All solder joints undergo aging with time, which results in the alteration of the
microstructure. Depending on the temperature to which the solder joint is exposed during
service, the rate of aging can differ. Higher temperatures naturally cause faster aging.
Solder joints in typical automotive under-the-hood service conditions are exposed to
temperatures of around 150°C, while those in computer related applications experience
temperatures of 50-80°C. Such high temperatures cause dynamic recrystallization and
grain growth to occur within the solder microstructure. This change in the microstructure
alters the properties of the solder joint and changes the way the solder material would
respond to further deformation processes.

In eutectic Sn-Ag solder joints aging produces coarsening of the Ag3Sn particles
in the solder matrix”. The intermetallic layers of Cu68n5 and Cu3Sn also grow in
thickness from approximately 0.7um to about 10pm after aging at 150°C for 1000
hours”. Jang et.al. observed a 211m thick Cu68n5 layer after a 60 seconds reflow of a
eutectic Sn-Ag solder at 250°C“.

The material in the joint configuration can undergo three basic types of stress /
strain imposition: 1) time dependent monotonic loading e. g. tensile loading, shear loading

and creep and 2) cyclic deformation as in fatigue“.

21

2) Creep:

Creep is the progressive deformation of a material under constant stress at an
elevated constant temperature. It is typically seen that the strength of a material
decreases with increase in temperature, which is due to a corresponding increase in
diffusion of atoms at elevated temperatures. This can strongly affect the mechanical
properties of the material. Higher temperatures also give additional mobility to
dislocations, which can move by the climb process and additional slip-systems can come
into play“. At elevated temperatures the strength of the material depends on both the
strain rate and the time for which it is being strained. Therefore the number of variables
increases as the temperature increases.

Creep deformation becomes important in human time frames at temperatures
greater than 0.5Tm (where Tm is the melting point of the material in absolute temperatue).
The creep experiment involves loading a tensile specimen at a constant temperature
(>0.5Tm) and at a constant load. The strain (extension) of the material is measured as a
function of time. Hence studies based on creep experiments can take several hours to
even years to achieve the desired information. A typical creep curve is shown in Figure
4. The curve can be ideally divided into three regions; primary, secondary and tertiary
creep. The creep rate given by de/dt decreases rapidly with time initially during primary
creep and is approximately constant in the secondary creep region. The initiation of
tertiary creep is an important point on the creep curve since after this point the creep rate
increases steadily until the specimen ultimately fractures. A long secondary creep period

or a very low minimal creep rate is essential for longer service life of the specimen.

22

Strain, a

 

 

 

 

 

 

 

Primary Secondary
Creep Creep
I II
(——)
de/dt = minimum creep rate
Time, t

Figure 4. Typical creep curve showing the three stages of creep. Curve A is
constant-load test; curve B, constant-stress test“.

23

Representation of the secondary creep deformation by a mathematical equation

commonly uses the Dom equation,37’38 which is given by:

42; = CGb (b/d)” (r/G)" Do exp(-Q/RT)
dt kT

where,

dys / dt = steady state creep rate,
G = shear modulus,

b = Burger’s vector,

T = absolute temperature,

d = grain size,

I = applied stress,

Do: frequency factor,

Q = activation energy for the deformation process,
11 = strain exponent,

p = grain size exponent, and

C = constant characteristic of the underlying mechanism.

Darveaux and Banerji39 developed constitutive relations, which describe the
behavior of solder joints under a wide range of conditions. They showed that eutectic Sn-
Ag solder absorbed larger strain prior to failure as compared to 60Pb-4OSn solder joints.

However, creep properties are affected by several factors. Higher melting
temperature solders exhibit lesser creep deformation if the applied strain is small (which
is usually the case in typical electronic packages)“. Guo et.al.4‘ and Choi et.al.42'43 have

shown that recently developed composite solders and alloyed solders are more creep

24

resistant than non-composite counterparts due to the intermetallic interphase layer formed
between the solder matrix and the composite reinforcement.

Testing solder joints rather than bulk solders is the best way to study the
deformation and microstructural effects of solder, since the microstructure of bulk
specimens is different from solder joints. Solder interconnect material in the joint
configuration experiences several convoluted and varied effects, which lead to their
deformation and ultimate failure that cannot be realized if solder material is tested
alone”. Darveaux and Murty’s44 test results show that creep properties of solder in joint
configuration is quite different than bulk solder, with joints showing better creep
resistance due to the effect of joint constraints.

Creep seems to be the dominant deformation process as one reaches temperatures

greater than 0.5Tm. Igoshev et.al.45

show that accumulation of grain boundary defects
start early during creep and last for 70-80% of the specimen’s life. Depending on the
stress states during creep at high temperatures, failure can take place via transcrystalline
(at lower stresses) or inter—crystalline (at higher stresses) cracking. Darvaeux and
Banerji39 have shown that dislocation climb is the main factor contributing to creep

deformation, however stress states in the solder joint can change and failure can occur by

fatigue.

25

3) Thermomechanical Fatigue (TMF):

Fatigue failures are those wherein the material subjected to repeated fluctuating
stress states fails at a much lower stress than that required to cause failure in a single
application of load”. Figure 5 gives some examples of fatigue cycles. Figure 5(a) shows
a sinusoidal curve with complete reversal of stresses. Figure 5(b) shows repeated
reversals in stress however the stress range is always on the positive (tensile) side. Figure
5(c) shows a random fatigue cycle and Figure 5(d) shows cyclic deformation with hold

times.

26

+

Stress

+

Stress

+

 

 

 

 

 

 

 

 

 

 

0a
6, ‘v'5
___1 _
Time —-—> Time —-—->
(a) (b)
.1.
a U
Time ——> Time —"
(C) (d)

Figure 5. Typical fatigue stress cycles. (a) Repeated reversed sinusoidal stress curve with
complete reversal of stresses, (b) repeated stress reversals on the positive (tensile) side,

(c) random fatigue cycle and (d) cyclic deformation with hold times.

27

Though Coffin-Manson’s law states that the fatigue cracking in steel is related to
the total plastic strain, in solder alloys with low melting temperatures, the fatigue
behavior is related to the equivalent strain amplitude and change in the properties with
temperature. The fracture is not only dependent on fatigue undergone by the joint but is
also dependent on creep at such temperatures“. Harada and Satoh46 have developed an
empirical equation to estimate the thermal fatigue life of 96.58n-3.5Ag solder. Their
equation gives a modeling approach to crack growth as a result of fatigue. It does not
attempt to model crack nucleation, which is a more critical phenomenon with reference to

solder interconnects1 "12. The equation is given by
Nf = C ln((Aaf+ B)/B)f" . exp (Q/kTmax) As eqmax'"

where,
Nf = thermal fatigue life,
As eqmax = maximum equivalent strain range,
Q = activation energy,
Tm = maximum temperature,
f = frequency of temperature cycle,
k = Boltzmann’s constant,
A = 5.87,
B = 1.40 x 103,
C = 0.234,
n = 1.2, and

m = 0.33.

28

Fatigue strength of a material usually increases with a decrease in temperature.
At higher temperatures, transition from fatigue failure to creep can occur and
transcrystalline fatigue failure may change to intercrystalline creep failure”. In general a
material with high temperature creep strength will have better fatigue properties at high
temperatures. Fine grain size gives better fatigue properties at lower temperature. As the
temperature increases, the differences in fatigue properties of coarse and fine grain sized
materials are reduced with increasing temperature until high temperatures are reached.
At high temperatures creep dominates and hence a large grain size is preferred for creep
resistance.

The stresses produced during fatigue need not only be mechanically induced.
Fluctuating thermal stresses induced by differential heating and cooling and due to
differences in the coefficient of thermal expansion (CTE) in the material can lead to
stress accumulation, which leads to failure of the material. Such repeated application of
thermal stresses of low magnitude that leads to failure is called thermomechanical
fatigue. A simple equation showing the stress developed in a constrained material cycled
between two different temperature extremes is given by:

a' = a E AT,

where,

a 2 stress developed in the material,

a = coefficient of thermal expansion,

E = elastic modulus, and

A T = change in temperature.

29

The life prediction of a solder joint is dependent on the susceptibility of a solder
joint to TMF. TMF in a solder joint can occur due to the cyclic changes in the
temperature experienced by the joint. Also the various constituents in the electronic
assembly play an important role during such temperature fluctuations, since different
constituents have different CTE. The plastic strain accumulation is thus a function of the
total change in the temperature, the rate and the magnitude at which this change occurs
and the inherent constraints in the electronic assembly and its interaction with the time
dependent and cyclic deformation processes occurring in the solder alloy“. A
constitutive equation taking into account these several processes is needed and a model

for this needs to be developed.

30

B) Eutectic Tin-Silver Solder

1) Crystal Structure and Directional Properties:

Eutectic Sn-Ag solder (96.5%Sn-3.5%Ag in wt.%) consists of two phases, B-Sn
and the Ag38n intermetallic phase. The B-Tin has a Body-Centered Tetragonal unit cell

with four atoms occupying the positions 0 0 0, 0 1/2 '/4, V2 0 3%, V2 1/2 1/2 in the unit cell as
shown in Figure 648. It is a squashed tetragonal cell with a=b=5.8197 A and c=3.l75

A 43, with c/a = 0.5456.

 

 

Figure 6. B-Sn unit cell (lattice parameters, a=b= 5.8197 A and c=3.l75 A 48).

31

The Sn unit cell has four closed packed directions”; [001], [111], [100] and [101]

and four closed packed planes”; (100), (110), (101) and (121). At different temperatures

different slip systems come into play. Table H shows the various possible slip systems at

different temperatures. Twin formation is seen frequently in tin and Table II also shows

the possible twinning plane and direction for tin. Twins have low energies associated

with them and if a twin is formed during solidification, internal strains at its boundaries

are so small or absent that recrystallization is not promoted in such cases

Table 11. Possible slip and twin systems in B-Sn.

50.5 1

 

 

 

 

 

 

 

 

Glide / Slip Systems Twinning Systems
Low Temp. (~20°C) High Temp. (~150°C)
Slip Slip Critical Slip Slip Planes" Direction“
Plane Direction Stress, Plane”53 Direction '
kg/mm2 ‘
(100) [001] 0.19 (110) [-111] (301) {-301]
(110) [001] 0.13
(101) [10-1] 0.16
(121) [10-1] 0.17 [

 

 

 

 

 

 

 

* Critical stress in kg/mm2 at 20°C and 0.01% impurity.
All data can be found in Ref.52, except the ones specially marked.

The Young’s Modulus in the a—direction is 54 GPa and in the c-direction is 85

GPa as shown in Table III“. The CTE for tin in the a-direction is 15.45 x 1045 /°C and

30.5 x 106 /°C in the c-direction54. However, tin is highly anisotropic and the value of

32

 

modulus changes with crystal direction as calculated by Lee et.al.9 The anisotropy of tin
in the solder joint can lead to very high stress accumulation, which can contribute to the

failure of the solder joint, assuming elastic deformation is imposed on bi-crystals.
The Ag33n has an orthorhombic structure with a=5.968 A, b=4.7802 A,

c=5.1843 A 55. The Ag3Sn undergoes a transformation at about 60°C55. However the
nature of this transformation is unknown and X-ray studies have shown that there is no

lattice change”.

33

Table III. Constants for various solder joint constituents“.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Cu Sn Cugsns Cu3Sn
(Polycrystal) (Single crystal) (Polycrystal) (Polycrystal)
a-dir. c-dir.

Young’s Modulus, GPa 117 85 54 85.56 108.3
Shear Modulus, GPa -- -- 50.21 42.41
Hardness, Gpa 2.94 0.98 3.71
Thermal Expansion, x 17.1 15.4 30.5 16.3 19.0
10‘I°C
Thermal Diffusivity, -- -- 0.145 0.24
cmzlsec
Resistivity, pQ-cm 1.7 11.5 17.5 8.93
Density, g/cc 8.9 7.3 8.28 8.9

 

34

 

2) Microstructure of Eutectic Tin-Silver:

The microstructure of eutectic Sn-Ag solder consists of Ag3Sn precipitated in a tin
matrix surrounding the so-called tin cells. The grain boundaries are difficult to reveal, as
effective etchants for this system are not well established. Depending on the cooling rate
one can obtain variations of this basic microstructure. Under equilibrium cooling the
most favorable growth direction for tin is along the [110]58 crystal direction, which gives
rise to dendritic arms in the microstructure. With rapid cooling one sees a more or less
equiaxed microstructure, with Dtin cells surrounded by the eutectic mixture.
Microstructures of eutectic Sn-Ag solder joint are given in Figure 7. It is evident that a
microstructure produced with a low soldering temperature and a fast cooling rate would
yield an optimal solder joint since low soldering temperature implies lesser superheat into
the system and similarly a fast cooling rate would prevent dendrite formation and

produce a more equiaxed microstructure33’59.

35

Solder

Solder
EquiaxedGrains’ , . . . ,

/Sn Dcndritcs

\ .
'1 Angn

.‘ f ' 'V‘CucSns
c - .A"

- . '- .~ . x

(c) 15pm (d) 8.6Em (e) 12um
Figure 7. SEM rrricrographs revealing microstructure of eutectic Sn-Ag solder.
(a) Solder joint showing equiaxed Sn-cells surrounded by Aggsn intermetallic, (b) same
joint revealing dendritic Sn-cells in some other region and (c,d,e and f) higher
magnification micrographs of particular regions of the same joint. These features are
common to all solder joints depending on the maximum temperature reached during

soldering and the cooling rate.

 

36

The microstructure in the joint configuration with copper substrates is slightly
different due to dissolution of copper into tin, which gives rise to scallop shaped Cu68n5
and Cu3Sn intermetallic phases at the copper-tin interphase as well as dispersed
hexagonal rod-like Cu6Sn5 particles in the tin matrix. Cu6Sn5 is found at the interface
with the Sn-rich phase and the Cu3Sn found between Cu and Cu6$n5 (and is closer to the

Cu-rich phase to maintain thermodynamic equilibrium). The lattice parameters for

hexagonal Cu68n5 are as follows: a = 4.192 A and C: 5.037 A 55. The thickness of this
intermetallic layer is dependent on the heating and cooling rate used during joint
fabrication. A higher temperature facilitates a thicker intermetallic layer. Depending on
the amount of heat input into the system during the entire soldering process as explained
by Guo et.al.°°, the total volume of the secondary intermetallic phases of Sn with Cu can
be controlled. Higher heat input (thermal flux) allows greater diffusion and hence thicker
intermetallic interphase layers. Aging at higher temperatures also increases the thickness
of this layer as well as the size of Cu68n5 particles due to the increased solubility and
faster diffusion of copper into tin.

The properties of the solder are affected by the microstructure and the constraints
imposed by the copper substrate in the joint configuration. The microstructure can be
changed and controlled by addition of several alloying elements (Cu, Ni, Ag, Bi, Sb, In)
in small proportions. The Ag3Sn in the eutectic Sn-Ag solder matrix increases the
hardness and strength of the solder. Copper addition (up to 1wt.%) slightly adds to the
strength of Sn-3.5Ag solder joint“. The intermetallic Cu6Sn5 formed due to the
dissolution of the Cu substrate increases the strength of the solder joint even more with a

loss in ductility.

37

C) Lead-based Solders

1) Microstructure of Lead-based Solders:

Lead-free solders have posed several metallurgical challenges to the research
community. Addition of secondary constituents like copper, nickel, bismuth, etc. to the
eutectic Sn-Ag solder matrix to enhance wettablility and decrease the melting point, has
led to the formation of intermetallics at the interphase / boundary and in the solder
matrix. These intermetallics change I affect the microstructure of the joint during
formation and results in variation of performance. It has been observed that the
microstructure in case of Pb-based solders affects the fatigue properties of the solder”.
Hence there is need to study the evolution and changes that occur in the microstructure
and mechanical properties due to such additions. Lead-based solders are well studied in
this regard and though there is a distinct difference in the behavior of lead-based solders
and lead-free solders with respect to microstructure and its evolution, the knowledge and
insight gained from studying lead-based solders can greatly enhance our understanding of
how the microstructure of lead-free solders evolve / change.

Microstructure of the Sn-Pb eutectic alloy (63%Sn-37%Pb): The solder joint
is a composite with solid, hard metallic elements bound in a relatively softer solder
matrix forming the bulk of the interconnect. Interrnetallics formed in the solder joint,
affect and present different properties than those exhibited by the matrix tested alone.
The solidification microstructure is governed essentially by the rate of cooling. Faster
cooled joints reveal a fine. equiaxed microstructure whereas slower cooling leads to a
lamellar microstructure. Synonymously, smaller joints cool faster and therefore exhibit a

finer rrricrostructure as compared to thicker joints (~0.5-1mm thick), which reveal a

38

coarse lamellar microstructure. Faster cooling rate implies a lesser time for diffusion and
hence slower growth of the lamellaez. Since solder joints are used at high homologous
temperatures in most cases, the microstructure evolves with time and hence affects the
way the joint behaves and contributes to be a strong interconnect.

Eutectic microstructure: Eutectic Sn-Pb is the most popular solder being used.
The microstructure is well studied and it gives valuable information to base our studies
upon. Though there is no direct correlation between Sn—Pb solders and Sn-Ag solders,
the information and data we can obtain from Sn-Pb solders is invaluable.

1.14 have studied the microstructure of Sn-Pb solders and have seen

Morris et.a
how the microstructure affects the joint properties. On relatively slow cooling, eutectic
Sn-Pb solders give rise to a microstructure shown in Figure 8(a), which consists of
lamellae of the two solid solutions simultaneously crystallizing and forming parallel
plate-like colonies when the two phases are present in equal volumes. This is the classic
“eutectic” microstructure. If one of the two phases dominates then the other forms a rod-
like morphology within the matrix of the larger volume phase.

Mei et.a1.62

has also compared the effect of cooling rate on the microstructure of
the Sn-Pb solder. Slow cooling gives the eutectic microstructure as above. Very rapid
cooling however results in the Pb-rich and Sn-rich phases, which solidify as equiaxed
grains mixed with each other (See Figure 8(c)). Intermediate cooling rate gives rise to
variations between the eutectic and the rapid solidification rrricrostructure. Eutectic

lamellar microstructure is typically observed on the PCB and on ceramic chip leads

whereas the fine equiaxed microstructure is seen on surface mount components“ (surface

39

mount components have a smaller mass and faster heat dissipation as compared to PCBs

and large ceramic chip leads).

4O

 
  

  
  
   

, ‘2‘“

1 \.
. Pen" ..
:Hr’ 21‘7‘;A \
'- “it”;

Figure 8. Effect of cooling rate on the rrricrostructure of eutectic Sn-Pb solder.
(a) Furnace cooling, (b) air cooling and (c) quenching (from Ref.l4).

41

2) Evolution of Sn-Pb Microstructure:

During solidification of the solder, when the temperature is lowered below the
eutectic temperature, the equilibrium solute content of the primary solution is greatly
decreased. The super saturation of the solute results in the precipitation of the solute in
the matrix as fine particles since solid-state diffusion is relatively slow. Hence one finds

small crystallites of Sn distributed in the Pb-rich phase2

. The Sn-rich phase is more
“pure” than the Pb-rich phase due to lesser dissolution of Pb in Sn. The volume of the Sn
rich phase to the Pb rich phase is 73:27 for 63Sn-37Pb soldersz.

The eutectic microstructure with plate-like lamellae is out of equilibrium with
respect to lowering the total surface energy of the interfacial area per unit volume. There
are two ways to address this issue to achieve thermodynamic equilibrium with respect to
surface and interfacial energy. Firstly, the lamellae can be converted into spheroidal
particles, which would coarsen and grow with time. Such spherodization usually initiates
at the boundary between the so-called colonies of the eutectic microstructure, where there
are several differently oriented colonies approaching each other. The spherodization
once initiated at such boundaries slowly consumes the entire grain. The second way the
microstructure can change is when the joint undergoes plastic deformation at high
homologous temperatures. In such a case the solder material may recrystallize and
evolve into finer equiaxed grains°367. The recrystallization occurs along bands of shear
that develop due to inhomogeneous deformation in the solder joint. This sudden change
can deteriorate the fatigue life of such solder drastically.

As Morris et.al.l4 point out, fine, equiaxed microstructures obtained by rapid

solidification have smaller interfacial surface area per unit volume, e.g. Figures 8(a and

42

c), which in turn helps to lower interfacial surface energy. Such grains do not undergo
recrystallization under load, since deformation causes grain boundary sliding and
dislocation activity that helps keep the grain size small. However they can grow and
coarsen which can affect the creep properties and other properties related to grain size.
Finally, at high homologous temperatures, the rate of diffusion, especially in the
intermetallic layer in case of Cu (from component) and Sn (from the solder), is very high.
This causes increase in the intermetallic layer and simultaneous depletion of the Sn from
the near intermetallic region, which gives rise to a Pb-rich layer/band near the interphase.
This Pb-rich layer is comparatively very soft to the Cu68n5 intermetallic layer and hence
there is a greater chance of crack nucleation, de-bonding and failure in this region. Thus

a chemically inhomogeneous solder is created near the joint interfaces.

3) Effect of Eutectic Sn-Pb Microstructure on the Mechanical Properties of Solder
Joints:

a) Creep: Figure 9 shows the creep curve adapted from Ref. 68 to show the creep
behavior of a fine-grained eutectic Sn-Pb solder. In the high stress regime, the stress
exponent is in the range of 4-7 and the activation energy is close to that of bulk diffusion.
The deformation within the grains is controlled by bulk diffusion and it is stated that
dislocation climb within the grains is the controlling creep mechanism. At slightly lower
stresses, the stress exponent is 2 and the activation energy is close to grain boundary
diffusion. One sees deformation predominantly concentrated at the grain boundaries,
which makes grain boundary sliding the creep rate / deformation controlling mechanism.

At still lower stresses the stress exponent has a value of about 3. The activation energy

43

has a value close to that of bulk diffusion. The creep rate controlling mechanism is
believed to be bulk deformation, from dislocations that drag solute atoms, which
accommodates deformation concentrated near the grain boundaries and hence maintains

contact between grains.

  
  
 
  

n=4-7
AQ = BulkDifi‘usion

n=2

AQ = on Diffusion

     
 

/ I
f ’ 11:3
’1 / AQ = Bulk Diffusion

Log Steady State Creep Rate

I

 

 

Log Stress

Figure 9. Schematic illustrating the creep properties of fine-grained eutectic Sn-Pb solder
from Ref. 68.

45

The rrricrostructure of the solder affects the creep behavior and creep rate. An
increase in the size of the colony of the eutectic Sn-Pb solder causes hardening of the
solder, especially at lower strain rates as seen in Figure 969 and the intermediate creep
rate in this case disappears (See dashed line in Figure 9). This phenomenon is particularly
seen in eutectic Sn-Pb compositions, where the microstructure is relatively sensitive to
the cooling rate. Addition of other elements can affect the creep rate by changing the
grain size and solidification microstructure. Reynolds et.al.70 have reason to believe that
the creep behavior is affected by the creep behavior of the individual phases present in
the joint”. The phase dominating the creep behavior can be identified by the
microstructure. Hence it is essential to customize the microstructure to obtain the desired
mechanical properties from the solder.

b) Shear Strength: Similar to dependence of creep behavior on microstructure, the
shear stress is also affected by the microstructural changes. A fine grained joint in shear
deforms by grain boundary sliding and it can sustain large deformations prior to failure.
In this case the solder behaves in the superplastic manner. In case of the eutectic Sn-Pb
microstructure, the shear strain is heterogeneously distributed throughout the
microstructure, which allows partial recrystallization and shear band formation in the
solder. These bands have finely divided grains, which then undergo superplastic
deformation. The mechanical inhomogeneity causes further redistribution of straining in
the joint and finally failure occurs along these shear bands”. It is observed that
superplastically deformed material can sustain larger amount of strain to failure and

hence crack growth rates are not fast.

46

c) Fatigue: Morris and Reynolds have stated in their paper14 that “microstructure should
resist the formation of the persistent slip bands that concentrate cyclic deformation and
nucleate fatigue cracks. To achieve this goal, one would have to homogenize the
deformation and avoid the development of local stress concentrations within the
material.” From this point of view eutectic Sn-Pb solders are rather not suitable,
especially due to the fact that solders usually experience high homologous temperatures
in service. Recrystallization due to inhomogeneous deformation into a fine grain size
under such conditions would lead to a soft microstructure. This creates early crack
nucleation and subsequent failure in the interconnect. To achieve better fatigue
properties in eutectic Sn-Pb solders, it is recommended that the eutectic microstructure be
converted into a more equiaxed nricrostructure to homogenize the strain. This can be
achieved by using a fast enough cooling rate so that a more equiaxed and homogeneous
microstructure is obtained. However, to achieve a fine equiaxed microstructure so that
the joint would be able to undergo superplastic deformation (which is possible in
electronic circuitry owing to the usually low strain rates) and to prevent grain growth
(due to the high temperatures experience by the solder joints) which will lead to decrease
in the fatigue resistance of the solder joint, addition of other elements, which inhibit the
formation of the eutectic microstructure, can prove very useful. Another way to improve
fatigue resistance is to introduce a dispersed second phase, which will defer deformation
of the matrix, however being softer than the matrix this secondary phase should be able to
undergo deformation“.

To achieve better creep and fatigue properties it is important to achieve a stable

fine grain microstructure, which does not coarsen with time, so as to facilitate

47

homogeneous deformation in the solder joint. This is comparable to a similar
phenomenon occurring in high temperature superalloys, which were developed for
aerospace applications. Hence approaches used by researchers for aerospace alloys could
also be used for solder joints. Out of the many such approaches, dispersion strengthening
and precipitation hardening are two possible techniques. In precipitation hardening a fine
secondary phase precipitates out homogeneously throughout the microstructure from the
solid solution. In case of dispersion hardening, a suitable phase needs to be dispersed in
the matrix by external means. These dispersed particles have to be of the appropriate size
and the distance between the dispersoids have be to optimized so that the hard particles
can stop the movement of the dislocations and hence hinder slip72'73. Betrabet et.al.72
discuss the use of such approaches in their paper with respect to the advantages and
disadvantages of such dispersoids and properties inherently required by the secondary
phases in the eutectic Sn-Pb system.

(1) Comparison of Sn-Pb and Sn-Ag solders: Satoh et.al.74, Hwang et.al.75 and Thwaites

et.al,7°

have reviewed the tensile behavior of Sn-Pb solder. On comparison of the two
solders for tensile properties, Sn-3.5Ag solders have comparable or slightly higher tensile
strength than Sn-Pb solders2’74'76.

Shear strengths of Sn-3.5Ag are comparable to those of Sn-Pb. In shear the
plastic instabilities of the solder do not interfere with strengthz. During elongation

l.76 and Timlinson et.al.77, Sn-Ag

experiments carried out by Satoh et.al.74, Thwaites et.a
had comparable elongation to Sn-Pb at room temperature and moderate strain rates,
however Sn-Ag is less strain rate sensitive i.e. there will be greater elongations at higher

strain rate and lower amount of elongations at lower strain rate”.

48

Creep resistance of Sn-Ag solder is better than Sn-Pb in the 25-100°C range. In
case of isothermal fatigue, eutectic Sn—Pb with a fine-grained equiaxed microstructure has
a better fatigue life as compared to one with a lamellar structure. Sn-Ag is much better in
fatigue as compared to Sn-Pb at high shear strain amplitudes as indicated by Guo et.al.78.
He attributes the better fatigue resistance of Sn-Ag solder to the resistance of Sn-Ag to
crack initiation, rather than crack propagation, because Sn-Ag has the lowest crack
growth resistance for the alloys studied by him. Other studies also show that Sn-Ag is
more fatigue resistant at room temperature and at about 100°C, compared to Sn-Pb

solders76

. In Sn-Pb solders localized microstructural coarsening occurs which decreases
its fatigue resistance and leads to failure in the joint, which is not the case in Sn-Ag

solders”. However, more detailed studies are warranted in this respect to assess the

mechanisms of thermomechanical fatigue damage in lead free solder.

49

1.3 AIM

Reliability of Sn-Ag solders as interconnects is vital to electronic packaging. So
far there has been no model explaining physical understanding of failure mechanisms
persistent in Sn-Ag solder. Scanning electron rrricrographs by themselves give no
information on the crystallographic texture of the solder joint. Characterizing the
rrricrostructure crystallographically is critical to understand deformation processes
occurring in the solder joints, as most of the mechanical properties are affected in some
way or other by the microstructure of the solder joint. OIM using EBSP is an effective
mean to identify physical changes in microstructure of Sn-Ag solder, which is different
from Sn-Pb solder. This can give an insight on how to enhance the mechanical properties
and achieve better solder interconnects. Hence, OIM is an ideal tool to study
crystallographic orientations, grain shape and grain boundary changes resulting from
solidification and subsequent deformation. Hence the subsequent investigations were
carried out.

“This research is the first attempt of its kind that aims at characterizing tin-
based eutectic Sn-Ag solder joints in the as-fabricated condition and subsequently
subjected to aging, creep and thermomechanical fatigue processes using the
Orientation Imaging Microscopy (OIM) technique, which utilizes Electron

Backscattered Patterns (EBSP .”

50

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51

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K-Baba Kishi and D.J.Dingley, AEM workshop, Inst. of Metals book 425, 71, 1987.

K-Baba Kishi and D.J.Dingley, “Application of Backscatter Kikuchi Diffraction in
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K-Baba Kishi, D.J.Dingley, and V.Randle, “A Crystallographic Atlas of Electron
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S.Jang, J.Wolf, O.Ehrmann, H.Gloor, H.Reichl, and K.W.Paik, “Investigation of
UBM System for Electroplated Sn/37Pb and Sn3.5Ag Solder ECTC”, Paper

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and Microstructure”, Israel University Press, Jerusalem, 255-342, 1969.

K.L.Murty and I.Turlik, “Deformation Mechanisms in Lead-Tin Alloys, Application
to Solder Reliability in Electronic Packages”, proceedings of 18’ joint conference on
electronic packaging, ASME/JSME, 1992.

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IEEE, 538-551, 1992.

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F.Guo, J.P.Lucas, and K.N.Subramanian, “Creep Behavior in Cu and Ag Particle-
Reinforced Composite and Eutectic Sn-3.5Ag and Sn-4Ag-0.5Cu Non-composite
Solder Joints”, Journal of Material Science: Materials in Electronics, 12, 27-35, 2001.

S.Choi, J.G.Lee, F.Guo, T.R.Bieler , K.N.Subramanian, and J.P.Lucas, “Creep
Properties of Sn-Ag Solder Joints Containing Intermetallic Particles”, JOM, 22-27,
June 2001.

53

43. K.N.Subramanian, A.Lee, S.Choi, P.Sonje, “Materials Issues in Electronic
Interconnects and Packaging”, J. Electron Mater., 30, 4, 372-378, 2001.

44. R.Darveaux and K.L.Murty, “Effects of Deformation Behavior on Solder Joint
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46. M.Harada and R.Satoh, “Mechanical Characteristics of 96.58n-3.5Ag Solder in
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47. C.H.Raeder, R.W.Messler,Jr., and L.F.Coffin, “Partially Constrained
Thermomechanical Fatigue of Eutectic Tin-Bismuth/Copper Solder Joints”, J.
Electron Mater., 28, 9, 1045-1055, 1999.

48. R.W.G.Wyckoff, ”Crystal Structures, Volume 1”, 2"‘1 Edition, Univ. of Arizona,
Tuscon, Arizona, Inter Science Publication, New York, 1963.

49. E.Schmid and W.Boas, “Plasticity of Crystals with Special Reference to Metals”, a
translation from the German by F.A.Hughes & Co., Limited, of “Kristallplastizitat
mit besonderer Berucksichtigung der Metalle”, London, 85, 1950.

50. B.Chalmers, “The Twining of Single Crystals of Sn”, Proc. Phy. Soc. London, 47,
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51. C.S.Barrett, Trans. AIME, 161, 15, 1945.

52. E.Schmid, “International Conference on Physics, Volume II, The Solid State of
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53. CS. Barrett, “Structure of Metals”, 2"d edition, Metallurgy and Metallurgical Series,
edited by R.F.Mehl, McGraw Hill Book Company, 337, 1952.

54. D.Frear and H.Morgan, “The Mechanics of Solder Alloy Interconnects”, edited by
J.H.Lau, 1994.

55. P.Villars and L.D.Calvert, “Pearson’s Handbook of Crystallographic Data for
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Transactions, Engg. Series, McGraw Hill Book Company, 1958.

54

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55

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56

EXPERIMENTAL PROCEDURES

2.1 SOLDER JOINT PREPARATION

Copper half dog bone specimens (shown in Figure 10) were made by electro
discharge machining (EDM) from a copper sheet of 0.5mm thickness. The copper dog
bones were cleaned in 50% Nitric Acid (HNO3) to remove the oxide layer that could
create pores and de-wetting and hinder joint formation. The dog bones were placed in the
apparatus developed by Rhee at Michigan State University, which eliminates the need for

a mask that was required in previous studies”.

This method facilitates the making of
solder joints of approximately 100nm with reasonable consistency (see fixture shown in
Figure 10). Once the lower dog bone piece was laid in the apparatus, the eutectic Sn—Ag
solder paste of approximately 0.2mm3 volume was placed on the free copper surface.
The upper dog bone piece was then placed on top and the entire assembly was placed on
a heated hot plate. The assembly was kept on the hot plate for about 50 seconds during
which time the temperature reached 221°C (the melting point of the eutectic Sn-Ag
solder). The temperature was further allowed to reach 260°C in another 5 seconds and
then the entire assembly was removed from the hot plate and transferred to an Aluminum
plate where it was allowed to cool down to room temperature. The initial cooling rate
was about 150°C/min till about 150°C, after which it took about 7 minutes to cool down
to room temperature.

The joint was taken out of the apparatus, taking care that no mechanical damage

was induced and mounted in a jig for polishing. Though most of the solder (0.2mm3

volume) was involved in making the joint, some of the solder made up the fillets on

57

either side of the joint and some was extruded out from the edges when the upper dog

bone was overlaid on the solder. This was ground off during polishing.

58

 

 

 

7' J

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3mm "/ _ 7
500m I .— l”...\ 1mm
I 4‘ 25mm 11 .mmS
Solder Joint ~ 100 pm thick
(a)
Glass Plate UPI)er Cfpper Dog Bone
600“!” l/ i —> f——“\ i
1
Lower Copper r \_
Dog Bone IL 7 f/ l
* v Glass Plate
600nm

 

 

 

 

 

 

Figure 10. (a) Solder joint configuration. (b) Fixture for manufacturing solder joints
used in this study. Copper dog bones were about 500nm in thickness, while the glass

plate was ground to about 600nm thickness, which facilitates making 100nm thick solder
joints.

59

Since OIM studies require the surface to be ideally free of oxide and deformation,
careful polishing is needed. Polishing was achieved by mounting the specimen in a
special jig (made of Aluminum) that prevents mechanical deformation during grinding
and polishing. Figure 11 illustrates the way the joint was placed in the jig for the
polishing operation. The jig was designed to support the joint on the flat edges, so that
no deformation or bending was induced in the joint. To accommodate for the thickness
of the joint, two identical copper strips (25mm x 3mm x 0.5mm, same as the dog bone
halves without the extension used to make the joint) were placed alongside the tail of the
copper dog bone on the joint side to prevent any bending or twisting of the joint during
polishing. The edges of these joints were metallographically polished progressively with
600 and 1000 grit sandpapers. The specimen / jig were handled carefully to prevent
specimen damage. Then, the same procedure was repeated on the other side of the
specimen, which was then progressively polished with a 0.3um alumina suspension
followed by 0.05pm silica in an alkaline suspension, which was the final step in
polishing. The side that underwent final 0.05am polishing was used to study the
microstructural evolution, whereas the other side, which had a flat surface, facilitated
mounting the specimen on the stage during OIM. The specimen was observed under an ’
optical microscope periodically while polishing. All specimens were metallographically
hand polished with minimal force application during polishing. The final two steps were
achieved by placing the joint (in the jig) with the surface to be polished on velvet paper
mounted on a 6cm x 1cm x 0.5cm Aluminum block, applying the polishing media and

then moving the jig back and forth without applying any force. The only force applied

60

was that of the weight of the jig, which is about 30 grams. Due to the hand support the

force actually applied was in the range of 0.196-0.245N.

61

Copper Piece Solder Joint

//

   
 
   

Solder . I“
Joint -

 

 

Copper Piece

 

 

 

 

 

 

 

 

 

 

 

 

Moveable /

Piece Moveable
/ Piece

Fixed __7

Backing

Piece

 

 

 

 

Screws

Figure 11. Jig used for polishing specimens showing a specimen with copper pieces used
as backing to avoid bending and twisting of the joint. Middle piece is not moved because
it supports the solder joint during polishing.

62

Preliminary OIM studies carried out on polished specimens indicated that no
additional electropolishing was necessary to enhance the sharpness of the EBSP’s, since

3'4'5 of the scanned

they were sharp enough to determine the crystal orientation for 60-90%
positions. The remaining 40-10% of the non-indexed positions were attributed to
porosity, grain or phase boundaries, second phases, oxidation or locally highly deformed
regions (for specimens after deformation). The solder joint specimen was then cleaned in
methanol or acetone in an ultrasonic cleaner and then dried in compressed air and stored
in a refrigerator until future testing. The single shear lap joints made with eutectic tin

silver (3.5 wt. %Ag) lead free solder had a solder area of about 1 mm2 and a thickness

ranging from 100-180um.

63

2.2 THERMAL AND MECHANICAL TESTING

OIM scans were carried out in the joint configuration on all specimens. The
solder joints used in this study along with their thermal and mechanical histories are
given in Table IV.

Aging was accomplished by placing the solder joint in a furnace maintained at a
steady temperature of 85° C for 100 hours. Creep test was carried out in a special
apparatus devised by Guo2 and Choi”, which facilitated the documentation of the
microstructural changes during creep. The load was applied to the joint through a cable
and pulley system. The entire loading assembly along with the solder joint was placed on
an optical microscope fitted with an attached closed circuit digital (CCD) camera. The
camera was previously setup in such a manner, so that the solder joint edge remained in
focus throughout the test. The computer controlled CCD camera took pictures at
specified time intervals so that the amount of local strain experienced by the solder joint
could be easily studied and documented. Specimens for elevated temperature creep tests
were heated by wrapping a heating element around the copper portion of one of the '
copper dog bones and heat was transferred to the solder joint by conduction, see Figure
12 for details. A constant load of 2.5 lb was applied to the specimen and for high
temperature creep; the temperature was controlled at 85°C with il°C of accuracy using a
variac. Thermocouple wires were wrapped around the dog bones at a distance of about 2
mm from the solder joint (not shown in Figure 12). Figure 12 shows the creep setup

used.

Table IV. Solder joint specimens used to characterize microstructural evolution.

 

 

 

 

 

 

 

 

Solder Composition Joint History Purpose of Investigation
Characterize as-cast microstructure
l Sn-3.5Ag As fabricated and microtexture as a baseline for
comparison
Crept at room Determine how rnrcrostructure and
o microtexture were changed due to
2 Sn-3.5Ag temperature (23
C) to Y"0 03 room . temperature creep
' deformation
Crept at high Determine how microstructure and
3 Sn-3.5Ag temperature (85° microtexture were changed due to
C) to y~0,06 high temperature creep deformation
Analyze same region before and
0 after aging to characterize change in
4 Sn-3.5Ag Aged at 85 C for a particular region of microstructure
100 hours .
and rrucrotexture due to thermal
history, minimal strain history
TMF 370 cycles .
5 Sn-3. 5 Ag between _15° C Deterrmne how TMF changed the
and 150° C rnrcrostructure and microtexture

 

 

 

 

65

 

Specimen ‘ Heating Pad

‘ 4 " ' 4""“"'-"1\'* '
Creep'Frame a“ ‘rr\

’Countcr _' Q. ”7‘ Light ~
fig-“Load; . ’ Microscope

 

Figure 12. Setup for dead weight loading miniature creep testing frame.

66

The thermomechanical fatigue (TMF) cycling was carried out by subjecting the
solder joints to thermal excursions between —15°C and 150°C with a heating ramp rate of
25°C/min and 20 min dwell time for the heating segment, and a cooling ramp time of
7°C/min and 300 min dwell time for the cooling segment7. This was carried out an
automated setup developed at Michigan State University7. The temperature profile
obtained with this setup provided 4 cycles per day using the cycle shown in Figure 13.
The TMF cycling was carried out for several cycles on a single solder joint, that were
removed periodically to assess the deformation and damage at intermediate cycling
stages by OIM analysis, after which they were put back into the cycling mode. The TMF
cycles were carried out for 370 cycles in the present study. The deformation generated
by TMF was due to the coefficient of thermal expansion (CTE) mismatch between the

copper substrates and the solder, and due to the intrinsic anisotropy of tins.

67

 

 

 

 

 

 

 

 

 

200, I I 1—!T I T I l I I I I l I I I I ! I I I I q
:9 150. °""""; .
° :

V .-
Q n-
‘5 - E : 2 -
.. 100 ------------ -—
cu -* z 3 E -
i-I ' . - -
Q) -
Q -
E 50 i
H . -
L .1

0:"" ':

+1 1 1 1 I r r 1 1 l r r r r l r 1 l 1 11 r r r .

-50

 

 

 

100 200 300 400 500
Time (min)

G

Figure 13. Temperature profile for thermomechanical fatigue cycling (-15°C
to 150°C)7.

68

tor
the
56p
[hill
nor
COL
one
abo
scre
Spfi‘
[hall
agjn
a”(til

OdeE

With 1

2.3 CRYSTALLOGRAPHIC DATA COLLECTION AND TEXTURE

MEASUREMENT

The OIM data was collected on a CAMSCAN 44FE SEM using hkl Channel
Acquisition software version 4.2 (HKL Technology, Inc., Blaakildevej, 17k, Hobro, DK-
9500, Denmark) run on a PC at Michigan State University. The flattened surface
(polished with 600nm paper) of the specimen was attached to the flat surface of a
standard Aluminum stub using a carbon tape so that the polished edge of the specimen
could be seen when observed from the top. The specimen was oriented and placed into
the microsc0pe the same way every time. Repeated mounting of the same specimen on
separate days resulted in crystal orientations in the same position that differed by less
than 2° (however, up to 5° difference occurred in the euler angle for rotations about the
normal axis associated with mounting the specimen holder on the microscope stage).
Coupled with the intrinsic 1° uncertainty in EBSP pattern indexing the absolute angular
orientation in a given specimen is known within :3°. The specimen was then tilted 70°
about the specimen x-axis so that one could view from the top to the bottom of the
screen, a solder joint sandwiched between two c0pper dog bones. A 25kV beam with a
specimen current of about 2.3mA was used to generate EBSP’S. A probe current greater
than 511A insured good scan conditions. However, with progressive high temperature
aging, the detection of EBSPs was degraded. A light polish with 0.05pm silica in an
alkaline suspension improved pattern sharpness, probably due to the removal of any
oxide layer.

Most OIM scans were overnight scans, collecting around 12,000 pixels of data

with lum step size over a 120x100 um2 area of the solder joint. Several regions of the

69

same specimen were scanned, to assess the similarities and differences in the
microstructure over the entire joint. The most representative maps for each type of
specimen are described in the results. The crystal orientation data was collected by
rastering the beam over the specimen in an automated manner. Crystal orientation
information obtained by these scans was processed to obtain an OIM map. Datasets from
the hkl scans were processed and converted to TSL datasets which could be processed by
the TexSEM software version 3.0 (TSL Laboratories, Draper, UT), which provided more
mapping and analytical tools than version 4.2 of the hkl software. To achieve
consistency in the x-y-z coordinate system between the hkl and TexSEM software, the
datasets obtained were rotated by +90° about the [001] direction (Normal Direction, ND)
in the TexSEM software version 3.0 (and this same effect is achieved by rotation of -90°
about the [001] direction (Normal Direction, ND) in the TexSEM software alpha version
3.0). Datasets were “cleaned-up” using the software using a nearest neighbor criterion,
so as to replace isolated unindexed pixels with the orientation of the nearest neighbor
pixel that had the highest degree of confidence in the crystal orientation. Orientation
maps, pole figures and misorientation plots were computed using PC version 3.0 of the
TexSEM analysis software and version 4.2 of the hkl software.

Since the easiest slip directions in tin are in the c-direction [001] on {100} and
{110} planes, crystals with the c-direction aligned with the solder joint x-axis will be
most easily sheared by mechanical or CTE driven stresses in the single shear lap joints.
This easy mode of deformation was used to identify a reference crystal orientation
scheme. The crystal orientations with the c-axis aligned with the specimen x-axis were

chosen as the reference direction and are displayed as red in the orientation maps. The

70

bll

C0

maps are based on the inverse pole figure color key shown in Figure 14. Increased c-axis
misorientation from the reference direction [001] by tilting towards the [110] crystal
direction is represented by adding blue and removing red, such that a red and a blue grain
are misoriented ~90° by a tilt about a <110> axis. Similarly tilting the [001] reference
direction towards the [100] crystal direction is represented by adding green and removing
red, such that a red and a green grain are misoriented ~90° by a tilt about a <100> axis.
Further, a [100] (green) crystal direction tilted towards a [110] crystal direction is
represented by adding blue and removing green, such that a green and a blue grain are
misoriented ~45° by a tilt about a <110> crystal direction. Any crystal rotation about the
specimen x-axis would give the same color. In a different perspective, when the dot
product of x- and c-axis unit vectors is equal to unity the representation is red, and when
it is equal to zero; the representation could be blue or green or blue-green. Orientations
in-between these two are represented by orange, yellow, and various combinations of red,
blue and green as seen in Figure 14. Black is used to represent regions where patterns
could not be indexed. The colors on these OIM maps do not completely define the
crystal orientation (in three dimension), to present a complete three dimensional
representation of crystal orientations, 2 such OIM maps are needed, e.g. with different
specimen perspectives separated by 90°. Thus the actual crystal orientation is shown in
some places using the tetragonal prism (tin has a body centered tetragonal structure),

which provides a better understanding to the reader.

71

 

Figure 14. Inverse pole figure color key for an inverse pole figure orientation maps in the
[010] direction with sample crystal orientations for grains having a particular color.

72

2.4 REFERENCES

1. S.Jadhav, Master’s Thesis, Michigan State University, East Lansing, 2001.
2. F.Guo, Ph.D. Thesis, Michigan State University, East Lansing, 2002.

3. D.J.Jensen, “Applications of Orientation Mapping by Scanning and Transmission
Electron Microscopy”, Ultrarrricroscopy, Elsevier Science, 67, 25, 1997.

4. D.P.Field, “Recent Advances in the Application of Orientation Imaging”,
Ultramicroscopy, Elsevier Science, 67 , 1, 1997.

5. B.L.Adams, “Orientation Imaging Microscopy-Application to the Measurement of
Grain-Boundary Structure”, Materials Science and Engineering, A166, 59, 1993.

6. S.Choi, Ph.D. Thesis, Michigan State University, East Lansing, 2002.

7. S.Choi, J.G.Lee, K.N. Subramanian, J.P.Lucas, and T.R.Bieler, “Microstructural
Characterization of Damage in Thermomechanically Fatigued Sn-Ag based Solder
Joints”, J. Electron Mater., 31, 4, 292, 2002.

8. J .G.Lee, A.U.Telang, K.N.Subramanian, and TR. Bieler, “Modeling
Thermomechanical Fatigue Behavior of Sn-Ag Solder Joints”, J. Electron. Mater., 31,
11, 2002.

73

RESULTS AND DISCUSSION

OIM provides a technique that can be used to study the microstructure and its
evolution with time after deformation and heat treatment processes. This study is the first
of its type with respect to solder, and this technique has tremendous potential to identify
the solder joint microstructure evolution. The OIM maps are interpreted with the help of
pole figures, misorientation density functions (MODF) and misorientation distribution
histograms. The most representative data sets are presented and described here. The
results follow the same order as in Table IV on page 65 for a logical presentation and
interpretation of the changes that occur with different rrricrostructural evolution paths.

As-fabricated eutectic Sn-Ag specimens were used to characterize the as-cast
microstructure and microtexture to establish a baseline for comparison. A specimen was
crept at room temperature (23° C) to a global shear strain (7) of ~0.03. This determined
how microstructure and microtexture changed due to room temperature creep
deformation. A second specimen with an as-fabricated OIM scan was then crept at high
temperature (85° C) to global shear strain y~0.06, which determined how microstructure
and microtexture changed due to high temperature creep deformation. A third specimen
was used to analyze the same region before and after aging (aged at 85° C for 100 hours)
to characterize the change in a particular region of microstructure and microtexture due to
thermal history without any externally imposed strain. Another specimen was used to
determine how TMF (TMFed for 370 cycles between -15° C and 150° C) changed the
microstructure and microtexture. Hence, differences in the behavior of the solder after
deformation (creep) or isothermal aging alone were studied, and compared to the role of

TMF (thermal and mechanical stresses acting together).

74

3.1 CREEP

Room Temperature Creep of Eutectic Sn-Ag Solder Joints
Before creep

The SEM and OIM scans of as-fabricated unaged eutectic Sn-Ag solder joints are
shown in Figure 15 and 16 respectively. Figure 15(a) is from an area near the center of
the joint and Figure 15(b) shows the SEM image of a region 170nm to the right of Figure
15(a). Figure 16(a and b) are the OIM scans corresponding to the boxed regions in
Figure 1, which show one dominant orientation in Figure 16(a) and two secondary
orientations. The same dominant and secondary orientations are present in Figure 16(b).
This dominant orientation has its c-axis tilted from the specimen normal by about 55°
towards specimen negative x-axis, whereas the secondary orientation shown by dark
orange color has its c-axis tilted from the specimen normal by about 65° towards the
positive x-axis. For both these orientations the c-axis is close to the specimen x-axis
(which can also be seen from the pole figures in Figure 17(a and b)) and tilted away by
about 15°. This orientation is expected to deform easily in shear, since the c-axis vector
is a Burgers vector. The secondary orientation shown by purple color has its c-axis tilted
from the specimen normal by about 55° towards the negative y-axis. The purple color
bands have an orientation with the c-axis pointing nearly out of the page, i.e., the c-axis
for this orientation is aligned to resist shear along the specimen x-direction. Thus there
appears to be three orientations that are twin related that could be generated by rotating
the unit cell about the specimen y-axis by about 60°, however, the region with bluish-

purple coloration has the weakest texture intensity (also seen from the pole figure). The

75

regions, which have the red color, have their c-axis, oriented along the x-direction, which
aligns the c-axis Burgers vector along the specimen shear direction. The dominant
orientation shown by a light orange color in Figure 16(a) and a ‘+’ on the pole figure in
Figure 17(a) has a texture intensity peak of 41.9 times that of a random texture: whereas
the dominant orientation in Figure 17(b) has a texture intensity of 110.8 x random.

The secondary (dark orange and purple) orientations are represented by a ‘o’
symbol in Figure 17(a). The secondary orientation represented by the dark orange color
is related to the dominant orientation by a rotation of about 120° (or 60°) about the
specimen y-direction.

Low angle and high angle grain boundaries are evident in the map. High angle
grain boundaries are easily evident in places where there is a discontinuity in color.
There are more high angle grain boundaries representing a range of 55-65° grain
misorientations than any other ones. These boundaries are indicated by white lines.
These boundaries have been identified as twins‘. Many high angle grain boundaries are
linked to low angle grain boundaries (thin for 3-5°, thick black lines for 5-15°) in several
locations of the OIM map.

Figure 16(a and b) reveals peculiar texture bands starting from the top right and
ending at the bottom left. The secondary orientations, which are the banded texture
components visible in the OIM scan, appear to be solidification twins. The dominant
orientation throughout this joint had a lighter shade of orange, whereas the minority

orientation bands have either a darker orange shade or a purple color. However, within

 

' A sample with truly random texture would have the same intensity of 1 x random in all orientations on a
pole figure. Hence 111 x random is a strong texture that implies a highly preferred crystal orientation.
Texture intensities were computed from discrete orientations by representing each orientation with a
Gaussian peak and then summing and normalizing using the default setting in the hkl software.

76

the bands of dark orange there are some regions, which show the lighter shade for the
circled region (top middle) in Figure 16(a). The orientations of the crystals in the dark
orange bands in Figure 16(b) (lower middle region) are somewhat similar to each other
(closely consistent within the band) and are misoriented by 55-65° from the dominant
orientation in the joint. The OIM map shown in Figure 16(b), has lesser number of bands

as compared to the OIM map in Figure 16(a) (which shows distinct bands).

77

Copper dog
bone

     

Copper dog ’ ‘
6011 m

6011 m

(b)

Figure 15. SEM micrographs of as-fabricated eutectic Sn-Ag solder joint. Figure 15(b) is
170m to right of Figure 15(a) used for room temperature creep study.

78

Shear
Direction

Shear

Diregtion

 

 

F iguf' e 16. OIM maps of as-fabricated eutectic Sn-Ag solder. Figure 16(b) is 170 pm to
b1 e right of Figure 16(b). White boundaries 55-65°, are twin boundaries; thin and thick
ack lines correspond to 3-5° and 5-15° misorientations respectively.

79

The pole figures" in Figure 17 corresponding to the two regions in Figure 16 also

show a single dominant orientation along with 2-3 secondary misorientations. The c-axis

of the dominant orientation is about 55° from the sample normal. This dominant

orientation corresponds to the majority of the matrix, which has a lighter shade of orange.

The secondary orientations correspond to c-axis being oriented at 65 and 55° from the

sample normal.
Figure 18 shows the misorientation distribution function (MODF) for the as-

fabricated specimen. The MODF indicates that there is large number (~298 x random) of

62° rotation about the [100] crystal direction. Additional peaks found for other grain

boundary angle / axis pairs for this as-fabricated specimen are listed in Table V.

 

.\\

P
Ole figures were calculated by TSL software using the “discrete binning” method with 5° bin size.

80

Table V. Angle / axis pairs as seen in MODF for the eutectic Sn-Ag as-fabricated

 

 

 

 

 

 

 

 

 

 

specimen (Figure 18).
r Angle in degrees Axis Intensity (x random)
r 20° [110] 1.2
F 30° [100] 8.6
F 45° [110] and[111] 4.1 and 7.3
I 62° [100] 298
I 70° [110] 50.5
I 77.5° [829] 7.7
L 87.5° [001] 24.4

 

81

 

 

(a) Max = 41.9 (b) Max = 110.8

Figure 17. [0 0 1] and [0 l 0] equal area pole figures of as-fabricated Sn-Ag eutectic
specimens. 17(a and b) correspond to Figures 16(a and b) respectively.

82

max: 298.381
115.427
44.653
17.274

6.682

2.585

. 1.000

1 0.387

 

2 5' 5' 7 5' 10‘ 12 5‘ 15'

 

 

77.5’ 80' 82 5' 85' 87 5’ 90'

 

Figure 18. Misorientation distribution function for as-fabricated specimen with 2.5° bin
size.

83

For each dataset, the number of boundary pixels with a particular misorientation
angle between two grains, (using a 1° bin size for misorientations larger than 3°) are
plotted as a misorientation histogram. The histogram is represented as a line plot to allow
easy comparison between similar misorientation histograms plotted for different
specimens (e. g. Figure 19(a and b) that compares histograms before creep and after creep
described later). Figure 19(a and b) shows the grain boundary misorientation distribution
corresponding to the OIM maps in Figure 16(a and b) respectively for the as-fabricated
specimen before creep. There are a large number of pixel pairs (~750) having low angle
boundaries <3° and one can see notable peaks at 43, 62 and around 70° misorientations.

Maximum number of 62° misorientation is seen throughout the joint, followed by the 70

and 43° peaks respectively. Other peaks corresponding to 30 and 75° are also present but
are less intense.

As with misorientation histograms, the area of grains with a particular size’ is
compared in the specimens before and after creep in Figure 20. For region (a)
corresponding to Figure 16(a), one sees that there are a large number of 6-10, 15 and
25pm grains. The region (b) corresponding to Figure 16(b) (which has less number of
solidification bands) has a large number of 6 and 60pm grains. Both regions show a large

number of small grains <10um.

 

. The software does not count unbounded grains, whose size is not measurable. Consequently, area is
presented in actual area units for bounded grains within the scanned area (which was the same for each
scan). Thus changes can be reliably compared.

84

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1000 Region (a) after Global Creep Shear Strain of 0.03
E 900 - II
it
“800 ‘ —Before RT Creep
$700 4 —After RT Creep
1:
§ 600 J
3
c 500 "
Ti
3400 -
3 300 -
8
E 200 - - /
E 100 ~ I ,

, A/
O l T T T
O 20 40 60 80 100
Misorientation angle in degrees (1 deg bin size)
Figure 19(a). Misorientation profile for as-fabricated and room temperature crept

specimens corresponding to Figure 16(a).

85

 

Region (b) after Global Creep Shear Strain of 0.03

 

 

— Before RT Creep
— After RT Creep

 

 

 

 

 

 

 

 

 

 

O 20 40 60 80 100
Misorientation angle in degrees (1 deg bin size)

 

 

 

Figure 19(b). Misorientation profile for as-fabricated and room temperature crept
specimens corresponding to Figure 16(b).

86

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2500
— Region (a) Before RT Creep
— Region (a) After RT Creep
— Region (b) Before RT Creep
2000 q —Region (1)) After RT Creep
’0?
t:
9 1500 - ‘
.2
E
9
to
3 .1
303-, 1000
m .
9 .
< LI
500 - ’ '
.11
\II / v
o .4 ......4, .Wfi
. . . . 1.0 . . . 100
Grain Size (diameter) In morons (Logarithmc bins)
Figure 20. Grain size distribution for as-fabricated and room temperature crept
specimens.

87

 

After Room Temperature Creep

Figure 21(a and b) are the SEM micrographs of the same regions of the same joint
as Figure 15(a and b) after undergoing a global room temperature creep to a shear strain
of about 0.03 (The scratch in Figure 21(a) was intentionally put on the specimen after the
initial OIM scan on the as-fabricated specimen to assist in the measurement of the
amount of creep the specimen had undergone and is not a result of deformation. All OIM
scans have been appropriately adjusted and cropped so that the scratch does not affect the
interpretation). OIM scans corresponding to the regions shown in SEM micrographs of
Figure 21(a and b) are shown in Figure 22(a and b) respectively. On comparison of
Figure 16(a and b) and Figure 22(a and b) one sees that room temperature creep does not
change the crystal orientation and texture of the solder joint after a global creep shear
strain of 0.03. One still sees one dominant orientation and two secondary orientations in
both OIM maps. The texture intensity in Figure 23(a) is 35.5 x random which is a slight
decrease compared to 41.9 for the as-fabricated specimen. The texture intensity in Figure
23(b) is 115.8 x random which is a slight increase but not a drastic one compared to
110.8 x random in Figure 17(a) for the as—fabricated specimen. These small changes
imply that room creep deformation did not cause drastic changes in texture.

However there are subtle changes in the position of both low and high angle grain
boundaries. The overall texture remained unchanged and the high and low angle grain
boundaries persisted and no major changes in grain shape were observed. There are also
minor changes in the texture intensity as indicated in Figures 23(a and b). There was a
slight decrease in the texture intensity in the region ‘a’ (the region with more

polycrystalline texture bands) and a slight increase in the texture intensity in region ‘b’,

88

the region with fewer texture bands. The increase in texture intensity of region ‘b’ can
be attributed to the decrease in the purple colored orientation, especially the band of
purple in the lower part in Figure 16(b). There have also been slight changes in the grain
boundary misorientation distribution as illustrated in Figure 19(a and b). In region ‘a’,
the boundaries with 60° misorientation seem to have decreased while increasing the
number of boundaries with a higher 70° misorientation angle. No such features were
observed in region ‘b’. Also, from comparison of pole figures in Figure 17 and 23, there
is a slight rotation of the dominant orientation by about 5-10°. This change is also
evident in the prisms in the lower right comer of region b in Figures 16 and 22, by a
rotation about an axis close to the specimen normal in the direction of the shear
deformation. This observation (lattice rotation and slight changes in maximum texture
intensity) shows that the preferred orientation is spread out slightly with deformationz.
Figure 24 shows the MODF for the specimen after room temperature creep. The
MODF has a maximum of 300 x random for the 62° rotations about the [100] direction.
There has been some grain coarsening of 2-10um grains in the region scanned.
The 0.03 global shear strain room temperature creep deformation in region ‘a’ (region
with more bands) increased the number of 2-3um grains and caused the coarsening of 5-
7pm grains to 10pm. Similarly, in region (b) there was a coarsening of 5-711m grains to
10pm, increase in the number of 20m grains and a emergence of 45m grains with a
corresponding decrease in the 60am grains. However these changes are subtle and this
implies that no significant grain boundary motion that would cause a change in the
misorientation between crystals (such as subgrain coalescence or recrystallization)

occurred during room temperature creep deformation to a shear strain of ~0.03.

89

With room temperature and global shear strains of 0.03, there is not enough
thermal energy or local deformation, which would cause significant grain boundary
motion. The dominant and secondary orientations in the specimen are twin related, and
they exhibit some degree of symmetry with respect to the sample coordinate system.
Thus room temperature creep deformation occurs by a dislocation creep mechanism,
which is consistent with the interpretation from conventional creep experiments3 with a
stress exponent greater than 5. The strong texture implies that small solder joints are
multicrystals rather than polycrystals, and this accounts for the greater variability of creep
resistance in our specimens consisting of single solder joints, as compared to the studies

with specimens containing multiple solder joints“.

9O

Copper dog
bone

 

 

(b)

Figure 21. SEM micrographs of as-fabricated eutectic Sn-Ag solder joint after a global
shear creep strain of 0.03. (a) Center and (b) Right of the joint. The scratch in Figure
21(a) was intentionally put on the specimen to assist in the measurement of the amount of
creep the specimen had undergone and is not a result of deformation.

91

Shear
Direction

Shear
Direction

 

 

Figure 22. OIM scans of eutectic Sn-Ag solder after room temperature creep of 0.03
global shear strain.

92

 

(a) Max = 35.5 (b) Max =115.8

Figure 23. [0 O 1] and {0 1 0] equal area pole figures of Sn-Ag eutectic specimens after
room temperature global creep to 0.03 shear strain. Figures 23(a and b) correspond to
Figures 22(a and b) respectively.

93

max: 300.157
116.000
44.830

17.325

6.695

2.588

1.000

0.386

 

2 5' 5‘ 7 5‘ 10‘ 12.5' 15'

 

001

 

Figure 24. Misorientation distribution firnction with 2.5° bin size for specimen after
global creep to 0.32 shear strain.

94

High Temperature Creep of Eutectic Sn-Ag Solder Joints

Before Creep

Figure 25(a and b) shows the SEM micrographs before high temperature creep for
an as-fabricated eutectic Sn-Ag solder joint. Figure 26 shows the corresponding OIM
scans of the two regions shown in these SEM micrographs. Figure 26(a) is from the
center of the joint and Figure 26(b) is 323 um to the left. Figure 26(a) shows a number of
high angle grain boundaries with a few isolated grains with high angle boundaries. One
can also see low angle grain boundaries traversing through the large grains shaded in
pink, with mostly the pink color on either side of the low angle (5°) grain boundary. An
isolated region shown by a green color has its c-axis pointing about 20° from the
specimen normal whereas the majority of the matrix (pink color) has its c-axis about 65°
from the specimen x-direction (Figure 26(8)). The purple orientation in the upper region
of Figure 26(a) has the c-axis about 80-85° from the positive x-axis and the majority of
the blue orientation in Figure 26(b) has its c-axis pointing 90-95° from the positive x-
axis. These preferred orientations are readily seen in the pole figures in Figure 27. The
region shown in Figure 26(b) encompasses a much larger region as compared to Figure
26(a) and shows predominantly three to four shades of blue separated by low angle grain
boundaries. The pole figures shown in Figure 27(a and b) show that in both the scans
there is only one dominant orientation (corresponding to the pink and blue colors in the
solder matrix of Figures 26(a and b) respectively) with 2 other orientations very close to
the dominant one (misoriented by about 10-20°), forming a cluster. These two other
orientations are common to both regions and are represented by blue and purple colors in

the OIM maps. The pink and blue colors represent orientations, which are very similar,

95

but they are misoriented by a twin rotation of about 62°. In Figure 26(a), the pink
orientation is related to the blue color, by a twin rotation of about 62° about the [100]
crystal direction and to the purple (top part of Figure 26(a)) orientation by a rotation of
about 40° about an axis near [111] as inferred from the MODF shown later in Figure 28.
The OIM map in Figure 26(b) shows blue as the dominant orientation and secondary
orientations are different shades of blue. Comparison of the pole figures in Figure 27(a
and b) show these relationships, where the dominant pink orientation in Figure 26(a) and
27(a) is about 60° from the dominant blue orientation in Figure 27(b) (that is also present
in Figure 26(b)). The texture intensity has a value of 89.8 x random in the scan shown in
Figure 27(a) whereas the one in Figure 27(b) has an intensity of 52.9 x random, a lower
value due to the clustered blue peaks, which tend to distribute the intensity.

Figure 28 shows the MODF for the as-fabricated specimen. The MODF has a
maximum of 198. It shows prominent rotations of about 62° about the [100] direction
and a second strong rotation of about 70° about the [110] crystal axis. These peaks are
very similar to those observed with the room temperature creep specimen.

Figure 29(a and b) show the misorientation plots corresponding to Figure 26(a
and b) respectively. As seen in Figure 29(a and b), there are notable peaks at 43, around
60, around 70, 75 and 80°, with an additional peak at 90° in Figure 29(b).

The grain size plots shown in Figure 30 are similar to Figure 20, showing a

bimodal population of very small grains of ~2um and grains larger than lOum.

96

 

(b)

Figure 25. SEM micrographs of as-fabricated eutectic Sn-Ag solder joint used for 85°
creep study.

97

Shear Direction

   

., T’ fiLf Shear Direction
14'“... _,- ‘ 1W“.

2 5 11m (a) Center )

 

45 um 09 Left

Figure 26. OIM maps of as-fabricated eutectic Sn-Ag solder joint used for 85° creep
study. Figure 25(b) is 324m to the left of Figure 25(8).

98

 

 

 

 

Max=89.8 32

 

 

 

 

(a) (b)

Figure 27. [0 0 1] and [1 0 0] pole figures of as-fabricated Sn-Ag solder joint specimen
used for 85° creep study.

99

m max: 219.569
--—-I 89.394
—-— 36.395
—- 14.818
—-- 6.033
2.456

0.407

 

 

If"?!
i:— 1.000
Lil—kl

 

 

 

001 100 001 ‘00 001 100 001 100

Figure 28. Misorientation distribution before high temperature creep.

100

 

 

 

 

 

 

 

 

 

 

 

Region (a) after HT Global Creep Shear Strain of 0.06
400
% 350 I —Before HT Creep
.3 300 _ —After HT Creep
Z:
to
‘8 250 —
8
c 200 T
'6 l
f.” 150. -
o .
g 100 —
a ' .
Z 50 - \I I
0 ’ "M‘u/‘r . . ~
0 20 4O 60 80 100
Misorientation angle in degrees (1 deg bin size)

 

 

 

Figure 29(a). Misorientation profile for as-fabricated and high temperature crept
specimen corresponding to Figure 26(a).

101

 

Region (b) after HT Global Creep Shear Strain 010.06

 

700

 

600 _ — Before HT Creep
— After HT Creep

 

 

 

 

 

 

W
100 — U

0 l l I I
0 20 40 60 80 1 00

Misorientation angle in degrees (1 deg bin size)

 

 

Nurrber of grain boundary pixels
b
O
O

 

 

 

 

 

 

Figure 29(b). Misorientation profile for as-fabricated and high temperature crept
specimen corresponding to Figure 26(b).

102

 

 

 

 

 

 

 

 

 

 

 

5000
4500 a — Region (a) Before HT Creep
— Region (3) Mar HT Creep
4000 d — Region (b) Before HT Creep
— Reglon (b) Mer HT Creep
3500 -
’Q
9 3000 -
.2
E
9 2500 r
(U
3
£9, 2000 -
8
a 1500 ~
1000 r
500 r
0
. . . ' . 10 . . . 100
Gram SIZB (diameter) In microns (Logarithmic buns)

 

 

Figure 30. Grain size distribution for as-fabricated and high temperature crept specimen.

103

After High Temperature Creep

Figure 31(a and b) shows the SEM micrographs of the same regions as in Figure
25(a and b) after high temperature creep at 85°C with a global shear strain of about 0.06.
Figure 32(a and b) shows the OIM maps of the corresponding regions. The scans after
creep look similar to the ones before creep with respect to the color representation of
texture, however one can easily see the effect of creep by comparing the before and after
maps. There is still one dominant orientation with 2 other orientations close to the
dominant one, similar to the as-fabricated specimen and shown by the pole figure in
Figure 33(a and b). The maximum intensity in the pole figures decreased slightly and all
dominant peaks have rotated systematically toward the negative y—direction by about 10°.
Also the sharpest peak in 33(b) has the orientation of the secondary peak in Figure 27(b),
and vice-versa.

High temperature processes cause grain boundary motion. After high temperature
creep (TITm = 0.72) to a global shear strain of 0.06, the specimen does show changes with
respect to grain boundary locations, particularly in Figure 26(a), but there is not a
significant change in the mesotexture. There are changes in the positions of high and low
angle grain boundaries which implies that they have moved due to creep that are easily
seen by comparing Figures 26(a) and 32(a). The high angle grain boundaries have
moved during shear and the isolated minority orientations (shown by circles in Figure
26(a and b)) have been consumed by the larger grains to reduce the number of small
grains. The gross texture components remain unchanged, though there is a systematic
rotation of all components by about 10° about the x-axis. Also in Figure 32(a), many low

angle grain boundaries have become more prominent and small grains have disappeared.

104

The motion of low angle boundaries implies that recovery has led to dissolution of other
low angle grain boundaries to incorporate smaller subgrains, which are separated only by
a few degrees, into the larger misorientation. This can be seen in the top right of Figure
32(a) where the low angle grain boundary no longer exists in comparison to Figure 26(a)
(arrow shown top right of the OIM map). This shows that the initial dominant orientation
grows at the expense of other orientations due to the high temperature. Also, in Figure
32(a) the vertical high angle grain boundary separating the pink and the blue orientations
has ‘smoothened out’ and ‘straightened up’. This is also indicative of grain growth
indicative of mass movement, which might be temperature assisted or shear strain
assisted during creep deformation or a combination of the two.

Figure 34 shows the MODF after high temperature creep. It is similar to the one
before creep. However there is a noted addition of 20° rotation about the [110] crystal
direction. The maximum intensity after high temperature creep is about 219 x random.

Figures 29(a and b) show the corresponding plots for the misorientation angle. In
Figure 29(a) one sees a slight decrease in the 43, 60, 70, 75 and 80°. However, in Figure
29(b) there is a more systematic decrease in all the peaks with minimal retention of the
20, 43 and 70° peaks. In Figure 29(b) one can see an increase in the 10 and 20° peaks.
The reduction in peaks implies that grain boundary length decreased, such that the grain
boundary energy has been reduced more by high temperature creep than at room
temperature (Figures 16 and 22). This means that there is some amount of grain growth
accompanying high temperature creep at 85°C.

Cracks develop in high angle boundaries that are not twin boundaries. On

examination of the SEM micrograph in Figure 31(a) of the creep specimen after high

105

temperature deformation a discontinuous crack traversing horizontally in the upper region
is observed. This crack is located at high angle grain boundaries in Figure 32(a). Figures
35 and 36 show the lattice from the two regions on either side of this high angle grain
boundary before and after high temperature creep respectively (the orientations before
creep are the corresponding regions from Figure 26(a) on either side of the high angle
grain boundary which developed into a crack seen in Figures 31(a) and 32(a)). The (110)
plane for both lattices has a misorientation of about 35-40° about the [110] crystal
direction. A possible glide system for Sn-crystals is (110) [111]. The [111] crystal
directions are aligned along the direction of applied shear strain for the purple and pink
orientations in Figure 35. The plane normals are not close to the plane of shear, so these
are relatively hard orientations. In Figure 36, the purple orientation has its plane normal
nearly perpendicular to the plane of shear, while the pink orientation has slip planes for
(110)[lll] as well as other c-axis slip systems that could operate to allow a more
arbitrary shape change to occur. Thus the pink orientation is soft, and it is adjacent to the
purple hard orientation that resists deformation. Such heterogeneity in deformation may
account for the formation of the crack.

Crystal rotations of 8-l2° developed during high temperature exposure. This
must be due to recovery processes and grain boundary motion since small strains cannot
cause such large crystal rotations. Figures 35 and 36 illustrate such rotations about the
specimen x-axis. Systematic crystal rotation is indicative of slip deformation. Since the
solder joint does not deform heterogeneously in all regions during deformation, the
observed rotations are rather large for region with local shear strain of 0.06 (seen in the

central region of Figure 31(a) and also the lower right comer of Figure 31(b)). which

106

implies a homogeneous rotation of only 3.4° for e.g. the maximum homogeneous
translation to the right of a microstructural feature (region circled in Figure 31(b)) in the
lower half of the specimen due to shear is about 9pm (based upon a 150m thickness),
which would result in a local shear strain of 0.06. Portions of the vertical grain boundary
between the pink and blue grains moved as much as 20pm (by comparing Figures 25(a)
and 31(a)), with a shear strain value of 0.3 which implies there was localized shear in this
region. Since it is unlikely that the specimen could have been mounted at a different
orientation by more than a couple degrees (see Appendices), the 10° rotation and the
large amount of boundary motion implies that there must have been more microstructural
change due to recovery/annealing effects rather than by shear strain alone.

Modest growth of moderate sized grains occurs with creep at higher temperatures.
Figure 30 shows the grain size changes after creep at 85°, in comparison to the as-
fabricated specimens. There is a conversion of grains into larger 20-30um grains in
region 32(a) and a similar trend is seen in region 32(b) with a large number of 33m and
50pm grains and a decrease in the 20m grains. The growth indicates motion or
elimination of some of the grain boundaries, which removed some of the smaller grains,
but did not result in a significant change of the misorientation relationships between
crystals during high temperature creep deformation.

These observations show that the single shear lap specimens are multicrystals
rather than polycrystals, and hence creep behavior may be made more repeatable by
causing a finer grains size with a random texture which would homogenize the plastic
deformation properties of the solder interconnect. The substantial motion of grain

boundaries as well as crystal rotations support the general view that high temperature

107

creep deformation occurs by a dislocation climb mechanism assisted by glide, which is

consistent with the interpretation from conventional creep experimentsz.

108

Copper
dog hone

LocalShear " H
Strain~0.3 ‘ '

Local
Shear
Strain
~ 0.01

Copper
dog bone

 

Local
Shear
7; Strain
‘ “ of 0.06

 

(b)
Figure 31. SEM micrographs of the same regions as shown in Figure 25(a and b), after
global creep of 0.06 shear strain at 85°C.

109

Shear Direction

 

45 um
Figure 32. OIM scans of eutectic Sn-Ag solder joint afier high temperature creep with a
global shear strain of 0.06.

110

{001} -\ {00'} 5’"
2:31

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5 "'3
10 8.
\. / 15 '3" .. / 1:. w
. EU I'M \ ,7 .. ,5 (-4:

\n/ ‘3 \Qb g ‘
24

{m} Max — 84.3 .3 Max = 55.3 2;
/\ 5° 33
/ \ E3 m\\ :33
\ 4s
43
51
54

 

 

M
\\_L,__./

 

\

 

 

/
\
/
K

(a) (b)
Figure 33. Pole figures of eutectic Sn-Ag solder joint after high temperature creep with a

global shear strain of 0.06. Figures 33(a and b) correspond to Figures 32(a and b)
respectively.

111

{PW-w max=198.?40
i-—- 82.269
5— 34.056
— 14.098
—— 5.836

m 2.415
5—— 1.000

0.414

 

 

 

 

. j _ ‘
001 100 001 100 001 100 001 $00 001 100 001 ‘00

 

001

Figure 34. Misorientation distribution after high temperature creep with a global shear
Strain of 0.06.

112

  
  
 
 

As-fabricated
specimen

 

 

Grain /
Boundary

Figure 35. Lattice orientations for as—fabricated specimen. The lattice show orientations
corresponding to Figure 26(a) before the crack development seen after high temperature
creep.

113

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Boundary Pink

Figure 36. Lattice orientations corresponding to various colors on either side of crack in
Figure 32(a) that developed after high temperature creep. The lattice are taken from the
Satne region as in Figure 35.

114

3.2 AGING

Isothermal Aging of Eutectic Tin-Silver Solder

Eutectic tin-silver, with its low melting point undergoes aging at room
temperature since this temperature is above 0.5Tm. Aging at a temperature of 85°C
allows us to carry out experimentation possible in reasonable length of time. By
obtaining OIM maps of the same region of a solder joint before and after aging at 85°C,
as illustrated in Figure 37(a and b), microstructural evolution due to aging in a particular
location can be examined. Figure 37(a) shows the OIM map of the as-fabricated joint
overlaid on the SEM image, and Figure 37(b) shows the OIM map of the same region
after aging at 85°C for 100 hours. SEM observations reveal coarsening of the Ag38n
particles, evident in the regions adjacent to the OIM scans, and discussed in more detail
in Ref. 1. Prior to aging, the OIM scan indicated a single dominant orientation in the
joint with fragments of low angle boundaries scattered throughout (essentially a single
crystal in the region scanned). Within this orientation, there were many small grains with
misorientation angles greater than 15° represented by the white boundaries. Only one

continuous low angle boundary was observed (a twist boundary about the c-axis near the

bottom in Figure 37 (a)).

After aging, (Figure 37(c)) the dominant single crystal orientation was about the
same, but the number of small grains with high misorientation angle decreased, and a
number of 5-15° low angle boundaries (thicker black lines) developed. The one

continuous low angle boundary present near the bottom of the micrograph of the as-

fabricated specimen was no longer in the same position after aging.

115

The pole figures shown in Figure 37(b and d) for as-fabricated and aged
specimens are very similar. Subtle changes did occur that reflect substantial motion of
low angle grain boundaries. Point plots of the pole figures of both specimens are inserted
in-between Figures 37(a and b) with as-fabricated orientations shown in black and the
aged orientations in gray (each point represents one or more pixels of the scan). The
orientations of the aged specimen in the (001) pole figure show 3 or 4 groups of
orientations clustered near that for the unaged specimens. These groups show that the
majority orientation is spread out over a larger angular space, such that the intensity of
this composite peak is reduced, even though the minority orientations have largely
disappeared. These disappearing minority orientations marked with a “+” (near (110)) or
a “*” on the pole figures in Figure 37(a) are diminished in Figure 37(b).

The misorientation distributions of the as-fabricated and aged specimen given in
Figure 38 shows an increase in the number of low angle misorientations of around 6-10°,
and a decrease in the number of high angle misorientations of 43, 60 and 70°. The
increase in the number and misorientation of low angle boundaries (thick black lines in
Figure 37(a and b)), and the fact that the (001) peak is split into 3-4 distinct sub-peaks
rotated by about 15° from the as-fabricated orientation, indicate that low angle
boundaries have swept through the microstructure one or more times. The decrease in
the number of high angle misorientations is probably due to the energy advantage that
large grains have to consume small grains with highly misoriented grain boundaries”.

The high angle misorientation peaks in Figure 24 are similar to those in Figure
19(a and b) and 29(a and b). Such misorientation distribution for the as-fabricated

Specimens used in creep and aging studies, suggest that certain misorientations are

116

energetically favored during the solidification process. These misorientations correspond
to special boundaries and twins]: A coincident site lattice is seen when there is a 223°
rotation about a [110] axis, or with a 43 or 71° rotation about a [010] axis. A 59 or 62°
rotation about [010] axis gives a (011)[o‘1‘1] or (031)[0T3] twin, respectively, and both
of these twins are evident as overlapping peaks in Figures 19 and 29 (misorientation
histogram of as-fabricated creep specimens) and Figure 38.

A few of the highly misoriented small grains did not disappear, particularly if they
were part of a cluster with other highly misoriented grains, such as the circled clusters in
Figure 37(a and b). These clusters appear to have existed in a smaller size in almost the
same location prior to aging in Figure 37(a). A careful investigation of these clusters
indicated a higher incidence of misorientations near 60°, than any other misorientation.
Twins are known to persist even with long annealing times due to the low energy of their
boundary structure‘5 and Figure 38 shows that 60° twins were retained more than the other
special boundary misorientations.

A similar OIM scan in a slightly overlapping region to the right of Figure 37(a
and b) showed the same type of crystal orientations and changes due to aging, with
differences only in the finest details.

A comparison of the MODF before and after aging (Figures 39 and 40
respectively) reveals a decrease in the intensity of the 43° misorientations and an increase
in the 0-15° misorientations (blue color) after aging, which is consistent with the result
seen from the misorientation distribution histogram in Figure 38. The 5-15°
misorientations are concentrated preferentially about the [100] crystal direction, though

O-5° misorientations have no preferred rotation axis (see Figure 40, 0° triangle). As

117

dislocations are absorbed into low angle grain boundaries to increase the misorientation,

some boundaries are more stable than others.

Figure 41 presents the grain size distribution for the as-fabricated and aged
specimen. The area of the small grains appears to have decreased as peaks in the
distribution have shifted from Sum to 8pm.‘ Since large grains are unbounded in the
OIM map, the OIM software was not able to characterize grains larger than 10pm so they

are not shown in the grain size distribution.

Low angle grain boundaries of about 8-12° developed due to high temperature
exposure, without stress. In Figure 42, the change in orientation from the bottom location
is plotted along a trace as one moves to the top along the vertical red line in Figures 37(a
and b). Whereas the majority crystal orientation changes monotonically from bottom to
top in the as-fabricated joint (spikes are the small highly misoriented grains), the
orientation after aging is nearly the same at the top and bottom, but the center of the joint
is misoriented from the top and bottom by about 10-15°. Two steps (see arrows) are

correlated with the vertical red line crossing a black low angle boundary.

The observed changes in the microstructure such as the elimination of small
grains and the polygonization resulting in low angle boundaries are consistent with
general physical metallurgy principles. Thus isothermal aging caused strongly preferred
orientations to persist, so that the joint maintained a nearly single crystal or multicrystal

microstructure. Further aging causes growth and continuance of such multicrystals and

 

. Since all plots are made using the same bin definitions, small differences are statistically meaningful for
comparison.

118

may cause coalescence of smaller crystals into the most dominant of the multicrystals

present in the joint.

119

 

 

 

 

 

    

5-15° Low Angl\e\§b
Grain Boundary Max = 108 ‘ ithax = 89

(100) vo
/ \ / \\
/ \\ / .\
3-5° Low Angle Z @ \ ‘ C

 

 

 

Grain Boundary

(b) (d)

Figure 37. Effect of isothermal aging on as-fabricated eutectic Sn—Ag joint made fi'om
paste solder. (a) As—fabricated condition and with overlay of OIM map on SEM
micrograph and (b) corresponding pole figures to (a), (c) aged condition with overlay of
OIM map on SEM micrograph and ((1) corresponding pole figures to (0). Small highly
misoriented gains with a white boundary disappeared (near [110], marked with a “+” on
the pole figure in (b), is diminished in (d)). Point plots of the pole figures of both
specimens are inserted in-between (b and d) with as-fabricated orientations shown in
black and the aged orientations in gay (each point represents one or more pixels of the
scan). The aged orientations in the (001) pole figure show 3 or 4 clusters of orientations.

120

 

 

 

 

 

 

 

 

 

 

 

 

 

 

700
ii .
a 600 ~ .
'a —As-fabricated
8
c
3 400 —
.n
.E
E 300 ~
or
‘8 200 -
a
‘e
g 100 -
O T A“ l l l
0 20 4O 60 80 100
Misorientation angle in degrees (1 deg bin size)

 

Figure 38. Misorientation angle histogams before and after isothermal aging. The
number of misorientations at 43, 60 and 70° decrease after aging, and the number of
misorientations in the 6-10° range increased.

121

 

 

100

Figure 39. Misorientation distribution function for as-fabricated specimen showing 43°
misorientations rotated about a [101] crystal direction and 60° misorientations rotated
about a [101] crystal direction.

122

r— max: 53.839
s—a 120.000
-— 64.000
—— 32.000
—— 16.000
.—- 8000
r7! 4.000
t 2.000
1.000
Inn-l

 

 

 

 

 

001 ‘ 001

Figure 40. Misorientation distribution function after aging showing decrease in the
intensity of the 43° misorientations and an increase in the <15° misorientations.

123

 

 

200
180 -

 

— As-fabncated
1 60 ‘ — After Aging

140 ~
120 r
100 r
80 2
60 r
40 r
20 r

O t i i r i

 

 

 

Area (square microns)

 

 

 

 

 

1 10
Grain Size (diameter) in microns (Logarithmic bins)

 

Figure 41. Grain size distribution for as-fabricated and aged specimen corresponding to
the OIM maps in Figure 37. Aging causes an increase in the size of the smaller gains.

124

 

100

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(I)

g 90% —Unaged

'8 30 2 —Aged

.5 7o . l

g 60 —

g 50 —

.2 40 —

.3 30 -

E, 20 — . r , p
E 10 «

§ 0 T l T l l l l

0 20 40 60 80 100 120 140
Vertical Position in microns

Figure 42. Effect of isothermal aging on relative misorientations starting from the bottom
to the top of the red line shown in Figure 37(a,b). Aged specimens had a misorientation
of about 10° from the as-fabricated orientation using the orientation at the bottom as a
reference orientation.

125

3.3 THERMOMECHANICAL FATIGUE

TMF of Eutectic Sn-Ag Solder Joints

Figure 43 shows the SEM microgaphs after 370 TMF cycles for eutectic Sn-Ag
solder joint. After obtaining the OIM scans for the as-fabricated Sn-Ag eutectic solder
joint in three regions of the same specimen, the OIM scans of the same regions after TMF
treatments of 150 and 370 TMF cycles were also obtained. OIM of region 1 is shown in
Figure 44(a-c), region 2 is shown in Figure 49(a-c) and region 3 in Figure 53(a-c).
Region 1 is close to the center of the joint, whereas region 2 is 362p.m to the left of
region 1 and region 3 is 229um to the right of region 1.

Region 1: The OIM scan from region 1 of the as-fabricated joints is shown in
Figure 44(a). It reveals a dominant orientation (light pink) with a secondary orientation
(lilac). These 2 major orientations present in the joint are spread throughout the joint
intermingled with one other. The dominant orientation (light pink) is related to the
secondary orientation (lilac) by a rotation of 60° about the [100] crystal direction. The
secondary orientation gives a banded appearance to the OIM scan, from the top left
toward the bottom right, consistent with the heat flow direction through the copper —
solder - copper assembly during solidification. A schematic showing the positioning of
the copper strips during the joint fabrication that can result in such a heat flow pattern is
shown in Figure 43(d). The banded appearance of the texture is less apparent in this joint
due to the fact that these two orientations have similar colors with respect to the sample

coordinate systems.

126

I... .-Lmfl
( _ A .

Other than these two orientations, there are a large number of speckled
orientations amongst the primary and secondary orientations with a red or a geen color.
The red and geen colored regions are separated from the matrix by high angle gain
boundaries (not shownin the figure due to large number of high angle gain boundaries
present in the scan). One can also see very few low angle gain boundaries (black lines)
in most regions of the joint. The majority (light pink) orientation has the c-axis aligned
45° from the negative x-direction towards positive y-axis, whereas in the secondary
orientations (lilac) the c-axes are aligned 45° with respect to the positive x-direction and
towards negative y-direction. Note that these two orientations have prisms that appear to
have the same orientation, but they do not — this visual illusion is due to the perspective
of the unit cell drawing with respect to the normal direction, which can be confirmed with
reference to the pole figures in Figure 45. The red and geen colored regions, which are
scattered amongst the texture bands, have their c-axis aligned along the specimen x-axis
and z-axis respectively. The reason for the presence of such small highly misoriented
gains in the as-fabricated joint is not clear at present. The primary and secondary
orientations are evident on the pole figures in Figure 45.

The OIM scans for region 1 after 150 and 370 TMF cycles are shown in Figure
44(b and c). There is no major change with respect to crystal orientation after 150 TMF
cycles, and the bands have persisted and gown after 370 TMF cycles, as seen in Figure
44(c). There are more interconnected low angle gain boundaries after 370 TMF cycles
as compared to the as-fabricated specimen or the one that has completed 150 TMF
cycles. There are fewer red and green colored orientations after 150 TMF cycles, as is

quite evident from looking at the OIM scan in Figure 44(b), and they are further reduced

127

after 370 TMF cycles. This result may be due to the effect of isothermal aging of 50
hours at 150°C during the first 150 TMF cycles, and another 70 hours at 150°C for the
next 220 TMF cycles. The heat input during isothermal aging at such high temperature
causes the stress to be reduced by recovery processes, and gain gowth. These processes
consume small grains seen as speckled geen and red regions as seen. prominently in the
OIM scans of the specimen after 370 TMF cycles. The secondary orientations became
more distinct in shape, and larger in size with a significant decrease in the small red and
geen colors at the same time.

The pole figures for region 1 are provided in Figure 45. The pole figure for the
as-fabricated specimen showed a dominant orientation and a secondary orientation. The
pole figures showed no change in the overall texture of the joint after 150 and 370 cycles.
However after 150 TMF cycles there is a new lighter shade of gay (shown by an arrow)
in Figure 45(b) which disappears after 370 TMF cycles as in Figure 45(c). The
maximum texture intensity for the as-fabricated specimen was 72.5 x random, which
decreased to 49.1 x random for the 150 TMF cycles specimen, but increased to 89.3 after

370 TMF cycles.

128

 

(a)

 

(d) Joint
configuration

(C)
Figure 43. SEM microgaphs after 370 TMF cycles. (a) Region 1 is near the center of the
joint, (b) region 2 is 362nm to the left of (a), (c) region 3 is 229nm to the right of (a) and
(d) joint configuration.

129

p. :- ~/ - ;u'—
-r .x 2.1»,I.

F'r; . '3‘ F- '7 l 'hn

L: J‘ {35.41.

 

(a)

 

Figure 44. Effect of TMF on as-fabricated eutectic Sn-Ag joint made from paste solder
fi'om region 1 in Figure 43(a). (a) OIM map of as-fabricated condition (b) OIM map of
same region after 150 TMF cycles, and (c) OIM map of same region after 370 TMF
cycles.

130

 

{010}

 

Max = 72.5

 

Figure 45.

. \

 

(a)

{or 0}

 

Max =49.1

 

 

 

(b)

“—J

 

{0m}

 

 

Max = 89.3

 

 

 

(C)

(a) Pole figures corresponding to OIM map of as-fabricated specimen in

Figure 44(a), (b) pole figure after 150 TMF cycles, and (c) after 370 TMF cycles. The
dominant orientation has persisted after 370 cycles, which is evident on comparison of
the (001) pole figures.

131

 

Figure 46 provides the misorientation histogram for region 1 with peaks at 20, 43,
60, 70, 75 and 80° for the as-fabricated specimen. After 150 TMF cycles one sees a
reduction in the 60° peak and an increase in the 43 and 70° peak. After 370 TMF cycles,
there is a decrease in the number of the 43, 60, 70 and >75° peaks. However, the 60°
peak is still persistent and there is no change in the 20° peak. Figure 47(a) shows the
corresponding MODF for the as-fabricated specimen. The MODF reveals that the 60°
misorientations are rotations about the [100] crystal direction, 70° misorientations are
rotations about the [110] crystal direction and higher angle misorientations (>70-85°) are
rotations concentrated close to a [313] crystal direction. After 370 TMF cycles, one sees a
larger intensity corresponding to <15° misorientations as seen in Figure 47(c) (see 0-15°
triangles in Figure 47(c)). This is consistent with misorientation distribution given in
Figure 46 and implies that the grain boundaries corresponding to the misorientation
angles less than 15° increase.

Figure 48 shows the gain size distribution for Region 1. At the end of 370 TMF
cycles there was an increase in the gain size of the 20pm gains and a decrease in the
2pm gains. The grain size distribution shows a bimodal distribution similar to the as-
fabricated specimens used for creep studies (see footnote on p. 86). The data
corresponding to the larger grains are not included in this plot since the software could

not consider unbounded gains for this analysis.

132

 

 

 

— As-fabricated
— After 150 TMF Cycles
— After 370 TMF Cycles (1

 

 

 

euro)
888

 

00

O

O
%

 

 

N

O

O
(

Number of grain boundary pixels
0
O

 

 

 

O
1
I
t
i
W

 

r f f r I I r ]

0 20 40 60 80 100
Misorientation angle in degrees (1 deg bin size)

 

 

 

Figure 46. Misorientation angle histogam corresponding to region 1 in degrees for as-
fabricated, 150 and 370 TMF cycled specimen. The number of misorientations at 43, 60,
70 and >75° diminish after 370 TMF cycles and there is an increase in the number of
<10° misorientations and no change in the 20° misorientations after 370 TMF cycles.

133

max: 32.698
64.000
32.000
16.000

8.000

.4 4.000

2.000

1.000

0.500

 

 

 

 

100

Figure 47(a). Misorientation distribution function for as-fabricated specimen showing
60° misorientations rotated about a [100] crystal direction. Misorientations >75° are
rotated about an axis close to a [313] crystal direction.

134

 

Figure 47(b). Misorientation distribution function after 150 TMF cycles showing
decrease in the >75° misorientations and a slight increase in the <15° misorientations as
compared to Figure 47(a).

135

max: 48.697
64.000
32.000
16.000

8.000

4.000

2.000

1.000

0.500

g] l l l l]

 

 

 

 

 

 

 

Figure 47(c). Misorientation distribution function after 370 TMF cycles showing an
increase in the intensity of <1 5° misorientations.

136

 

1 200

 

 

 

 

 

 

 

 

 

 

— As-fabricated
— After 150 TMF Cycles
1000 ~ — After 370 TMF Cycles
73800 —
C
9
.2
E 600 r
9
<11
3
g 400 r
m .
9 .
< . \t
' if,“
0 T t r f r r i l I l ' ' T l
1 1 o 1 00

 

 

Grain Size (diameter) in microns (Logarithm'c bins)

 

Figure 48. Grain size distribution corresponding to region 1 for as-fabricated, 150 and
370 TMF cycled specimen and OIM maps shown in Figure 44. TMF caused an increase
in the gain size from 10pm to 20pm and a decrease in 2pm gains.

137

There has been no obvious microcracking on the surface of the SEM microgaphs,
after 370 TMF cycles. OIM scans show some degree of grain gowth for 10-20um
gains, similar to observations for elevated temperature creep. In contrast, the number of
smaller gains has remained relatively constant in TMF, unlike in the crept and
isothermally aged conditions (Figures 30, 41, 48, 52, and 56). Thus it appears that TMF
up to this stage retains small gains, while allowing larger gains to gow in a manner
similar to high temperature creep and isothermal aging conditions.

Up to 370 cycles this joint can be considered to undergo stabilization by gain
gowth probably due to reduction of the number of high interfacial energy gain
boundaries present in the as-fabricated specimen (not the 22, 60 and 70° which are
considered as low energy boundariesl). The heat input at the high temperature aids this
stabilization and after 370 cycles the joint has spent enough time at the high temperature
extreme to substantially reduce the higher energy gain boundary area. This is apparent
in the histogam in Figures 46, 51 and 55 (described later), which shows a reduction in
the number of non-special boundaries, and an increase in the number of special
boundaries. The decrease in gain boundary area implies that gain gowth occurred, to
reduce the total energy of the gain boundaries7

The SEM microgaphs in Figure 43(a-c) show coarsening of the Aggsn particles,
with no other significant changes. Though the microstructure from the SEM microgaphs

does not show changes, the mesotexture obtained from the OIM shows changes.

138

Region 2 showed similar features and changes as seen in Region 1. The OIM
maps, pole figures, misorientation histograms and grain size distribution are shown in
Figures 49-52 respectively. Observations corresponding to region 3 are provided in

Figures 53-57.

139

from region 2 in Figure 43(b). (a) OIM map of as-fabricated condition (b) OIM map of
same region after 150 TMF cycles, and (c) OIM map of same region after 370 TMF

cycles.

Figure 49. Effect of TMF on as-fabricated eutectic Sn-Ag joint made from paste solder

 

140

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 50. (3) Pole figures corresponding to OIM map of as-fabricated specimen in
Figure 49(a), (b) pole figure after 150 TMF cycles, and (c) after 370 TMF cycles . The
dominant orientation has persisted after 370 cycles, which is evident on comparison of
the (001) pole figures.

141

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

600
—As-fabricated

-"3 — After 150 TMF Cycles
92 500 -
'5. — After 370 TMF Cycles
2‘
8400 4
C
6 ll
.5 300 —
CO
e (\I
“5200 -
g .
3100 ~ .\
2

O “‘ I I r l ‘1‘

0 . 20 . 40 . 60 _80_ 100
Misorientation angle In degrees (1 deg bin suze)

 

Figure 51. Misorientation angle histogram corresponding to region 2 in degees for as-
fabricated, 150 and 370 TMF cycled specimen. The number of misorientations at 43, 70,
75 and 80° diminish after 370 TMF cycles and there is an increase in the number of <10
and 60° misorientations after 370 TMF cycles.

142

 

 

 

—As-fabricated
1600 -
A —— After 150 TMF Cycles
C 1400 “ —— After 370 TMF Cycles

 

 

 

h1000 ~

Area (squa

 

N -> O) 03
O O O 8
O O O

1 l 1 1

 

 

 

O

 

'lIiIII

Grain Size (diameter) in1r(r)licrons (Logarithmic bins) 100

 

 

 

Figure 52. Grain size distribution corresponding to region 2 for as-fabricated, 150, and
370 TMF cycled specimen and OIM maps shown in Figure 49. TMF caused an increase
in the gain size from 10 to 20pm) and decrease in the 2pm gains.

143

‘0

- 31* . TIE-"'1'“. ‘

20.00 pm (C)

 

Figure 53. Effect of TMF on as-fabricated eutectic Sn-Ag joint made from paste solder
from region 3 in Figure 43(c). (a) OIM map of as-fabricated condition (b) OIM map of
same region after 150 TMF cycles, and (c) OIM map of same region after 370 TMF
cycles. The primary orientation in the as-fabricated specimen was consumed by the
secondary orientation afier 370 TMF cycles.

{001} W

 

 

 

 

/\

 

 

Max= 108 Max=91

{010}

 

{010}

\

 

 

 

 

 

 

(a) (b) (C)

Figure 54. (a) Pole figures corresponding to OIM map of as-fabricated specimen in
Figure 53(a), (b) pole figure after 150 TMF cycles and (c) after 370 TMF cycles. The

dominant orientation switched places after 370 cycles, which is evident on comparison of
the (001) pole figures.

145

 

e

-i‘

 

 

 

8

 

— As-fabricated
500 r — After 150 TMF Cycles
[1 — After 370 TMF Cycles

 

 

 

é

 

300 - l

 

Number of grain boundary pixels
8
O

l
200 a \ ‘\ ,' \ §‘V‘

l l l

 

 

 

0 100

 

 

2 40 0 O
Misonoentation angle in degrges (1 deg an size)

 

Figure 55. Misorientation angle histogam corresponding to region 3 in degees for as-
fabricated, 150, and 370 TMF cycled specimen. The number of misorientations <10° and
at 43° diminish after 370 TMF cycles and there is an increase in the number of 60,70 and
75° misorientations after 370 TMF cycles.

146

 

 

 

 

 

 

 

 

 

 

 

 

 

1000

900 " —As-fabricated

800 _ —After150TMF Cycles
Tn‘ — After 370 TMF Cycles
5 700 —
.9
E 600 ~
on
26 500 ~
3
3, 400 -
5:3 300 -
< 1

200 ~

100 — ‘ ’

O T I l I T I I T I I T I I I I I T
. . . . 10 . . . 100
Grain Size (diameter) tn morons (Loganthmc bins)

 

 

 

Figure 56. Grain size distribution corresponding to region 3 for as-fabricated, 150, and
370 TMF cycled specimen and OIM maps shown in Figure 52. TMF caused an increase
in the gain size from 10 to 20pm gains and a decrease in the 2pm gains.

147

 

Tables VI, VII and VIII compare the microtextural development (Table VI),
distribution of misorientation angles between gains, and gain size distribution as a
function of TMF cycles in the three regions of the same specimen studied.

Table VI indicates that regions 1 and 2 are similar; both have one dominant and a
secondary orientation and large number of speckled orientations in the as-fabricated
condition. Region 3 has one predominant orientation and few speckled orientations.
Progessively after 150 and 370 TMF cycles, regions 1 and 2 show a decrease in the
number of speckled orientations, and the banded texture becomes more distinct. Region
3 shows emergence of a secondary orientation after 150 TMF, which gows and
dominates at 370 TMF cycles.

As can be seen in Table VH, after 370 TMF cycles in regions 1 and 2 there is a
tendency for increase in the low angle gain boundary misorientations (<10°). Region 3
does not exhibit this trend. All regions show a decrease in the special gain boundary
misorientation angles (45, 70 and >70°) after 370 TMF cycles. However the 60° peak
decreases for region 1 (central region) and increases for regions 2 and 3 (edge regions).
It should also be noted that the trend presented for the specimen that has experienced 370
TMF cycles is not consistent with the observations on the same specimen during the
course of 150 TMF cycles. He reason for this behavior is not clear at this time.

Table VH1 indicates a significant increase in the area of small grains (<10um)
after 150 cycles. After 370 TMF cycles there is a decrease in the 2pm grains and an
increase in the area of larger grains (25pm for regions 1 and 3, and 18pm gains for
region 2). With increasing number of TMF cycles one can envision that some amount of

grain growth occurs at the end of 370 TMF cycles. Small gains with larger

148

 

misorientations are consumed with reduction is the gain boundary length, and the
energetically favored twin—boundaries have persisted at the end of 370 TMF cycles.
However, it is not clear why there is an opposite trend in the gain size distribution at the
end of 150 TMF cycles in contrast to 370 TMF cycles.

Deformation in TMF is a complicated process and is different from isothermal
aging and creep. In addition the highly inhomogeneous behavior of the heterogeneous

solder joint complicates the overall behavior.

149

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table VI. Comparison of Microtextural Features for the Three Regions after
Several TMF Cycles.
R990“ Fem" As-fabricated 150 TMF cycles 37" TMF
cycles
. . . Present (Pink)
Dominant Present.(Whrtrsh- Present (Pink) and more
Orientation Pink) . .
distinct
1
Present (Lilac)
(Middle 3‘80“?” Present (Lilac) Present (Lilac) and more
Orientation . .
distinct
Region)
Large number
Speckled scattered throughout Reduced in
Orientation (red and geen number Almost absent
colored)
. Present (Pink)
(1)):mrnant Present (Pink) Present (Pink) and more
entatron . .
2 distinct
. . Present (Lilac)
Secondary Present (W hrtrsh- .
(Edge Orientation Green) Present (Lilac) and more
distinct
Region) Large number Reduced in
Speckled scattered number but not Almost absent
Orientation throughout (red and si . ficantl
geen colored) gnr y
Reduced further
and becomes
Dominant Decrease secondary
3 Orientation Present (Yellow) (Y ellow-Orange) orientation
(Yellow-
(Edge Orange)
Increases .
. Secondary Very small amount . . Dornrnates
Regen) . . Significantly
Orientation (Purple) (Purple) (Purple)
Seen scattered .
SPGCH‘TA throughout (red and Reduced m Almost absent
Orientation number
geen colored)

 

150

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table VII. Comparison of Misorientation Angles for the Three Regions after
Several TMF Cycles.
Misorientation Number of Grain Boundary Pixels
Region Angle
(deg) As-fabricated 15¢:wa 31:32:17
<10 200 200 300
20 200 200 200
1 30 60 80 40
(Middle 45 270 280 200
Region) 60-62 400 300 350
70 325 520 280
>70 ~200 ~200 ~50
<10 120 80 280
20 300 100 250
2 30 60 100 40
(Edge 45 170 200 100
Region) 60-62 350 210 500
70 400 400 150
>70 ~200 ~200 ~100
<10 250 280 120
20 70 50 50
3 30 50 50 30
(Edge 45 210 250 120
Region) 60-62 240 280 490
70 320 250 380
>70 ~220 ~180 ~180

 

 

 

 

 

 

 

 

 

 

 

151

 

 

Table VIII. Comparison of Grain Size for the Three regions after Several TMF
Cycles.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Grain Size Area
Region (square um)
( )
Pm As- fabricated 150 TMF 370 TMF
cycles cycles
2 600 1000 400
1 3-8 200 250 80
(Middle 10 250 400 100
Region) 18-22 400 550 200
25 - - 400
2 650 1600 450
2 3-8 200 225 225
(Edge 10 100 - 200
Region) 18 - 200 400
25 400 - -
2 550 850 550
3
3-8 100 225 200
(Edge
10-12 80 400 125
Region)
20 - - 300

 

 

 

 

 

152

 

3.4 REFERENCES

1. A.U.Telang, T.R.Bieler, S.Choi and K.N.Subramanian, “Orientation Imaging Studies
of Sn-Based Electronic Solder Joints”, J. Mater. Res., 17, 9, 2294, 2002.

2. R.W.Cahn and P.Haasen, Physical Metallurgy 4th ed., Elsevier Science, 28, 1996.

3. R.Darveaux and K.Banerji, “Constitutive Relations for Tin-Based-Solder Joints”, 42“d
Electronic Components and Technology Conference (ECT C), IEEE, Piscataway, NJ,
538, 1992.

4. S.Choi, J.G.Lee, F.Guo, T.R. Bieler, K.N.Subramanian, and J.P.Lucas, “Creep
Properties of Sn-Ag Solder Joints Containing Intermetallic Particles”, JOM, 53/6, 22,
2001.

 

5. I.L.Dillamore, P.L.Moriis, C.J.E.Smith, and B.W.Hutchinson, Proc. Roy. Soc. 329A,
405, 1972.

6. K.L.Merkle and D.Wolf, “Structure and Energy of Grain-Boundaries in Metals”,
MRS Bulletin, 15/9, 42, 1990.

7. V.Randle and B.Ralph, “Local Texture Changes Associated with Grain Growth”,
Proceedings of the Royal Society of London, Series A, Mathematical and Physical
Sciences, 415, 1848, 239, 1988.

153

SUMMARY

The results obtained by OIM provide significant insight into the solder
microtexture, which could not be observed by ordinary microscopic techniques.
Almost all of the as-fabricated specimens showed texture bands, however the
orientation of the dominant crystals in the joint varied from joint to joint. There was
typically a dominant and secondary orientation in as-solidified specimens that were
twin related, which often exhibited some degee of symmetry with respect to the
sample coordinate system. Most specimens tend to have the c-axis not close to the
length direction of solder/substrate interface. The strong texture implied that small
solder joints are multicrystals instead of polycrystals. Certain misorientations are
energetically favored during the solidification process such as the 60° twins and 70°
misorientations (Z boundaries).

The gross texture components remain unchanged after creep, aging, or TMF
up to 370 cycles. High temperature processes like creep and aging cause gain
boundary motion. Low angle grain boundaries of about 8-12° developed due to high
temperature exposure, with or without stress. Also, crystal rotations of 812°
developed during high temperature exposure, with or without stress. Creep studies
have shown that no major crystallographic changes have occurred after room
temperature creep of 0.03 global shear strain, whereas high temperature creep with
0.06 global shear strain does show some changes in the crystal orientation but with no
major change in the texture of the solder joint. Also, during high temperature creep,

cracks nucleated along the high angle grain boundaries (that are not twin type gain

154

 

boundaries) aligned in the direction of shear. Twin boundaries persist more than
other boundary types after high temperature exposure, with or without stress. Aging
studies revealed grain coarsening with an increase in the number of low angle gain
boundaries and decrease in the number of high angle grain boundaries. Up to 370

TMF cycles the joint reveals grain gowth.

155

 

Suggestions for future work:

1.

Is localized deformation caused by generation of small gains that decrease the
creep resistance locally? Do the boundaries provide more interfacial locations for
recovery processes?

Do twin boundaries cause near neighbor boundaries to be more likely to crack?
Are twin boundaries resistant to absorbing dislocations so that neighboring
boundaries have to absorb more, and hence are more highly strained? Are 2
boundaries less likely to slide, and hence more likely to crack?

Do non-twin misorientation peaks change in the opposite sense (or differently) as
compared to the other 2 boundaries?

With increasing number of thermal cycles, is there more nucleation of small
grains in gain boundaries or development of cracks? Which types of boundaries
cause cracking vs. nucleation of small gains?

Does damage nucleation depend on the dominant crystal orientation from
solidification and their misorientations with neighboring grains and how is

damage nucleation related to ultimate failure and breakdown of the interconnect?

156

APPENDIX

Specimen Mounting Error Calculation: The tables below show euler angle data

recorded after mounting the same specimen over and over again. It is found that a

maximum of 35° is seen about euler angle 1. All euler angles are in degees.

Specimen: High Temperature Creep Region A

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Before After
Euler 1 Euler 2 Euler 3 Euler 1 Euler 2 Euler 3
Set 1 1 61 80 58 1 63 80 58
162 81 57 163 81 56
162 81 57 164 80 57
162 80 57 163 80 58
Average 161.75 80.5 57.25 163.25 80.25 57.25
Difference
Euler 1 Euler 2 Euler 3
-1.5 0.25 0
Before After
Euler 1 Euler 2 Euler 3 Euler 1 Euler 2 Euler 3
Set 2 1 50 80 25 151 80 24
151 80 24 152 80 24
150 80 25 151 81 25
148 81 25 150 81 26
Average 149.75 80.25 24.75 151 80.5 24.75
Difference
Euler 1 Euler 2 Euler 3
-1.25 -O.25 0

 

 

 

 

 

157

 

 

SET 1: First Iteration:

Specimen: High Temperature Creep Region B

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Before After
Euler 1 Euler 2 Euler 3 Euler 1 Euler 2 Euler 3

8611 102 110 46 102 110 46
101 110 47 103 110 46

102 110 46 103 110 46

101 110 46 102 110 46

Average 101.5 110 46.25 102.5 110 46

Difference
Euler 1 Euler 2 Euler 3
1 0.5 0.5
Second Iteration:
Before After
Euler 1 Euler 2 Euler 3 Euler 1 Euler 2 Euler 3

$911 102 110 46 105 112 46
101 110 47 105 111 46

102 110 46 105 112 46

101 110 46 105 111 46

Average 101.5 110 46.25 105 111.5 46

Difference
Euler 1 Euler 2 Euler 3
~35 -1.5 0.25

 

 

 

 

 

158

SET 2: First Iteration:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Before After
Euler 1 Euler 2 Euler 3 Euler 1 Euler 2 Euler 3
Set 2 264 93 55 267 93 55
265 93 55 266 93 54
265 94 54 266 93 54
Average 255 93 55 267 93 55
Difference
Euler 1 Euler 2 Euler 3
-1.75 0.25 0.25
Second Iteration:
Before After
Euler 1 Euler 2 Euler 3 Euler 1 Euler 2 Euler 3
Set 2 264 93 55 268 91 55
265 93 55 268 91 54
265 94 54 268 91 54
Average 265 93 55 268 91 55
Difference
Euler 1 Euler 2 Euler 3
-3.25 2.25 0.25

 

 

 

 

 

159

Specimen: High Temperature Creep Region C

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Before After
Euler 1 Euler 2 Euler 3 Euler 1 Euler 2 Euler 3
Set 1 249 1 01 51 248 1 00 50
249 100 51 249 101 50
250 101 51 248 99 51
252 79 54 251 79 54
Average 250 95.25 51 .75 249 94.75 51 .25
Difference
Euler 1 Euler 2 Euler 3
1 0.5 0.5
Before After
Euler 1 Euler 2 Euler 3 Euler 1 Euler 2 Euler 3
Set 2 236 115 45 234 114 46
236 1 16 52 235 1 15 51
236 1 16 51 234 1 16 50
236 116 51 234 115 50
237 1 16 52 235 1 15 52
234 116 46 234 115 47
Average 235.83 115.83 49.5 234.33 115 49.33
Difference
Euler 1 Euler 2 Euler 3
1.5 0.83 0.17

 

 

 

 

 

160

 

 

Specimen: Thermomechanical Fatigue

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Before After
Euler 1 Euler 2 Euler 3 Euler 1 Euler 2 Euler 3
Seti 135 115 84 135 115 84
134 115 86 136 115 85
Average 134.5 115 85 135.5 115 84.5
Difference
Euler 1 Euler 2 Euler 3
-1 O 0.5

 

 

 

 

 

161