3Y=l
w a i a
no. 3T3 ;
DIFFUSION KINETICS AND MICROSTRUCTURE OF EUTECTIC AND
COMPOSITE SOLDER/COPPER JOINTS
DISSERTATION
Presented to the Graduate Council of the
University of North Texas in Partial
Fulfillment of the Requirements
For the Degree of
DOCTOR OF PHILOSOPHY
By
Yujing Wu, B.S., M.S.
Denton, Texas
May, 1994
3Y=l
w a i a
no. 3T3 ;
DIFFUSION KINETICS AND MICROSTRUCTURE OF EUTECTIC AND
COMPOSITE SOLDER/COPPER JOINTS
DISSERTATION
Presented to the Graduate Council of the
University of North Texas in Partial
Fulfillment of the Requirements
For the Degree of
DOCTOR OF PHILOSOPHY
By
Yujing Wu, B.S., M.S.
Denton, Texas
May, 1994
Wu, Yujing, Diffusion Kinetics and Microstructures of Eutectic and
Composite Solder/Copper Joints. Doctor of Philosophy, May 1994, 294 pp.,
28 tables, 95 illustrations, bibliography, 140 titles.
Sn/Pb solders are widely used by the electronics industry to provide both
mechanical and electrical interconnections between electronic components and
printed circuit boards. Solders with enhanced mechanical properties are required
for high reliability for Surface Mount Technology (SMT) applications. One
approach to improve the mechanical properties of solder is to add metallic or
intermetallic particles to eutectic 63Sn/37Pb solder to form composite solders.
Cu6Sn5 and Cu3Sn form and grow at the solder/copper substrate
interface. The formation and growth of these intermetallics have been proposed
as controlling mechanisms for solderability and reliability of solder/copper joints.
The goal of this study was to investigate the diffusion kinetics and
microstructures of six types of composite solder/copper joints.
Scanning electron microscopy (SEM), transmission electron microscopy
(TEM), x-ray dispersive spectroscopy (XEDS), scanning TEM with XEDS and
in-situ TEM were used to study the microstructures and the chemical
compositions of the specimens.
The growth and morphology of the intermetallic phases at composite
solder/copper substrate interfaces were examined as functions of time,
temperature and particle additions. The anneal times range from 0 (as soldered)
to 64 days and the anneal temperatures range from 110 to 160°C. The
activation energies for the formation of Cu6Sn5 and Cu3Sn at the solder/copper
substrate interface were determined and were compared to the values for
eutectic solder/copper system. The addition of particles to eutectic solder
strongly affects the microstructure and kinetics of the interfacial layers.
Compared to eutectic solder, the addition of Cu-containing particles increases
the activation energy for Cu6Sn5 formation and decreases the activation energy
for Cu3Sn formation. The activation energies for formation of Cu6Sn5 and Cu3Sn
are both decreased with Au or Ag particle additions. In Ni composite solder the
Cu3Sn formation is suppressed, and the activation energy for Cu6Sn5 formation
is dramatically increased.
The effect of the particle additions on the diffusion behavior of Sn in the
composite solder matrix and thus on the microstructures of the intermetallic
interface were examined. A Sn diffusion model and the Sn diffusion
mechanisms affected by particle additions in composite solders are proposed.
TABLE OF CONTENTS
Page
LIST OF TABLES vii
LIST OF ILLUSTRATIONS ix
Chapter
1. INTRODUCTION 1
CHAPTER 1 REFERENCES 10
2. BASIC THEORY
2.1 Phase Diagrams 14
2.1.1 The Lead-Tin System
2.1.2 The Copper-Tin System
2.2 Surface Wetting 16
2.3 Diffusion in Solids 19
2.4 Solidification 26
2.4.1 Nucleation
2.4.2 Eutectic Solidification
2.5 Phase Growth 29
CHAPTER 2 REFERENCES ! 40
3. SAMPLE PREPARATION
3.1 Cu/Solder/Cu Joint Fabrication 42
3.2 Annealing Procedure 44
3.3 SEM Sample Preparation 45
3.4 TEM Sample Preparation 47
3.4.1 Ultramicrotomy
3.4.2 Electropolishing
3.4.3 Conventional Cross-sectional (XTEM) Sample
Preparation
3.5 Thin Film Preparation 54
3.6 In-Situ Heating 56
CHAPTER 3 REFERENCES 72
4. INTERMETALLICS AT THE INTERFACES OF COMPOSITE
SOLDER/COPPER JOINTS
4.1 Introduction 74
4.2 Microstructure of Composite Solder/Copper Substrate
Interface 74
4.3 The Formation of Microvoids 80
4.4 Activation Energies of Intermetallic Formation in Eutectic
Solder and Composite Solders 81
4.5 In-Situ Thin Film Diffusion Couple Studies 84
4.6 Diffusion Mechanism 89
4.7 Microstructures of Fe and Pd Composite Solders 98
4.8 Summary and Conclusion of Chapter 4 99
CHAPTER 4 REFERENCES 164
IV
5. THE MATRIX OF EUTECTIC AND COMPOSITE SOLDERS
5.1 Introduction 167
5.2 The Microstructure of Eutectic Solder 168
5.3 Eutectic Microstructures in the As-Soldered State 171
5.4 The Microstructures of Composite Solders 175
5.4.1 The Matrix of Cu-Containing Composite Solders
5.4.2 The Matrices of Au and Ag Composite Solders
5.4.3 The Matrix of the Ni Composite Solder
5.4.4 The Pb-Rich and Sn-Rich Phases in Composite
Solder
5.5 Summary and Conclusion of Chapter 5 179
CHAPTER 5 REFERENCES 203
6. SUMMARY 205
APPENDIX A. CRYSTAL STRUCTURES 211
APPENDIX A REFERENCES 231
APPENDIX B. SCANNING ELECTRON MICROSCOPY AND X-RAY
MICROANALYSIS 233
APPENDIX B REFERENCES 261
APPENDIX C. PRINCIPLES OF TRANSMISSION ELECTRON
MICROSCOPY 263
APPENDIX C REFERENCES 277
v
APPENDIX D. STATISTICAL ANALYSIS 278
APPENDIX D REFERENCES 284
BIBLIOGRAPHY 285
VI
LIST OF TABLES
Page
2.1 Diffusion Parameters of Cu, Ag, Au and Ni in /?-Sn and
Parameters of /?-Sn Self-diffusion 31
3.1 Compositions and Particle Size Ranges of the Composite Solders . 58
3.2 Cooling Rates of Different Sample Sets 59
3.3 Composite Solder Sample Matrix 60
3.4 XTEM Sample Preparation Procedure 61
3.5 Thin Film Sample Matrix 62
4.1 Statistical Parameters for the Thickness Measurements 101
4.2 Intermetallic Thickness (jum) and Diffusion Coefficients for
Eutectic Solder 102
4.3 Intermetallic Thickness (/xm) and Diffusion Coefficients for
7.6 w t% Cu Composite Solder Diffusion Coefficients 103
4.4 Intermetallic Thickness (/*m) and Diffusion Coefficients for
20 wt% Cu3Sn Composite Solder 104
4.5 Intermetallic Thickness (/xm) and Diffusion Coefficients for
20 w t% Cu6Sn5 Composite Solder 105
4.6 Intermetallic Thickness (/xm) and Diffusion Coefficients for
4 wt% Ag Composite Solder 106
4.7 Intermetallic Thickness (/im) and Diffusion Coefficients for
4 wt% Au Composite Solder 107
vii
4.8 Intermetallic Thickness (j«m) and Diffusion Coefficients for
4 wt% Ni Composite Solder 108
4.9 Activation Energies for Intermetallic Formation for the Eutectic
Solder and Composite Solders 109
4.10 The Ratio of the Area Contacted by the Pb-rich Phase to the
Total Interfacial Area of the Solder/Cu Interface 110
4.11 Thickness (jum) of Cu6Sn5 and Cu3Sn at the Solder/Cu Interface
for the 10 wt% and 20 wt% Cu6Sn5 Composite Solder 111
5.1 Thickness (jam) of Cu6Sn5 and Cu3Sn Layers at the Solder/Copper
Particle and Solder/Copper Substrate Interface 182
5.2 Thickness (^m) of Cu6Sn5 Layers After Annealing at 140 °C . . . 183
A.1 Lattice Spacings and Indexed Planes of Pb 217
A.2 Lattice Spacings and Indexed Planes of Sn 218
A.3 Lattice Spacings and Indexed Planes of Cu, Ag, Au, and Ni . . . . 219
A.4 Lattice Spacings and Indexed Planes of Cu6Sn5 220
A.5 Lattice Spacings and Indexed Planes of Cu3Sn 221
A.6 Lattice Spacings and Indexed Planes of AuSn4 222
A.7 Lattice Spacings and Indexed Planes of Ag3Sn 223
A.8 Lattice Spacings and Indexed Planes of Ni3Sn4 224
C.1 JEOL JEM-100 CX and JEOL JEM-200 CX Electron Microscope
Performance Specifications 271
VIII
LIST OF ILLUSTRATIONS
Page
1.1 Cross-Section View of Solder/Copper Joint 9
2.1 Lead-Tin Phase Diagram 32
2.2 Copper-Tin Phase Diagram 33
2.3 The Equilibrium Shape of a Droplet 34
2.4 Schematic Illustration of Elementary Jump of Interstitial
Mechanism 35
2.5 Schematic Illustration of Elementary Jump of Vacancy
Mechanism 36
2.6 Schematic Illustration of the Free Energy and Configurations
of a Jump of Vacancy Mechanism 37
2.7 Schematic Illustration of the Free Energy Change Associated
with Nucleation of a Sphere 38
2.8 Schematic Illustration of Various Eutectic Structures 39
3.1 Sample Configuration of Copper/Solder/Copper Joint and
Silicon Blocks 63
3.2 Buehler Minimet Polisher/Grinder with Sample Holder 64
3.3 A Typical Ultramicrotome 65
3.4 Schematic of Sample Sectioning Using Ultramicrotomy 66
3.5 Schematic of Sample Rough Trimming and Re-embedding 67
3.6 Schematic of Precise Trimming of Embedded 68
3.7 South Bay Technology Model 550C Jet Polisher 69
IX
3.8 VE-400 Evaporator 70
3.9 Schematics of Thin Film Sample Configurations 71
4.1 SEM Microstructure and XEDS Spectra of Eutectic Solder/Copper
Substrate Sample after Annealing at 120 °C for 32 Days 112
4.2 SEM Microstructures of Cu Composite Solder/Copper Substrate
Sample as a Function of Annealing Time 115
4.3 SEM Microstructures of Ag Composite Solder/Copper Substrate
Samples as a Function of Annealing Temperature 117
4.4 SEM Microstructures of the Eutectic Solder and Composite
Solder/Copper Substrate Interfaces after Annealing at 140°C
for 16 Days 119
4.5 TEM Micrograph of a Eutectic Solder/Copper Joint after
Annealing at 140 °C for 4 Days 123
4.6 Selected Area Diffraction Patterns of Cu6Sn5, Cu3Sn and Cu
Phases in Figure 4.5 124
4.7 SEM and TEM Micrographs of the Interfacial Area of the
As-Soldered Cu6Sn5 Composite Solder/Copper Joint 125
4.8 TEM Micrograph of the As-Soldered Cu3Sn Composite
Solder/Copper Joint 126
4.9 TEM Micrograph of the As-Soldered Cu6Sn5 Composite
Solder/Copper Joint 128
4.10 TEM Micrograph of the As-Soldered Cu Composite
Solder/Copper Joint 130
x
4.11 TEM Micrograph of the As-Soldered Ag Composite
Solder/Copper Joint 131
4.12 TEM Micrograph of the As-Soldered Au Composite
Solder/Copper Joint 132
4.13 TEM Micrograph of the As-Soldered Ni Composite
Solder/Copper Joint 133
4.14 TEM Micrograph of Cu Composite Solder/Copper Joint after
Annealing at 140 °C for 4 Days 134
4.15 TEM Micrograph of Cu3Sn Composite Solder/Copper Joint after
Annealing at 140 °C for 4 Days 135
4.16 TEM Micrograph of Ag Composite Solder/Copper Joint after
Annealing at 140 °C for 4 Days 136
4.17 TEM Micrograph of Ni Composite Solder/Copper Joint after
Annealing at 140 °C for 8 Days 137
4.18 SEM Micrograph of Au Composite Solder/Copper Joint after
Annealing at 120 °C for 64 Days 138
4.19 SEM Micrograph of Ni Composite Solder/Copper Joint 140
4.20 Intermetallic Thicknesses at the Solder/Copper Substrate
Interface versus the Square Root of Annealing Time for
Eutectic Solder at 140 °C 141
4.21 Intermetallic Thickness at the Solder/Copper Substrate
Interface versus the Square Root of Annealing Time
for Cu Composite Solderat 120 °C 142
XI
4.22 Plots of Ln(D) versus 1/T for Cu6Sn5 and Cu3Sn Formation at the
Solder/Copper Substrate Interface of Cu Composite Solder . . . . 143
4.23 Plots of Ln(D) versus 1/T for Cu6Sn5 and Cu3Sn Formation at the
Solder/Copper Substrate Interface of Au Composite Solder . . . . 144
4.24 TEM Micrographs of Cu, Sn, Ni, Ag and Au Thin Films 145
4.25 A Time Series of TEM Micrographs of Cu/Sn Thin Film
Showing Cu-Sn Intermetallic Growth 148
4.26 TEM Micrograph of Cu/Sn/Ni Sample Showing no Intermetallic
Growth after Annealing at 250 °C for 2 Hours, Followed by
200 °C for 12 Hours 155
4.27 XEDS Peak Intensity Ratios of Ni to Sn for the Cu/Sn/Ni Sample . 1 56
4.28 Model for the Growth of the Two Interfacial Intermetallics 157
4.29 The Thicknesses of the Intermetallic Layers at the Solder/Copper
Substrate Interface for Eutectic Solder and All Composite Solders
in the As-Soldered Condition 158
4.30 The Thicknesses of the Intermetallic Layers at the Solder/Copper
Substrate Interface for Eutectic Solder and All Composite Solders
after Annealing at 140°C for 16 Days 159
4.31 TEM Micrograph of the Matrix of Au Composite Solder after
Annealing at 140°C for 4 Days 160
4.32 XEDS Peak Intensity Ratio of Sn to Au along AuSn4/AuSn4
Grain Boundaries and AuSn4/Au Phase Boundaries 161
4.33 SEM Micrograph of 4 wt% Fe Composite Solder/Copper Joint
after Annealed at 140°C for 4 Days 162
XII
4.34 SEM Micrograph of 4 wt% Pd Composite Solder/Copper Joint
after Annealed at 140°C for 16 Days 163
5.1 SEM and TEM Microstructures of the Eutectic Solder Matrix in
the As-soldered State 184
5.2 Selected Area Diffraction Patterns of Pb-rich Phase and Sn-rich
Phase 186
5.3 SEM Microstructure of the Eutectic Solder Matrix After Annealing
at 140 °C for 8 days 187
5.4 The Size of the Pb-Rich Phase of Eutectic Solder as a Function of
Anneal Time at 140 °C 188
5.5 TEM Microstructure of Eutectic Solder Matrix in the As-soldered
State Showing the Amorphous Pb Oxide Phase and SADP of Pb
Oxide Phase 189
5.6 TEM Microstructure of Eutectic Solder Matrix after Solidification
with Fast Cooling Rate Showing a Highly Lamellar Structure . . . 190
5.7 TEM Microstructure of Eutectic Solder Matrix After Solidification
with Fast Cooling Rate May Showing a Colony Structure 191
5.8 Dark Field TEM Micrograph of Eutectic Solder Matrix After
Solidification with Moderate Cooling Rate 192
5.9 SEM Microstructure of Cu, Cu3Sn and Cu6Sn5 composite Solder
Matrix in the As-Soldered State 193
5.10 TEM Micrograph of Cu Composite Solder Matrix in the As-
Soldered State shows a Cu Particle and Surrounding
Intermetallics 195
XIII
5.11 SEM Microstructures of Cu, Cu3Sn and Cu6Sn5 Composite
Solder Matrix after Annealing at 140 °C for 16 Days 196
5.12 TEM Micrograph of Cu6Sn5 Composite Solder Matrix in the
As-Soldered State 198
5.13 SEM Microstructure of Au Composite Solder Matrix in the
As-Soldered State and after annealing at 140 °C for 16 Days . . . 199
5.14 SEM Microstructure of Ag Composite Solder Matrix in the
As-Soldered State and after annealing at 140 °C for 16 Days . . . 200
5.15 SEM Microstructure of Ni Composite Solder Matrix in the
As-Soldered State and after annealing at 140 °C for 16 Days . . . 201
5.16 TEM Microstructure of Ni Composite Solder Matrix in the As-
Soldered State, showing a Ni Particle and Surrounding Ni3Sn4 . . 202
A.1 Schematic of the Principle Structures of Metals 225
A.2 Schematic of the Diffraction Camera Geometry 226
A.3 Schematic of the Unit Cell of /?-Sn 227
A.4 Schematic of the Interstitials Octahedral Voids in the cph
Structure 228
A. 5 Crystal Structure of Ordered Cu6Sn5 229
A.6 Crystal Structure of Cu3Sn 230
B.1 Schematic Drawing of the Electron and X-ray Optics of a SEM . . 246
B.2 Configuration of a Typical Self-Biased Electron Gun 247
B.3 Schematic Diagram of an Electromagnetic Lens 248
B.4 Ray Diagram Illustrating Lensing Action 249
XIV
B.5 Lensing Action of the Three Lenses of a Scanning Electron
Microscope 250
B.6 Schematic Illustration of Scattering Processes 251
B.7 Monte Carlo Electron Trajectory Simulation of the
Electron-Sample Interaction in Iron 252
B.8 Detailed Single Scattering Monte Carlo Electron Trajectory
Simulation for a Copper Target 253
B.9 Variation of the Backscatter Coefficient as a Function of Atomic
Number 254
B.10 Schematic Illustration of the Origin of the X-ray Continuum . . . . 255
B.11 Schematic Illustration of the Processes of Inner-Shell Ionization
and Subsequent Deexcitation 256
B.12 Schematic Illustration of Scanning System of the Scanning
Electron Microscope 257
B.13 The Principle of Information Display by Image Scanning 258
B.14 The Principle of Intensity or Z Modulation Used to Display the
Magnitude of the Signal Produced by Electron-Specimen
Interaction at the Locations Scanned in Figure B.13 259
B.15 Schematic Representation of an X-Ray Energy-Dispersive
Spectrometer 260
C.1 The Basic Structure of the Transmission Electron Microscope . . . 272
C.2 Formation of Image and Diffraction Pattern by the Objective Lens 273
C.3 Bright Field and Dark Field Image Formation 274
xv
C.4 (a) Reflection at Bragg Angle 6 from Crystal Planes
(b) Relationship between Incident, Transmitted and Diffracted
Beams 275
C.5 JEOL JEM-200 Internal Structure 276
XVI
CHAPTER 1
INTRODUCTION
Soldering is a simple operation. It consists of the relative positioning of
the parts to be jointed, wetting the surfaces with molten solder, and allowing
the solder to cool down until it has solidified. Soldering is an important
technique in the assembly of electronic products. In the electronics industry,
63Sn/37Pb eutectic solder is widely used as a joining material. It acts as both
electrical and mechanical connection within and among the different packaging
levels in an electronic assembly. The advances in packaging technologies driven
by the desire for miniaturization and increased circuit speed have resulted in
severe operating conditions for the solder joints and inevitably to solder joint
reliability problems.1 An understanding of the physical metallurgy of solders and
soldering is therefore of great interest, both from a fundamental scientific
perspective and because of its technological importance.
The reliability of the solder joints is associated with the wettability of the
surfaces to be joined and the joint's subsequent ability to retain good
performance.2 Understanding the reactions that occur during soldering and
subsequent aging must come from a fundamental knowledge of the
microstructures, thermodynamics and kinetics of the solder-substrate system.
When two metal parts are joined by solder, a metallic continuity is
established at the two interfaces that form where the solder is bonded to both
1
2
metal parts.3 This metallic continuity, or joining interface, contains an
intermetallic layer or layers. An intermetallic compound is a distinguishable
homogeneous phase having a relatively narrow range of composition with
simple stoichiometric proportions.4 In most cases, the formation of an
intermetallic compound, by the reaction of the solder with the substrate, occurs
during the wetting process. Intermetallic compounds grow at the interface of
the solder and the substrate during long term storage at ambient temperature
and more rapidly at high temperatures.5,6 The manner by which a solder joint
ages is an important aspect of its reliability. If the intermetallic phases that form
are excessively brittle, the joint may not be able to withstand normal operating
strains. If the intermetallic layer grows too quickly, the solder joint may become
depleted of the elemental constituent used to form the intermetallics and
thereby change the properties of the joint. The interdiffusion processes which
produce the intermetallic layer can also produce Kirkendall porosity which can
degrade the mechanical properties of the joint. Therefore, solder-substrate
reactions are critical parts of solder joint behavior.
Cu-Sn intermetallics are the most common intermetallic layers observed
between solder and substrate because of the frequency with which Sn/Pb
solder is used with copper substrates. There are two intermetallic phases which
occur in this system. As illustrated in Figure 1.1, the layer that forms adjacent
to the copper substrate is Cu3Sn, and the layer that forms adjacent to the
solder is Cu6Sn5.4,7,8,9
The effects of intermetallic growth within solder joints are not entirely
understood. While the presence of intermetallic compounds are an indication
that a good metallurgical bond has formed, the fact that these compounds are
3
brittle may also make them deleterious to a joint's mechanical integrity. When
these compounds form as continuous layers at the solder/substrate interface,
the intermetallic can interrupt electrical currents due to their high resistivity,
effectively isolating the metals that were to be electrically joined.10 In addition,
if these intermetallic compounds become too thick, the reliability of the joint
can be in jeopardy due to cracking, which may begin in these compounds.5
Because of the important contribution that the intermetallics make to the
stability of the solder connection, understanding their formation and growth is
important. Solder/substrate reactions fall into two categories: molten
solder/substrate reactions and solid state growth of intermetallic compounds.2
During wetting, molten solder comes into contact and reacts with the solid
substrate. At this point, two processes occur simultaneously: the base metal
dissolves into the molten solder, and the active constituent in the solder reacts
with the base metal. Both processes will form intermetallic compounds in the
interfacial region between the molten solder and the base metal. Many studies
have been published that examine the reactions between the molten solder and
the substrate.2,11,12,13,14 The solid state growth of intermetallic compounds is
generally more complex and includes the problem of long term growth of
intermetallic layers at the interface during the service life of the connection.
Two types of solid state growth kinetics may be observed: linear and parabolic.
One interpretation is that linear growth is limited by the reaction rate at the
growth site, i.e., it is reaction controlled, and parabolic growth is limited by
diffusion of reactant to the reaction interface, i.e., it is diffusion controlled.2
The microstructure and kinetics of intermetallic growth in the Sn/Pb
solder/substrate system have been widely studied. For copper in contact with
4
Sn and either 60Sn/40Pb or 63Sn/37Pb solder, the two intermetallic phases
previously described are generally observed as a result of long-term aging:
Cu6Sn5 adjacent to the solder, followed by Cu3Sn adjacent to the copper
substrate. Cu6Sn5 is always observed in optical metallographic cross sections
of as-soldered samples, whereas the Cu3Sn is not. It is thermodynamically
predicted that both intermetallics are present in the as-soldered state.
Numerous investigations15'16,17'18,19'20'21'22'23'24'25'26 have generated data on the
solid state growth of the Cu-Sn intermetallics at temperatures less than the
melting point of eutectic Sn/Pb solder (183°C). In most of these studies, the
total intermetallic layer thickness is reported as a function of time at
temperature, as opposed to measurements of the discrete thicknesses of the
two Cu-Sn intermetallic phases. There are a few references where individual
measurements have been performed,19,21 however, the data in these references
usually only covers either isolated temperatures or relatively short ranges in
time and aging temperature. The most comprehensive investigations of
intermetallic growth kinetics for samples of tin/copper and 60Sn/40Pb
solder/copper were conducted during the early 70s by MacKay and coworkers
at the International Tin Research Institute (ITRI).15,18 The majority of the ITRI
data were generated on specimens consisting of electroplated layers of either
Sn or 60Sn/40Pb on annealed wrought copper substrates, followed by aging
treatments in air furnaces at temperatures between 70°C and 170°C for times
as long as 1 year. A least squares analysis was performed27 on the ITRI data.
The results show that a parabolic growth law is an appropriate description of
the intermetallic growth process for both intermetallic layers.
The literature is in general agreement on several findings: the solid state
5
growth kinetics of Cu3Sn and Cu6Sn5 for Sn-based solder alloys in contact with
copper can be described by parabolic growth laws. The activation energy for
the growth of Cu3Sn is about twice that of Cu6Sn5, and the Cu3Sn layer is
always thinner than the Cu6Sn5 layer over the temperature range of 90° to
170°C. The relatively thick intermetallic layers are associated with mechanically
weak connections. Some conclusions, however, remain in dispute: does the
Cu3Sn form during soldering or later during aging; is the dominant diffusing
species Cu or Sn; and what are the morphologies of the intermetallic phases?
Surface mount technology (SMT) has been widely adopted in recent
years by the electronics industry, brought on by the need to produce small,
dense electronic packages. The solder joint in SMT is responsible for both
electrical and mechanical connection. Sn/Pb solder does not have adequate
ductility to sustain the repeated relative component displacements caused by
the mismatch between the expansion coefficients of the chip carrier and the
circuit board.28 Solders with enhanced mechanical properties are required for
high reliability.29 One approach is to add metallic or intermetallic particles to
eutectic 63Sn/37Pb solder to form composite solders.30,31 If the added particles
have a higher melting point than the solder matrix, the composite will melt at
the same temperature as the matrix. If the added particles have superior
mechanical properties compared to the matrix, the composite solder is expected
to be stronger than the matrix solder alone. Hence, SMT solder joints made
with composite solder should be stronger and more reliable than SMT joints
made using standard solder. Initial studies of these materials have shown that
this is indeed the case.32 Although kinetic and microstructural data for the new
composite solder/substrate systems are needed, only a few studies have been
6
conducted to date.33,34,35
The main purpose of this work is to explore the kinetics and
microstructures of eutectic solder and six types of composite solder used with
copper substrates. The six types of composite solder contain 7.6 w t% Cu, 20
w t% Cu3Sn, 20 wt% Cu6Sn5, 4 wt% Au, 4 wt% Ag, and 4 w t% Ni.
In Chapter 2, the basic theories of solid state phase transformations are
discussed. The phase diagram summarizes the temperature and composition
range in which the various phases are stable in an alloy, and gives a systematic
description of the melting and solidification behavior.36 Wetting, in which
specific interactions take place between the liquid solder and solid surface of
the part to be soldered, is an essential prerequisite for soldering. It depends on
the surface tensions acting between the interfaces involved. During soldering,
the solder transforms from a liquid to a solid. Solidification occurs by the
nucleation and growth of new phases and involves a complete structural
change at the advancing liquid-solid interface. The microstructure of the solder
matrix in the as-soldered state depends on the solidification cooling rate.37
During annealing, the intermetallic layers at the solder/copper substrate
interface grow thicker. The diffusion of Sn through the solder matrix and the
intermetallic phases, followed by reaction with Cu must occur for intermetallic
growth to take place. The particles added to the eutectic solder matrix affect
the diffusion behavior of the Sn, and thus affect the formation and growth of
the intermetallic layers at the composite solder/copper interface.
Scanning electron microscopy (SEM), transmission electron microscopy
(TEM), X-ray energy dispersive spectroscopy (XEDS) and scanning transmission
electron microscopy (STEM) are the major characterization techniques used to
7
analyze the microstructures of the solder/copper joints. The sample preparation
details for formation of the copper/solder/copper joints, SEM samples, TEM
samples, and thin film samples are presented in Chapter 3. Ultramicrotomy was
the primary method for TEM sample preparation and is the only method that
allows all phases of the solder/copper joint be simultaneously analyzed by
TEM.38
In Chapter 4, the results of the studies of solid state diffusion kinetics
and microstructural evolution during intermetallic formation and growth in
copper/composite solder/copper joints are discussed. The intermetallics at the
solder/copper interface are examined as functions of time, temperature and
particle composition. The activation energies for the formation of Cu6Sn5 and
Cu3Sn for the six types of composite solder/copper system are determined and
compared to the values for the eutectic solder/copper system. A diffusion
model based on the SEM and TEM studies and in-situ TEM thin film
observations is discussed. The effects of the particle additions on the diffusion
behavior of Sn in the composite solder matrix and thus on the microstructures
of the interfacial intermetallic layers are also discussed.
The microstructures of the eutectic solder and composite solder matrix
are discussed in Chapter 5. The relationship between the microstructure of the
eutectic solder matrix in the as-soldered state and the solidification cooling rate,
and the annealing behaviors of the two phases in the matrix are examined. The
effects of the particles added to the solder matrix on matrix solder phases and
Sn diffusion are also discussed.
The crystal structures of the metals and intermetallic phases are briefly
described in Appendix A. The basic principles of scanning electron microscopy
8
and transmission electron microscopy are given in Appendix B and Appendix C,
respectively. The statistical analysis methods used in this study are discussed
in Appendix D.
Cu Strap
63/37 Sn/Pb Solder 01 Composite Solder
Cu Strap
7ZZZZZZZZZZZZ22ZZZZ. WZZZZL
Figure 1.1. Cross-sectional view of solder/copper joint.
CHAPTER 1 REFERENCES
1. J.W. Morris, D. Tribula, T.S.E. Summers and D. Grivas, Solder Joint
Reliability Theory and Application, J.H. Lau Ed., (Van Nostrand Reinhold,
New York, 1991), Chapter 7.
2. A.D. Roming, Jr., Y.A. Chang, J.J. Stephens, D.R. Frear, V. Marcotte
and C. Lea, Solder Mechanics: A State of the Art Assessment, D.R.
Frear, W.B. Jones and K.R. Kinsman Ed., (TMS, PA, 1990), Chapter 2.
3. H.H. Manko, Solder and Soldering, 2nd Ed., (McGraw-Hill, New York,
1979), Chapter 1.
4. C.S. Barrett and T.B. Massalski, Structure of Metals, 3rd Ed., (Pergamon
Press, New York, 1980), Chapter 10.
5. P.E. Davis, M.E. Warwick and P.J. Kay, Plating and Surface Finishing,
69, 72 (1982).
6. R.W. Woodgate, Handbook of Machine Soldering, (Wiley, New York,
1983), Chapter 2.
7. R.J.K. Wassink, Soldering in Electronics, 2nd Ed., (Electrochemical
Publications, Scotland, 1989), Chapter 4.
8. P.E. Davis, M.E. Warwick and S.J. Muckett, Plating and Surface
Finishing, 70, 49 (1983).
9. M.E. Warwick and S.J. Muckett, Circuit World, 9, 5 (1983).
10. E.W. Brothers, The Western Electric Engineer, 49 (1981).
11. I. Okamoto and T. Yasuda, Trans. JWRI, 15, 73 (1986).
10
11
12. Z.P. Saperstein and M.A. Howes, Welding Journal, 47, 162s (1968).
13. M.A. Howes and Z.P. Saperstein, Welding Journal, 48, 80s (1969).
14. W.G. Bader, Welding Journal, 48, 551s (1969).
15. P.J. Kay and C.A. MacKay, Trans. Inst. Metal Finishing, 51, 85 (1973).
16. L. Zakraysek, Welding Journal, 51, 536s (1972).
17. M. Onishi and H. Fujibuchi, Trans. Japanese Inst. Metals, 16, 539
(1975).
18. D.A. Unsworth and C.A. MacKay, Trans. Inst. Metal Finishing, 51, 85
(1973).
19. K. Kumar, A. Moscaritolo and M. Brownwell, J. Electrochemical
Society, 128, 2165 (1981).
20. V.C. Marcotte and K. Schroder, Mater. Res. Soc. Symp. Proc. 19, 403
(1983).
21. D.S. Dunn, T.F. Marinis, W.M. Sherry and C.J. Williams, Electronic
Packaging Materials Science, E.A. Geiss, K.N. Tu and D.R. Uhlman,
Eds., (MRS, Pittsburgy, 1985), p 129.
22. E.K. Ohriner, Welding Journal, 66, 191s (1987).
23. Q. Yiyu, F. Hongyuan, C. Dinghua, F. Fuhua and H. Lixia, Brazing and
Soldering, 13, 39 (1987).
24. A.J. Sunwoo, J.W. Morris, Jr. and G.K. Lucey, Jr., Metallurgical
Transactions A, 23A, 1323 (1992).
25. J.A. Clum and T.J. Singler, Proc. 3rd Elec. Mater. Proc. Congress, 175
(1990).
12
26. S.S. Tamhankar, E.K. Chang, R.J. Wolf and M.J. Kirschner, J.
Microcircuits & Electronic Packaging, 16, 23 (1993).
27. J.J. Stephens, Internal Memorandum, March 2, 1989, Sandia National
Laboratories, Albuquerque, NM.
28. T.J. Kilinski, J.R. Lesniak and B.I. Sandor, Solder Joint Reliability, J.H.
Lau Eds., (Van Nostrand Reinhold, New York, 1991), Chapter 13.
29. K.R. Kinsman, Solder Mechanics: A State of the Art Assessment, D.R.
Frear, W.B. Jones and K.R. Kinsman, Eds., (TMS, PA, 1991), p. XIX.
30. D.R. Frear, D. Grivas and J.W. Morris, Jr., J. Electr. Mat., 16, 181
(1987).
31. J.L. Marshall, J. Calderon, J.A. Sees, G. Lucey and J.S. Hwang, IEEE
Trans. CHMT, 14, 698 (1991).
32. S.M.L. Sastry, T.C. Peng, R.J. Lederich, K.L. Jerina and C.G. Kuo, Proc.
NEPCON West '92, III, 1266 (1992).
33. R.F. Pinizzotto, Y. Wu, E.G. Jacobs and L.A. Foster, Proc. NEPCON
West '92, III, 1284 (1992).
34. R.F. Pinizzotto, E.G. Jacobs, Y. Wu, J.A. Sees, L.A. Foster and C.
Pouraphabagher, 31 st Annual Proceedings, Reliability Physics 1993, 209
(1993).
35. Y. Wu, J.A. Sees, C. Pouraghabagher, L.A. Foster, J.L. Marshall, E.G.
Jacobs and R.F. Pinizzotto, J. Electron. Mat., 22, 769 (1993).
36. R.E. Smallman, Modern Physical Metallurgy, 4th Ed., (Butterworths,
London, 1985), Chapter 3.
13
37. J.W. Morris, Jr., D. Tribula, T.S.E. Summers and D. Grivas, Solder Joint
Reliability, J.H. Lau Ed., (Van Nostrand Reinhold, New York, 1991),
Chapter 7.
38. E.G. Jacobs, L.A. Foster, Y. Wu, A.R. Wilson and R.F. Pinizzotto, J.
Mater. Res., 8, 87 (1993).
CHAPTER 2
BASIC THEORY
2.1 Phase Diagrams
In any alloy at equilibrium, the free energy of the alloy system will be a
minimum. In principle, equations for the free energy of the various phases as
a function of composition and temperature can be calculated and used to
determine the phases present at equilibrium, and the composition of these
phases. In fact, the available theory is not precise enough for such refined
calculations in even the simplest case. As a result, the phases which form at
various temperatures and compositions are determined empirically and recorded
in the form of a phase diagram. A phase diagram summarizes the temperature
and composition range in which the various phases are stable and gives a
systematic description of the melting and solidification behavior of an alloy.1
Depending on the nature of the two metals involved (i.e. the crystal
structure, the size of the atoms, the valency, etc.), several basic types of
binary equilibrium diagrams exist. The binary phase diagrams have been
discussed in details in many books.1,2 Here only the Pb-Sn and Cu-Sn systems
which are the systems interested in this study will be discussed.
2.1.1 The Lead-Tin System
Figure 2.1 is the Lead-Tin phase diagram,3 a typical eutectic phase
diagram. In this diagram the temperature is plotted along the vertical axis and
14
15
the composition along the horizontal axis. The compositions are specified in
both atomic and mass percentage.
Point P in Figure 2.1 represents the melting point of pure lead; point S
is the melting point of pure tin. Point E is the melting point of the alloy with
eutectic composition, tin62-lead38. This point is called the eutectic point and
is at 183°C. Sometimes tin63-lead37 is specified as the eutectic composition,
especially in the catalogues of solder manufacturers.
Above the liquidus in the diagram, only liquid exists. Below the solidus,
exclusively solid exists. In the intermediate range, solid and liquid exist
together. If, for instance, the high lead-bearing alloy, Iead65-tin35, cools down
from the liquid state, then at approximately 245°C (point A), segregation of
lead-rich crystals commences. These lead-rich crystals are not 100% lead, but
have a composition corresponding to point B in the diagram. As a result, the
composition of the liquid shifts to the tin-rich side, and its solidification
temperature is lowered. Upon continued cooling, this shift continues,
accompanied by continuing segregation of lead-rich crystals. In this process the
composition of the liquid moves along the line A-E, and that of the lead moves
along the line B-D, that is, on continued cooling the lead-rich crystals absorb
more tin. When the liquid reaches the composition of point E at a temperature
of 183°C, it is in equilibrium not only with the lead-rich crystals of composition
D, but also with tin-rich crystals of composition G. The composition of the
liquid now ceases to shift, whereas crystallization continues at constant
temperature and composition: the eutectic temperature and the eutectic
composition. Thus the solidification process of Iead65-tin35 solder stretches
over a range of temperatures.
16
A solder of eutectic composition does not have a solidification
temperature range, but has a single solidifying or melting point. Other elements
may be added to the solder. With low contents of these other elements, their
influence remains insignificant and is usually neglected. However, the precise
positions of the characteristic points in the phase diagram are then uncertain.
2.1.2 The Copper-Tin System
The Copper-Tin phase diagram,3 shown in Figure 2.2, like most other
alloy systems, contains more than one of the characteristic reactions. Cu-Sn
phase diagram contains several secondary solid solutions, i.e. phases which
occur in the middle of the diagram with a fairly wide range of compositions.
There are several phases which become unstable with cooling. For example, the
6 phase decomposes by a eutectoid change into a + e near 350°C. e and rj are
the only intermetallic phases that can form and exist at temperatures below
350°C. There is a A7-phase order-disorder transformation which occurs at
227°C. Above 227°C, the rj-phase exists as a disordered solid solution, but at
low temperatures the r/'-phase has a structure that is a supperlattice on the
NiAs (B82) type structure.4
2.2 Surface Wetting
Wetting is an essential prerequisite for soldering. Wetting means that a
specific interaction takes place between the liquid solder and the solid surface
of the part to be soldered. The extent to which a liquid solder will spread across
a surface, or flow into a gap between two or more surfaces, depends, among
other things, on the surface tensions acting between the interfaces involved.5
17
The surface tension is determined by the interatomic bond energies of
the atoms. In the bulk of a liquid metal, each atom has a certain number of
nearest neighbors, and the total internal energy may be considered as a
summation of these interatomic bond energies. The atoms in the surface layer
possess a higher potential energy than the bulk atoms, because they are
incompletely surrounded by the other atoms. If the surface area is enlarged,
more atoms take up positions on the surface at the expense of increasing their
energy. At the interface of two metals, the atoms have two types of bonds:
bonds with atoms of their own kind and bonds with atoms of the other metal.
It depends on the various metal-metal bond energies whether these interfacial
atoms have a higher or lower energy than the bulk atoms. The higher the
energy of these atoms at the interface, the higher the interfacial tension.6
The surface tension of a liquid, y„ is a thermodynamic quantity, and is
equal to the amount of work needed to isothermally enlarge the liquid surface
area. A system strives toward a minimum value of its free energy, and hence
to a minimum surface area. A floating droplet therefore assumes the shape of
a sphere, because this shape has the minimum surface area at a given volume.
This tendency to reduce the surface area implies that there exists a pressure
difference, AP, between the two sides of a spherical surface:5
A P = - t ± (2.1) R
The surface tension, y„ is not a function of R, the sphere radius, as long as R
is much greater than the interatomic distance.
Figure 2.3a shows the situation of a liquid-solder droplet on a solid
18
surface.5 When gravity is negligible, which is the case with small droplets, the
shape of the droplet is determined solely by surface tensions. The pressure is
the same everywhere in the liquid, the curvature is constant along the liquid
surface, and the shape is therefore that of a spherical cap.
The droplet selects the shape for which the total surface free energy,
Fsurface
Fsurface = ysxAs + yisxAi + yixAl ( 2 " 2 )
has its minimum value, where: 7, - surface tension of the liquid, ys - surface
tension of the solid, yls - surface tension of the liquid-solid interface, As - solid
surface area, At - interfacial area, and A[ - liquid spherical area. From this
condition Eq. 2.3 can be obtained:5
Y is + Y / C O S 0 = y s ( 2 . 3 )
The shape of Figure 2.3a is the result of a calculation in which it was
assumed that gravity could be ignored and that the solid surface is flat.7 In
practice, the solid material will dissolve in the molten solder and the final
equilibrium shape will always tend towards that of Figure 2.3b, since this has
a lower total surface free energy.5
From Eq. 2.3 it is clear that wetting , i.e., a small contact angle Q, is
promoted by small values of 7, and 7ls in combination with a relatively large
value of 7S. The surface tension of oxides are distinctly lower than the values
for the corresponding metals.8 Therefore, it is difficult to wet the surface of a
solid metal as long as it is oxidized. The reaction of a flux with the oxide on a
solid surface causes an increase of the surface tension ys by removal of the
19
oxide, and thus promotes wetting of the metal surface by the solder.
2.3 Diffusion in Solids
Diffusion is a process in which atoms move from one region to another
due to a driving force to lower the free energy of the system. If there is a
chemical potential gradient in the system, atoms will tend to move from a
region of high chemical potential to a region of low chemical potential. In most
cases, the chemical potential gradient is in the same direction as the
concentration gradient of the diffusing species.9 Therefore, it is convenient to
describe a diffusion process in terms of the concentration gradient.
Consider a one-dimensional system. If the atomic concentration is C(x),
the flux of the diffusing atoms can be expressed as10
J - D 0 , i 2 A )
Where J is the net flux of atoms, D is the diffusion coefficient with units of
cm2/sec, and 8C/dx is the concentration gradient, assumed to be constant over
time. Equation 2.4 is called Fick's first law. It shows that the number of atoms
passing through a plane of unit area per unit time is simply proportional to the
concentration gradient.
When atoms diffuse from one area to another area inside a solid, the
concentration C(x) usually varies with time. The continuity equation of the atom
flow then leads to10
20
dC(x,t) _ (PC (2.5) dt ax2
Equation 2.5 is called Fick's second law, whore C, the concentration, is a
function of time t and position x.
Consider a system, its scale is much larger than the mean diffusion
distance of the atoms with a fixed concentration Cs at the surface of the
specimen. As given by P.G. Shewmon10, by assuming that the diffusion
coefficient D is a constant, the solution to the diffusion equations give the
relationship between the depth of the diffusion-affected zone, d, and the
diffusion time:
d'y/Di ( 2 6 )
A detailed derivation and discussion of this relation was also given by J.R.
Manning.11 Equation 2.6 gives a quantitative measurement of diffusion and thus
is of practical importance. It is the form that will be used throughout this
dissertation.
During diffusion, atoms move from one region in a solid to another.
Microscopically, during diffusion the atoms jump from site to site in a random
fashion, known as random walk.11,12 In the presence of a concentration
gradient, more atoms are moving away from the high-concentration region due
to random walk than are moving away from the low-concentration region.
Diffusion through various mechanisms including (1) interstitial mechanism, (2)
interstitialcy mechanism, (3) crowdion mechanism, (4) vacancy mechanism, (5)
dislocation pipe diffusion mechanisms, (6) grain boundary diffusion
mechanisms, (7) surface diffusion mechanisms, and so on.11 The first four
21
mechanisms listed above are possible means of volume or bulk diffusion. Of
these, the vacancy and the interstitial mechanisms are most frequently
encountered. Atoms diffusing in different chemical systems may have different
diffusion mechanisms, and in a single diffusion process, several mechanisms
may operate simultaneously. The elementary atomic motions in a crystal for
interstitial and vacancy mechanisms are shown in Figures 2.4 and 2.5.
Interstitial Mechanism: When there are imperfections such as interstitial
atoms, the interstitial mechanism can operate. Here, an atom moves through
the crystal by moving directly from one interstitial site to another, as shown in
Figure 2.4.11 This mechanism is particularly likely for diffusion of small impurity
atoms which easily fit into interstitial sites and do not greatly displace the
solvent atoms from their normal lattice sites.
Vacancy Mechanism: In thermal equilibrium, any crystal at a temperature
above absolute zero contains a certain number of vacant lattice sites. These
vacancies provide an easy path for diffusion. The elementary jump in the
vacancy mechanism is the jump of an atom into a neighboring vacancy, as
shown in Figure 2.5.11 The site previously occupied by the atom is the vacant,
so that in effect the atom and vacancy merely exchange positions. Each atom
moves through the crystal by making a series of exchanges with the various
vacancies which from time to time are in its vicinity.
Consider a randomly diffusing entity. If the jump frequency of the particle
is independent of jump direction, we have10
22
D = -Ya2 (2.7) 6
where T is the jump frequency, and a is the interatomic distance of two atomic
planes.
Consider the diffusion of vacancies. As seen in Figure 2.6, a vacancy
moves whenever one of the atoms next to it jumps into the vacant site. These
neighboring atoms oscillate about their equilibrium site, in the direction of the
vacancy, with a frequency v. After some time, one of the atoms will make an
especially severe oscillation at about the time the four-atom window separating
it from the vacancy opens up. The magnitude of the local free-energy
fluctuation required for such a jump is called AGm. AGm is much greater than
the mean thermal energy of the atoms, RT. The frequency with which such a
large fluctuation occurs depends on the ratio AGm /RT, the ratio of the required
energy fluctuation to the mean thermal energy of the atoms. A statistical
mechanical treatment13 of the problem indicates that the fraction of the
oscillations which lead to a jump is exp( -AGm/RT), where AGm is made up of
a relatively large activation enthalpy, AHm, and a smaller TASm term.
The mean vibrational frequency v is essentially temperature independent,
though the vibrational amplitude increases with T. As a result, the expression
vexp(- AGm/RT) gives the jump frequency for each of the atoms neighboring a
vacancy. If the vacancy has z nearest neighbors, then r „ for the vacancy is
r ^ v e x p ^ - (2.8) RT
So D„ is given by
23
Ya2 a2 A5m A/ / f A Q »
Z)v=——— = ——zv exp—-exp - (2.9) v 6 6 R RT
where the equation AGm = AHm -TASm is used. Let
D0 = — v e x p - ^ 5 - (2-10) 6 R
So
D=D0exp—2- (2.11) 0 RT
is obtained, where D0 is called a pre-exponential constant, and Q the activation
energy. Though Equation 2.11 was derived using a vacancy mechanism, it is
empirically correct for other diffusion mechanisms. In a solid, Q has values
between 0.1 and 5.0 eV, depending on the system and the diffusion
mechanism. Generally, Q is smaller for an interstitial diffusion mechanism than
for a vacancy diffusion mechanism. The values for D0 are generally in the
vicinity of unity, although they can be rather small for interstitial diffusion.
The noble metals (copper, silver, gold, and nickel) have been found to
diffuse extremely rapidly in a polyvalent metal matrix, such as lead, tin, indium,
or thallium. The diffusivity of these dilute impurities is from 102 to 105 times
that of self-diffusion. The values of the activation energies and D0 value for
Cu,14 Ag,15 Au,15 and Ni16 diffusion in /?-Sn and for Sn self-diffusion,17 along the
a and c axes of Sn, are listed in Table 2.1.
The very low activation energies for Cu, Ag, Au and Ni diffusion in Sn,
make a striking contrast with the activation energies for Sn self-diffusion. An
examination of the geometrical configuration in /?-Sn (discussed in Appendix A)
24
reveals that the atoms in the /?-Sn structure form a set of relatively open square
channels along the c axis, while passages transverse to the c axis are more
restricted.14,15 An interstitial mechanism is usually invoked to explain the high
mobility of the fast diffusers. Interstitial solid solutions are thought to occur
only when the ratio of the solute atomic diameter/solvent atomic diameter is in
the range 0.4-0.6,18 whereas in these systems this ratio is in the range 0.7-0.8.
However, Dyson, Anthony and Turnbull19 have pointed out that it may be
possible to account for the tendency toward interstitial formation in the fast-
diffuser systems if the packing or the host metal is limited by ionic rather than
by atomic size. For example, the radius of channels along the c axis of Sn
bounded by the Pauling ion cores of Sn would be 2.20 A for quadruply ionized
Sn. Therefore it appears that noble-metal and Ni atoms (atomic radii:20 Cu,
1.278 A; Ag, 1.445 A; Au, 1.442 A; Ni, 1.246 A) could be placed in the
channels along the c axis of Sn with little or no distortion. Here the Ni atomic
size (1.246 A) is the smallest, compared with other elements, and its diffusivity
is the largest of all the impurities in tin.
It is found experimentally that diffusion along grain boundaries can also
be described by
D „ ' D w e x (2.12)
where Db is the grain boundary diffusivity and Db0 is the frequency factors. Qb
is the experimentally determined values of the activation energies for diffusion.
In general, at any temperature, the magnitudes of Db relative to the diffusivity
through defect-free lattice D, are
25
Db>D{ (2.13)
This mainly reflects the relative ease with which atoms can migrate along
interior boundaries and through the lattice. Rapid diffusion along the grain
boundaries increases the mean concentration in a thin volume around the
boundary and thereby produces an increase in the apparent diffusivity in the
material as a whole. If the grain boundary has an effective thickness 6 and the
grain size is d, the apparent diffusion coefficient in this case, as given by D.A.
Porter et al.2 will be
D ^ D . + D f i l d (2.14)
It can be seen that the relative importance of lattice and grain boundary
diffusion depends on the ratio Db<5/D,d. When Dbtf > D,d, diffusion through the
lattice can be ignored in comparison to grain boundary diffusion and grain
boundary diffusion makes a significant contribution. The effective width of a
grain boundary is ~0 .5 nm. The order of grain sizes can vary from ~ 1 to 10
jam in our composite solder/copper systems and the effectiveness of the grain
boundaries will vary accordingly.
The relative magnitudes of Db<5 and D,d are sensitive to temperature.
Although Db > D, at all temperatures, the difference increases as temperature
decreases. This is because the activation energy for diffusion along grain
boundaries (Qb) is lower than that for lattice diffusion (Q,). In fee metals it is
generally found that Qb ~ 0.5 Q,. This means that when the grain boundary
diffusivity is scaled by the factor 616 (Eq. 2.14) the grain boundary contribution
to the total, or apparent, diffusion coefficient is negligible in comparison to the
26
lattice diffusivity at high temperature, but dominates at low temperature. In
general it is found that grain boundary diffusion becomes important below
about 0.75-0.8 Tm, where, Tm is the equilibrium melting temperature in degrees
Kelvin.2
The rate at which atoms diffuse along different boundaries is not the
same, but depends on the atomic structure of the individual boundary. This in
turn depends on the orientation of the adjoining crystals and the plane of the
boundary. Also the diffusion coefficient can vary with direction within a given
boundary plane. In the composite solder/copper system, there are Sn-rich and
Pb-rich phases, and metallic or intermetallic particles in the solder matrix. The
metallic and intermetallic phases have much higher melting temperatures than
eutectic solder. The diffusion of the Sn or Pb through these phases may be
dominated by grain boundary diffusion in the temperature range used in the
work reported here, which is below the melting temperature of eutectic solder
(183°C).
2.4 Solidification
Solidification is the term used to describe the transformation from the
liquid to the solid state. Solidification is a process that occurs by the nucleation
and growth of a new phase; that is, the structure changes suddenly and
completely at the advancing liquid-solid interface.10
2.4.1 Nucleation
In solidification, nucleation involves the ordering of a group of atoms in
the liquid to form a very small crystal of the solid. Such fluctuations occur
27
abdve the melting point, but at these temperatures the liquid is more stable
than solid so the crystallites or nuclei always decompose back to liquid. Even
when the temperature of the liquid is lowered to just under the melting point,
the nuclei formed still tend to decompose back to liquid again. This remelting
of the crystallites stems from the surface energy associated with the liquid-solid
interface of these small nuclei.
Consider a given volume of liquid at a temperature AT below the melting
temperature Tm with a free energy G,. If some of the atoms of the liquid cluster
together to form a small solid sphere of radius r, the free energy of the system
will change to G2. A free energy change AG = G2 - GT is given by:
AG(r) = -AGV—rcr3 + YSi4n:r2 (2.15) 3
and
A G = G L - G S = ̂ - (2.16) Te
where Gs and GL are the free energies per unit volume of solid and liquid
respectively, ySL is the solid/liquid interfacial free energy, and L is the latent
heat of fusion per unit volume. A plot of AG(r) in Figure 2.72 shows that for r
< r* , a critical nucleus size, growth of the crystallite increases the free energy
of the material involved. However, if the fluctuation is great enough to form a
crystallite of r > r* , continued growth of the particle will decrease the free
energy of the system. By solving for d(AG)/dr = 0
r* = 2 Y s l (2.17)
28
AG' = 1 6 " ( Y ^ 3 12.18) 3(A Gvf
is obtained. The larger the undercooling AT, the smaller the fluctuation in free
energy required to create a supercritical particle.
2.4.2 Eutectic Solidification
In the solidification of a binary eutectic composition two solid phases
form cooperatively from the liquid. The reaction L -» a + /3 is called eutectic
solidification.10
In a eutectic the two phases can have various morphologies. These are
shown in Figure 2.8.10 As discussed by P.G. Shewmon,10 the shape that
minimizes the amount of free energy going into ct-0 interface might appear to
be the globular form. However, discrete globules require repeated nucleation of
the second phase. The process proceeds with less supercooling if the second
phase grows continuously as rods or lamellae. If the surface energy of the a-/3
interface, ya/j, is independent of the orientation of the interface, rods form, since
these have a lower surface-volume ratio. However, in crystals ya/3 is rarely
independent of interface orientation, so a lamellar structure is often observed,
with the lamellae oriented to have a low ya/3.
The rod and lamellar eutectic occur in those cases where both phases
grow with an atomically rough surface, giving an interface mobility that is high
and isotropic. The liquid and solid are thus in equilibrium at each interface, so
the rate of growth is determined by the rate of diffusion in the liquid. In the
case of the acicular eutectic, the matrix phase grows with an atomically rough
29
surface, but the growth of the acicular phase is determined by the rate of
incorporation of atoms into the atomically smooth crystal surface. The phase
thus grows only in certain directions, grows rather independently of the matrix,
and seems to nucleate frequently. In our eutectic solder system, both the
lamellar and globular eutectic microstructures are observed.
2.5 Phase Growth
The control of grain size by annealing arises in a variety of situations.
During high temperature (>0 .5 Tm) anneals, the smaller grains shrink and
disappear so that the mean grain diameter D of the specimen increases with
time.
Since grain growth occurs spontaneously, it must correspond to a
decrease in the free energy. In grain growth the energy and perfection of the
lattice of a region is not changed by the passage of a grain boundary through
it. Thus in grain growth the decrease in free energy comes from the decrease
in total grain-boundary area. The free energy per unit volume associated with
the grain boundaries is:
G „ ' A ^ b (2.19)
where Ab is the area of grain boundary per unit volume. The surface area per
grain is proportional to D2, while its volume is proportional to D3. Thus Gb oc
7b/D. Consider a spherical grain of radius r. If the grain diameter is increased by
the infinitesimal dr, then dn atoms are transferred across the grain boundary
from the surrounding grain. The free-energy change for this transfer can be
written2
30
dG = y dA = A (j, dn (2.20)
A | a = Y — <2-21> dn
where A/* is the chemical potential drop across a grain boundary. For a sphere
the number dn of atoms is the volume divided by the atomic volume Q, so
Qdn-dV=4izr2dr (2.22)
The area change accompanying dr is -87rrdr, so
An - " 2 y Q (2.23) r
This is often called the Gibbs-Thomson equation. The difference in chemical
potential Aju, across the boundary drives the atoms across the boundary, thus
allowing the grain to grow. Eq. 2.22 tell us that free energy decreases as the
grain grows. In the case of solder matrix, with annealing, the grain sizes for the
Sn-rich and Pb-rich regions increase, as fast as the atoms can diffuse to them
from the surrounding matrix.
31
Table 2.1. Diffusion Parameters of Cu, Ag, Au and Ni in /?-Sn
and Parameters of /?-Sn Self-diffusion
element atomi
c radii
o (A)
parallel c axis parallel a axis element atomi
c radii
o (A)
Q» °o||
(cm2/s)
Qi Dox
(cm2/s)
element atomi
c radii
o (A)
Kcal eV
°o||
(cm2/s) Kcal eV
Dox
(cm2/s)
Cu 1.28 ~ 4 0.17 ~ 10"3 7.9 0.34 2.4x10"3
Ag 1.45 12.3 0.53 7.1x10"3 18.4 0.80 1.8x10"1
Au 1.44 11.0 0.48 5.8x10"3 17.7 0.77 1.6x10"1
Ni 1.25 4.3 0.19 2.0x10"2 12.9 0.56 1.9x10"2
Sn 1.62 26.0 1.13 7.7x10'2 25.9 1.12 1.1x10'1
32
10 20 30 40 WEIGHT PER CENT LEAO 50 60 70 80 85 90 95
327J
232* A B/ 232*
\G 183* CD (Pb) /1.45(2.! hs*i
>t 26.1 (3« L11 7 <8
s \ s \
96.81 98.1)4 I I
0 S*
10 20 30 40 50 60 70 ATOMIC PER CENT IEAO
80 90 100 Pfc
Figure 2.1. Lead-Tin phase diagram, showing the eutectic temperature of 183°C
and the eutectic composition of about 62 weight % tin.3
33
10 20 30 40 J I , I
WEIGHT PER CENT TIN 50 60 TO 80 90
J I I L
20 25 30 35 40 900 1 L - j 1 j - J -
798° \ 153 (25.5)
586*
S355
-350® 20.5(32.55)
I I V 700 10 15
43.1(58.6)
&0r(Cn)
43.5 (59.0) 86.7 92.4
45.5 60.9) 98.7(993) •—44l8(60l3
232#
10 20 30 40 50 60 TO 80 90 100 ATOMIC PER CENT TIN $r
Figure 2.2. Copper-Tin phase diagram.
34
atmosphere
solder
base / m e t a l Ys
Yh
(a) droplet on a flat plate
liquid solder
(b) equilibrium shape of a droplet in practice
Figure 2.3. (a) Droplet on a flat plate and (b) the equilibrium shape of a droplet
in practice.
35
Figure 2.4. Interstitial mechanism, elementary jump 11
36
Figure 2.5. Vacancy mechanism, elementary jump. 11
37
(a)
o o o o
(a) (b) (c)
Figure 2,6. Free energy G arid configurations (a, b, c) in going through the
saddle point of a jump.10
38
interfacial energy ccr2
Volume free energy c c r T
Figure 2.7. The free energy change associated with nucleation of a sphere of
radius r.2
39
Top free surface
Growth direction Solid-liquid
interface
Top free surface
Growth direction
Top free
surface
Growth direction Solid-liquid
interface
\ ^Sol id- l iquid
interface
Growth
direction
Top free surface
w l \ -vs
,S?X<N \ \N
^ V . I / x / */>
- \ N I v 1 / ^)^Solid*liquid
\ /— \ I , / interface
(d)
Figure 2.8. Schematic illustration of various eutectic structures: (a) lamellar, (b)
rodlike, (c) globular and (d) acicular.10
CHAPTER 2 REFERENCES
1. R.E. Smallman, Modern Physical Metallurgy, 4th Ed., (Butterworths,
Boston, 1985), Chapter. 3.
2. D.A. Porter and K.E. Easterling, Phase Transformations in Metals and
Alloys, 2nd Ed., (Chapman & Hall, New York, 1992).
3. M. Hansen and K. Anderko, Constitution of Binary Alloys, 2nd Ed.,
(McGraw-Hill, New York, 1958).
4. A. Westgren and G. Phragmen, Z. anorg. Chem., 175, 80 (1928).
5. R.J.K. Wassink, Soldering in Electronics, 2nd Ed., (Electrochemical
Publications, Scotland, 1989), Chapter 2.
6 A.R. Miedema and F.J.A. den Broeder, Z. Metallk. 70, 14 (1979).
7 E.E. Braudo, E.N. Michalow and W.B. Tolstogusow, Z. Phys. Chem.,
Leipzig, 253, 369 (1973).
8 A. Bondi, Chem. Rev. 52, 417 (1953).
9 J.W. Mayer and S.S. Lau, Electronic Materials Science: For Integrated
Circuits in Si and GaAs, (Macmillan, New York, 1990).
10. P.G. Shewmon, Transformation in Metals, (McGraw-Hill, New York,
1969).
11. J.R. Manning, Diffusion Kinetics for Atoms in Crystals, (Van Nostrand,
New York, 1968).
12. R.J. Borg and G.J. Diences, An Introduction to Solid State Diffusion,
(Academic Press, New York, 1988).
40
41
13. K. Huang, Statistical Mechanics, (Wiley, New York, 1987), Chap. 7.
14. B.F. Dyson, T.R. Anthony and D. Turnbull, J. Appl. Phys. 38, 3408
(1967).
15. ibid. 37, 2374 (1966).
16. D.C. Yeh and H.B. Huntington, Phys. Rev. Lett., 53, 1469 (1984).
17. F.H. Huang and H.B. Huntington, Phys. Rev. B9, 1479 (1974).
18. W. Hume-Rothery and G.V. Raynor, The Structure of Metals and Alloys,
(Pergamon Press, New York), p.97.
19. B.F. Dyson, T.R. Anthony and D. Turnbull, J. Appl. Phys., 37, 2370
(1966).
20. W.B. Peatson, The Crystal Chemistry and Physics of Metals and Alloys,
(Wiley, New York, 1972), p. 135.
CHAPTER 3
SAMPLE PREPARATION
3.1 Cu/solder/Cu Joint Fabrication
Commercial eutectic 63/37 Sn/Pb New Generation Solder Paste
consisting of 88% metal plus 12% water soluble RMA flux by weight, Grade
W-P-9-4, from International Electronic Materials Corporation, lot #1022 701 \
was used throughout this work. The composite solders were fabricated by
mixing preweighed quantities of the solder paste and the powered metals or
intermetallics. Cu6Sn5 and Cu3Sn intermetallic particles were obtained from the
National Institute of Standards and Technology (NIST).2 Cu, Ag, Au, Ni and
other metal particles were obtained from Aesar.3
The Cu6Sn5 and Cu3Sn composites were each ground by hand using an
agate mortar and pestle for 15 minutes prior to mixing. The same mortar and
pestle were used to grind each intermetallic but they were cleaned with
Kimwipes between each use. The other composites, Cu, Ag, Au, and Ni, etc.,
were mixed directly without grinding.
Pre-weighed quantities of the solder paste and particles were then mixed
by hand using a ceramic crucible and plastic spatula for about 30 minutes to
ensure homogeneous distribution of the particles. The weight percentage of the
particulate was calculated on a metal only basis; the weight of the RMA flux
was not included. The weight percentage of each particle type was based on
our ability to fabricate uniform materials and not on the physical characteristics
42
43
of the composite solders. Seven solders were studied, as listed in Table 3.1.
SEM micrographs of the as-received or after grinding particles were taken in the
secondary electron imaging mode. The sizes of the particles were then
measured.
The copper substrates used in this work were fabricated from copper
pipes with a wall thickness of 1 mm. The pipes were cut using a Buehler
Isomet low speed saw equipped with a diamond blade into rings approximately
2 mm thick. The rings were cut open with tin-snips and flattened. They were
then cut to their final size, approximately 2 mm by 10 mm by 1 mm. These
copper straps were cleaned with acetone and methanol, then cleaned in HCI to
remove surface oxides and contaminates, rinsed in isopropanol in an ultrasonic
cleaner and air dried.
An alumina ceramic susceptor plate, used for more uniform heating, was
preheated on a laboratory hot plate to 250°C. Two copper straps with solder
(or composite solder) paste inbetween (about 1 -2 mm thick) were placed on the
alumina susceptor for 1 to 1.5 minutes for the solder to reflow and form a
soldered connection. The sample was removed from the susceptor and allowed
to cool in air to ambient temperature. The completed copper/composite
solder/copper joint samples were about 3-4 mm thick. After the samples
reached room temperature, they were ultrasonically cleaned in acetone for
about 2 minutes to remove flux residues, and then ultrasonically cleaned in
isopropanol and air dried.
The preceding describes the standard procedure used to prepare
copper/solder/copper joints. For comparing the effect of the cooling rate on the
solder microstructure, two additional sets of copper/eutectic solder/copper
44
joints were made using different cooling rates, as listed in Table 3.2.
Set I: After the solder joint was formed, the sample was immediately
removed from the hot plate and placed on a large stainless steel plate to cool.
This led to the fast cooling rate. It took less then 1 minute to cool the sample
from 250°C to 50°C.
Set II: After the solder joint was formed, the sample was immediately
removed from the hot plate and placed on a table with wood top and allowed
to cool in air to room temperature. This led to the medium cooling rate. It took
about 5 minutes to cool the sample from 250°C to 50°C.
Set III: After the solder joint was formed, the hot plate was turned off.
The sample remained on the hot plate until it reached room temperature. This
led to the very slow cooling rate. It took about 30 minute to cool the sample
from 250°C to 50°C.
3.2 Annealing Procedure
Both the tops and bottoms of the copper/solder/copper joint samples
were polished with 600 grit silicon carbide paper to remove excess solder.
Blank silicon slabs, about 5 mm thick, were cut with the low speed diamond
saw into pieces approximately 12 mm by 5 mm by 5 mm in size. They were
cleaned in acetone to remove any oil buildup from the saw and were put on the
hot plate which was heated to about 140°C. The silicon pieces were joined to
the top and bottom of the solder joint sample using wax, creating a layered
silicon/copper/solder/copper/silicon sample. The silicon blocks increase the
sample thickness and hardness and facilitate subsequent handling. Cross-
sectional slices about 0.5 mm thick were cut from the coupled block using the
45
low speed diamond saw. The slices were cleaned with acetone and methanol,
ultrasonically cleaned in Dl water and dried in air. The sample configuration is
illustrated in Figure 3.1.
The slices were annealed in three different, small, benchtop box furnaces
capable of maintaining the temperature to ±3°C. All Cu-containing and Ni
composite solder samples were annealed for 0, 4, 8, 16, 32 and 64 days (0,
96, 192, 384, 768 and 1536 hours) at 110, 120, 130, 140 and 160°C. In
addition to these conditions, Eutectic Solder Only (ESO) samples were annealed
for 0, 4, 8, 16, 32 and 64 days at 150°C, and Cu6Sn5 composite solder
samples were annealed for 0, 4, 8, 16 and 32 days at 150°C. Ag and Au
composite solders were annealed for 0, 4, 8, 16, 32, and 64 days at 120, 140,
and 160°C, and for 0, 4, 8, 16 and 32 days at 110 and 150°C. The complete
sample matrix is shown in Table 3.3.
3.3 SEM Sample Preparation
After annealing (or after soldering for the unaged samples), the sample
was mounted with wax on a stainless steel disk 31 mm in diameter and 12.5
mm in height (called the sample holder) used by a Buehler Minimet
Polisher/Grinder. Since the solder has a low melting point, the temperature was
not allowed to exceed 150°C and the heating time was limited to about 1
minute.
It has been noted that the preparation of solder joints for metallurgical
examination is very much an art.4 Solders are typically soft, while the
intermetallic compounds which form tend to be very hard and brittle. The
substrate can be either soft or hard.4,5 The addition of hard metallic and
46
intermetallic particles to a soft solder matrix further complicates the situation.
During polishing, the softer phases tend to erode preferentially compared to the
harder phases. Standard metallurgical sample preparation technology was used
to polish these samples, with careful control of the polishing conditions such
as time and pressure.
An annealed sample slice was first ground with 240 grit Buehler silicon
carbide paper to level the face of the sample. The sample was then polished on
600 grit paper to smooth out the scratches introduced by the 240 grit paper.
At this point, a Buehler Minimet Polisher with Microcloth polishing cloths,
Metadi diamond compounds, and Metadi fluid were used to polish the sample
further. Figure 3.2 shows the polisher with a sample holder disk attached.6 The
sample surface touches the polishing cloth inside the bowl. 9 jwm and 15 jiim
diamond pastes were used for the majority of the polishing, followed by 1 and
0.25 /xm diamond pastes. The final polishing step used 0.05 //m alumina slurry,
and was considered complete when no visible scratches were observed on the
sample using an optical microscope at 10x magnification. The sample was
ultrasonically cleaned in Dl water for about 2 minutes between each polishing
step to remove particulate matter to prevent contamination of the polishing
cloths.
The polished samples were etched for 15 seconds in the vapor of reagent
grade (37.4%) HCI to delineate the microstructures of the solder and the
solder/copper interface. After etching, the samples were ultrasonically cleaned
in Dl water.
The polished and etched copper/solder/copper samples were examined
using a JEOL T-300 Scanning Electron Microscopy (SEM) operating at 1 5 kV.
47
Images were obtained using a Robinson backscattered electron detector and
were recorded on Polaroid Type 52 or 55 film. A Tracor Northern (TN-5500) X-
ray Energy Dispersive Spectroscopy (XEDS) system was used to analyze the
spectra and to identify the various phases observed.
3.4 TEM Sample Preparation
Transmission Electron Microscopy (TEM) was used to reveal the
nanostructural characteristics of the different phases within the sample and the
interfacial relationships between these phases. Three different TEM sample
preparation techniques were used for the experiments described here: (1) thin
sectioning by ultramicrotomy, (2) electropolishing and (3) conventional
mechanical polishing followed by ion milling. Ultramicrotomy was the primary
method used throughout the study. The other two sample preparation methods
were used to investigate the effects the sample preparation method on the
observed microstructures.
3.4.1 Ultramicrotomy
The TEM examination of a solder joint is actually somewhat routine, but
the preparation of solder specimens for TEM is perhaps the most difficult in the
realm of materials science.4 To date, there has been only limited success in
preparing solder samples for TEM by the methods traditionally used for
crystalline materials.7,8 The soft tin and lead rich phases are difficult to
mechanically polish without smearing or tearing, and the brittle intermetallic
phases fracture easily. Samples of Sn/Pb solder have been electropolished with
some success.7 However, electrochemical differences between the copper,
48
intermetallic phases, particulate phases and solder phases make it impossible
to successfully electropolish composite solder/copper samples. Ion milling is
difficult since large differences in the ion milling rates of the numerous phases
lead to preferential thinning of some phases compared to others, resulting in
some phases being electron transparent while others remain electron opaque.
Ultramicrotomy is a viable alternative to these methods because many
of the difficulties encountered with other sample preparation techniques are
avoided. It is possible to obtain sections that are uniformly thin across
heterogeneous phases, which is the primary advantage of this technique.
However, some mechanical damage is introduced which makes detailed studies
of dislocation substructure probbuatical.
Ultramicrotomy involves cutting thin sections with an extremely sharp
knife (usually a diamond knife) from a bulk sample by controlled gravity drop
or a powered motion of a specimen. A typical ultramicrotomy apparatus is
shown in Figure 3.3. During sectioning, the sample block moves past the knife
under the weight of the cantilever arm and the force of gravity. The thin
sections cut from the bulk sample float off the knife edge onto the surface of
a water bath in the knife trough for retrieval.
A key factor in successful ultramicrotomy is careful control of the cutting
conditions. A schematic of the sectioning process, shown in Figure 3.4,
illustrates the geometric parameters that affect material sectioning.
Optimization of the cutting angle (knife bevel angle plus tilt angle) is necessary
to minimize specimen deformation. While the cutting angle is an important
consideration, it is generally a fixed parameter optimized by the knife
manufacturer. The knife angle is chosen for the particular materials to be
49
sectioned, hard and brittle versus soft and ductile. Low angle knives ranging
from 25-35° are now being touted for reduced compression in ductile materials
but increased edge fragility for harder materials.9,10 Two diamond knives with
bevel angle of 35° or 45° were used throughout this work. The experimental
fine tuning of the sectioning process involves factors such as control of the
laboratory environment, the sectioning rate, and the preparation of the bulk
block sample for sectioning.
Copper/solder/copper joints were prepared as described in section 3.1.
The copper/solder/copper sandwiches were embedded in an epoxy block prior
to ultramicrotomy in order to support them during sectioning and to prevent
pieces of some of the phases from scrolling and detaching from the other
phases. The solder joints were cleaned in acetone to remove residual flux and
oils from handling. After air drying, the samples were carbon coated on both
sides using a JEOL JEE vacuum evaporator. Carbon evaporation was performed
using two ultrapure carbon rods.11 One rod, sharpened to a fine point,was held
by spring loading against the flat face of the second rod (5 mm diameter x 100
mm). In a vacuum of 4.0 x 10"4 torr, a current of 40 - 45 A was applied to the
rods causing carbon to evaporate from the sharpened rod and deposit onto the
sample surface. This process was continued for approximately 15 seconds, and
the carbon thickness was approximately 50 nm. After coating, the samples
were dipped in cyanoacrylate ester (Super Glue)12 and air dried. This treatment
was necessary to insure that the metal samples would adhere to the epoxy
block material and not delaminate during sectioning.
The coated samples were placed into BEEM capsules13 and embedded in
approximately 1 ml of Luft's Epon epoxy resin. Standard mixture "B",
50
consisting of 25 ml Epon resin 812, 24 ml nadic methyl anhydride hardener,
and DMP-30 accelerator at a ratio of 0.1 ml/5 ml of "B" was used. The resin
was polymerized for approximately 8-12 hours at 60°C.
The embedded block must be trimmed to present a small flat facet to the
knife edge in order to produce good thin sections, and the harder the material,
the smaller this facet must be. A single edged razor blade was used to remove
excess resin from the tip of the solder sample. Once the sample was exposed,
the copper/solder/copper strap was rough trimmed with the razor blade to form
a pyramid whose top was approximately 0.5 mm square which included one
copper/solder interface. The sides of the pyramid sloped at 35-40° angles from
the top. This trimming step, however, resulted in the resin cracking away from
the sides of solder sample, thus requiring a second coating of carbon and re-
embedding with the same Epon epoxy. This sequence is illustrated in Figure
3.5.
The re-embedded sample was trimmed again as follows. The sample was
mounted in the ultramicrotome and a standard 45° glass knife was used to
precisely trim the sample face to its final shape (Figure 3.6). Excess resin was
removed from the sample by manually moving the sample past the knife while
simultaneously advancing the knife holder. When the tip of the sample became
exposed, the knife was positioned at a 30° angle with respect to the tip of the
sample. Excess resin was then gently removed from the sides of the sample.
When enough resin was removed from one side, the block was rotated 90° and
the next side was trimmed. This was repeated until all four sides of the
embedded sample were trimmed. The finished sample face was trapezoidal with
a thin strip of resin surrounding the exposed solder tip.
51
A Sorval Model MT 6000 Ultramicrotome was used for sectioning the
samples. Figure 3.3 shows the ultramicrotome with an embedded sample
positioned for sectioning. The sample chuck supports the block and is equipped
with 360° x-y and 30° y-z rotational motion for exact positioning along the
knife edge. The chuck is placed into a socket on the cantilever arm. The
solder/copper interface was oriented perpendicular to the parallel sides of the
knife edge. A diamond knife with a bevel angle of 35° was used at a tilt angle
of 6° on a metal base with a trough located behind it. This trough, or "knife
boat" was filled with deionized water. The cutting thickness was set at 20 nm
with a cutting speed of 0.1 mm/sec. During sectioning, the thin sections float
off the knife onto the surface of the water bath because of the surface tension.
Once cut, the thin sections were picked up from the water surface using a thin
metal loop. The sections were placed on 50 or 75 mesh copper grids that were
coated with Formvar and carbon. (Formvar is a polymer coating that supports
the sections on the copper grid.) Excess water was wicked away using the
edge of a sheet of filter paper. The samples were air dried before observation
in the TEM.
Luft's Epon required an overnight oven cure at 60°C. It was thought that
any additional heat treatments might change the microstructures of interest in
the sample. To eliminate questions about how sample preparation might alter
the microstructure, another embedding formulation which cures at room
temperature was developed at the final stage of this study. Elmers Epoxy,14
Resin and Hardener were used to embed the as-soldered eutectic solder/copper
joints, and samples of the bulk eutectic solder which were used to study the
relationship between the solder microstructure and the cooling rate. This epoxy
52
formulation cures at room temperature in 12 - 24 hours.
3.4.2 Electropolishing
Bulk samples of Sn/Pb eutectic solder were prepared by jet
electropolishing to compare the microstructures observed in samples made
using different preparation techniques. A photograph of a South Bay
Technology Model 550C jet polishing apparatus15 is shown in Figure 3.7. It
includes a chemical container, a chemical pump, a jet nozzle, an LED control
unit, two sapphire light rods, a photodetector, a sample stage and a power
supply. Electropolishing was performed using 85% ethyl alcohol (200 proof) +
5% 2-Butoxyethynol + 10% perchloric acid.7 Immediately before jet polishing,
both sides of the sample were mechanically polished using 600 grit sandpaper
to remove the surface oxide that inhibits smooth electropolishing. The samples
were thinned to a thickness of 100 to 150 jum. Electropolishing was performed
with a bias of 30-34 volts and 80 mA current. During electropolishing, the final
thickness of the sample was automatically controlled using an appropriate
sensitivity setting on the automatic shut-off system. When the sample was thin
enough for light to pass through or when a small hole was made in the sample,
a photodetector automatically turned off the pump motor and terminated the
voltage across the sample. As soon as polishing stopped, the sample was
removed from the stage and rinsed in deionized water to prevent further
thinning or etching. After electropolishing, the sample was immediately
transferred to the TEM for observation. Around the holes electropolished in the
sample are thin areas that are sufficiently electron transparent for TEM
observation.
53
3.4.3 Conventional Cross-sectional (XTEM) Sample Preparation
Copper/eutectic solder (63Sn/37Pb)/copper samples were prepared using
a conventional cross-sectional TEM sample preparation method, which uses
mechanical polishing followed by ion milling. Again, the goal was to compare
the microstructural differences caused by different sample preparation
techniques.
The basic procedures for preparing an XTEM sample are summarized in
Table 3.4. First, the copper/solder/copper joint and two pieces of silicon about
the same size as the joint sample were cleaned with acetone and methanol, and
then glued together with M-Bond 610 epoxy.16 After gluing, the sample block
was squeezed tightly from both sides using a special vise equipped with Teflon
blocks to make the glue lines between the solder joint and the two pieces of
silicon as thin as possible. The entire sample block held by the vise was heated
in an oven at 120°C for one hour to cure the epoxy. Cross-sectional pieces
about 0.5 mm thick were cut from the block using a low speed saw with a
diamond blade, and 3 mm diameter discs were cut from these pieces using a
Sonic-Mill Model-150 ultrasonic cutter.
Next, standard metallurgical polishing procedures, the same as those
described in section 3.3, SEM Sample Preparation, were used to mechanically
thin the sample disc. After polishing both sides, the disc was usually less than
50 //m thick. Since the 50 /xm thick sample was too fragile to withstand the
rest of the preparation procedure without additional support, a copper ring, 3
mm in diameter, with a hole (2 mm by 1 mm) in the center was attached to the
thin disk using a very small amount of M-Bond epoxy before it is removed from
the stainless steel sample holder. This copper ring is used to support the sample
54
disc sample during polishing and protects the thin sample from breakage. After
removing the sample from the polishing holder, the sample was mounted on a
glass slide with the copper ring on the bottom. Then the sample was
"dimpled", that is, one surface was made concave using ball grinding. A ball 13
mm in diameter touches the sample surface and rotates with 1 jum diamond
paste and lubricating liquid. A concave dimple is made at the center of the
sample.
The final step of conventional TEM sample preparation is ion milling. A
Gatan Dual Ion Mill Model 600 was used. A polished and dimpled sample is
thinned to electron transparency by sputtering both sides of the sample using
heavy ions (argon). Argon ions are introduced from two ion guns. These two
guns are mounted on a rotatable wheel so that they can be rotated at an angle
relative to the sample surface. The sample stage is continuously rotated during
sputtering to maintain uniformity. The operation conditions of the Ion Mill are:
gun voltage = 3 kV, ion beam current = 0.5 mA/gun, gun tilt angle = 14°,
base vacuum pressure < 1 x 10"6 torr, operation time = 4 - 8 hours. Upon
finishing, the samples were ion milled for 15 minutes at the gun tilt angle ~
8.5°to decrease the ion mill damage. After ion milling, areas of the sample less
than 100 nm thick could be analyzed in the TEM.
3.5 Thin Film Preparation
Since the formation and growth of Cu-Sn intermetallics at the
solder/copper substrate interface during soldering and system use have been
proposed as controlling mechanisms for the solderability and reliability of solder
joints,17,18 there is scientific interest in the diffusion and reaction behavior near
55
the solder/substrate interface. To determine the mechanisms of intermetallic
formation and the effect of particle additions on diffusion, thin film samples
were observed in-situ in real time using a hot stage in the TEM.
Pure solder is composed of tin and lead. Since tin is the more reactive
species and reacts with Cu, Ni, Ag, Au, etc. to form intermetallics, and since
lead is essentially inert with respect to these metals, the focus of these
experiments was on the direct reaction of Sn with Cu, and the effects of other
elements such as Ni, Au and Ag on these reactions.
Thin films were evaporated using a Veeco 400" Series Evaporator,19
which is shown in Figure 3.8. The base vacuum was 10"5 torr to 10"6 torr (~
1 mPa to 0.1 mPa) and the sources were 99.9% pure metal, each on an
electrically heated tungsten wire. The samples were allowed to cool to room
temperature immediately after evaporation.
Thin amorphous carbon films with a density of 5 ± 3 jug/cm2
(corresponding to 20 ± 10 A thickness) were placed on standard TEM grids
(200 mesh). The carbon films are strong, conductive substrates for subsequent
film deposition. Next, several grids with the carbon films were placed in the
evaporating chamber and held upside down using a copper plate with 3 mm
diameter holes. A continuous 500 A thick layer of copper was evaporated onto
the top surface of the grids. A 500 A thick layer of tin was deposited on the
copper using another TEM grid (50 or 75 mesh) placed under the original
sample as a shadow mask. This resulted in a checkered pattern of square Sn
islands on top of a continuous Cu film. To study the effects of particle
additions, 100 A thick layers of X (X = Ni, Ag or Au) were evaporated. There
were four different configurations as shown in Figure 3.9.
56
Configuration 1: After evaporating Cu and Sn, X was evaporated on top
of the samples after shifting the shadow mask grid. This resulted in the
samples consisting of continuous Cu films, plus isolated Sn islands, plus X
islands which only partially overlap the Sn islands.
Configuration 2: After evaporating Cu and Sn, without the shadow mask
grid, X was evaporated on top of the samples. This resulted in a continuous X
layer on top of the continuous Cu and Sn islands.
Configuration 3: After evaporating Cu and Sn, without shifting or
eliminating the shadow mask grid, X was evaporated. This resulted in X exactly
on top of the Sn islands.
Configuration 4: X was evaporated after the Cu but before the Sn. This
resulted in samples consisting of continuous Cu, then continuous X, plus
isolated Sn islands.
There were also Sn/Y (Y = Cu, Ni, Ag or Au) samples, which consisted
of 500 A thick Y islands on top of continuous 500 A thick Sn films. The
complete matrix of thin film samples is shown in Table 3.5.
3.6 In-Situ Heating
The samples were placed in a Gatan Single Tilt Heating Holder Model
628 and were observed in a JEOL 100CX TEM. The hot stage is a side entry,
furnace type, single tilt, heating TEM specimen holder which is water cooled
to extend its operating temperature range and to reduce specimen drift by
maintaining a local constant temperature heat sink. The furnace is mounted on
two insulating ceramic balls set in jewelled mounts. The whole suspension
system is spring loaded to accommodate the expansion and contraction which
57
occur during heating and cooling. The furnace contains a miniature
encapsulated 10 watt heater which is spot welded to two terminal posts in the
specimen tip. One of the terminals is grounded to the specimen rod which acts
as the return current conductor for the heater, and the other is connected via
a copper wire to a 5 pin vacuum feed-through mounted at the end of the
specimen rod. The furnace temperature is measured with a platinum/platinum-
13% rhodium thermocouple spot welded to the furnace body. The
thermocouple leads are anchored by terminals in the specimen tip and are then
fed along the axis of the specimen rod to the five pin vacuum feed-through. A
30 watt current regulated DC power supply provides ripple-free power to the
heater. The furnace temperature is controlled by setting the heater current to
the desired value. A complete calibration of heating stage temperature vs
current was performed in our laboratory.
58
Table 3.1. Compositions and Particle Size Ranges of the Composite Solders
Particle Type Weight % Particle Size Range Ot/m) Particle Type Weight %
Before Grinding After Grinding
Eutectic solder
only
0 0 N/A
Cu6Sn5 20 1 8 - 4 6 0.7 - 24
Cu3Sn 20 25 - 69 0.7 - 24
Cu 7.6 8 - 1 1 N/A
Au 4 2 - 5 N/A
Ag 4 4 - 7 N/A
Ni 4 2 - 3 N/A
N/A: not applicable.
59
Table 3.2. Cooling Rates of Different Sample Sets
Sample
Set
Cooling
Rate
Time (seconds) from Start Temp (252°C). Sample
Set
Cooling
Rate 183°C 150°C 100°C 50°C 32°C
1 fast 6.7 10.5 21.5 51.9 143.8
II medium 31.8 54.4 114.7 313.9 759.4
III very slow 279.4 451.1 792.8 1732 2561
Table 3.3. Composite Solder Sample Matrix
X: samples annealed for 0, 4, 8, 16, 32 and 64 days
A: samples annealed for 0, 4, 8, 16 and 32 days
60
Particle
Type
Anneal temperature (°C) Particle
Type 110 120 130 140 150 160
ESO X X X X X X
Cu X X X X X
Cu6Sn5 X X X X A X
Cu3Sn X X X X X
Ni X X X X X
Au A X X A X
Ag A X X A X
61
Table 3.4. XTEM Sample Preparation Procedure
Step 1. gluing and cutting • solder joint and two piece of silicon are
glued together.
• cross-sectional pieces are cut from glued
block and 3 mm discs are ultrasonically
milled from these pieces.
Step 2. polishing • sand papers, microcloths with diamond
pastes and 0.05 //m Al203 are used to thin
the sample to about 50 //m.
Step 3. dimpling • a rolling ball with 1 //m diamond paste
ground the sample center to form a concave
surface.
Step 4. ion milling • sample was sputtered with argon ions at
14° until its center was less than 100 nm
thick.
62
Table 3.5. Thin Film Sample Matrix
Type Configuration
Cu/Sn square Sn islands on top of a continuous Cu film
Cu/Sn/Ni config. 1 config. 2 config. 3 config. 4
Cu/Sn/Ag config. 1 config. 2 config. 3
Cu/Sn/Au config. 1 config. 2
Sn/Cu square Cu islands on top of a continuous Sn film
Sn/Ni square Ni islands on top of a continuous Sn film
Sn/Ag square Ag islands on top of a continuous Sn film
Sn/Au square Ag islands on top of a continuous Sn film
The configurations are as shown in Figure 3.9.
63
Copper/Solder/Copper Joint
Cu Strap
Solder
Cu Strap
t t Silicon Joint Silicon
Glue Togther
Cut Slice
! o>!
CO U i S j 3 O! 9 Q 0 )
CO I
Figure 3.1. Sample configuration of copper/solder/copper joint and silicon
blocks.
6 4
££ UlJ Q -J O X yj —j a.
O m (3 z X CO
u
0 S X (/)
c o V; "35 o a CD c 1c w "o a 0 C o +-» CO k. 0 TJ o x: -92 o. CO CO
0 "D C u. o I— 0 J= CO o a. +-» 0 E
JC 0 D CD
CNj CO 0 u. D CD
65
Cantilever Arm
Sample Sample Holder
Diamond Knife
Knife Trough
Figure 3.3. A typical ultramicrotome.
66
Sample Polymerized Block
Tilt Angle Bevel Angle Rake Angle
t I
Knife
Top Down View of Knife Trough
Thin Sections
Water 111
Figure 3.4. Schematic of sample sectioning using ultramicrotomy.
67
I Sample
Polymerized Block
;j|x
Rough Trimming
• Rough
Trimming
ft
After Rough Trimming
Sample Re-embedding
Figure 3.5. Sample rough trimming and re-embedding.
68
Finished Sample Face After Trimming
Figure 3.6. Schematic of steps need for precise trimming of embedded
materials to produce a small facet on the block face.
69
LED CONTROL UNIT & PHOTO DETECTOR
'kmtmm
j rr mmmw mntvwtm M M MO
auto
pcwe* scwHTwr* auto poitmrr mw
POWER SUPPLY
CHEMICAL CONTAINER
Figure 3.7. South Bay Technology Model 550C jet polisher. 15
70
Figure 3.8. Veeco VE-400 Evaporateor 19
71
Figure 3.9. Schematics of thin film sample configurations.
CHAPTER 3 REFERENCES
1. International Electronic Materials Corporation, 30275 Bainbridge Road,
Cleveland, OH 44139.
2. National Institute of Standards and Technology, Gaithersburg, MD
20899.
3. Aesar, Inc., 30 Bond Street, Ward Hill, MA 01835.
4. A.D. Roming, Jr., Y.A. Chang, J.J. Stephens, D.R. Frear, V. Marcotte
and C. Lea, In Solder Mechanics: A State of the Art Assessment, D.R.
Frear, W.B. Jones and K.R. Kinsman Eds., (TMS, PA, 1990), Chpter 2.
5. ASM Metals Handbook, Metallography and Microstructures, 9th ed,
(ASM International, 1985).
6. Instruction Manual for 69 - 1000 Minimet Polisher/Grinder, Buehler Ltd.,
41 Waukegan, Lake Bluff, IL 60044.
7. D.R. Frear, Ph.D. Thesis, University of California at Berkeley, 1987.
8. S.F. Dirnfield and J.J. Ramon, Welding Journal, 48, 373 (1990).
9. J.-C. Jesior, J. Ultrastr. and Mol. Str. Res., 95, 210 (1986).
10. J.-C. Jesior, Scanning Microscopy Supplement, 3, 147 (1989).
11. JEOL SVC, JEOL Engineering Service Company, Ltd., Tokyo, Japan.
12. Duro, Loctite Corp., Cleveland, OH 44128.
13. Ted Pella, Inc., 4595 Mountain Lakes Blud., Redding, CA 96003.
14. Borden, Inc., HPPG, Columbus, OH 43215.
72
73
15. South Bay Technology, Inc., 1120 Via Callejon, San Clemente, CA
92672.
16. Micro-Measurements Division, Measurements Group, Inc., Raleigh, NC
27611.
17. D.S. Dunn, T.F. Marinis, W.M. Sherry and C.J. Williams, Mater. Res.
Soc. Symp. Proc., 40, 129 (1985).
18. P.E. Davis, M.E. Warwick and S.J. Muckett, Plating and Surface
Finishing, 70, 49 (1983).
19. Veeco Instruments Inc., Terminal Drive, Plainview, NY.
CHAPTER 4
INTERMETALLICS AT THE INTERFACES OF
COMPOSITE SOLDER/COPPER JOINTS
4.1 Introduction
Intermetallic compounds such as Cu6Sn5 and Cu3Sn are known to form
and grow at solder/copper substrate interfaces during soldering and system
use.1The formation and growth of these intermetallics have been proposed as
controlling mechanisms for the solderability and reliability of solder joints.2 In
this chapter, the results of solid state diffusion kinetic and microstructural
studies of intermetallic formation in copper/composite solder/copper samples
are reported. The intermetallics at the solder/copper interface were examined
as functions of time, temperature and particle composition. The samples were
prepared according to the experimental procedures outlined in Chapter 3, and
were characterized using scanning electron microscopy (SEM), transmission
electron microscopy (TEM), x-ray energy dispersive spectroscopy (XEDS) and
scanning transmission electron microscopy (STEM) as described in Appendix
B and Appendix C.
4.2 Microstructure of Composite Solder/Copper Substrate Interface
Figure 4.1a is an SEM micrograph of the intermetallics formed at the
interface between eutectic solder and the copper substrate after annealing for
32 days at 120°C. Starting at the bottom of the micrograph, the observed
74
75
phases are the copper substrate (A), Cu3Sn (e-phase) adjacent to the copper
substrate (B), Cu6Sn5 (rj-phase) adjacent to the solder (C), the light contrast Pb-
rich phase (D) and dark contrast Sn-rich phase (E) in the solder matrix. These
phases were unambiguously identified using XEDS in the SEM and the spectra
are shown in Figure 4.1b. These phase identifications were verified using
selected area electron diffraction patterns (SADP) in the TEM. Since the
diffraction line intensities were not recorded, in this study rj (unordered) and r\'
(ordered) Cu6Sn5 phase (discussed in Appendix A) are treated as the same
phase.
Figures 4.2 and 4.3 are two series of micrographs which demonstrate
the growth of the intermetallic layers with annealing. Figure 4.2 shows the
microstructure of the as-soldered (unaged) Cu composite solder and the
microstructures after 8 and 64 days at 120°C. Figure 4.3 shows the
microstructure of the Ag composite solder after 32 days at 120, 140, and
160°C. Two intermetallic layers form at the solder/copper interface. The two
intermetallics increase in thickness with time and elevated temperature. The
Cu6Sn5 layer is generally thicker than the Cu3Sn layer. As shown in Figure 4.2a,
a thin and irregular Cu6Sn5 layer, but no Cu3Sn layer, is visible in the as-
soldered state, and this Cu6Sn5 layer is already continuous. It should be noted
that similar to Figure 4.2a, Cu3Sn was never observed in unaged sample using
SEM. Annealing was always required for the Cu3Sn to become thick enough to
be visible in the SEM.
In Figure 4.2b, a copper particle is visible surrounded by a layer of
Cu3Sn, followed by a layer of Cu6Sn5. These two intermetallics formed in a
manner similar to the intermetallics at the solder/copper substrate interface. If
76
the anneal time is long enough and a large amount of Sn is present, the Cu
particles completely transform to the thermodynamically favored Cu6Sn5 phase
(Figure 4.2c). The Ag particles in the Ag composite solder react with Sn to
form Ag3Sn during soldering and annealing. There are Ag or Ag3Sn particles in
the composite matrix. With annealing, more and more Ag particles transform
to Ag3Sn. The eutectic solder matrix and composite solder matrices will be
discussed in detail in the next chapter.
Figure 4.4 shows the solder/copper interface for the eutectic solder
(Figure 4.4a), Cu3Sn (Figure 4.4b), Cu6Sn5 (Figure 4.4c), Cu (Figure 4.4d), Au
(Figure 4.4e), Ag (Figure 4.4f), and Ni (Figure 4.4g) composites after annealing
at 140°C for 16 days. Except for the Ni composite solder (Figure 4.4g), these
results are similar to the Sn/Pb eutectic solder case. However, the particles
added to the solder affect the thicknesses and morphologies of the intermetallic
layers. The Cu6Sn5 layers in the Cu, Cu3Sn and Cu6Sn5 composite solders are
all slightly thinner than in the eutectic solder only sample, and the Cu3Sn layers
are thicker. The opposite effects occur for Ag, Au, and Ni composite solders:
the Cu6Sn5 layers are thicker and the Cu3Sn layers thinner than for the eutectic
solder.
To address the issues regarding the nanostructure of the interfacial
intermetallics and the solder matrix, it is necessary to examine the
solder/copper joints using transmission electron microscopy. As described in
Chapter 3, it is possible to prepare the solder/copper joint sample for
examination by TEM using ultramicrotomy. All phases are uniformly thin. For
the first time, the copper substrate, Pb-rich and Sn-rich phases of the solder,
the metallic and intermetallic particles in composite solder, and the intermetallic
77
layers at the solder/substrate interface were observed and analyzed by TEM
simultaneously in a single sample.
A TEM micrograph of a eutectic solder/copper joint aged at 140°C for 4
days is shown in Figure 4.5. In this micrograph, the copper, solder, and
intermetallic phases are visible and variations in the grain morphology of each
phase are readily distinguishable. The intermetallics probably extend upwards
from the interface. Electron diffraction studies were performed and the patterns
for the Cu, Cu3Sn, and Cu6Sn5 phases are shown in Figure 4.6. These patterns
were indexed and the phases were positively identified with at least 10 d-
spacings in agreement with the literature values.3 The interplanar d-spacings for
these phases are listed in Appendix A.
For as-soldered samples before annealing, only a thin, irregular Cu6Sn5
layer was observed using SEM. Cu3Sn was not visible in any of the samples,
including the eutectic solder. Similar observations have led some researchers
to conclude that Cu3Sn does not form during soldering, but only during high
temperature annealing.4,5,6,7 Cu3Sn should occur immediately, however, based
on the Cu/Sn phase diagram and classical solid state phase transformation
theory. Figures 4.7a and 4.7b are SEM and TEM micrographs of a Cu6Sn5
composite solder joint in the as-soldered state showing the solder/copper
substrate interface. In a TEM micrograph (Figure 4.7b), two intermetallic layers
are visible between the solder matrix and the copper substrate. The Cu3Sn layer
is about 0.2 to 0.3 fim thick and cannot be seen in the SEM micrograph of a
similar area (Figure 4.7a). These results confirm that Cu3Sn forms during
soldering, but may not be visible because of the spatial resolution limits of
SEM. The Cu3Sn becomes observable by SEM only after intermetallic growth
78
occurs.
Figures 4.8 to 4.13 show the interfacial region between the solder and
copper substrate for different types of solder in the as-soldered state. The
Figures are for Cu3Sn, Cu6Sn5, Cu, Ag, Au, and Ni composite solders,
respectively. Except for the Ni composite, a thin Cu3Sn intermetallic layer exists
between the Cu6Sn5 and the Cu substrate for all the solders. The Cu3Sn layer
in the Ag and Au composites is much thinner than in the eutectic solder and
Cu, Cu3Sn, Cu6Sn5 composites. The Cu3Sn layer is 0.07 - 0.15 fim thick in Ag
and Au composites and 0.2 - 0.3 j»m thick in eutectic and Cu, Cu3Sn, Cu6Sn5
composite solders. For the Ni composite solder in the as-soldered state, no
continued Cu3Sn layer was observed.
The microstructures of the solder/copper interfacial regions after
annealing for 4 days at 140°C for Cu, Cu3Sn and Ag composite solder are
shown in Figures 4.14, 4.15 and 4.16, respectively. Figure 4.17 shows the
interfacial area of the Ni composite after annealing for 8 days at 140°C. For the
eutectic and composite solders, two intermetallic layers increase in thickness
with annealing. After annealing at 140°C for 4 days, the thickness of the Cu3Sn
layer is on the order of 0.3 jum (0.2 - 0.4 jum) for the Ag composite (Figure
4.16), and 0.4 jum (0.2 - 0.6 jum) for the Au composite, which is much less
than the 1 .0 - 1.2 jum thickness of the Cu (Figure 4.14), Cu3Sn (Figure 4.15)
and Cu6Sn5 composites, and the eutectic solder (Figure 4.5). The Cu3Sn layer
may be very thin, if it exists at all, in the Ni composite solder after annealing
at 140°C for 8 days (< 0.2 - 0.3 jum).
The observed grain size are widely different for each phase. The solder
79
matrix consists of Pb-rich regions within very large Sn-rich regions, which will
be discussed in Chapter 5. The copper substrate is extremely fined grained
material. The Cu6Sn5 phase has columnar (rod-like) grains, whereas the Cu3Sn
phase has a more equiaxed grain structure. The as-soldered Cu3Sn phase has
a grain size on the order of 0.2 - 0.3 jum, and the grain size of the Cu6Sn5
phase is on the order of 0.5 - 1 j«m. With annealing, coarsening occurs. After
140°C for 4 days, the Cu6Sn5 grains were much rounder and larger, and their
diameters increased to 1 - 2 jiim. The Cu3Sn phase only increased to 0.3 - 0.4
jum. The Cu3Sn grains may be seen in Figures 4.5, 4.8 and 4.9. The columnar
morphology of the Cu6Sn5 is shown in Figures 4.8 and 4.9. These grains are
each a single crystal of Cu6Sn5. This morphology for Cu6Sn5 has also been
observed by Warwick and Muckett.8
Some of the small microstructural features visible in these TEM
micrographs may be due to artifacts caused by the ultramicrotomy used for
sample preparation.9 Contamination or dulling of the knife blade is often the
source of extraneous features. Striations were observed at relatively evenly
spaced intervals parallel to the direction of sectioning. These knife marks may
result from a dull knife that has microchipping or contamination along the blade
edge. In some areas, tearing of the intermetallic phases was observed.
Intermetallic tearing could be avoided by cleaning the blade or by using an area
of the blade free of pieces of resin or metal. Brittle phase tearing similar to that
shown in the TEM micrographs has been observed by others.10,11 This is
attributed to a combination of shearing and brittle fracture.7
Another common sectioning artifact is "chatter," characterized by
80
regularly spaced areas of light and dark contrast aligned perpendicular to the
sectioning direction. This is caused by vibration of the specimen during
sectioning. The chatter is minimized if sectioning is performed in the early
morning or late at night when people were rarely in the laboratory. It is
hypothesized that in our laboratory, chatter is caused by floor and building
vibrations.
4.3 The Formation of Microvoids
It was suggested by Lucey et al.12 that microvoids may form either
within the intermetallic layers or at their interfaces, and extend to the surface
of the solder joint. The microvoids could link together to form a conduit for
impurities and oxygen diffusion from the external environment to interact with
the subsurface intermetallic layer, resulting in a loss of solderability. However,
there is no experimental evidence that clearly supports this model.
After careful examination the SEM and TEM micrographs, it was
determined that microvoids do not form at the solder/copper substrate interface
for eutectic solder and composite solders in the as-soldered state, except for
the Ni composite solder. After long time, high temperature annealing,
microvoids may form. At this point, as shown in Figure 4.18, the Cu3Sn layer
might transform totally or partially to Cu6Sn5 with additional annealing. The
Cu3Sn layer stops growing. The thickness data for samples in this condition
were not used for calculation of the diffusion coefficients.
The microstructure of the Ni composite solder is different than the
microstructure of any the other samples. Under certain annealing conditions,
as shown in Figure 4.4g and Figure 4.19b, Cu3Sn is not observed and there is
81
a large concentration of voids in the Cu6Sn5, especially in the lower half of the
intermetallic layer where Cu3Sn is expected to occur. Even though for some
anneal conditions microvoids are not present, the Cu3Sn layer at the interface
is extremely thin compared to other solders (Figure 4.19a) or even completely
invisible. There are no clear rules about the conditions under which microvoids
are present and no Cu3Sn layer exist.
The microvoids discussed above are Kirkendall voids generated when
different chemical components in a system have unequal diffusion coefficients.
They form along a line at the intermetallic/copper substrate interface. These
voids do not link and extend through the intermetallic layers to the
intermetallic/solder interface. They are different than those "microtunnels"
proposed by Lucey et al.12
4.4 Activation Energies of Intermetallic Formation in Eutectic Solder and
Composite Solders
There are two limiting conditions for intermetallic formation and growth
in the solder/copper substrate system. First, when diffusion through the
growing intermetallic layer may be the rate-limiting factor (diffusion controlled
growth). Second, an interfacial reaction is the rate-limiting step (reaction
controlled growth).
The thicknesses of the Cu3Sn and Cu6Sn5 were measured with a
digitizing tablet interfaced to a personal computer. SEM micrographs of the
solder/copper interface region were placed on the digitizer pad and a calibrated
pointer was used to encode pairs of points representing a single measurement
of the intermetallic thickness. A minimum of 100 such measurements, equally
82
spaced along the interface, were made for each thickness reported. This
procedure results in high quality data that can be reliably analyzed with
statistical significance. After digitization, the distributions of the measurements,
the average thickness, the standard deviation, and the maximum and minimum
thickness values were calculated. The average thickness values were used to
represent the thickness of the intermetallic layers. Table 4.1 is an example of
the statistical parameters calculated for the thickness measurements of Cu6Sn5
in Au composite solder.
Figures 4.20 and 4.21 are plots of the solder/copper interface
thicknesses versus the square root of annealing time for Cu6Sn5 and Cu3Sn in
eutectic solder at 140°C and Cu composite solder at 120°C, respectively. The
linear correlation coefficients for the data, in Figures 4.20 (R2 = 0.94 for Cu6Sn5
and R2 = 0.95 for Cu3Sn), and 4.21 (R2 = 0.95 for Cu6Sn5 and R2 = 0.98 for
Cu3Sn), as well as for other anneal temperatures and in other types of
composite solders suggests that the growth of these intermetallics is diffusion-
controlled over the temperature range 110 to 160°C and that it follows a simple
parabolic relationship. In more general terms, intermetallic formation is a
thermally activated process.
As derived in Chapter 2, the diffusion coefficient may be calculated using
d = {Dt <4-1>
where d = layer thickness, D = diffusion coefficient and t = time. Values for
D are calculated by plotting the intermetallic thickness versus the square root
of the anneal time. The diffusion coefficients for Cu6Sn5 and Cu3Sn in eutectic
solder at 140°C and in Cu composite solder at 120°C were calculated using
83
Equation 4.1 and are shown in Figure 4.20 and Figure 4.21, respectively. The
measured intermetallic thicknesses and the diffusion coefficient at each
temperature for each type of solder are listed in Table 4.2 (eutectic solder),
Table 4.3 (Cu composite solder), Table 4.4 (Cu3Sn composite solder), Table 4.5
(Cu6Sn5 composite solder), Table 4.6 (Ag composite solder), Table 4.7 (Au
composite solder), and Table 4.8 (Ni composite solder). The correlation
coefficients, R2, are generally found to be greater than 0.9 for all the eutectic
and composite solders, except the Ni composite solder. The excellent linear
correlations demonstrate that the diffusion model is valid. The lower correlation
for the Ni composite solder may be attributed to the increased irregularity of the
Cu6Sn5 intermetallic layer. Great difficulty was encountered in measuring the
thickness of this layer due to its highly irregular and porous nature, and to the
uncontrolled occurrence of microvoids, as described above.
The activation energies for the formation of Cu6Sn5 and Cu3Sn may be
calculated using the relation:
D=DQe-MT (4.2)
which was derivated in Chapter 2. D = diffusion coefficient, D0 = diffusion
constant, Q = activation energy, k = Boltzmann constant and T = absolute
temperature.
Figures 4.22 and 4.23 are plots of ln(D) versus 1/T for intermetallic
formation in the Cu composite and Au composite solders, respectively. Again,
the linear correlation coefficients, R2, for the activation energy plots for all
solders are greater than 0.9. The linear fits are very good, demonstrating that
the model is indeed appropriate. The activation energies for formation of Cu6Sn5
84
and Cu3Sn for eutectic solder in the temperature range 110 to 160°C are 0.84
eV (18.5 Kcal/mol) and 1.63 eV (44.9 Kcal/mol), respectively. The values are
in reasonable agreement with previously published data.13,14,15,16,17 The
activation energies for intermetallic formation for the eutectic solder and
composite solders are listed in Table 4.9. The growth of the intermetallic layers
at the interface is strongly affected by the particle type added to the solder. Cu-
containing particle additions increase the activation energy for Cu6Sn5 formation
and decrease the activation energy for Cu3Sn formation compared to the
eutectic solder alone. Ag and Au particles decrease the activation energies for
both Cu6Sn5 and Cu3Sn formation. Ni particles drastically increase the activation
energy for Cu6Sn5 formation.
4.5 In-Situ Thin Film Diffusion Couple Studies
As a general rule for binary diffusion couples, the element with the lower
melting point has the larger diffusion constant. Therefore, for the Cu-Sn
system, Sn should be the faster diffuser in the Cu-Sn system. Diffusion couple
experiments in the literature18,19,20 proved that Sn is the faster diffuser.
Experiments reported in the literature for diffusion couples of Cu and Sn have
found that Cu6Sn5 and Cu3Sn intermetallics form in the Cu substrate below any
diffusion barrier layers (Sn, Ni, Co, Cu6Sn5, etc.) added between the Cu and
Sn.21 This implies that the Sn diffuses into the Cu much more rapidly than the
Cu diffuses into the Sn. To obtain direct information about the mechanisms of
Cu/Sn intermetallic formation and growth at the solder/substrate interface and
the effect of other particle additions, Cu/Sn and Cu/Sn/X (X = Ni, Ag or Au)
thin film samples were observed in real time in the TEM while annealing the
85
samples using a hot stage.
The types of thin film samples and the sample preparation methods were
described in Chapter 3. Since thin films were deposited by evaporation, the Cu,
Sn, Ni, Ag and Au films are polycrystalline. The morphologies of these thin
films are shown in Figure 4.24. It is clear that the grain sizes and morphology
are so different for each element that they can be easily distinguished.
For Sn-islands on a Cu substrate, intermetallic formation and growth with
annealing are demonstrated in Figure 4.25, which is a time series of TEM
micrographs showing the Cu-Sn intermetallic growth. As shown in Figure 4.25,
intermetallic formation begins at the Sn/Cu boundary and progresses laterally
from the Sn into the Cu. The original Sn/Cu boundary remained stationary. This
is an expected result since Sn is the faster diffuser in the system. Lateral
growth is observable because the Cu and Sn are extremely thin (500 A)
compared to their length and width. It is also possible that the oxygen and
carbon present on the surface of the Cu (because the films were deposited in
a conventional vacuum system) prevents the interdiffusion of the metallic films,
as proposed by Dufner.22
There are two distinct intermetallics after annealing. As shown in Figure
4.25c the growth nearest the Sn is most likely Cu6Sn5, whereas the one
adjacent to the Cu is probably Cu3Sn. The intermetallic phases were identified
using selected electron diffraction patterns from each region. Furthermore,
these two phases can also be easily distinguished by their grain sizes, i.e. the
grain size of Cu3Sn is smaller than that of Cu6Sn5, as in the TEM cross-sectional
micrograph of solder/copper joints.
Heating also causes microstructural changes in the Cu and Sn layers. The
86
Cu layer undergoes a rapid microstructural change when it is first heated, and
becomes more uniform. The Sn layer density decreases with time as the
intermetallic layers grow and become thicker. In addition, the Sn layer near the
Sn/Cu boundary becomes thinner with longer anneal times and, in extreme
cases, scattered void formation was observed in the Sn closest to the interface.
All these results indicate that Sn diffusion into the Cu must occur for
intermetallic formation to take place. The growth of the intermetallics requires
the diffusion of Sn through Cu6Sn5 and Cu3Sn followed by reaction with Cu. Cu
does not diffuse into the solder to any appreciable extent.
There are several other characteristics of the intermetallic regions shown
in Figure 4.25. First, microvoid formation occurs at the Cu/intermetallic
interface. The void formation was prolific at the intermetallic growth front, and
the voids continuously evolved and preceded this front. Second, there was a
formation of "finger-like" projections regions. These protrusions are one or both
of the intermetallics. With annealing, these regions expanded and joined
together laterally. Third, in the Cu6Sn5 intermetallic region, "electron dense,"
structures formed. The formation of these structures was sensitive to the
temperature. With higher anneal temperature, they formed faster. This "electron
dense" was also observed by Pouraghabagheret al. at high temperature range
(350°C - 450°C).23
For Cu islands on top of a continuous Sn layer, intermetallic formation
took place where the Cu and Sn overlapped, and no lateral intermetallic
formation was observed. Since this is a Sn rich system, the intermetallic was
mainly Cu6Sn5.
For Cu/Ni/Sn samples, when a continuous Ni barrier is deposited
87
inbetween the Cu and Sn, (thin film sample configuration 4, Chapter 3, page
58 and 73), or deposited on top of the Cu and Sn islands, (thin film sample
configuration 2 and configuration 3), lateral intermetallic formation is
completely suppressed, even when the Ni layer is only 100 A thick. No
intermetallics were observed after annealing at 250°C for several hours. This
is in agreement with the use of Ni plating of copper printed circuit board
conductors to maintain solderability after long storage times.24 Since Ni
minimizes Cu-Sn intermetallic formation, it enhances solderability.
For samples consisting of continuous Cu films plus isolated Sn islands,
plus Ni islands which only partially overlap the Sn (configuration 1), at 250°C,
intermetallic formation begins in some areas at the Sn/Cu boundary. The
annealing behavior is the same as for the Cu/Sn samples described above. In
other areas, as shown in Figure 4.26, there was no intermetallic growth even
after annealing at 250°C for 30 minutes followed by 200°C for 24 hours. XEDS
was used to identify the chemical composition. XEDS spectra show that in the
areas with intermetallic growth, there is no Ni on top of the Sn or at the
interface. For the areas without intermetallic growth, Figure 4.27 shows the
XEDS peak intensity ratio of Ni to Sn as function of probe positions. The probe
was placed on the Cu side, at the Cu/Sn interface, and at several positions on
the Sn side, as labeled in Figure 4.26. The XEDS results demonstrate that Ni
is present at the Cu/Sn interface and that there is a lateral Ni concentration
gradient from the interface into the Sn. This implies that the Ni diffuses through
the Sn layer to the Sn/Cu interface. Once the Ni reaches the interface, it may
act as a barrier which prevents Sn from diffusing into the Cu, and thus inhibits
Sn/Cu intermetallic reactions, even though it is present in extremely small
88
concentrations.
Previous published data indicates that diffusion of Au and Sn in Au-Sn
alloys is strongly concentration dependent.25 For the Sn/Au thin film sample,
in the Sn-rich region, Au atoms diffuse rapidly into the tin matrix via an
interstitial mechanism.26 In the Au-rich region, however, Au can diffuse only via
a vacancy mechanism and thus the diffusivities of Au and Sn in Au are
generally small. When Au and Sn are brought into contact with each other,
even at room temperature, the Au diffuses rapidly into the Sn via an interstitial
mechanism and forms the intermetallic phase AuSn4. This process is enhanced
with high temperature (200-250°C) annealing. For the Cu/Sn/Au sample, with
annealing, the Au first diffuses rapidly into the Sn and forms AuSn4
intermetallic. The diffusion of Sn into the Cu is inhibited until all of the Au is
reacts with Sn to form AuSn4.
For the Sn/Ag sample, similar to the Sn/Au sample, Ag diffuses into the
Sn and forms Ag-Sn intermetallic. This process is slower than in the Sn/Au
sample, since the diffusivity of Ag in Sn is smaller than that of Au in Sn.25 For
the Cu/Sn/Ag sample, with annealing, the diffusion of the Sn into the Cu and
the Ag into the Sn occurs simultaneously.
For the Sn/Ni sample, with high temperature annealing, Ni diffuses into
the Sn and forms a Ni-Sn intermetallic. With in-situ TEM observation, it was
found that the rate Ni-Sn intermetallic formation is slower than Au-Sn
intermetallic, and even slower than Ag-Sn intermetallic formation. In the
temperature range from room temperature to 400°C, the diffusivity of various
elements in Sn is: Ni > Au > Ag.27 The low Ni-Sn intermetallic formation rate
may be explained as follows. There are two factors related to X-Sn intermetallic
89
formation in the Sn/X thin film samples (X = Au, Ag and Ni). One is the
diffusivity of X in Sn. The other is the nucleation rate for intermetallic
formation. The X-Sn intermetallics may be formed by nucleation directly from
the Sn phase.28 For the cases of Sn/Au and Sn/Ag thin films, the limiting factor
for the formation of the intermetallic phase is the diffusivity of Au and Ag in
Sn, respectively. For the case of Sn/Ni thin films, the limiting factor is the
nucleation rate. This explanation is consistent with the observations of the
Cu/Sn/Ni thin film samples that the Ni does not completely react with Sn to
form Ni-Sn intermetallic, but diffuses rapidly to the Sn/Cu interface and acts as
a barrier preventing Sn from diffusing into the Cu.
4.6 Diffusion Mechanisms
The diffusion and reaction of the Sn and Cu result in the formation and
growth of the Cu6Sn5 and Cu3Sn intermetallics at the solder/copper substrate
interface. Based on the studies of these intermetallic layers using SEM and
TEM, and the in-situ observations, the formation of the intermetallics is thought
to occur via the following mechanisms, which are diagrammed in Figure 4.28.
Initially after soldering, thin layers of both Cu6Sn5 and Cu3Sn are formed at the
solder/copper substrate interface. The 17-phase, Cu6Sn5, forms adjacent to the
solder and the e-phase, Cu3Sn, forms adjacent to the copper substrate. With
annealing, Sn diffuses through the Cu6Sn5 phase to the tj/e interface, and reacts
there with the Cu3Sn to form Cu6Sn5. The Sn also diffuses through the Cu3Sn
phase to the e/Cu interface and reacts there with the Cu causing the Cu3Sn
layer to grow in thickness as well. Based on the morphology of the 17 and e
90
phases, Sn diffusion mainly occurs through the grain boundaries.
Additional evidence of the tin being the mobile species in the
solder/copper system is provided by the AuSn4 and Ag3Sn particles which are
in the solder side and along the solder/Cu6Sn5 interface in the Au and Ag
(Figure 4.3b) composite solders, respectively. Although these particles could
have been deposited here by transfer from the solder during the mechanical
polishing used for sample preparation, it is more likely that they are a residue
of the reaction between the added particles and the solder. These intermetallic
particles can act as diffusion markers. If Cu is the faster diffuser, the particles
should be inside the Cu6Sn5 or Cu3Sn intermetallic layers, or along the
copper/Cu3Sn interface. This is not the case. Their position on the solder side
of the interface is consistent with Sn being the mobile species.
Another phenomenon observed in this system is Pb enrichment at the
solder/Cu6Sn5 interface after annealing. The solder near this region is depleted
of Sn, as shown in Figure 4.1. The total length of the intermetallic/solder
interface and the length of the interface contacted by the Pb-rich phase were
measured using a digitizing tablet. The ratios of the area contacted by the Pb-
rich phase to the total interfacial area were calculated for various anneal
conditions and are listed in Table 4.10. For the eutectic solder before annealing,
the ratio was approximately 0.16. After annealing for 4 days at 160°C, this
ratio increased to approximately 0.9. This ratio did not increase after additional
annealing at 160°C. One explanation for this behavior is that at the start of
annealing, there is a large amount of Sn at the interface that can readily react
with the Cu. With continued annealing, the amount of immediately available Sn
decreases, creating a Sn concentration gradient in the solder and increasing the
91
ratio of Pb-rich phase contact area to total interfacial area. Subsequently, the
Sn supply at the interface becomes dependent on Sn diffusion through the
solder to the interface. At equilibrium, a Sn concentration gradient is formed in
the solder and the ratio of Pb-rich area to total interface area is approximately
constant over time.
The particles in the composite solders strongly affect the diffusion
behavior of Sn, and therefore affect Cu-Sn intermetallic formation at the
solder/copper substrate interface. The thicknesses of the intermetallic layers for
all seven samples in the as-soldered state and after annealing for 16 days at
140°C are shown in Figures 4.29 and 4.30. The measurements were performed
from SEM micrographs as previously described, except for the thicknesses of
the Cu3Sn layer before annealing which were measured from TEM micrographs.
One interesting feature of the data is that none of the particles, except Ni,
strongly affect the initial thickness of the Cu6Sn5 layer. However, after annealing
for 16 days at 140°C, trends are evident in both the Cu6Sn5 and Cu3Sn
thicknesses. The composite solders with Cu-containing and Fe particles all
reduce the Cu6Sn5 thickness and increase the Cu3Sn thickness with respect to
the eutectic solder. Ag, Au, Ni and Pd all reduce the amount of Cu3Sn at the
interface. The Fe and Pd samples will be discussed later.
As listed in Table 4.9, all of the Cu-containing particles increase the
activation energy for Cu6Sn5 formation, but reduce the activation energy for
Cu3Sn formation compared to eutectic solder. The Au and Ag composite
solders have smaller activation energy values for the formation of Cu6Sn5 and
Cu3Sn. The activation energy for the formation of Cu6Sn5 in the Ni composite
solder is very large and the activation energy for Cu3Sn formation can not be
92
determined because Cu3Sn is not always observed.
Intermetallic formation is a strong function of the activation energy: For
large values of Q, the temperature dependence is enhanced. Depending on the
D0 values and the initial intermetallic thicknesses, Cu6Sn5 can be the dominant
phase at low temperatures, but Cu3Sn can dominate at high temperatures. This,
in fact, is what is experimentally observed. For the short time soldering
sequences, the exposure to high temperature is minimal and the Cu6Sn5 is
preferentially formed. The formation of Cu3Sn is kinetically limited and may or
may not be observable using optical microscopy or SEM depending on the exact
soldering conditions used. During high temperature processing, however, more
Cu3Sn is formed than Cu6Sn5 (compared to the initial amounts) and both
intermetallics become observable. The TEM observations confirm this model,
since Cu3Sn is always observed in as-soldered samples, even though it is very
thin. Cu3Sn growth dominates at high temperature because its activation
energy is larger than that of Cu6Sn5.
Au and Ag composite solders have smaller Cu6Sn5 and Cu3Sn activation
energies than eutectic solder. The Cu3Sn is very thin after the initial soldering
operation (< 0.2 ixm) and it always remains thinner than the Cu6Sn5 layer, even
after high temperature and long time annealing. Au can rapidly diffuse by an
interstitial diffusion mechanism in the Sn matrix.26 During soldering, all the Au
particles in the solder matrix react completely with Sn to form AuSn4, thus
reducing the amount of Sn that is able to reach the solder/copper interface. The
initial thickness of Cu6Sn5 and Cu3Sn after soldering are thinner than for the
eutectic solder only sample and Cu-containing composite solder samples
(section 4.2). After soldering, the AuSn4 particles are distributed uniformly in
93
the solder matrix. (The microstructure of the solder matrix will be discussed in
chapter 5 in detail). Buene et al29 studied the room temperature diffusion of
Au/Sn thin film couples and found that Sn might diffuse through the Au-Sn
intermetallic very quickly via the grain boundaries. The diffusion coefficient of
Sn through Au-Sn intermetallic is about 105 larger than Sn self-diffusion. Figure
4.31 is a TEM micrograph which shows the Au composite solder matrix after
annealing at 140°C for 4 days. There are two AuSn4 particles in contact with
each other. Both AuSn4 grains contact the Sn-rich phase of the solder. These
phases were all identified using selected area electron diffraction patterns. The
AuSn4/AuSn4 grain boundary (labeled 1) and AuSn4/Sn phase boundary (labeled
2) are clearly visible. XEDS in STEM mode was used to determine the Sn/Au
ratios along the AuSn4/AuSn4 grain boundary and AuSn4/Sn phase boundary,
and these were compared to the Sn/Au ratios inside the AuSn4 phase, which
were measured 200 A away from the boundary toward the center of the AuSn4
grain. The results of these measurements are shown in Figure 4.32. The
average XEDS peak intensity ratio of Sn to Au at the boundaries is 2.3, much
larger than the average value of 1.1 inside the AuSn4 grains. This means that
the AuSn4 grain boundaries and the AuSn4/Au phase boundaries may act as
enhanced diffusion pathway for Sn. Since the Sn can diffuse easily along these
boundaries after soldering, the Sn supply to the solder/copper interface is
greater than for the eutectic solder only. The Sn moves via normal bulk
diffusion of the Sn in the areas without AuSn4, and via the much faster
boundary diffusion through AuSn4/AuSn4 grain boundaries and AuSn4/Au phase
boundaries. This enhances the Sn diffusion and reduces the activation energies
for the formation of both Cu6Sn5 and Cu3Sn at the Au composite solder/copper
94
interface compared to the eutectic solder only.
The difference between the Ag and Au composite solders is that all of
the Au particles react completely with Sn to form AuSn4, whereas the Ag
particles are not completely transformed to Ag3Sn during the soldering
operation. After soldering, both Ag and Ag3Sn particles occur in the solder
matrix. The remaining Ag particles may act as Sn-sinks. They remove Sn from
the solder and reduce the amount of Sn available for reaction at the substrate
interface. The Ag particles continue to react with the Sn until the terminal
phase Ag3Sn formed. The Sn-sink and enhanced diffusion through Ag3Sn/Ag3Sn
grain boundaries and Ag3Sn/Sn phase boundaries diffusion mechanisms are
competive processes. In the case of Ag composite solder, the increase in
boundary diffusion is dominant, and the overall effect is that the Cu6Sn5 and
Cu3Sn activation energies are smaller than for the eutectic solder, but larger
than for the Au composite solder.
Compared to eutectic solder alone, the Cu-containing particles all
increase the activation energy of Cu6Sn5 formation and, therefore reduce its
thickness. These particles also decrease the activation energy for Cu3Sn
formation and enhance its thickness. There are two possible mechanisms which
can occur in the solder matrices of these alloys. The Cu and Cu3Sn particles act
as Sn-sinks. They remove Sn from the solder and reduce the amount of Sn
available for reaction at the substrate interface. The particles continue to react
with the Sn until the terminal phase Cu6Sn5 is formed. Thus, the amount of Sn
that reaches the solder/copper substrate interface in a given period of time is
reduced.
However, this mechanism may not be the only way in which the
95
activation energies are affected. Sn-sinks do not explain why the presence of
Cu6Sn5 particles (the terminal phase) also alters the kinetic data. Cu6Sn5
particles do not directly react with the solder. It has been experimentally
verified that they do not change shape or phase with annealing, so it may be
assumed that they are chemically inert in Sn/Pb solder and do not act as Sn-
sinks. To investigate the effect of Cu6Sn5 particle additions on Sn diffusion, a
10 w t% Cu6Sn5 composite solder was fabricated. These samples were
annealed at 150°C for 0, 4, 16 and 32 days, and the Cu6Sn5 and Cu3Sn
intermetallics at the solder/copper interface were examined. Table 4.11 gives
the intermetallic thicknesses and diffusion coefficients at 150°C for both 10
w t% Cu6Sn5 composite solder and 20 wt% Cu6Sn5 composite solder. From
Table 4.11 it can be seen that all the intermetallic thicknesses of Cu6Sn5 and
Cu3Sn for the 20 wt% Cu6Sn5 composite solder/copper interface are thicker
than the corresponding thicknesses for 10 wt% Cu6Sn5 composite solder under
the same annealing conditions. Therefore, the diffusion coefficients are larger
for 20 wt% Cu6Sn5 composite solder than for 10 wt% Cu6Sn5 composite
solder. Since the Cu6Sn5 phase is the terminal phase in the system, the Cu6Sn5
phases do not react with Sn. The only difference between these two composite
solders is that there are more Cu6Sn5 particles in the 20 wt% Cu6Sn5 composite
solder and therefore there are more Cu6Sn5 grain and phase boundaries. These
boundaries enhance Sn diffusion. It is postulated here that enhanced boundary
diffusion exists in all-Cu containing composite solders. The values of the
activation energies in Cu-containing composite solders support this postulate.
20 wt% of intermetallic particles were added to the solder matrix for both the
Cu3Sn and Cu6Sn5 composite solders. Comparing these two composite solders,
96
the activation energy changes for 20wt % Cu3Sn composite solder are larger
than those for 20 wt% Cu6Sn5 composite solder compared to the eutectic
solder alone. For the 7.6 wt% Cu composite solder, since fewer particles were
added to the solder matrix, there are fewer boundaries that can enhance the Sn
diffusion, hence the changes in activation energy are smaller than for 20 wt%
Cu6Sn5 composite solder. Since Cu, Cu3Sn and Cu6Sn5 particles are larger than
the AuSn4 and Ag3Sn particles, the ratio of the areas of the Cu-containing
phase/Sn boundary are smaller than for the Au and Ag composite solders. Thus
the enhanced boundary diffusion effects are also smaller.
Intermetallic formation for the Ni composite solder is quite different than
for the other composite solders. Cu3Sn formation is almost completely
suppressed. The thickness of the Cu6Sn5 layer is increased over that observed
for the eutectic solder alone and other composite solders, but a substantial
fraction of the volume is void space.
One way of analyzing the activation energy data for the Ni composite
solder is to note that the activation energies for the formation of Cu3Sn and
Cu6Sn5 intermetallics are both greatly increased. Since Cu3Sn is not usually
observed, its activation energy may be assumed to have been raised to a very
large value. The activation energy for Cu6Sn5 formation is 1.58 eV, an increase
of 1.9 over that observed for the eutectic solder alone. It should also be noted
that the Ni particles are only 4 wt% of the composite solder, which makes their
effectiveness even more marked.
Ni acts as an extremely effective diffusion barrier making it difficult for
the Sn to diffuse into the Cu. The excess Sn on the solder side of the interface
makes the Sn-rich intermetallic phase favored, hence Cu6Sn5, the intermetallic
97
with the largest Sn/Cu ratio, is formed. During annealing, or even during
soldering, Ni from the added particles diffuses to the interface and blocks any
additional Sn from moving from the solder into the Cu. This effect is observed
in the in-situ thin film annealing experiments. Ni drastically inhibits intermetallic
formation when it is placed between the Cu and the Sn, and also when it is
placed on top of the Sn without direct contact with the substrate Cu. The voids
in the intermetallic layer, as shown in Figure 4.19, may be due to the
Kirkendahl Effect, that is, due to differences in the diffusivities of the two
species, Cu and Sn. The voids occur in the area where Cu mass transport is
greatest, closest to the Cu substrate. The Ni diffuses rapidly through the solder
via an interstitial mechanism to the interface where it prevents Sn diffusion.
However, Cu may not be prevented from diffusing through the Ni barrier layer
quite so effectively. Kirkendahl voids would be formed as the Cu closest to the
substrate diffuses to the solder and reacts with the Sn there to form Cu6Sn5.
This is consistent with the microstructural observation that there are Pb-rich
phases and Ni3Sn4 intermetallic phases inside the Cu6Sn5 interface layer (Figure
4.19) which means that Cu diffuses into the solder. This is also consistent with
the XEDS spectra inside the Cu6Sn5 interface layer where a small Ni peak is
observed.
There is an observed tendency that the thicknesses of the intermetallics
depart from the d proportional to t,/2 behavior, typically after high temperature
and long time annealing. It appears that it is the supply of Sn to the Cu
substrate which is in some way restricted. One possibility is the presence of
the voids at the intermetallic/copper substrate interface, as shown in Figure
4.19. Voids would limit the flow of the Sn into the Cu substrate. Another
98
possibility is that coarsening is occurring in the two intermetallic layers,
inhibiting the movement of Sn via grain boundaries since with coarsening the
ratio of the grain boundary areas to a given volume decreases. With TEM,
coarsening of the two intermetallic phases with annealing is observed, as
discussed in section 4.2. Another possibility is that the segregation of an
impurity to the grain boundaries of the intermetallic phases is limiting the rate
of reaction of the Sn, so that the system is no longer diffusion controlled. Lead
is one possible candidate, since no impurities were detected in this study.
4.7 Microstructures of Fe and Pd Composite solders
After comparing the equilibrium phase-diagrams30 and diffusion
characteristics of Cu-Sn with Fe-Sn, and of Ni-Sn with Pd-Sn (and many
others), the prediction was made that the microstructures of the intermetallic
interface at the solder/copper substrate should be similar for Fe and Cu-
containing additions, and similar for Ni and Pd composite solders. For example,
Fe, like Cu, forms a number of intermetallic phases with Sn. However, Pd
behaves more like Ni, forming a solid solution with Cu. Figure 4.33 shows the
interface of the Fe composite solder after annealing at 140°C for 4 days. Figure
4.34 shows the intermetallic interface of the Pd composite solder after
annealing at 140°C for 16 days. The similarities of the microstructures of the
Cu to the Fe, and the Ni to the Pd composite solders are striking, in keeping
with the predictions. Likewise, the intermetallic thickness data for Fe and Pd
composite solders, included in Figure 4.30, are similar to the Cu-containing
composites and Ni composite, respectively.
99
4.8 Summary and Conclusions of Chapter 4
During soldering, both Cu6Sn5 and Cu3Sn form at the solder/copper
substrate interface. The 77-phase Cu6Sn5 forms adjacent to the solder and the
e - p h a s e Cu3Sn is adjacent to the Cu substrate. Cu6Sn5 and Cu3Sn both increase
in thickness with increasing anneal time and temperature. The activation
energies for the formation of Cu6Sn5 and Cu3Sn at the interfaces of eutectic
solder and six types of composite solders/copper substrate were determined.
The growth of the intermetallic layers at the interface is strongly affected
by the particle type added to the solder. Cu-containing particle additions reduce
the thickness of Cu6Sn5 and increase the thickness of Cu3Sn. They increase the
activation energy for Cu6Sn5 formation and decrease the activation energy for
Cu3Sn formation compared to the eutectic solder alone. Ag and Au particles
decrease the activation energies for both Cu6Sn5 and Cu3Sn formation. Ni
particles drastically reduce the Cu3Sn thickness to near zero and increase the
thickness of Cu6Sn5. However, the Cu6Sn5 contains a substantial volume
fraction of voids close to the Cu substrate.
TEM was used to investigate the nanostrucutres of the eutectic and
composite solder/copper systems and the interfacial relationships among the
different phases. Studies of the intermetallic layers in TEM showed that the e-
phase has a columnar morphology while ij-phase has a rod like faceted
morphology. Cu3Sn was observable at the solder/copper interface in as-soldered
samples only by using TEM. It was not observable using SEM.
To determine the mechanisms of intermetallic formation at the
solder/copper interface and the effect of particle additions on intermetallic
growth, Cu/Sn, Cu/Sn/Ni, etc. thin film samples were annealed in the TEM in-
100
situ using a hot stage. For the Cu/Sn thin film sample, it was found that
intermetallic formation begins at the Sn/Cu boundary and progresses laterally
from the Sn into the Cu. It was also found that Ni may act as a barrier which
prevents Sn from diffusing into Cu, thus inhibiting Cu-Sn intermetallic
formation.
Based on the SEM and TEM studies and in-situ TEM thin film
observations, a Sn diffusion model and the Sn diffusion mechanisms affected
by particles in composite solders were proposed. The growth of Cu-Sn
intermetallics at the solder/copper substrate interface requires the diffusion of
Sn through Cu6Sn5 and Cu3Sn followed by reaction with Cu; Cu does not
diffuse into the solder to any appreciate extent.
There are two mechanisms which explain the effects of the particle
additions on the kinetics of intermetallic formation. First, the grain boundaries
of the intermetallic particles and the intermetallic particle/Sn phase boundaries
in the solder matrix may act as enhanced diffusion pathways for Sn, thus
increasing the Sn supply at the solder/copper interface. Second, the Cu, Cu3Sn
and Ag particles act as Sn-sinks which remove Sn from the solder and decrease
the amount of Sn available for reaction at the solder/substrate interface.
Ni is an extremely effective diffusion barrier which completely prevents
Sn from diffusing into Cu. The activation energy for Cu6Sn5 formation is
dramatically increased compared to the eutectic solder samples.
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109
Table 4.9 Activation Energies (eV) for Intermetallic Formation
for the Eutectic Solder and Composite Solders
Solder Alloy Type Cu6Sn5 Cu3Sn Solder Alloy Type
Q R2 Q R2
eutectic solder 0.84 0.98 1.63 0.96
7.6 wt% Cu 1.00 0.92 0.96 0.95
20 wt% Cu3Sn 1.31 0.99 0.81 0.94
20 wt% Cu6Sn5 1.23 0.94 0.91 0.94
4 wt% Ag 0.73 0.95 1.18 0.99
4 wt% Au 0.65 0.98 0.85 0.99
4 wt% Ni 1.55 0.92 N/A
110
Table 4.10 The Ratio of the Area Contacted by the Pb-rich Phase
to the Total Interfacial Area of the Solder/Cu Interface
Solder Type Anneal Condition Ratio
eutectic solder as-soldered 0.16 eutectic solder
4 days at 160°C 0.92
eutectic solder
8 days at 160°C 0.92
20 wt% Cu6Sn5 composite 4 days at 160°C 0.78 20 wt% Cu6Sn5 composite
8 days at 160°C 0.77
20 wt% Cu6Sn5 composite
16 days at 160°C 0.80
20 wt% Cu3Sn composite 4 days at 160°C 0.78 20 wt% Cu3Sn composite
8 days at 160°C 0.90
20 wt% Cu3Sn composite
16 days at 160°C 0.90
4 wt% Au composite as-soldered 0.24 4 wt% Au composite
4 days at 160°C 0.70
4 wt% Au composite
8 days at 160°C 0.74
111
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(a) SEM microstructure
Figure 4.1. (a) SEM microstructure and (b) XEDS spectra of eutectic
solder/copper substrate sample after annealing at 120°C for 32 days. (A) Cu
substrate, (B) Cu3Sn, (C) Cu6Sn5, (D) Pb-rich phase, and (E) Sn-rich phase.
113
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(b) XEDS Spectra
114
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(b) XEDS Spectra
115
m
s
(a) as-soldered
Figure 4.2. SEM microstructures of Cu composite solder/copper substrate
samples as a function of annealing time, (a) as-soldered state, (b) 120°C for 8
days, (c) 120°C for 64 days. The Cu6Sn5 layer is general thicker than the Cu3Sn
layer. A Cu particle is visible in (a) surrounded by Cu6Sn5. Another Cu particle
is visible in (b) surrounded by Cu3Sn and Cu6Sn5. The particle visible in (c) has
completely transformed to Cu6Sn5. (A) Cu substrate, (B) Cu3Sn, (C) Cu6Sn5, (D)
Pb-rich phase, and (E) Sn-rich phase.
116
(b) 120°C for 8 days
(c) 120°C for 64 days
117
(a) 120°C
Figure 4.3. SEM microstructures of Ag composite solder/copper substrate
samples as a function of annealing temperature, (a) 120°C, (b) 140°C and (c)
160°C for 32 days. The particles in the matrix are Ag and Ag3Sn. (A) Cu
substrate, (B) Cu3Sn, (C) Cu6Sn5, (D) Pb-rich phase, and (E) Sn-rich phase.
118
1
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(b) 140°C
(c) 160°C
119
(a) eutectic solder
Figure 4.4. SEM microstructures of the eutectic solder and composite
solder/copper substrate interfaces after annealing at 140°C for 16 days, (a)
eutectic solder, (b) 20 wt% Cu3Sn composite solder, (c) 20 w t% Cu6Sn5
composite solder, (d) 7.6 wt% Cu composite solder, (e) 4 w t% Au composite
solder, (f) 4 w t% Ag composite solder, and (g) 4 wt% Ni composite solder. The
particle additions affect the thicknesses and morphologies of the intermetallic
layers at the interface. (A) Cu substrate, (B) Cu3Sn, (C) Cu6Sn5, (D) Pb-rich
phase, and (E) Sn-rich phase.
120
t n i B i
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(b) 20 wt% Cu3Sn
(c) 20 wt% Cu6Sn5
121
15 5 0 8 i-St.
(d) 7.6 wt% Cu
(e) 4 wt% Au
122
(f) 4 wt% Ag
void
(g) 4 wt% Ni
123
Figure 4.5. TEM micrograph of a eutectic solder/copper joint after annealing at
140°C for 4 days. The copper, solder and intermetallic phases are all visible. (A)
Cu substrate, (B) Cu3Sn, (C) Cu6Sn5, (D) Pb-rich phase, and (E) Sn-rich phase.
124
(a) Cu6Sn6
(b) Cu3Sn
TMWMlif
(c) Cu
Figure 4.6. Selected area diffraction patterns of the (a) Cu6Sn5, (b) Cu3Sn, and
(c) copper phases in Figure 4.5.
125
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126
(a) TEM, Cu3Sn composite, as-soldered, low magnification
Figure 4.8. TEM micrograph of the as-soldered Cu3Sn composite solder/copper
joint, (a) low magnification and (b) higher magnification. (A) Cu substrate, (B)
Cu3Sn, (C) Cu6Sn5, (D) Pb-rich phase, and (E) Sn-rich phase.
127
a s s y s s a
(b) TEM, Cu3Sn composite, as-soldered, higher magnification
128
(a) TEM, Cu6Sn5 composite, as-soldered, low magnification
Figure 4.9. TEM micrograph of the as-soldered Cu6Sn5 composite solder/copper
joint, (a) low magnification and (b) higher magnification. (A) Cu substrate, (B)
Cu3Sn, (C) Cu6Sn5, (D) Pb-rich phase, and (E) Sn-rich phase.
129
(b) TEM, Cu6Sn5 composite, as-soldered, higher magnification
130
«
Figure 4.10. TEM micrograph of the as-soldered Cu composite solder/copper
joint. (A) Cu substrate, (B) Cu3Sn, (C) Cu6Sn5< (D) Pb-rich phase, and (E) Sn-rich
phase.
131
2
hi frj "Ji WW,
Mum J';,- •' /I;. ; :w'y my/
Figure 4.11. TEM micrograph of the as-soldered Ag composite solder/copper
joint. (A) Cu substrate, (B) Cu3Sn, (C) Cu6Sn5, (D) Pb-rich phase, and (E) Sn-rich
phase.
132
'¥ # v f / ; * q f . / M
d ?.. u'fzvfr&i
Figure 4.12. TEM micrograph of the as-soldered Au composite solder/copper
joint. (A) Cu substrate, (B) Cu3Sn, (C) Cu6Sn5, (D) Pb-rich phase, and (E) Sn-rich
phase.
133
r J %
Figure 4.13. TEM micrograph of the as-soldered Ni composite solder/copper
joint. (A) Cu substrate, (C) Cu6Sn5, (D) Pb-rich phase, and (E) Sn-rich phase.
134
mKMMm •Vt l ; ,if' I ih'rJ . > , \ \ I- • . - 1 , X f | ? J ; i . ! . - 1 | i I . .V J t / ' J>i •', •
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Cu6Sn5/Cu3Sn interface
Figure 4.14. TEM micrograph of Cu composite solder/copper joint after
annealing at 140°C for 4 days. (A) Cu substrate, (B) Cu3Sn, (C) Cu6Sn5, (D) Pb-
rich phase, and (E) Sn-rich phase.
135
Cu6Sn5/Cu3Sni interface
m
i
S s f i
Figure 4.15. TEM micrograph of Cu3Sn composite solder/copper joint after
annealing at 140°C for 4 days. (A) Cu substrate, (B) Cu3Sn, (C) Cu6Sn5, (D) Pb-
rich phase, and (E) Sn-rich phase.
136
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f
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f - c . _ ^ • Vvr,
Figure 4.16. TEM micrograph of Ag composite solder/copper joint after
annealing at 140°C for 4 days. (A) Cu substrate, (B) Cu3Sn, (C) Cu6Sn5, (D) Pb-
rich phase, and (E) Sn-rich phase.
137
m
J
Figure 4.17. TEM micrograph of Ni composite solder/copper joint after
annealing at 140°C for 8 days. (A) Cu substrate, (B) Cu3Sn, (C) Cu6Sn5> (D) Pb-
rich phase, and (E) Sn-rich phase.
138
J f Z J I J 2 S ! t r *
microvoids
Figure 4.18. SEM micrograph of Au composite solder/copper joint after
annealing at 120°C for 64 days. Microvoids are present along the
intermetallic/copper substrate interface (indicated by the arrors). The Cu3Sn is
partially transformed to Cu6Sn5. (A) Cu substrate, (B) Cu3Sn, (C) Cu6Sn5, (D)
Pb-rich phase, and (E) Sn-rich phase.
139
IB
(a) 120°C, 32 days
Figure 4.19. SEM micrographs of a Ni composite solder/copper joint, (a)
annealed at 120°C for 32 days and (b) annealed at 160°C for 16 days. (A) Cu
substrate, (B) Cu3Sn, (C) Cu6Sn5, (D) Pb-rich phase, (E) Sn-rich phase, (F) voids,
(G) Ni, and (H) Ni3Sn4.
140
(b) 160°C, 16 days
141
8
E 3 CO CO 0 c o 'sz
D(Cu6Sn5) = 3.98 x 10"1 cm 2/s
D(Cu3Sn) = 1.49x10~1/bm /s
500 1000 1500 2000 2500
Square Root of Annealing Time (sec1/2)
3000
Figure 4.20 Intermetallic thicknesses at the solder/copper interface versus the
square root of aging time for eutectic solder at 140°C. The slope of the line is
the square root of the diffusion coefficient.
142
E 3
D(CueSn^ = 2.09 x 101 cm2/s
D(CUjjSn) = 0.90 x 1014cm2/s
500 1000 1500 2000 2500 3000
Square Root of Annealing Time (sec1/2)
Figure 4.21 Intermetallic thicknesses at the solder/copper interface versus the
square root of aging time for Cu composite solder at 120°C. The slope of the
line is the square root of the diffusion coefficient.
143
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°
-
- Q(Cu3Sn) = 0.96 eV/atom
I I •
I 2.3 2.4 2.5
1/T (x 1000)
2.6
Figure 4.22 Plots of ln(D) versus 1/T for Cu6Sn5 and Cu3Sn formation at the
solder/copper substrate interface of Cu composite solder. The slope of the line
is the activation energy.
144
Q c
Q(Cu6Sn5) = 0.65 eV/atom
Q(Cu3Sn) = 0.85 eV/atom
2.4 2.5
1/T (x 1000)
Figure 4.23 Plots of ln(D) versus 1/T for Cu6Sn5 and Cu3Sn formation at the
solder/copper substrate interface of Au composite solder. The slope of the line
is the activation energy.
145
(a) Cu
Figure 4.24. TEM micrographs of (a) Cu, (b) Sn, (c) Ni, (d) Ag, and (e) Au thin
films. The morphologies for each element are different.
146
(b) Sn
(c) Ni
147
(d) Ag
(e) Au
148
r * JPf
&itmm
(a) unaged
Figure 4.25. A time series of TEM micrographs of Sn islands on a continuous
Cu layer showing the Cu-Sn intermetallic growth, (a) unaged, (b) 250°C for 9
min, (c) 250°C for 18 min, (d) 250°C for 31 min, (e) 250°C for 32 min,
followed by at 200°C for 72 min, (f) 250°C for 32 min, followed by at 200°C
for 286 min, (g) 250°C for 32 min, followed by at 200°C for 703 min.
149
(b) 250°C, 9 min
150
(c) 250°C, 18 min
151
£
(d) 250°C, 31 min
152
(e) 250°C, 32 min + 200°C, 72 min
153
(f) 250°C, 32 min + 200°C, 286 min
154
(g) 250°C, 32 min + 200°C, 703 min
155
Sill
Figure 4.26. TEM micrograph of the Cu/Sn/Ni sample showing no intermetallic
growth after annealing at 250°C for 2 hours, followed by 200°C for 12 hours.
Ni was detected at the Sn/Cu interface. 1, 2 and 3 are the probe positions for
XEDS analysis.
156
0.2 c
CO
o
o o +5 CO
0) c £ (0 c
(0 a> a
0.1
Cu side interface 1 probe position
Figure 4.27. XEDS peak intensity ratios of Ni to Sn for the Cu/Sn/Ni sample.
t = 0
solder
Cu substrate
157
1 l<_ Cu3Sn
t > 0
solder
wmm
iau
CugSri
Cu substrate
Figure 4.28. Model for the growth of the two interfacial intermetallics.
158
E
(A <0 <D C
o
Cu3Sn Cu^n, Cu eutectic Au Ag
• CUgSn » C u ^ S n 5
Figure 4.29. The thicknesses of the iritermetallic layers at the solder/copper
substrate interface for eutectic solder and all composite solders in the as-
soldered condition.
159
8
E
<ft <0 d) c o
CU3S11 Cu6Sn5 Cu Fe eutectic Au Ag
•Cu3Sn flCueSns
Figure 4.30. The thicknesses of the intermetallic layers at the solder/copper
substrate interface for eutectic solder and all composite solders after annealing
at 140°C for 16 days. (Note scale change from Figure 4.29.)
160
Figure 4.31. TEM micrograph of the matrix of Au composite solder after
annealing at 140°C for 4 days. The AuSn4/AuSn4 grain boundary is labeled as
1 and AuSn4/Sn phase boundary is labeled as 2. (D) Pb-rich phase, (E) Sn-rich
phase and (F) AuSn4.
161
< o c
CO
o o CO cn
(O c a>
CO Q LU X
0
^ / Valong boundary /
—9T . _
I I
within AuSn4
i i i i i i I 4 5 6 7 8
Measurement Number
10 11
Figure 4.32. XEDS peak intensity ratio of Sn to Au along an AuSn4/AuSn4 grain
boundary and an AuSn4/Au phase boundary compared to the ratio within the
AuSn4.
162
Figure 4.33. SEM micrograph of 4 wt% Fe composite solder/copper joint
annealed at 140°C for 4 days. Compare Figure 4.33 and Figure 4.2b. There are
two intermetallics at the solder/copper interface in both micrographs. The Cu
particles are surrounded by Cu-Sn intermetallic. The Fe particles are surrounded
by Fe-Sn intermetallic. (A) Cu, (B) Cu3Sn, (C) Cu6Sn5, (D) Pb-rich, (E) Sn-rich
and (F) Fe.
163
Figure 4.34. SEM micrograph of 4 wt% Pd composite solder/copper joint
annealed at 140°C for 16 days. Compare Figure 4.34 and Figure 4.4h. There
is no Cu3Sn layer and voids occur at the solder/copper interface in both
samples. (A) Cu, (C) Cu6Sn5, (D) Pb-rich, (E) Sn-rich (F) voids, and (G) Pd-Sn
intermetallic.
CHAPTER 4 REFERENCES
1. D.S. Dunn, T.F. Marinis, W.M. Sherry and C.J. Williams, Mat. Res. Soc.
Symp. Proc. 40, 129 (1985).
2. P.E. Davis, M.E. Warwick and S.J. Muckett, Plating and Surface
Finishing, 70, 49 (1983).
3. Elemental and Interplanar Spacing Index, (U.S. Department of Commerce,
NIST and JCPDS International Center for Diffraction Data, 1989).
4. W.G. Bader, Welding Journal, 54, 370s (1975).
5. P.E. Davis, M.E. Warwick and S.J. Muckett, Plating and Surface
Finishing, 70, 49 (1983).
6. K.N. Tu, Acta Met., 21, 347 (1973).
7. D.A. Unsworth and C.A Mackay, Trans. Insts. Metal Finishing, 51, 85
(1973).
8. M.E. Warwick and S.J. Muckett, Circuit World, 9, 5 (1983).
9. E.G. Jacobs, L.A. Foster, Y. Wu, A.R. Wilson and R.F. Pinizzotto, J.
Mater. Res. 8, 87 (1993).
10. T. Malis and D. Steele, Mat. Res. Soc. Symp. Proc., 254, 257 (1992).
11. 0 .0 . Popoola, J.J. Copper, B.P. Jakstys and W.M. Kriven, Mat. Res.
Soc. Symp. Proc., 254, 271 (1992).
12. G.L. Lucey, J.L. Marshall, C. Handwerker, D. Tench and A. Sunwoo,
Proc. NEPCON WEST '91, 1, 3 (1991).
164
165
13. D.S. Dunn, T.F. Marinis, W.M. Sherry and C.J. Williams, Mat. Res. Soc.
Symp. Proc., 40, 129 (1985).
14. R.J.K. Wassink, Soldering in Electronics, 2nd Ed., (Electrochemical
Publications, Ltd., Scotland, 1989), Chapter 4.
15. K.N. Tu and R.D. Thompson, Acta Met., 30, 947 (1982).
16. P.W. Dehaven, Mat. Res. Soc. Symp. Proc., 40, 123 (1985).
17. P.J. Kay and C.A. Mackay, Trans. Inst. Metal Finishing, 54, 68 (1976).
18. W. G Bader, Welding Journal, 48, 551s (1969).
19. M. Omishi and A. Fujibuchi, Trans. JIM, 16, 539 (1972).
20. H. Oikawa and A. Hosoi, Scripta. Met., 9, 823 (1975).
21. P.J. Kay and C.A. Mackay, Trans. Inst. Metal Finishing, 57, 169 (1979).
22. D.C. Dufner, "Imaging of Chemical Reactions in Binary Alloys by High-
Resolution TEM", Presented at the Texas Society for Electron
Microscopy Symposium, San Marcos, TX, March 27, 1992.
23. C. Pouraghabagher, E.G Jacobs and R.F. Pinizzotto, "In situ
Transmission Electron Microscopy of Sn/Cu Intermetallic Formation",
Presented at the Texas Society for Electron Microscopy Symposium,
Austin, TX, October 22, 1992.
24. H.N. Keller, IEEE Trans. CHMT, 9, 433 (1986).
25. S. Nakahara, R.J. McCoy, L. Buene and J.M. Vandenberg, Thin Solid
Films, 84, 185 (1981).
26. B.F. Dyson, J. Appl. Phys. 37, 2375 (1966).
27. D.C. Yeh and H.B. Huntington, Phys. Rev. Lett., 53, 1469 1984.
166
28. L. Buene, H. Falkenberg-Arell and J. Tafto, Thin Solid Films, 65, 247
(1980).
29. S. Nakahara, R.J. McCoy, L. Buene and J.M. Vandenberg, Thin Solid
Films, 84, 185 (1981).
30. Metals Handbook 8th Ed., Vol. 8, Metallograph, Structures and Phase
Diagrams, (American Society for Metals, Metala Park, OH, 1973).
CHAPTER 5
THE MATRIX OF
EUTECTIC AND COMPOSITE SOLDERS
5.1 Introduction
The reliability of solder joints often depends directly on the mechanical
properties of the solder alloy. The mechanical properties of metals and alloys
depend on their microstructures and solder alloys are no exception. The
behavior of solder alloys is complex because unlike most structural alloys, they
are used at such high temperature relative to the melting temperature that the
microstructures change and evolve during service. Application conditions that
involve thermal cycling may produce cyclic microstructural evolution, depending
on the temperatures and frequencies involved.
The elements of the microstructure that are typically important are the
grain size and shape, the spacing of second phase particles, and the dislocation
density. In eutectic solders the grain size and the second-phase size and
spacing are directly related because at least two phases are always present. In
this chapter, the as-soldered eutectic and composite solder microstructures and
their evolution during annealing are reported. The study concentrates on a
fundamental understanding of the microstructure of the solder matrix and its
dependence on processing, solidification and annealing. The particles in the
composite solder matrix, their reaction with the solder, and their effect on Sn
diffusion are also discussed.
167
168
The samples were prepared as described in Chapter 3. The standard
solidification cooling rate is the same for all samples, and is the same as that
used in the study of intermetallic layers at the solder/copper substrate interface.
The relationship of the matrix microstructure of as-soldered eutectic solder
samples with the cooling rate was also examined.
5.2 The Microstructure of Eutectic Solder
SEM and TEM micrographs of the eutectic solder matrix in the as-
soldered state are shown in Figure 5.1. The eutectic solder consists of two
phases. In the SEM micrograph*of Figure 5.1a, the Sn-rich phase appears dark
and the Pb-rich phase appears light. The matrix has a uniform globular
microstructure and does not show a lamellar or colony structure. The volume
ratio of the Pb-rich phase to Sn-rich in the eutectic 63Sn/37Pb solder is about
27:73.1 In the TEM micrograph of Figure 5.1b, the darker contrast Pb-rich
phase completely resides within the Sn-rich phase. Upon solidification at the
eutectic temperature, 19 wt% Sn is soluble in the Pb-rich phase2,3 and 2.5 wt%
Pb is soluble in the Sn-rich phase.4 On cooling to room temperature the
solubility drops to about 1 wt% Sn5 and less than 0.4 wt% Pb6 in the Pb-rich
phase and Sn-rich phase, respectively. The microstructure of eutectic solder is
highly dependent on the processing the alloy has received.7 The relationship
between the microstructure and the solidification cooling rate of eutectic solder
will be discussed in next section. At the standard cooling rate used throughout
the work, the typical microstructure is as in Figure 5.1. The selected area
diffraction pattern (SADP) of these phases are shown in Figure 5.2. The d-
spacings of the SADPs in Figures 5.2a and 5.2b match the d-spacing values
169
given in the literature8 to within 1 % for fcc-Pb and /?-Sn, respectively. These
phase identifications were also verified using x-ray energy dispersive
spectroscopy (XEDS) in both SEM and STEM modes. In contrast to the results
of Frear et al.9,10 the Sn was not found to precipitate out in the Pb-rich regions
of the matrix.
The microstructure of a two-phase alloy is unstable if the total interfacial
free energy is not minimized. If the alloy is held at a temperature where
diffusion can occur, small particles will coarsen into larger particles with a
smaller total interfacial area through a continuous, diffusion-controlled process.
However, such coarsening often produces undesirable degradation of
mechanical properties such as strength.11 As with grain growth, the rate of
coarsening increases with temperature and is of particular concern in the design
of materials for high temperature applications.
The effect of anneal time and temperature on coarsening of eutectic
solder was studied using both SEM and TEM. Figure 5.3 shows the matrix of
eutectic solder after annealing at 140°C for 8 days. The grains in the Sn-rich
region can be distinguished easily and each Pb-rich region appears to be a
single grain. While Sn-rich grains are regular in shape, the Pb-rich phase
becomes elongated and more irregular with annealing. Comparing Figures 5.1a
and 5.3, it is clear that the grain size increases with annealing. The average
grain sizes for the Sn-rich and Pb-rich regions increase from 0.5 fxm and 1 jum
in the as-soldered state to 1 jum and 3 jinn after annealing at 140°C for 8 days.
Figure 5.4 shows the average grain size of the Pb-rich phase as a function of
annealing time at 140°C.
For the as-soldered eutectic solder sample, a phase with bright contrast,
170
as shown in Figure 5.5a, was observed using TEM. The SADP of this phase is
shown in Figure 5.5b. XEDS spectra verify that this phase contains Pb. The
SADP in Figure 5.5b is characterized by broad rings. Ring broadening is typical
of amorphous or nanocrystalline materials. It is a totally unexpected result to
find an amorphous Pb-rich phase, because both the Pb-rich and Sn-rich phases
must solidify from the liquid as the sample cools. Since XEDS used here cannot
detect light elements (Z < Na), it cannot distinguish between metallic Pb and
Pb oxides. To identify the amorphous phase, eutectic solder samples in the as-
soldered state were sent to Oakridge National Laboratory and analyzed by Dr.
Mary McGivers using electron energy loss spectrascopy which can detect 0 .
The results showed that the amorphous areas are much thinner than the non-
amorphous areas (Sn-rich phase and crystalline Pb-rich phase), and contain lead
and oxygen. The existance of the very thin Pb oxide phase may due to
preferential removal of the Pb during the TEM sample preparation process of
ultramicrotomy, followed by the oxidation of the remaining thin Pb phase.
Alternatively, the Pb-rich phase may be totally removed from the sample leaving
the native PbO behind. To exam whether or not the Pb-rich phase can oxidize
easily, as-soldered eutectic solder samples were also prepared by
electropolishing and mechanical polishing followed by ion milling. Although the
quality of the samples prepared using these techniques were not as good as
those prepared by ultramicrotomy, broad ring diffraction patterns were still
obtained. These results confirmed that the Pb-rich phase can be oxidized very
easily.
171
5.3 Eutectic Microstructures in the as-Soldered State
A central principle of materials science states that a material's properties
originate not only from its atomic composition but also from the atomic
arrangements within the material i.e. the material microstructure. However, for
a material of a given chemical composition, the microstructure is not static but
can vary greatly with its processing history. In the case of solder, the
application dictates its use in the as-soldered state, and hence, the cooling rate
of the alloy is the primary processing parameter. The local cooling rates of a
solder joint depend on many factors, including the soldering process, the
specific solder joint thickness and geometry, the composition and configuration
of the carrier board, and the neighboring components.11 To understand the
effect of cooling rate on solder joint microstructure, the microstructures of
samples with a simple configuration of copper/eutectic solder/copper with
different cooling rates (described in Chapter 3) were studied.
In the case of the fastest cooling rate, there is preferentially oriented,
plane-front, steady-state growth. The eutectic Sn/Pb solder grows as
alternating lamellae of the two constituent phases parallel to the direction of
growth. Eutectic solidification is a cooperative growth process since the solute
rejected ahead of one phase region becomes immediately incorporated as the
solvent phase in the adjacent region, and the planes thus grow at the same
rate.11 Many lamellae constitute a lamellar grain. They will continue to grow in
a coupled manner until they contact an external interface or a similar grain. The
eutectic lamellar microstructure is shown in Figure 5.6. The lamellar spacing
within the eutectic grain is determined by the cooling rate. A fast cooling rate
results in fine lamellae. For a multigrained structure, the eutectic grains will be
172
smaller and the lamellar spacing within each grain will be finer with faster
cooling rates.12,13,14 The important microstructural parameters in this structure
are the eutectic grain size and the internal fine phase structure.
With this morphology, many individual phase regions, i.e., the lamellae,
constitute a single eutectic grain. Within a eutectic grain, all regions of the
same phase exhibit a single constant crystallographic orientation, and there is
a unique preferred crystallographic interface plane between the two constituent
phases.14,15,16,17,18 The lamellar grain described above is composed, in fact, of
single crystallites of the two constituent phases.18,19,20,21 The crystallographic
relationships for the two phases minimize the growth and interfacial energies
for a given set of solidification conditions. The stability of the liquid-solid
interface determines the inter- and intraphase crystallographic and
morphological perfection.15,16,17,18
A breakdown of the lamellar structure results from instabilities in the
advancing liquid-solid interface. The resultant morphology may be rod-like, or
globular (degenerate lamellar). It lacks the long-range perfection of the regular
lamellar structure.17 Interface instabilities arise from growth along unfavorably
oriented growth directions, local supercooling effects, etc.16,17,18 Solidification
under such conditions results in discontinuities and faults of the individual
phase regions and phase interfaces that disrupt the continued growth of the
aligned lamellar structure. Instead, as shown in Figure 5.7, only a short-range
phase alignment is maintained and a colony substructure develops within a
eutectic grain. A colony is a subset of a eutectic grain and is characterized as
a short-range phase alignment over a small region of the eutectic grain
separated from other eutectic colonies by a small crystallographic mismatch.11
173
The colony structure lacks the structural perfection of the lamellar eutectic,
especially at the colony boundaries. However, it does maintain a special and
unique crystallographic alignment with the growth direction and, as much as
possible, between the two constituent phases.
A different microstructure is obtained for moderate cooling rate samples,
(Figure 5.1b). Eutectic colony formation is suppressed and the microstructure
consists of a dispersion of the Pb-rich phase in a Sn-rich matrix. The phase size
and shape distribution are uniform throughout the entire specimen. Unlike the
lamellar grain structure described above, there is no crystallographic relationship
between the two phases.
When the slowest solidification cooling rate is used, as described in
Chapter 3, the amorphous Pb oxide phases are observed. This implies that the
sample preparation artifact of Pb removal by ultramicrotomy occurs more easily
when the solder/copper joint solidifies slowly.
Describing a eutectic microstructure is not straightforward. Unlike a
single-phase material, grain size is not readily apparent. Much of the published
work on solder microstructures uses the phase diameter (i.e., the average
diameter of a phase region in a two dimensional section) as the grain size. The
phase diameter may not be a true grain at all. Figure 5.8 is a dark field image
of a moderate cooling rate sample. The Pb-rich regions are embedded within the
Sn-rich phase. By definition, a grain refers to an element of a material within
which a single crystallography exists. In a eutectic structure, many individual
phase regions may constitute a single "eutectic grain". The terms that apply to
eutectic microstructures include the eutectic grain, the eutectic colony, and the
individual phase regions. The eutectic grain refers to that portion of the
174
structure that nucleated at a single site and that shares a specific and unique
crystallography. The eutectic colony may be a subset of a eutectic grain and
refers to a region within the microstructure where the phase particles have a
characteristic arrangement.12
The coarsening behavior of as-soldered eutectic solders varies
significantly with the various morphologies. The perfect lamellar structures
exhibit exceptionally high morphological stability at elevated temperatures.22,23
This contrasts greatly with the rapid coarsening of the more dispersed
structures and the irregularly shaped material which comprises the colony
boundaries. Coarsening always initiates in these less regular regions and very
slowly consumes the rest of the material. This is attributed to the higher
interfacial energies of the less favorably aligned structures and the enhanced
diffusion afforded by the greater fault and grain boundary areas.12
5.4 The Microstructures of Composite Solders
5.4.1 The Matrix of Cu-Containing Composite Solders
SEM microstructures of the Cu, Cu3Sn and Cu6Sn5 composite solder
matrices in the as-soldered state are shown in Figures 5.9a, 5.9b and 5.9c,
respectively. The copper particles (Figure 5.9a) and Cu3Sn particles (Figure
5.9b) are surrounded by a layer of Cu6Sn5. The TEM micrograph in Figure 5.10
shows the interfacial region between a copper particle and the solder of the Cu
composite solder in the as-solddred state. Similar to the interfacial layers
between the solder and copper substrate, two intermetallic layers, Cu3Sn and
Cu6Sn5, are visible between the copper particle and the solder matrix.
SEM microstructures of the Cu, Cu3Sn, and Cu6Sn5 composite solder
175
matrix after annealing at 140°C for 16 days are shown in Figures 5.11a, 5.11b,
and 5.11c, respectively. With annealing, the Cu and Cu3Sn particles react with
Sn to form Cu-Sn intermetallics. If the anneal time is long enough and large
amounts of Sn are present (as is the case of the samples used in these
experiments), the particles completely transform to the thermodynamically
favored terminal phase Cu6Sn5. In the Cu composite solder, the thicknesses of
the intermetallics surrounding the Cu particles are relatively constant,
independent of the particle size. The intermetallic thicknesses were measured
using the same computerized digitization technique as used for measuring the
intermetallic thicknesses at the solder/copper substrate interfaces. Table 5.1
compares the thicknesses of the Cu3Sn and Cu6Sn5 layers around the copper
particles with the intermetallic thicknesses at the solder/copper substrate
interface for Cu composite solder annealed at 140°C. It was found that the
thicknesses of Cu6Sn5 and Cu3Sn at the solder/copper particle interface after
annealing at 140°C for 0 (the as-soldered state), 4, 8 and 16 days are larger
than the corresponding thicknesses at the solder/copper substrate interface.
Therefore, the diffusion coefficient is larger at the solder/copper particle
interface than at the solder/copper substrate interface. The diffusion of Sn
through Cu6Sn5 and Cu3Sn followed by reaction with Cu must occur for
intermetallic formation and growth to take place. Copper particles (or other
metallic/intermetallic particles) are distributed uniformly in the composite solder
matrix and are surrounded by the solder. The pathways for the Sn to diffuse to
the copper particles are shorter than to the solder/copper substrate interface.
Thus the Sn flux at the solder/copper particle interface is greater than at the
solder/copper substrate interface. This is consistent with the diffusion
176
mechanism proposed for the formation and growth of Cu6Sn5 and Cu3Sn
interfacial layers presented in Chapter 4. Table 5.2 compares the thicknesses
of the Cu6Sn5 layer around the Cu3Sn particles with the Cu6Sn5 thicknesses
around the copper particles and at the solder/copper substrate interfaces for Cu
and Cu3Sn composite solders after annealing at 140°C. The thickness of the
Cu6Sn5 layer around the Cu3Sn particles is larger than that around the Cu
particles or at the solder/copper substrate interface. This is because of the Sn
reacts with the Cu3Sn phase directly and transforms it to Cu6Sn5. It is not
necessary to transform Cu to Cu3Sn first. This observationt is also consistent
with the proposed diffusion mechanism.
With annealing, the Cu particles react with the Sn. After the
consumption of all the Cu, the Sn reacts with Cu3Sn until it is all transformed
into Cu6Sn5. In the Cu3Sn composite solder, Cu3Sn reacts with the Sn to form
Cu6Sn5 directly. Both Cu and Cu3Sn particles act as Sn-sinks. They remove Sn
from the matrix which reduces the amount of Sn that diffuses to the
solder/substrate interface. This is one mechanism that causes the change in
activation energies for the formation of Cu6Sn5 and Cu3Sn at the solder/copper
substrate interface in Cu and Cu3Sn composite solders compared to the
eutectic solder alone.
Since Cu6Sn5 is the thermodynamically favored terminal phase, the
Cu6Sn5 particles in the Cu6Sn5 composite solder do not react with the Sn as the
Cu and Cu3Sn particles do. With annealing, the Cu6Sn5 particles remain the
same, as shown in Figures 5.9c and 5.11c, except possibly for a small amount
of coalescence. These Cu6Sn5 particles, therefore, do not react with Sn to any
appreciable extent. As discussed in Chapter 4, the Cu6Sn5/Cu6Sn5 grain
177
boundaries (labeled 1 in Figure 5.12) and Cu6Sn5/Sn phase boundaries (labeled
2 in Figure 5.12) enhance the Sn diffusion in the solder matrix.
5.4.2 The Matrices of Au and Ag Composite Solders
Figures 5.13a and 5.13b are SEM micrographs of the Au composite
solder matrix in the as-soldered state and after annealing at 140°C for 16 days.
The gray contrast, needle-like structures are AuSn4 intermetallic. Dyson et
a l 24,25,26 studied the diffusion of noble metals in Sn and Pb, and found that Au
impurities diffuse rapidly in Sn by an interstitial mechanism. Since Sn self-
diffuses via vacancy diffusion, the diffusivities of Au diffusing in Sn and Sn
self-diffusion are very different. At 140°C, the Au diffusivity is on the order of
10"7 cm2/sec,24 while the diffusivity of Sn is on the order of 10"12 cm2/sec.27
During soldering Au rapidly diffuses through the solder matrix and reacts with
Sn to form AuSn4 intermetallic. In the as-soldered state, the Au particles have
completely transformed into AuSn4. AuSn4 phase is the terminal phase in this
system according to the Au-Sn phase diagram.28 With additional annealing, the
AuSn4 does not react with the Sn or Pb. As discussed in Chapter 4, XEDS in
STEM mode revealed that there were enhanced diffusion pathways for Sn along
the AuSn4/AuSn4 grain boundaries and AuSn4/Sn phase boundaries.
The matrices of the Ag composite solder in the as-soldered state and
after annealing at 140°C for 16 days are shown in Figures 5.14a and 5.14b.
The Ag particles react with Sn to form Ag3Sn intermetallic during the soldering
operation and with annealing. The rates for the formation of the Cu-Sn, Au-Sn
and Ag-Sn intermetallics are: Au-Sn > Ag-Sn > Cu-Sn. The Ag and Ag3Sn
particles have almost the same contrast in the SEM and can be distinguished
178
only by XEDS analysis. In addition, the Ag and Ag3Sn particles appear similar
in the TEM, but have different SADPs. The particles shown in Figures 5.14a
and 5.14b are Ag and Ag3Sn. With annealing more and more Ag particles
transform into Ag3Sn.
5.4.3 The Matrix of the Ni Composite Solder
Figures 5.15a and 15b are SEM micrographs of the Ni composite solder
matrix in the as-soldered state and after annealing at 140°C for 16 days. In the
as-soldered state, the Ni particles are surrounded by a layer of Ni3Sn4. A TEM
micrograph of a Ni particle surrounded by Ni3Sn4 is shown in Figure 5.16. The
Ni3Sn4 phase was identified by XEDS in the SEM and by SADP in the TEM.
While the Ni3Sn4 layer in the as-soldered state is thicker than the Cu6Sn5 layer
surrounding the Cu particles in Cu composite solder (Figure 5.9a), the
subsequent growth of Ni3Sn4 around the Ni particles is similar to the growth of
Cu6Sn5 around the Cu particle. With soldering and annealing, the Ni reacts with
the Sn until the Ni transforms completely to the terminal phase Ni3Sn4. As
discussed in Chapter 4, during soldering Ni diffuses extreme quickly in Sn by
an interstitial mechanism29 to the solder/copper substrate interface and stays
there. This Ni barrier layer inhibits the Sn from reaching the copper substrate
and thus prevents the Sn from reacting with Cu to form Cu-Sn intermetallic.
5.4.4 The Pb-Rich and Sn-Rich Phases in Composite Solder
The metallic or intermetallic particles added to the composite solders are
distributed in the solder matrix and are imbedded in the Pb-rich and Sn-rich
regions. As shown in Figure 5.12, a TEM micrograph of the Cu6Sn5 composite
179
solder matrix in the as-soldered state, the morphology and the size of the Pb-
rich and Sn-rich regions in composite solders are the same as in the eutectic
solder matrix. In as-soldered state, all the composite solder matrices have a
uniform globular microstructure (Figure 5.9, 5.13a, 5.14a and 5.15a), except
for Cu6Sn5 composite solder which has a two phase eutectic lamellar
microstructure due to a different local solidification cooling rate. The coarsening
behavior of the composite solder matrices are same as that of the eutectic
solder matrix. The coarsening rates are also similar. As shown in Figure 5.11,
5.13b, 5.14b and 5.15b, the sizes of the Pb-rich and Sn rich regions in
composite solders after annealing at 140°C for 16 days are not significantly
different for the in eutectic solder. In addition, precipitation of metallic or
intermetallic particles within the solder phases, or Sn precipitation within the
Pb-rich regions were not observed.
5.5 Summary and Conclusions of Chapter 5
The eutectic solder matrix consists of two phases, Pb-rich and Sn-rich.
The matrix has a uniform globular microstructure in the as-soldered state and
no precipitation was found within the Pb-rich or Sn-rich regions or along the
grain boundaries.
With high temperature and long time annealing, the two solder phases
coarsen. The sizes of the Pb-rich and Sn-rich regions increase with time, and
the rate of coarsening increases with temperature.
An amorphous Pb oxide phase was observed in the eutectic and
composite solder matrices. The existance of this phase may due to removal of
the Pb during the ultramicrotomy used for TEM sample preparation.
180
The microstructure of solder matrix in the as-soldered state is related to
the solidification cooling rate. With faster cooling, the eutectic Sn/Pb solder
grows as alternating lamellae of the two constituent phases. With slower
cooling, the eutectic solder matrix forms a dispersion of Pb-rich regions in the
Sn-rich matrix. This microstructure is uniform in phase size and shape.
The Cu and Cu3Sn particles in the Cu and Cu3Sn composite solders react
with Sn until all Cu and Cu3Sn particles transform into the terminal phase
Cu6Sn5. The particles act as Sn-sinks which remove Sn from the solder. The
formation and growth of Cu-Sn intermetallics at the solder/copper particle
interface are similar to that at the solder/copper substrate interface.
Cu6Sn5 is the terminal intermetallic phase. Cu6Sn5 particles in the Cu6Sn5
composite solder do not react with the solder. The Cu6Sn5/Cu6Sn5 grain
boundaries and Cu6Sn5/Sn phase boundaries may enhance the Sn diffusion to
the solder/copper substrate interface.
Au diffuses rapidly in solder via an interstitial mechanism. During
soldering, all Au particles react completely with Sn and form the terminal
intermetallic phase AuSn4. The AuSn4/AuSn4 grain boundaries and AuSn4/Sn
phase boundaries act as enhanced diffusion pathways for Sn.
During soldering and with annealing, Ag reacts with Sn to form Ag3Sn
in Ag composite solder.
Ni can diffuse rapidly to the solder/copper substrate interface where it
acts as barrier layer and inhibits Sn diffusion. Ni also reacts with Sn to form
Ni3Sn4 in the Ni composite solder.
The morphology and the sizes of the Pb-rich and Sn-rich regions in the
composite solders are similar to those of the eutectic solder matrix. The
181
coarsening behavior of the Pb-rich and Sn-rich phases are not affected by the
particle additions in the composite solders.
182
Table 5.1. Thicknesses (ji/m) of Cu6Sn5 and Cu3Sn layers
at the Solder/Copper Particle Interface and Solder/Copper Substrate Interface
for 7.6 wt% Cu Composite Solder Annealed at 140°C
Intermetallic Position Anneal Time (days) Intermetallic Position
0 4 8 16
Cu6Sn5 around copper
particle
1.01 2.00 2.64 4.93 Cu6Sn5
at solder/copper
interface
0.96 1.64 2.19 3.61
Cu3Sn around copper
particle
0 1.83 2.20 2.83 Cu3Sn
at solder/copper
interface
0 0.82 1.37 2.46
183
Table 5.2. Thicknesses (//m) of Cu6Sn5 Layers After Annealing at 140°C
Position Anneal Time (days) Position
0 4 8 16
around Cu3Sn particles 0.90 3.17 7.82 11.48
around Cu particles 1.01 2.00 2.64 4.93
at Cu3Sn composite solder/copper
substrate interface
0.98 1.65 2.23 2.58
at Cu composite solder/copper
substrate interface
0.96 1.64 2.19 3.61
184
(a) SEM
Figure 5.1. (a) SEM and (b) TEM microstructures of the eutectic solder matrix
in the as-soldered state. (A) Pb-rich phase and (B) Sn-rich phase.
185
(b) TEM
186
(a) Pb-rich phase
(b) Sn-rich phase
Figure 5.2. Selected area diffraction patterns (SADP) of (a) Pb-rich phase and
(b) Sn-rich phase.
187
Figure 5.3. SEM microstructure of the eutectic solder matrix after annealing at
140°C for 8 days. (A) Pb-rich phase and (B) Sn-rich phase.
188
E 5
c o
" 5 > a> 2 4
sz o "C • JQ 0.
a> N CO
0 as-soldered 4 days 8 days
Anneal time
16 days
Figure 5.4. The size of the Pb-rich phase of eutectic solder as a function of
anneal time at 140°C.
189
(a) TEM micrograph
(c) SADP
Figure 5.5. (a) TEM microstructure of eutectic solder matrix in the as-soldered
state shows the amorphous Pb oxide phase and (b) SADP of Pb oxide phase.
(A) Pb oxide phase and (B) Sn-rich phase.
190
Figure 5.6. TEM microstructure of eutectic solder matrix after solidification with
fast cooling rate shows a highly lamellar structure. The dark regions are the Pb-
rich phase and the light regions are the Sn-rich phase.
191
Figure 5.7. TEM microstructure of eutectic solder matrix after solidification with
fast cooling rate may show a colony structure. The dark regions are the Pb-rich
phase and the light regions are the Sn-rich phase.
192
Figure 5.8. Dark field TEM micrograph of eutectic solder matrix after
solidification with moderate cooling rate. The Sn-rich grains are clearly visible.
193
(a) Cu
Figure 5.9. SEM microstructures of (a) Cu, (b) Cu3Sn and (c) Cu6Sn5 composite
solder matrix in the as-soldered state. (A) Pb-rich phase, (B) Sn-rich phase, (C)
Cu, (D) Cu6Sn5 and (E) Cu3Sn.
194
(b) CiuSn
(c) CugSrig
195
Figure 5.10. TEM micrograph of Cu composite solder matrix in the as-soldered
state shows the a particle and surrounding Cu-Sn intermetallics.
196
(a) Cu
Figure 5.11. SEM microstructures of (a) Cu, (b) Cu3Sn and (c) Cu6Sn5
composite solder matrix after annealing at 140°C for 16 days. (A) Pb-rich
phase, (B) Sn-rich phase, (C) Cu, (D) Cu6Sn5 and (E) Cu3Sn.
197
(b) Cu3Sn
(c) CiigSrig
198
m
Figure 5.12. TEM micrograph of Cu6Sn5 composite solder matrix in the as-
soldered state. Cu6Sn5/Cu6Sn5 grain boundaries (labeled with 1) and Cu6Sn5/Sn
phase boundaries (labeled with 2) are visible. (A) Pb oxide phase, (B) Sn-rich
phase and (C) Cu6Sn5 .
199
— -r ̂ M St* -** ^
ft** c oJ0Jk
"K»Tk .*"1
(a) as-soldered
(b) 140°C, 16 days
Figure 5.13. SEM microstructure of Au composite solder matrix (a) as-soldered
arid (b) after annealing at 140°C for 16 days. (A) Pb-rich phase, (B) Sn-rich
phase and (C) AuSn4.
200
(a) as-soldered
. I m
(b) 140°C, 16 days
Figure 5.14. SEM microstructure of Ag composite solder matrix (a) as-soldered
and (b) after annealing at 140°C for 16 days. (A) Pb-rich phase, (B) Sn-rich
phase, (C) Ag and (D) Ag3Sn.
201
f« CSS t
(a) as-soldered
(b) 140°C, 16 days
Figure 5.15. SEM microstructure of Ni composite solder matrix (a) as-soldered
and (b) after annealing at 140°C for 16 days. (A) Pb-rich phase, (B) Sn-rich
phase, (C) Ni and (D) Ni3Sn4 phase.
202
Figure 5.16. TEM micrograph of Ni composite solder matrix in the as-soldered
state showing a Ni particle and surrounding Ni3Sn4.
CHAPTER 5 REFERENCES
1. Z. Mei and J.W. Morris, Jr., J. Elec. Mater., 21, 599 (1992).
2. D. Stockdale, J. Inst. Metals, 49, 267 (1932).
3. G. Borelius, Trans. AIME, 191, 477 (1951).
4. A. Stockburn, J. Inst. Metals, 66, 33 (1940).
5. I. Obinata and E. Schmid, Metallwirtschaft, 12, 101 (1933).
6. H.S. Kalish and F.J. Dunkerley, Trans. AIME, 180, 637 (1949).
7. W.A. Tiller, R. McDjenovich, J. Appl. Phys., 34, 3639 (1963).
8. Elemental and Interplannar Spacing Index, (U.S. Department of
Commerce, NIST and JCPDS International Center for Diffraction Data,
1989).
9. D.R. Frear, Ph.D. Dissertation, University of California, Berkeley, 1987.
10. D.R. Frear, J.B. Posthill and J.W. Morris, Jr., Metal. Trans. A, 20A,
1325 (1989).
11. J.W. Morris, Jr., D. Tribula, T.S.E. Summers and D. Grivas, Solder Joint
Reliability Theory and Application, J.H. Lau Eds., (Van Nostrand
Reinhold, New York, 1991), Chapter 7.
12. M. McLean, Directionally Solidified Eutectic, (The Metals Society,
London, 1983).
13. P.G. Shewmon, Transformations in Metals, (McGraw-Hill, New York,
1969).
203
204
14. R. Elliott, Eutectic Solidification Processing, (Betterworths, London,
1983).
15. J.D. Verhoeven, D.P. Mourer and E.D. Gibson, Met. Trans. A, 8A, 1239
(1977).
16. J.D. Hunt, J. Inst. Met., 94, 125 (1964).
17. R.H. Hopkins and R.W. Kraft, Trans. AIME, 242, 1627 (1968).
18. B. Labulle and C. Petipas, J. Cryst. Growth, 28, 279 (1975).
19. M. Cagnon, M. Suery, A. Eberhardt and B. Baudelet, Acta Met. 25, 71
(1977).
20. J.P. Chilton and W.C. Winegard, J. Inst. Met., 89, 162 (1960).
21. H.W. Weart and D.J. Mack, Trans. Met. Soc. AIME, 10, 664 (1958).
22. B.P. Kashyap and G.S. Murty, Mat. Sci. & Eng., 50, 205 (1981).
23. M. Frebel and B. Otte, Scripta Met., 9, 1317 (1975).
24. B.F. Dyson, J. Appl. Phys., 37, 2375 (1966).
25. B.F. Dyson, T.R. Anthony and D. Turnbull, J. Appl. Phys. 38, 3408
(1967).
26. B.F. Dyson, T.R. Anthony and D. Turnbull, J. Appl. Phys. 37, 2370
(1966).
27. J.D. Meakin and E. Klokholm, Trans. AIME, 218, 463 (1960).
28. M. Hansen and K. Anderko, Constitution of Binary Alloys, 2nd Ed.,
(McGraw-Hill, New York, 1958), p.232.
29. D.C. Yeh and H.B. Huntington, Phys. Rev. Lett., 53, 1469 (1984).
CHAPTER 6
SUMMARY
In this dissertation, the studies of diffusion kinetics and microstructures
of eutectic and composite solder/copper joints were described in detail. Sn/Pb
solders are widely used by the electronics industry to provide both mechanical
and electrical connections within and among the different packaging levels in
an electronic system. In an effort to improve the mechanical properties of
solder, metallic and intermetallic particles were added to a eutectic solder
matrix to form composite solders. When solder reacts with the copper
substrate, the intermetallics Cu6Sn5 and Cu3Sn form and grow at the
solder/copper interface. The formation and growth of these intermetallics have
been proposed as controlling mechanisms for solderability and reliability of
solder/copper joints. It is important to investigate the kinetics and
microstructures of the new composite solder/copper joints and to understand
the mechanisms behind the experimental results, which could lead to better
control of the solderability and reliability.
Scanning electron microscopy (SEM), transmission electron microscopy
(TEM), x-ray energy dispersive spectroscopy (XEDS) and scanning transmission
electron microscopy (STEM) were used to examine the microstructures of
solder/copper joints. Samples used for SEM examination were prepared using
standard metallurgical sample preparation techniques with careful control of the
polishing conditions. Ultramicrotomy was the primary TEM sample preparation
205
206
technique developed during this project.
The diffusion kinetics and microstructures of six types of composite
solder/copper joints were studied. These composite solders are: 7.6 w t % Cu,
20 w t% Cu6Sn5, 20 w t% Cu3Snf 4 w t% Au, 4 w t% Ag and 4 w t % Ni. The
growth and morphology of the intermetallic phases at the composite
solder/copper substrate interface were examined as functions of time,
temperature and particle additions. The activation energies for the formation of
Cu6Sn5 and Cu3Sn at the interface were determined for these composite
solders, and were compared to the published values for the eutectic
solder/copper system. The microstructures and the anneal behavior of the
eutectic solder and composite solder matrix were studied. The effect of the
particle additions on the diffusion behavior of Sn in the composite solder matrix
and thus on the microstructures of the intermetallic interface were also
examined.
Conclusions from this work are:
1. During soldering, both Cu6Sn5 and Cu3Sn form at the solder/copper
substrate interface. The rj-phase Cu6Sn5 forms adjacent to the solder and
the e-phase Cu3Sn is adjacent to the copper substrate. Cu6Sn5 and Cu3Sn
both increase in thickness with increasing anneal time and temperature.
2. The activation energies for the formation of Cu6Sn5 and Cu3Sn at the
eutectic solder and six types of composite solder/copper substrate
interfaces were determined.
3. The addition of particles to eutectic solder strongly affects the
microstructure and kinetics of the interfacial intermetallic layers at the
solder/copper substrate interface. Compared to the activation energy for
207
Cu6Sn5 formation (0.84 eV) and Cu3Sn formation (1.63 eV) for the
eutectic solder alone:
(1) Cu-containing particle additions (Cu, Cu6Sn5 and Cu3Sn) reduce
the thickness of the Cu6Sn5 and increase the thickness of the
Cu3Sn. They increase the activation energy for Cu6Sn5 formation
and decrease the activation energy for Cu3Sn formation.
(2) Au and Ag particles decrease the activation energies for both
Cu6Sn5 and Cu3Sn formation.
(3) Ni particle additions drastically increase the activation energy for
Cu6Sn5 formation. Cu3Sn formation is suppressed. Its thickness is
reduced to almost zero. The Cu6Sn5 layer contains a substantial
volume fraction of voids adjacent to the copper substrate.
TEM was used to investigate the nanostructure of the eutectic and
composite solder/copper systems and the interfacial relationships among
the different phases.
(1) Ultramicrotomy was successfully used to section thin slices of
solder/copper joints in cross-section for TEM analysis. For the first
time, the Pb-rich and Sn-rich phases of the solder, the copper
substrate, the particles in the composite solders, and the metallic
and intermetallic interfacial layers were observed and analyzed by
TEM in a single sample.
(2) The e -phase Cu3Sn has a columnar morphology while the tj-phase
Cu6Sn5 has a rod faceted morphology. The grain size of the
Cu6Sn5 phase is larger than that of the Cu3Sn phase.
(3) Cu3Sn was observable at the solder/copper interface in as-
208
soldered samples only by using TEM. It was not observable using
SEM.
5. Thin film samples were annealed in the TEM in-situ using a hot stage,
and were observed in real-time to determine the mechanisms of
intermetallic formation at the solder/copper interface and the effect of
particle additions on the intermetallic growth.
(1) For the Cu/Sn thin films, intermetallic formation begins at the
Sn/Cu boundary and progresses laterally from the Sn into the Cu.
(2) For the Cu/Sn/Ni thin films, Ni acts as a barrier which prevents Sn
from diffusing into Cu, thus inhibiting Cu-Sn intermetallic
formation.
6. The eutectic solder matrix consists of two phases, Pb-rich and Sn-rich.
(1) The eutectic solder matrix has a uniform globular microstructure
in the as-soldered state. With annealing, the two solder phases
coarsen.
(2) The microstructure of solder matrix in the as-soldered state is
related to the solidification cooling rate. With fast cooling,
alternating lamellae of the two constituent phases are formed.
With slow cooling, the eutectic solder matrix is a dispersion of Pb-
rich region in a Sn-rich matrix.
7. For the particles added to the solder matrix:
(1) Cu and Cu3Sn particles react with Sn until all Cu and Cu3Sn
transform to the terminal phase, Cu6Sn5. These particles act as
Sn-sinks which remove Sn from the solder.
(2) Cu6Sn5 particles do not react with the solder. The Cu6Sn5/Sn
209
phase boundaries and Cu6Sn5/Cu6Sn5 grain boundaries enhance
the Sn diffusion to the solder/copper substrate interface.
(3) Au diffuses rapidly in the solder via an interstitial mechanism.
During soldering, all the Au particles react completely with the Sn
to form the terminal phase AuSn4. The AuSn4/Sn phase
boundaries and AuSn4/AuSn4 grain boundaries act as enhanced
diffusion pathways for Sn.
(4) During soldering and with annealing, the Ag particles react with
the Sn to form Ag3Sn.
(5) Ni can diffuse rapidly to the solder/copper substrate interface and
act as a barrier layer to inhibit Sn diffusion. Ni also reacts with the
Sn to form Ni3Sn4.
8. Based on the SEM and TEM studies, and in-situ TEM thin film
observations, a Sn diffusion model and Sn diffusion mechanisms in
composite solders were proposed.
(1) The growth of Cu-Sn intermetallics at the solder/copper substrate
interface requires the diffusion of Sn through Cu6Sn5 and Cu3Sn
followed by reaction with Cu; Cu does not diffuse into the solder
to any appreciable extent.
(2) There are two mechanisms which explain the effects of the
particle additions on the kinetics of intermetallic formation. First,
the grain boundaries of the intermetallic particles and the
intermetallic particle/Sn phase boundaries in the solder matrix act
as enhanced diffusion pathways for Sn, thus increasing the flux
of Sn to the solder/copper substrate interface. Second, the Cu,
210
Cu3Sn and Ag particles act as Sn-sinks which remove Sn from the
solder and decrease the amount of Sn available for reaction at the
solder/substrate interface.
(3) Ni is an extremely effective diffusion barrier which completely
prevents Sn from diffusing into the copper substrate.
APPENDIX A
CRYSTAL STRUCTURES
211
212
This appendix describes the crystal structures of the metals and
intermetallics discussed in this study.
Metals usually have one of the three basic crystal structures: face-
centered cubic (fee) (Strukturbericht A1), body-centered cubic (bcc)
(Strukturbericht A2), or closed-packed hexagonal (cph) (Strukturbericht A3).
These forms result from simple ways of packing spheres. Figure A.1 illustrates
the unit cells in perspective with the atomic positions indicated by spheres.1
The shadowed planes are the closest-packed planes. In the fee and cph
structures, the coordination number is 12, each atom being surrounded by 12
nearest neighbors at a distance &/2H = 0.707a in fee (where a is the length
of the cube edge), and a distance of a in cph (where a is the length of the edge
of the hexagon). In the bcc structure the coordination number is 8, with 8
nearest neighbors at a distance ah/3/2 = 0.866a (where a is the length of the
cube edge), and with an additional 6 next nearest neighbors at a distance a.
The electron diffraction pattern from a specific region of a specimen
viewed in the transmission electron microscope (TEM) is known as a Selected
Area Diffraction Pattern (SADP). SADPs are routinely used for phase
identification. The SADP on the final viewing screen is the magnified image of
the back focal plane of the objective lens. The magnification factor is defined
as an equivalent camera length that would be necessary to produce the same
magnification in a diffraction camera without the lenses. This is shown
schematically in Figure A.2 using reflection from crystal planes at a Bragg angle
9 to generate a diffracted beam.2 As discussed by J.W. Edington,2 if the
distance from the transmitted to the diffracted spot is R, and the camera length
is L:
213
Rd = XL (A.1)
where XL is the camera constant which describes the magnification of the
diffraction pattern. The distance R in the SADP is characteristic of the
interplanar spacing d(hk)) of the reflecting plane and the camera constant. After
obtaining a SADP, the interplanar spacing (d-spacing) is calculated by:
d = (A.2) R
The interplanar spacings, d(hk„, may be used for phase identification using the
data compiled by the International Center for Diffraction Data.3
The crystal structure of Pb is fee with a = 4.9502 A (where a is the
length of the cube edge as shown in Figure A. 1a).4 Sn has two possible
phases: grey a-Sn and white /?-Sn. Grey Sn is cubic and is the low temperature
phase. It was not observed in this study. (According to the equilibrium phase
diagram cr-Sn should form below 13°C in pure Sn, but this transformation is
greatly inhibited by the presence of Pb or Sb in Sn alloys.) /?-Sn, as shown in
Figure A.3, has a body-centered tetragonal structure with 2 atoms per unit cell
and a = 5.8315 A, c = 3.1814 A.4 Tables A.1 and A.2 show the lattice
spacings and indexed planes for Pb and /?-Sn.
The d-spacings in Tables A.1 to A.3, and the calculated d-spacings in
Tables A.4 to A.8 are calculated values using the lattice parameters and the
crystallographic formulae for interplanar spacings given by J.W. Edington.5 The
handbook values of the d-spacings in Tables A.4 to A.7 are the d-spacings
published by the International Center for Diffraction Data.3 The experimental
values of the d-spacings in Tables A.4 to A.8 were calculated from data
214
obtained during this project.
The crystal structures of Cu, Ag, Au, and Ni are all face-centered cubic.
Table A.3 lists the lattice spacings4 and indexed planes for these elements.
When atoms of two or more elements can be intermixed over a range of
concentrations on the sites of a given crystal structure, a solid solution is
formed. Many solid solutions become ordered at low temperatures. Ordering
involves a change from the nearly random distribution of the different types of
atoms at each atomic site to a more regular arrangement whereby designated
lattice sites are occupied predominately by one kind of atom.1 In a disordered
alloy of composition AB, for example, all the lattice sites are occupied by both
A and B atoms. On ordering, A and B atoms segregate to specific lattice sites,
so that the resulting arrangement can be described as a lattice of A atoms
interpenetrating a lattice of B atoms. The segregation of atoms to particular
lattice sites may take place with little or no deformation of the lattice, creating
an ordered solid solution, or superlattice, from a random solid solution.1
In a disordered solid solution, crystallographically equivalent atomic
planes are statistically identical, but in an ordered superlattice this need not be
true. For example, alternate planes of a set may become A-rich and B-rich
planes, respectively, and the distance between identical planes may become
twice the distance between identical planes of the disordered alloy (or some
other multiple of this distance). Hence, the structures of ordered alloys usually
produce diffraction patterns that have additional Bragg reflections. The
superlattice lines are associated with the new, larger atomic plane spacings
which are not present in the disordered alloys.
Interstitial solid solutions are formed when atoms with small radii are
215
accommodated in the interstices of the lattice of a solvent. In a truly interstitial
solid solution the smaller atoms are merely deposited in the interstitial voids
(holes) between the bigger atoms, which may be assumed to be in contact. The
cph structure has two types of interstitial voids. As shown in Figure A.4, the
larger voids are surrounded by six atoms and are called octahedral voids.1 The
octahedral holes are of particular importance in the NiAs structure because
which they are occupied by Ni atoms while the As atoms lie on the close-
packed planes of the cph lattice.
The ordered Cu6Sn5 phase (IJ')6,7 has a structure that can be regarded as
a superlattice of the NiAs (B82) type, either with a = 20.83 A , c = 25.15 A,
c/a = 1.204,1 or with a = 20.89 A, c = 25.48 A, c/a = 1.214.2 As illustrated
in Figure A.5, the octahedral interstitial holes between the Cu atoms at 000
and 00>2 are sites 2c and 2d. Sites 2c are filled by Sn atoms, and sites 2d are
occupied by a mixture of 20% Cu atoms and 80% vacancies.8 Each layer is a
cph (0001) plane. The dimensions of the hexagonal pseudo-cell were reported
as a = 4.198 A, c = 5.096 A, c/a = 1.214.9 The orthorhombic unit cell
contains 230-250 Sn atoms and 300-280 Cu atoms, for an overall composition
of Cu6Sn5. The high-temperature modification 17 is possibly isotopic with NiAs.
Table A.4 lists the lattice spacings and indexed planes for the Cu6Sn5 phase.
The Cu3Sn phase (e) is orthorhombic, with 64 atoms per unit cell and a
= 4.34 A , b = 5.56 A, c = 38.18 A,1 or a = 4.382 A, b = 5.521 A , c =
33.25 A , 2 as shown in Figure A.6. The pseudo-cell has a = 4.34 A , b = 5.56
A , c = 4.765 A . Table A.5 lists the lattice spacings and indexed planes for
Cu3Sn phase.
The structure of AuSn4 is the same as PtSn4 and PdSn4 and has an
216
orthorhombic unit cell, containing 20 atoms, with a = 6.44 A , b = 7.04 A and
c = 11.60 A.10 Table A.6 lists the lattice spacings and indexed planes for
AuSn4.
The Ag3Sn phase has a slightly rhombically deformed cph superlattice
with 4 atoms per unit cell,11,12,13 and a = 2.995 A, c = 4.780 A , c/a = 1 . 5 9 6 .
The Ag3Sn phase was found to undergo a transformation at about 60°C.14 X-
ray investigation showed that it is not accompanied by a lattice change.15 Table
A.7 lists the lattice spacings and indexed planes for Ag3Sn phase.
Ni3Sn4 is monoclinic, with 14 atoms per unit cell, similar to the CoSn
(B35) structure. At higher temperatures, the narrow homogeneity range shifts
to higher Ni contents: a = 12.22 A , b = 4.06 A , c = 5.33 A, /? = 105°3' at
57.3 at.% Sn; a = 12.31 A , b = 4.06 A , c = 5.18 A , £ = 103°48' at 54.8
at% Sn.16,17 Table A.8 lists the lattice spacings and indexed planes for Ni3Sn4.
Since the d-spacings are not listed in the handbook3, the d-spacings in Table
A.8 are the first 20 possible d(hk„ calculated using the lattice parameters.
Table A.1. Lattice Spacings and Indexed Planes of Pb
face-centered cubic, a = 4.9502 A
217
d (A) hkl
2.858 111
2.475 002
1.750 022
1.493 113
1.429 222
1.238 004
1.136 133
1.107 024
1.011 224
0.953 333 or 115
0.875 044
0.837 135
0.825 006 or 244
0.783 026
0.755 335
0.746 226
0.715 444
Table A.2. Lattice Spacings and Indexed Planes of /?-Sn
body centered tetragonal, a = 5.8315 A, c = 3.1814 A
218
d (A) hkl d (A) hkl
2.915 002 1.0252 125
2.793 101 0.9824 312
2.062 022 0.9718 006
2.017 112 0.9310 303
1.695 103 0.9280 215
1.484 211 0.9218 026
1.458 004 0.9178 116
1.442 123 0.8868 323
1.304 024 0.8755 145
1.292 114 0.8485 314
1.205 213 0.8466 235
1.0950 105 0.8386 136
1.0434 301 0.8086 046
1.0401 233 0.8058 107
1.0309 044
219
Table A.3. Lattice Spacings and Indexed Planes of Cu, Ag, Au and Ni
face-centered cubic
hkl Cu Ag Au Ni hkl
a = 3.6150 A a = 4.0862 A a = 4.0780 A a = 3.5238 A
111 2.087 2.359 2.355 2.0345
002 1.808 2.044 2.039 1.7619
022 1.278 1.445 1.442 1.2460
113 1.090 1.231 1.230 1.0623
222 1.044 1.180 1.177 1.0172
004 0.904 1.022 1.020 0.8810
133 0.829 0.938 0.936 0.8084
024 0.808 0.914 0.912 0.7880
224 0.738 0.834 0.832 0.7193
333 or 115 0.696 0.786 0.785 0.6782
044 0.639 0.722 0.721 0.6229
135 0.610 0.691 0.689 0.5956
006 or 244 0.603 0.681 0.680 0.5873
026 0.572 0.646 0.645 0.5571
335 0.551 0.623 0.622 0.5374
226 0.545 0.616 0.615 0.5313
444 0.590 0.590 0.589 0.5086
220
Table A.4. Lattice Spacings and Indexed Planes of Cu6Sn5
d-spacing (A) Indexed as
ordered
cph lattice
a = 4.198 A
c = 5.096 A
Indexed as
long period
superlattice
a = 20.83 A
c = 25.15 A
Calculated
from lattice
parameters
Handbook
value3
Experimental
value
Indexed as
ordered
cph lattice
a = 4.198 A
c = 5.096 A
Indexed as
long period
superlattice
a = 20.83 A
c = 25.15 A
5.10 5.12 5.028 001 005
3.57 3.66 3.558 501
2.96 2.98 2.941 101 505
2.55 2.56 2.549 002 0,0 ,10
2.10 2.12 2.164 110 550
2.09 2.10 2.085 102 5,0,10
1.94 1.95 1.912 111 555
1.82 1.83 1.835 200 10,0,0
1.73 1.72 1.738 10,0,4
1.71 1.71 1.664 201 10,0,5
221
Table A.5. Lattice Spacings and Indexed Planes of Cu3Sn
d-spacing (A) Indexed as
ordered
orthorhombic
lattice
Indexed as
long period
superlattice
Calculated Handbook Experimental a = 4.24 A a = 4.34 A
from lattice value3 value b = 5.56 A b = 5.56 A
parameters c = 4.765 A c = 38.18 A
5.56 5.51 5.335 010 010
4.77 4.77 4.779 001 008
4.34 4.33 4.248 100 100
3.62 3.61 3.761 011 018
3.42 3.41 3.374 110 110
3.21 3.20 3.231 101 108
2.78 2.77 2.798 020 or 111 020 or 118
2.66 2.76 2.730 119
2.40 2.39 2.415 021 028
2.38 2.38 2.365 002 0,0,16
or 029
222
Table A.6. Lattice Spacings and Indexed Planes of AuSn4
d-spacing (A) Indexed as
ordered
orthorhombic
lattice
a = 6.44 A
b = 7.04 A
c = 11.60 A
Calculated from
lattice
parameters
Handbook value3 Experimental
value
Indexed as
ordered
orthorhombic
lattice
a = 6.44 A
b = 7.04 A
c = 11.60 A
5.80 5.80 5.892 002
4.31 4.25 4.200 102
3.31 3.24 3.260 103
3.22 3.22 3.166 200
2.98 2.95 2.926 121
2.93 2.90 2.905 210
2.90 2.83 2.866 004
2.82 2.82 2.847 202
2.79 2.80 2.807 220
2.60 2.59 2.618 023 or 212
223
Table A.7. Lattice Spacings and Indexed Planes of Ag3Sn
d-spacing (A) Indexed as
ordered
cph lattice
a = 2.995 A
c = 4 .780 A
Indexed as
long period
superlattice
a = 11.98 A
c = 4 .780 A
Calculated
from lattice
parameters
Handbook
value3
Experimental
value
Indexed as
ordered
cph lattice
a = 2.995 A
c = 4 .780 A
Indexed as
long period
superlattice
a = 11.98 A
c = 4 .780 A
5.19 5.18 5.124 200
3.92 3.91 4.046 210
3.73 3.73 3.719 111
3.52 3.51 3.494 201
3.03 3.03 211
2.99 2.98 2.956 220
2.59 2.59 2.591 100 400
2.39 2.39 2.427 002 002
2.33 2.38 2.329 102
2.28 2.28 2.283 101 401
224
Table A.8. Lattice Spacings and Indexed Planes of Ni3Sn4
d-spacing (A) Indexed as ordered monoclinic lattice
a = 12.22 A b = 4.06 A c = 5.33 A p = 105°3'
Calculated from lattice parameters
Experimental value
Indexed as ordered monoclinic lattice
a = 12.22 A b = 4.06 A c = 5.33 A p = 105°3'
11.80 100
8.87 200
5.15 5.124 001
4.33 4.522 101
4.06 010
3.93 300
3.84 3.833 110
3.46 3.391 201
3.34 210
3.19 3.159 011
3.00 2.995 301
2.96 2.956 111 or 400
2.82 2.812 310
2.63 2.650 211
2.57 2.574 002
2.39 102
2.36 500
2.32 2.315 401
2.30 311
2.17 2.174 012
225
(111) plane (110) plane
« / V 5 -
( a ) Face-centered cubic ( A l ) (6 ) Body-centered cubic (A2)
( 001 ) plane
(c) Close-packed hexagonal (A3 )
Figure A.1. The principal structures of metals; closest-packed planes are
indicated by shading, (a) faced-centered cubic (fee) (A1), (b) body-centered
cubic (bee) (A2), and (c) close-packed hexagonal (cph) (A3).1
226
(hkl) reflecting
planes
incident beam
specimen
transmitted
beam
diffracted beam
transmitted spot
diffracted spot
Figure A.2. The diffraction camera geometry used to simulate the magnification
of the diffraction pattern by the microscope lenses.2
227
Body-centered Tetragonal
2 atoms/unit cell
a = 5.8315 A
c = 3.1814 A
a / j 2
Figure A.3. The unit cell of yS-Sn.1
228
Yi
Q Metal atoms
O Octahedral interstices
Figure A.4. The interstitial octahedral voids in the cph structure with an ideal
axial ratio c/a = V8 / 3.1
229
(a)
2a Cu
2c Sn
0,1/2
0,1/2
2d Ordered mixture 20% Cu and 80% vacancies
(b) 0,1/2
Figure A.5. Crystal structure of ordered Cu6Sn5. (a) unit cell, (b) (0001)
projection with the distance above the projection plane indicated in units of c.8
230
Sn
Cu
Figure A.6. Crystal structure of Cu3Sn.
APPENDIX A REFERENCES
1. C.S. Barrett and T.B. Massalski, Structure of Metals, 3rd Ed., (Pergamon
Press, New York, 1980), Chapter 10.
2. J.W. Edington, Practical Electron Microscopy in Materials Science, (Van
Nostrand Reinhold, New York, 1976), Chapter 1.
3. Elemental and Interplanar Spacing Index, (U.S. Department of Commerce,
NIST and JCPDS International Center for Diffraction Data, 1989).
4. C.S. Barrett and T.B. Massalski, Structure of Metals, 3rd Ed., (Pergamon
Press, New York, 1980), Appendix.
5. J.W. Edington, Practical Electron Microscopy in Materials Science, (Van
Nostrand Reinhold, New York, 1976), Appendix 1.
6. J.D. Bernal, Nature, 122, 54, (1928).
7. 0. Carlsson and G. Hagg, Z. Krist, 83, 308 (1932).
8. W.J. Boettinger, Internal Memorandum, Metallurgy Division, NIST,
Gaithersburg, MD 20899.
9. A. Westgren and G. Phragmen, Z. anorg. Chem., 175, 80 (1928).
10. K. Schubert and U. Rosier, Z. Metallkunde, 41, 298 (1950).
11. 0. Nial, A. Almin and A. Westgren, Z. physik. Chem., B14, 83 (1931).
12. M.M. Umanskiy, Zhur. Fiz. Khim., 14, 846 (1940).
13. P. Michel, Compt. rend., 235, 377 (1952).
14. A.J. Murphy, J. Inst. Metals, 35, 107 (1926).
15. G.D. Preston, J. Inst. Metals, 35, 118 (1926).
231
232
16. H. Nowotny and K. Schubert, Naturwissenschaften, 32, 76 (1944).
17. H.Nowotny and K. Schubert, Z. Metallkunde, 37, 23 (1946).
APPENDIX B
SCANNING ELECTRON MICROSCOPY AND X-RAY MICROANALYSIS
233
234
The modern scientist is required to observe, analyze and explain
phenomena occurring on a micrometer (/xm) or submicrometer scale. The
scanning electron microscope (SEM) is a powerful instrument which permits the
observation and characterization of materials and surfaces on this scale. In the
SEM, the area to be examined is irradiated with a finely focused electron beam,
which may be static or swept in a raster scan across the surface of the
specimen. The types of signals produced when the electron beam impinges on
a specimen surface include secondary electrons, backscattered electrons, Auger
electrons, characteristic x-rays and photons of various energies. These signals
are obtained from specific emission volumes within the sample and can be used
to determine many of the characteristics of the sample. In SEM, the signals of
greatest interest are the secondary, backscattered electrons and characteristic
x-rays. The basic components of the SEM are the electron gun, the lens
system, the electron detector, the visual and recording cathode ray tubes
(CRTs), and the electronics associated with them.1 Figure B.1 shows a
schematic of the electron and x-ray optics of a scanning electron microscope.1
B.1 Electron Guns
Electron optical columns of the SEM include the electron gun and two or
more electron lenses. The electron gun provides a stable source of electrons
which is used to form the electron probe. These electrons are usually obtained
from a source by thermionic emission. At sufficiently high temperatures, a
certain percentage of the electrons in a solid become sufficiently energetic to
overcome the work function of the cathode material and escape. The filament
materials commonly used are W and LaB6. The filament has a pointed tip and
235
is heated directly or indirectly using a dc filament power supply. It is maintained
at a high negative voltage (1 -50 kV) during operation. At the filament operating
temperature, the emitted electrons leave the tip and are accelerated to ground
(anode) by the potential between the cathode and anode. The configuration of
a typical electron gun is shown in Figure B.2.2
Surrounding the filament is a grid cap or Wehnelt cylinder with a circular
aperture centered at the filament apex. The grid cap is biased negatively
between 0 and 2500 V with respect to the cathode. The electric field formed
with this gun configuration causes the emitted electrons from the filament to
converge to a crossover of dimension d0 with divergence angle a0 below the
Wehnelt cylinder, as shown in Figure B.2.
B.2 Electron Lenses
The condenser and objective lens systems are used to demagnify the
electron crossover (d0~ 10-50 /im) in the electron gun to the final spot size
used on the sample surface (5-200 nm). This represents a total demagnification
factor as large as 10,000. The condenser lens system, which is composed of
one or more lenses, determines the beam current which impinges on the
sample. The final probe-forming lens, called the objective lens, determines the
final spot size of the electron beam. Conventional electromagnetic lenses are
used and the electron beam is focused by the interaction of the electromagnetic
fields of the lenses with the moving electrons in the beam.
The magnetic lenses are similar to simple solenoid coils. Figure B.3
shows a schematic section of a cylindrical electromagnetic lens commonly used
as a condenser lens.2 The winding used to induce the magnetic field in the iron
236
core may be seen in the figure. The bore of diameter D of the electromagnetic
lens is parallel to the direction in which the electrons are traveling. The gap
located in the center of the iron core is the distance S between the north and
south pole pieces of the lens. The strength of the magnetic lens, that is the
intensity of the magnetic field in the gap, is proportional to Nl, where N is the
number of turns in the solenoid winding, and I is the current flowing through
the lens. As an electron moves through the magnetic field, it experiences a
radial force inward, which is proportional to the Lorentz force. The lensing
action is similar to that of an optical lens, in which a ray parallel to the axis of
the lens is bent to the lens axis at the focal length, f, of the lens (Figure B.4).
In an optical lens, the focal length is fixed by the curvature of the lens surface
and cannot be changed. In an electromagnetic lens, the focal length depends
on two factors: the accelerating voltage and the current through the coil.
Therefore, the focal length of and electromagnetic lens can be controlled by
adjusting the current supplied to it.
The lenses in a scanning electron microscope reduce the diameter of the
electron beam to a very small size on the sample surface. As shown in Figure
B.4, the demagnification is M = S'/S, where S is the distance between the
object plane and principal plane of the lens and S' is the distance between the
image plane and the principal plane of the lens. As the focal length f is reduced,
the S' is reduced and M becomes smaller. After passing through the first
condenser lens, the electron beam diameter is reduced from d0 to d1f where d!
= Md0.
Figure B.5 shows the coupling of the three lenses; the object for a given
lens is the image from the lens above it. The net result is that the diameter of
237
the electron beam at the sample surface, d3, is:
d3 = d0xM1xM2xM3 (B.1)
where IV^, M2, and M3are the demagnification factors for each lens.
The distance of the sample from the bottom of the objective lens is the
working distance, WD. Whenever WD is changed, the objective lens current,
and hence S3, must be adjusted to produce the minimum spot size on the
sample surface for the setting of condenser lenses C, and C2. This adjustment
is the focusing operation for the SEM.
B.3. Electron-Beam-Specimen Interactions
B.3.1. Scattering
Electron scattering is divided into two categories, elastic and inelastic
scattering, illustrated in Figure B.6.1 When elastic scattering occurs, the
direction of the electron is changed, but the magnitude of its velocity is
constant, so is the kinetic energy. Elastic scattering results from collisions of
the energetic electrons with the nuclei of the atom, partially screened by the
bound electrons. For a given thickness, elastic scattering is more probable for
high atomic number materials and at low beam energy.
The second general category of scattering is inelastic scattering. During
an inelastic scattering event, energy is transferred to the target atoms and
electrons, and the kinetic energy of the incident electron decreases. There are
a number of possible inelastic scattering processes. The principal processes of
interest in scanning electron microscopy are briefly described here. For a basic
reference, please see Kittel's Introduction to Solid State Physics.3
238
(a) Plasmon Excitation. The beam electron can excite simple harmonic
oscillations in the "free electron gas" which exists between the ionic cores in
a solid. This is a highly probable inelastic scattering process.
(b) Excitation of Conduction Electrons Leading to Secondary Electron
(Low-Energy) Emission. The interaction of the incident electron with the solid
can cause electrons from the solid to be ejected, these are called secondary
electrons. They have initial kinetic energies between 0 and 50 eV.
(c) Ionization of Inner Shells. A sufficiently energetic electron can interact
with an atom and cause the ejection of a tightly bound inner-shell electron,
leaving the atom in an ionized and highly energetic state. Subsequent decay of
this excited state results in the emission of characteristic x-rays and Auger
electrons.
(d) Bremsstrahlung or Continuum X-rays. An energetic incident electron
can undergo deceleration due to Coulombic interactions with the atoms. The
energy lost from the incident electron in this deceleration is converted into an
x-ray photon, known as a bremsstrahlung ("braking radiation"). The
bremsstrahlung x-rays form a continuous spectrum from zero energy up to the
beam energy. The angular distribution of intensity of this continuum is
anisotropic.
(e) Excitation of Phonons. A substantial portion of the energy deposited
in the sample by the incident electron is transferred to the solid by the
excitation of lattice oscillations (phonons), i.e., heat.
The processes of elastic and inelastic scattering operate concurrently.
Inelastic scattering is favored at low atomic numbers and elastic scattering at
high atomic numbers. Elastic scattering causes the beam electrons to deviate
239
from their original direction of travel, causing them to "diffuse" through the
solid. Inelastic scattering progressively reduces the energy of the beam electron
until it is captured by the solid, thus limiting the range of travel of the electron
within the solid. The region over which the beam electrons interact with the
solid, depositing energy and producing those forms of secondary radiation
which be measured, is known as the interaction volume. Monte Carlo
simulations of electron trajectories4,5,6 are especially useful in understanding the
size and shape of the interaction volume as a function of specimen and beam
parameters. An example of the Monte Carlo simulation is shown in Figure B.7.1
B.3.2. Backscattered Electrons
It is found experimentally that a significant fraction of the incident
electrons which strike a target subsequently escape from the target. These
reemergent incident electrons are collectively known as backscattered
electrons. The backscattered electron coefficient, a, is defined as the number
of backscattered electrons, nBS, divided by the number of beam electrons
incident on the target, nB; alternatively, electron currents may be used:
0 = _^BS=^BS (B.2)
Careful examination of the individual trajectories drawn using Monte Carlo
simulation reveals that the process of backscattering usually takes place as a
result of a sequence of elastic scattering events in which the net change in
direction is sufficient to carry the electron out of the specimen (Figure B.8).1 It
is possible for an electron incident normal to a specimen surface to scatter
240
through an angle greater than 90° and thus escape the specimen after a single
scattering event. Backscattered electrons are extremely useful for imaging in
SEM.7
The incident electrons generally penetrate some distance into the solid
before undergoing a sufficient number of elastic scattering events to reverse
their direction of travel. The emerging backscattered electrons thus carry
information about the nature of the specimen over a range of depth. As shown
in Figure B.9,8 the backscattered coefficient, a, increases with increasing
atomic number, Z, and is relatively insensitive to beam energy.9 As the tilt angle
of the specimen increases, the opportunity for backscattering events increases.
The backscatter coefficient is approximately described by10
t] (0) = — — (B.3) (1+COS0)P
where 6 is the tilt angle, p = 9/Z% for pure elements and Z is the atomic
number. Since more electrons mean brighter signals, Eq. B.3 tells us that the
constant of backscatter electrons proportional to Z, the atomic number. In this
work, the elements interested are Cu, Sn, Pb, Au, Ag, Ni, etc., whose atomic
numbers are in the range from 28 to 82. Figure B.9 shows that these elements
have sufficient backscatter coefficients.
B.3.2 Secondary Electrons
Secondary electrons are defined as those electrons emitted from the
sample with an energy less than 50 eV (an arbitrary cutoff). The secondary
electron coefficient, 6, is given by
241
5 = (B.4) nB iB
where nSE is the number of secondary electrons emitted from a sample
bombarded by nB incident electrons, and i designates the equivalent current.
Secondary electrons are produced as a result of interactions between energetic
beam electrons and weakly bound conduction electrons.11 The interaction
between the beam electron and the conduction band electron results in the
transfer of only a few electron volts of energy to the conduction band electron,
so they only come from the surface.
An important characteristic of secondary electrons is their shallow
sampling depth, a direct consequence of the low kinetic energy with which
they are generated. The mean free path of the secondary electrons is about 1
nm for metals and up to 10 nm for insulators. Compared to the behavior of
backscattered electrons, whose yield increases monotonically with the atomic
number of the specimen, the secondary electron coefficient is relatively
insensitive to composition and has no strong trend with atomic number. In
other words, the secondary electrons are sensitive to the surface topography,
but not the chemical composition.
B.3.3 X-Rays
During inelastic scattering of the incident electrons, x-rays can be formed
by two distinct processes: (1) Deceleration of the incident electron by the
Coulombic field of the atom core, which consists of the nucleus and tightly
bound electrons, leads to formation of a continuous spectrum of x-ray energies
242
from zero energy up to the value of the incident electron energy, as shown in
Figure B. 10.1 This is the x-ray continuum or bremsstrahlung. (2) The interaction
of a incident electron with an inner-shell electron can result in the ejection of
the bound inner-shell electron which leaves the atom in an excited state with
a vacancy in the electron shell, as shown in Figure B.11.1 During subsequent
deexcitation, an electron transition occurs from an outer shell to fill this
vacancy. The transition involves a change in energy, and the energy released
from the atom can manifest itself either in the form of an x-ray or an ejected
(Auger) electron. Since the energy of the emitted x-ray is related to the
difference in energy between the sharply defined levels of the atoms, it is
referred to as a characteristic x-ray. Their specific energies (and wavelengths)
are characteristic of the particular element which is excited. The x-ray energies
may be used to identify the atoms present in the sample. The x-ray intensities
are related to the atomic concentrations.
The intensity of the continuum radiation increases with increasing atomic
number of the target and with increasing beam energy. The level of the
continuum radiation plays an important role in determining the minimum
detectable level for a particular element, since the continuum forms a
background against which characteristic signals must be measured.
B.4 Image Formation in the Scanning Electron Microscope
At any given point in time, the electron beam, defined by beam current,
i, beam diameter, d, and beam divergence, a, enters the specimen chamber and
strikes the specimen at a single controlled location. Within the interaction
volume, both elastic and inelastic scattering occur, producing detectable signals
243
from backscattered electrons, secondary electrons, characteristic and
continuum x-rays, etc. These signals are related to the properties of the
specimen, i.e. local topography, composition, etc. By measuring the magnitude
of these signals with suitable detectors, the properties of the specimen can be
determined at the location of the electron beam impact. In order to study more
than a single location, the beam must be moved from place to place by means
of a scanning system, illustrated in Figure B.12.1 Scanning is usually
accomplished using electromagnetic coils arranged in pairs, one pair each for
deflection in the X and Y directions. The electron beam is moved over time to
sample the specimen properties at a controlled succession of points. In an
analog scanning system, the beam is moved continuously along a line (the line
scan), for example, in the X direction. After completion of the line scan, the
position of the line is shifted slightly in the Y direction (the frame scan), and the
process is repeated to produce a grid pattern. This process is known as
rastering.
In forming the SEM image, the beam is scanned on the specimen in an
X-Y pattern while the CRT is synchronously scanned in the same X-Y pattern,
as illustrated in Figure B.13.1 A one-to-one correspondence is established
between the set of beam locations on the specimen and the points on the CRT.
To display the electron interaction information, the signal intensity S derived
from the detector is used to adjust the brightness of the spot on the CRT
(intensity or Z modulation), as shown in Figure B.14.1 Thus, the creation of an
SEM image consists of constructing a map transforming information from
specimen space to CRT space.
Magnification in the SEM image is accomplished by adjusting the scale
244
of the map on the CRT, and depends only on the excitation of the scan coils
and not the excitation of the objective lens, which determines the focus of the
beam. The smaller the scan area on the specimen, the larger the magnification
on the CRT.
B.5 X-Ray Energy Despersive Spectrometer (XEDS)
Chemical analysis in the SEM is performed by measuring the energy and
intensity distribution of the x-ray signals generated by a focused electron beam.
The operating principles of the XEDS are illustrated in Figure B. 1 5.1 The
x-ray signal from the sample passes through a thin beryllium window into a
cooled, reverse-bias p-i-n (p-type, intrinsic, n-type) lithium-drifted silicon
detector (SiLi detector). (Most detectors have Be windows, but new ones may
have polymers, or none at all if the vacuum is good enough.) Absorption of
each individual x-ray photon leads to the ejection of a photoelectron which
gives up most of its energy to the formation of electron-hole pairs. They in turn
are swept away by the applied bias to form a charge pulse which is then
converted to a voltage pulse by a charge-sensitive preamplifier. The voltage
pulses produced by the detector are on average proportional in size to the
incoming x-ray photon energy. The signal is further amplified and sharped by
a main amplifier, and finally passed on to a multichannel analyzer (MCA), where
the pulses are sorted by voltage. The contents of the MCA memory either
reside directly in a computer or can be transmitted to a computer for further
processing, such as peak identification and quantification.
The first stage in the analysis of an unknown is the identification of the
elements present. The identification of the major constituents of a sample can
245
usually be done with a high degree of confidence. The quantitative analyses of
~1-jum3 regions of bulk samples can also be obtained using the x-ray
technology.
246
CATHODE
WEHNELT CYLINDER
ANODE
SPRAY APERTURE
FIRST CONDENSER LENS
SECOND CONDENSER LENS
DOUBLE DEFLECTION COIL
STIGMATOR
FINAL (OBJECTIVE) LENS BEAM LIMITING APERTURE
X-RAY DETECTOR (WDS OR EDS)
PMT AMP
SCAN GENERATORS
SPECIMEN
SECONDARY ELECTRON DETECTOR
TO DOUBLE DEFLECTION COIL
MAGNIFICATION CONTROL-
Figure B.1. Schematic drawing of the electron and x-ray optics of a SEM.
247
FILAMENT
WEHNELT^ CYLINDER \
EQUIPOTENTIALS
^ANOOE PLATE
BIAS RESISTOR
HIGH VOLTAGE SUPPLY
Raure B.2. Configuration of a typical self h i , ^ , y p , c a l se , f-b'ased electron gun.2
248
z
< 0
P r U)
VIEW TOWARD OBJECT SPACE
Figure B.3. Schematic diagram of an axially symmetric electromagnetic lens.
The magnetic field lines are plotted along with the components of the magnetic
field.2
2 4 9
Mognificotion, M = S'/ S
Principal plane
of lens Object plane Focal plane
Image plane
Y Lens axis
Figure B.4. Ray d iagram i l lustrat ing lensing act ion.
250
Spray apertures
Sample (7
Final aperture o
r 1 __Scan coil ^ J ~ location
Figure B.5. Lensing action of the three lenses of a scanning electron
microscope.
251
(o) ELASTIC E, *E„
(b) INELASTIC
Ej < E 0
4>j « 4 > e
Figure B.6. Schematic illustration of scattering processes which occur when an
energetic electron of energy E0 interacts with an atom, (a) Elastic scattering,
instantaneous energy E, after collision equals E0; (b) Inelastic scattering,
instantaneous energy E| less than E0.1
252
0.5 ftm
0.5 Jim
Figure B.7. Monte Carlo electron trajectory simulation of the electron-sample
interaction in iron. E0 = 20 keV, tilt = 0°. (a) Plot of five trajectories, showing
random variations, (b) Plot of 100 trajectories giving a visual impression of the
interaction volume.1
253
Figure B.8. Detailed single scattering Monte Carlo electron trajectory simulation
for a copper target, E0 = 30 keV, showing trajectories intersecting the sample
surface which result in backscattering.1
254
0.6 r-
0 . 5 -
0.4 -
0.3
0 . 2 -
0.1 ~ 10 ktV
— 4 9 kt V
SPECIMEN TILT • 0*
-4- +> 4 -10 20 30 4 0 50 60 70 80 90
Figure B.9. Variation of the backscatter coefficient as a function of atomic
number at En = 10 keV and En = 49 keV.1
255
WVVVVN
WVVVVIAA h v - E
Figure B.10. Schematic illustration of the origin of the x-ray continuum,
resulting from deceleration of the incident electrons by the Coulombic fields of
the atoms.1
256
INCIDENT • ELECTRON
EJECTED ORBITAL ELECTRON
• SCATTERED PRIMARY ELECTRON
ELECTRON RELAXATION AND PHOTON GENERATION
p X-RAY PI P EMITTED
PHOTON INTERNALLY CONVERTED AND AUGER ELECTRON EMITTED
X-RAY PHOrON EMITTED
Figure B. 11. Schematic illustration of the process of inner-shell ionization and
subsequent deexcitation by either Auger electron emission or x-ray photon
emission.
257
SCAN COILS
BACKSCATTERED X-RAY W.ED
CATHOOOUJMINESCENT I 23456789
- TRANSMITTED
DISPLAY AND RECORDING CRT's
VIDEO AMPLIFIERS
SECONDARY AND/OR BACKSCATTERED
Figure B. 12. Schematic illustration of scanning system of the scanning electron
microscope. FA, final aperture; SD, solid state backscattered electron detector;
ET, Everhart-Thornley detector composed of S, scintillator and PM,
photomultiplier; ED, energy dispersive x-ray spectrometer; CRT, cathode ray
tube. The numbers 1-9 indicate successive beam positions during a single
scanning sequence. Also: PM for cathodoluminescance, WD for wavelength
dispersive x-ray spectrometer.1
258
AREA SCANNED ON SPECIMEN
XXXXX XXXXX
' Z i
x x
X X X X X
INFORMATION TRANSFER
AREA SCANNED ON CATHODE RAY TUBE
Figure B.13. The principle of information display by image scanning. A
correspondence is established between a set of locations on the specimen and
on the CRT. Magnif ication = L//.1
259
SPECIMEN CRT DISPLAY
xxxx xxxx XXX
GU.y.D
Figure B.14. The principle of intensity or Z modulation used to display the
magnitude of the signal produced by electron-specimen interaction at the
locations scanned in Figure B. 13. Black represents low intensity; stippled,
intermediate intensity; white, high intensity.1
260
PILEUP REJECTOR ELECTRON
BEAM CRYOSTAT
DETECTOR
FET PREAMPLIFIER
B AS SUPPLY
DATA OUTPUT DEVICE
SPECIMEN
ULTICHANNEL ANALYZER
Aa^/ lL.
DISPLAY
COMPUTER
X-RAY SIGNAL
Figure B.15. Schematic representation of an x-ray energy-dispersive
spectrometer.
APPENDIX B REFERENCES
1. J.I. Goldstein, D.E. Newbury, P. Echlin, D.C. Joy, C. Fiori and E. Lifshin,
Scanning Electron Microscopy and X-Ray Microanalysis, (Plenum Press,
New York, 1981).
2. C.E. Hall, Introduction to Electron Microscopy, (McGraw Hill, New York,
1953).
3. C. Kittel, \r\troduction to Solid State Physics, 6th Ed., (Wiley, New York,
1986).
4. M.J. Berger, Methods in Computational Physics, Vol.1, B. Adler, S.
Fernback and M. Rotenberg Eds., (Academic, New York, 1963).
5. R. Shimizu and K. Murata, J. Appl. Phys., 42, 387 (1971).
6. K.F.J. Heinrich, D.E. Newbury and H. Yakowitz, National Bureau of
Standards Spec. Pub. 460, (Washington, DC, 1976).
7. O.C. Wells, SEM/1977/I, NT Research Institute, p.747, (Chicago, Illinois,
1977).
8. K.F.J. Heinrich, X-Ray Optics and Microanalysis, 4th Intl. Cong, on X-
Ray Optics and Microanalysis, R. Castaing, P. Deschamps and J.Philibert
Eds., p. 1509, (Hermann, Paris, 1966).
9. K.F.J. Heinrich, The Electron Microprobe, T.D. McKinley, K.F.J. Heinrich
and D.B. Wittry Eds., p.296, (Wiley, New York, 1966).
10. F. Arnal, P. Verdier and P-D. Vincinsini, C.R. Acad. Sci., 268, 1526
(Paris, 1969).
261
262
11. H.W.Streitwolf, Ann. Phys., 3, 183 (Leipzig, 1959).
APPENDIX C
PRINCIPLES OF TRANSMISSION ELECTRON MICROSCOPY
263
264
A number of the microstructural studies presented in this work were
performed using the Transmission Electron Microscope (TEM). The purpose of
this appendix is to provide some basic background on TEM.
C.1 Basic Principles of Transmission Electron Microscopy
A transmission electron microscope is similar to an optical microscope.
It has a source, which is an electron beam, and magnetic lenses (condenser,
objective and projector lenses). Figure C.1 illustrates the basic structure of the
TEM.1 The electron microscope uses an electron beam to illuminate a specimen
whereas an optical microscope uses a light beam. The theoretical resolution of
an optical system is determined by Rayleigh's criterion:2
a =1.22— (C.1) D
where a is the angular resolution, X is the wavelength of the source, and D is
the diameter of the objective aperture. The wavelength of visible light is 3600 -
7200 A.2 Electrons may be regarded as particle waves with wavelength X
given by the de Broglie relation X = h/mv. If the electron is accelerated to a
voltage Ve, the relativistically corrected wavelength is3
h '1 (c.2)
[2mFee(1 +eFe/2mc2)]1/2
where h is Planck's constant, m is the mass of the electron, e is its charge, and
c is the velocity of light. At 100 kV and 200 kV, the conventional accelerating
voltages for transmission electron microscopy, the relativistically corrected
wavelengths are 0.0371 A and 0.0251 A , respectively. It is this wavelength
265
difference that leads to the tremendous resolution difference between an
electron microscope and an optical microscope.
In Equation C.1, a is proportional to 1/D, which means that the
resolution can be improved by increasing the diameter of the objective lens
aperture. However, the resolution is also affected by the defects inherent in all
lenses. Three major lens defects are spherical aberration, chromatic aberration
and astigmatism, which are discussed in detail by J.W. Edington3 and A.W.
Agar et al.1 Chromatic aberration and astigmatism can be minimized in the TEM
by proper lens design. Hence, as given by J.W. Edington,3 the maximum
resolution of an electron microscope is determined by:
d . = j3/4C i/4 ( C 3 ) "min A s
where Cs is the spherical aberration coefficient of the objective lens and X is the
electron wavelength. Equation C.3 shows that the two most important
parameters affecting the resolution of a transmission electron microscope are
the wavelength and the spherical aberration coefficient of the objective lens.
This equation is the standard resolution criterion used for a TEM.
In principle, either electrostatic or magnetic lenses can be used to focus
a beam of electrons.4 Practical instruments exclusively employ magnetic lenses
since they can be made with smaller defects than electrostatic lenses.1 A
detailed discussion of magnetic lens theory is given by C.E. Hall.4 In brief, a
magnetic lens is made with soft-iron pole pieces. Highly concentrated magnetic
fields are generated by currents flowing through annular coils to focus the
electron beam. Electrons passing through the magnetic field travel in a helical
path. This additional rotary motion is a characteristic of magnetic lenses.
266
C.2 The Formation of Images and Diffraction Patterns
A transmission electron microscope can provide two types of
information, microstructural images and electron diffraction patterns. The
essential features of the imaging and diffraction modes in a TEM can be
explained in terms of a geometric optics treatment of the situation at the
objective lens as shown in Figure C.2.3 An electron beam parallel to the optic
axis passes through the specimen and forms an image at the image plane. The
action of forming this image brings both the transmitted and the diffracted
beams to a focus in the back focal plane of the objective lens. Since both a
diffraction pattern and an image of the specimen are always produced by the
objective lens at the same time, a magnified image of either may be produced
on the viewing screen by focusing the next lens in the magnification system on
either the image plane or the focal plane of the objective lens.
C.2.1 Bright and Dark Field Images
Several types of images can be obtained by appropriately using the
objective aperture, located in the back focal plane of the objective lens. Bright
field (BF) and centered dark field (DF) are the most commonly used imaging
modes for materials studies. Both types of image may be understood in terms
of the image forming characteristics of the objective lens and the use of the
objective aperture. As shown in figure C.3a, with a small aperture inserted in
the back focal plane of the objective lens, the diffracted beams are intercepted
and only the transmitted beam is allowed to pass. Thus the image formed on
the viewing screen is only from the transmitted beam, which is called the bright
field image. Alternatively, the objective aperture can be displaced away from
267
the optical axis to intercept the transmitted beam and allow a diffracted beam
to contribute to the image, forming a dark field image. However, when the
electron path is far away from the optical axis, a poor quality image is produced
because of the additional lens aberrations from off-axis rays. To retain the
resolution of the bright field mode, the illumination incident on the specimen is
tilted so that the diffracted electrons travel along the optic axis, as shown in
figure C.3b, and a centered dark field image is obtained. The purpose of using
BF and DF images is to improve the image contrast without losing detailed
information of the specimen. DF images also are used to identify regions of the
specimen that are composed of a specified phase.
C.2.2 Selected Area Diffraction Patterns
Electron diffraction patterns are routinely obtained in the transmission
electron microscope and are used to gain quantitative information on the
identity of phases and their orientation relationship to the matrix.
In practice, diffraction patterns are usually formed from specific regions
of the specimen, known as selected area diffraction patterns (SADP). As shown
in Figure C.2, an aperture is inserted coplanar with the image in the image
plane of objective lens to allow only the transmitted and diffracted rays
generated within the region AB of the specimen to pass into the remaining
imaging system. Those rays from outside this region are blocked by the
aperture and do not contribute to the diffraction pattern formed in the back
focal plane of the objective lens. Therefore, the diffraction pattern formed on
the viewing screen provides information only from material present in the AB
region.
268
When a beam of electrons is incident on the top surface of a thin
crystalline specimen, specific diffracted beams occur at the bottom exit
surface. Although each individual atom in the crystal scatters the incident
beam, the strong diffracted beams arise because scattered wavelets are in
phase in particular directions in the crystal, that is, the path difference is an
integral number of wavelengths. Consider the particular case shown in Figure
C.4 when the incident beam is made up of plane waves in phase and oriented
at an angle 6 relative to two (hkl) crystal Planes I and II.3 Let the two waves be
reflected by these crystal planes at an angle 0.
At the plane wavefront CD two situations may occur: (1) The two waves
may be in phase, as shown in Figure C.4, in which case reinforcement will
occur and a strong reflected beam will be present. (2) The waves may be out
of phase, that is they will destructurely interfere and there will be either a zero
intensity or a very weak reflected beam.
Case (1), that is a strong beam, will occur if the path difference POD is
an integral number of wavelengths, nX. PO = OD = OL sin 0. OL is the
interplannar spacing d(hk0. Thus for a strong reflection,
2dhkls\x\%=n'k (C.4)
which is Bragg's law. There will be a strong diffracted beam on the exit side of
the crystal only if there is a set of crystal planes oriented at a critical angle 6
relative to the incoming beam.
Electron diffraction patterns produced in transmission in the electron
microscope can be of three different types: ring patterns, spot patterns, and
board ring patterns, which correspond to polycrystalline, single-crystal, and
269
amorphous or nanocrystalline materials, respectively.
While spot patterns are from single-crystal regions of the specimen, ring
patterns arise from fine grain size polycrystalline material such as physically or
chemically vapor deposited or electrodeposited thin foils. For a given beam
direction a number of fine grain particles within the area illuminated by the
beam will be oriented to satisfy Bragg's law for all allowed reflecting planes.
However, one individual grain will produce a specific beam reflected from a
particular (hkl) plane, such that the angle between it and the incident beam is
28, satisfying Bragg's law. For randomly oriented particles and a specific
reflecting plane (hkl), these beams will lie in a cone with apex angle 4^(hk0
centered on the incident beam direction to produce a ring in the diffraction
pattern. Since a number of {hkl} planes will reflect, a series of concentric rings
will be produced, each one corresponding to a particular set of (hkl) reflections.
The diffraction pattern from amorphous materials is devoid of the sharp
lines characteristic of crystals and consists of broad features.5,6 The diffraction
from amorphous materials is weak, and is less quantitative.
Diffraction patterns are most commonly used for phase identification.
The diameter of the diffraction ring or the distance from the diffracted spot to
the transmitted beam in the spot pattern are characteristics of the interplanar
spacings, d(hkl), of the reflecting planes. The method of determining the d-
spacings from the SADP has been discussed briefly in Appendix A, and a
detailed discussion is given by J.W. Edington.3 After determining the d-
spacings, the phase can be identified using a published spacing index.7
270
C.3 JEOL JEM - 100 CX and JEM - 200 CX
Two transmission electron microscopes, the JEOL JEM -100 CX and
JEOL JEM - 200 CX, were used in this work. Except for different operating
voltage, magnification range, and resolution, which are compared in Table C.1,
these two microscopes have almost identical internal structures.8,9 As shown
in Figure C.5, both microscopes have 6 magnetic lenses: two condenser lenses,
one objective lens, two intermediate lenses and one projector lens. The JEM
100 - CX also has a scanning unit (STEM) and can be interfaced to an X-ray
energy dispersive spectrometer (XEDS) for chemical analysis. XEDS is described
in Appendix B.
271
Table C.1. JEOL JEM -100 CX and JEOL JEM -200 CX
Electron Microscope Performance Specifications
Property JEOL JEM - 100 CX8 JEOL JEM -200 CX9
accelerating voltage up to 100 kV up to 200 kV
resolution 1.4 A (lattice) 1.4 A (lattice) resolution
3.0 A (point to point) 3.5 A (point to point)
magnification up to 320,000x up to 450,000x
interfaced to XEDS yes no
272
Source \ j Filament
Condenser lens
Objective tens ~
Projector
lens *•"
Intermediate image
Viewing screen
Electron microscope
Figure C.1. The basic structure of the transmission electron microscope.1
273
back focal plane
diffraction J pattern
incident beam
specimen objective
lens
selected area aperture
Figure C.2. Formation of image and diffraction pattern by the objective lens.:
274
objective h 0 * * * 0 1
incident — beam — ^
diffrocted spot
transmitted spot
specimen
objective aperture
( o ) image
. . , back focal o b ie c , , w e plane
tilted incident beam
diffracted spot
specimen
transmitted spot
objective aperture
(b) image
Figure C.3. Bright field and dark field image formation, (a) Bright field and (b)
centered dark field.3
275
top of thin foil
crystal plane II
bottom of thin foil
incident electron beam
plane wave in phase
crystal plane I
1000-3000 X
incident electron beam
transmitted beam
diffracted beam
(b)
Figure C.4. (a) Reflection at the Bragg angle 6 from crystal planes in a thin foil
electron microscope specimen, (b) The relationship between incident,
transmitted and diffracted beams for a transmitting specimen.3
276
1
Lift
Electron gun
Wehnelt unit
Anode
Electron gun 2nd beam deflector coil
Anode chamber airlock valve
Condenser lens pole piece
Condenser lens aperture assembly
Beam displacement compensating coil
Condenser lens 1st beam deflector coil-
Condenser lens 2nd beam deflector coil Blanking plate Objective lens aperture assembly
Objective lens pole piece
Objective lens stigmator coil
Field limiting aperture assembly
Intermediate lens pole piece
Projector lens pole piece
Viewing window
Dispensing magazine
Receiving magazine
HV cable
Anode chamber
Gas inlet
Electron gun 1st beam deflector coil
-1st condenser lens coil
2nd condenser lens coil
Image wobbler coil
Condenser lens stigmator coil
Specimen chamber
Goniometer
Specimen holder
Objective lens coil
1st intermediate lens coil
2nd intermediate lens coil
Projector lens coil
Shutter
High resolution diffraction chamber
Viewing chamber airlock valve
Viewing chamber
Fluorescent screen
Camera chamber
Figure C.5. JEOL JEM - 200 internal structure.
APPENDIX C REFERENCES
1. A.W. Agar, R.H. Alderson and D. Chescoe, Principles and Practice of
Electron Microscope Operation, (North-Holland, Amsterdam, 1974).
2. F.G. Smith and J.H. Thompson, Optics, (Wiley, New York, 1971).
3. J.W. Edington, Practical Electron Microscopy in Materials Science, (Van
Nostrand, New York, 1976).
4. C.E. Hall, Introduction to Electron Microscopy, (McGraw-Hill, New York,
1966).
5. B.E. Warren, X-Ray Diffraction, (Addison-Wesley, Reading, 1969).
6. L.H. Schwartz and J.B. Cohen, Diffraction from Materials, (Springer-
Verlag, Berlin, 1987).
7. Elemental and Interplannar Spacing Index, (U.S. Department of
Commerce, NIST and JCPDS International Center for Diffraction Data,
1989).
8. Instruction Manual for JEM - 100 CX Electron Microscope, JEOL Ltd.,
Tokyo, Japan.
9. Instruction Manual for JEM - 200 CX Electron Microscope, JEOL Ltd.,
Tokyo, Japan.
277
APPENDIX D
STATISTICAL ANALYSIS
278
279
Experimental error or noise is one difficulty typically confronting the
scientific investigator. Variation produced by various factors, both known and
unknown, is called experimental error. Usually, only a small fraction of the total
error is directly attributable to error in measurement. Important effects may be
wholly or partially obscured by experimental error. Conversely, through
experimental error, the experimenter may be misled into believing in effects that
do not exist. The confusing effects of experimental error can be greatly reduced
by adequate statistical analysis of the experimental data. Furthermore,
statistical analysis can result in a measure of the precision of the measured
parameter under study.
D.1 Descriptive Measurement
When an experiment is repeated under what are, as nearly as possible,
the same conditions, the observed results are never quite identical. The
fluctuation that occurs from one repetition to another is called experimental
variation, experimental error, or merely error.
The total aggregate of measurements that conceptually might occur as
the result of performing a particular operation in a particular way is referred to
as the population of measurements. While it is sometimes convenient to think
of this population as infinite, the experiments are finite of size N, where N is
large. The actual experimental values are a sample from this population.
One important parameter of a sample is the average value. Given a set
of n measurements, x1f x2,..., xn, the arithmetic mean or the sample mean, x,
is defined by:
280
2 *< (D.1) i=1
x = -n
The mean describes the center of the probability distribution and the average
value of the sample.
If we imagine a hypothetical population as containing a very large
number of measurements, N, we can denote the corresponding average of the
population by:
N
2 *< (D.2) i=1
\x= N
To distinguish between the sample and population quantities, we call ju.
the population mean, and x the sample average. In general, a parameter like the
mean fi is a quantity directly associated with the population, and a statistic like
the average x is a quantity calculated from a set of data which is a sample from
the population. The mean of the population is also called the expected value.
The spread in a population is estimated by the standard deviation. The
standard deviation of n measurements is defined as:
n
2 fa - x f (D.3) i=1
n - 1
For n independent measurements drawn from a continuous population with
281
mean /*, if the distribution of the sample average x is normally distributed, then
the Central Limit Theory guarantees that the expected value of the
measurement (mean of the population) will be within the interval:
x - 1 . 9 6 - ^ - < \i ^x + 1 .96-^- (D.4) yfH ^
with probability 0.95.1
It can be seen from Eq D.4 that as the sample set, n, gets larger and
larger, the average, x, has a large probability of being closer and closer to the
mean of the population, fi, i.e. the expected value.
In the kinetic and microstructural studies of the interfacial intermetallic
layers at solder/copper substrate interfaces, the thickness measurements of the
intermetallic phases Cu6Sn5 and Cu3Sn were made using a digitizing tablet
interfaced to a personal computer. Micrographs of the solder/copper interface
region were placed on the digitizer pad and pairs of points representing a single
measurement of the intermetallic thickness were recorded. A minimum of 100
such measurements equally spaced along the interface were made for each
thickness reported. This procedure results in high quality data that can be
reliably analyzed with statistical significance. The distribution of the
measurements, the average thickness, the standard deviation, and the
maximum and minimum thickness values were calculated. One set of these
thickness measurement analyses are summarized in Table 4.1.
D.2. Simple Linear Regression
If there is a linear relationship between two variables, then a simple linear
282
regression model can be used to fit the data. A simple linear regression model
has the form:
Yr p0 + ^ + e(. i = 1,2, •••, n (D.5)
where Y ; is the value of the dependent variable for the ith measurement, X; is
the value of the independent variable for the ith measurement, (30 is the
intercept parameter, jSJ is the slope parameter, e; is an error term representing
deviations of the ith measurement from the line jSo+ft X; , and n is the number
of measurements.
The parameters 0O and /3t are estimated by the method of least square
fitting, which minimizes the squared distances of the measurements from the
expected linear relationship. Choose b0 and to minimize
s [ r, - (b0 • fc,x()]
Once b0 and bj have been determined, the estimated regression equation
becomes:
Y, *= f»„ • b,X, ID'6)
Equation D.6 is an approximation of the true relationship : Yj = |30+ &X,.
R2, called the linear correlation coefficient, is calculated as:1
283
I)(y!-rf fl2=_£z1 (D.7)
n
h(Y,-Y)z
i=1
where Y; is the value of the dependent variable for the ith measurement, Y is
the average mean of Y; (i = 1 to n), Yj* is the regression value which
corresponds to Y;. R2 is a measure of the quality of the regression analysis and
represents the fraction of the variation about the mean that is explained by the
fitting. It is often used as an overall measure of the fit attained. The value of
R2 is between 0 and 1. R2 is close to 1 if the independent variable explains a
relatively large amount of variability in the dependent variable, i.e., there is an
excellent linear correlation between the two variables, X; and Yf.
The values of the diffusion coefficient for each intermetallic at a given
temperature were calculated by measuring the thicknesses of the intermetallic
layers and applying the standard diffusion model, Eq. 4.1. The excellent linear
relationships between the variables in the model, described by the R2 values
(generally greater than 0.9 except for the Ni composite solder, which was
greater than 0.75), demonstrates that the model is valid. When calculating the
activation energies, the linear correlation coefficients, R2, for the activation
energy plots are all greater than 0.9. Again, the good linear fit indicates a valid
model.
APPENDIX D REFERENCES
1. G.E.P. Box, W.G. Hunter and J.S. Hunter, Statistics for Experimenters:
An Introduction to Design, Data Analysis, and Model Building (Wiley,
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284
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Ray Optics and Microanalysis, Eds. Castaing, R; Deschamps, P. and
Philibert, J., p. 1509, (Hermann, Paris, 1966).
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