Kinetics in Nanoscale Materials

PREFACE ix
CHAPTER 1 INTRODUCTION TO KINETICS IN NANOSCALE MATERIALS 1
1.1 Introduction 1
1.2 Nanosphere: Surface Energy is Equivalent to Gibbs-Thomson Potential 3
1.3 Nanosphere: Lower Melting Point 6
1.4 Nanosphere: Fewer Homogeneous Nucleation and its Effect on Phase Diagram 10
1.5 Nanosphere: Kirkendall Effect and Instability of Hollow Nanospheres 13
1.6 Nanosphere: Inverse Kirkendall Effect in Hollow Nano Alloy Spheres 17
1.7 Nanosphere: Combining Kirkendall Effect and Inverse Kirkendall Effect on Concentric Bilayer Hollow Nanosphere 18
1.8 Nano Hole: Instability of a Donut-Type Nano Hole in a Membrane 19
1.9 Nanowire: Point Contact Reactions Between Metal and Silicon Nanowires 21
1.10 Nanowire: Nanogap in Silicon Nanowires 22
1.11 Nanowire: Lithiation in Silicon Nanowires 26
1.12 Nanowire: Point Contact Reactions Between Metallic Nanowires 27
1.13 Nano Thin Film: Explosive Reaction in Periodic Multilayered Nano Thin Films 28
1.14 Nano Microstructure in Bulk Samples: Nanotwins 30
1.15 Nano Microstructure on the Surface of a Bulk Sample: Surface Mechanical Attrition Treatment (SMAT) of Steel 32
References 33
Problems 35
CHAPTER 2 LINEAR AND NONLINEAR DIFFUSION 37
2.1 Introduction 37
2.2 Linear Diffusion 38
2.2.1 Atomic Flux 39
2.2.2 Fick's First Law of Diffusion 40
2.2.3 Chemical Potential 43
2.2.4 Fick's Second Law of Diffusion 45
2.2.5 Flux Divergence 47
2.2.6 Tracer Diffusion 49
2.2.7 Diffusivity 51
2.2.8 Experimental Measurement of the Parameters in Diffusivity 53
2.3 Nonlinear Diffusion 57
2.3.1 Nonlinear Effect due to Kinetic Consideration 58
2.3.2 Nonlinear Effect due to Thermodynamic Consideration 59
2.3.3 Combining Thermodynamic and Kinetic Nonlinear Effects 62
References 63
Problems 64
CHAPTER 3 KIRKENDALL EFFECT AND INVERSE KIRKENDALL EFFECT 67
3.1 Introduction 67
3.2 Kirkendall Effect 69
3.2.1 Darken's Analysis of Kirkendall Shift and Marker Motion 72
3.2.2 Boltzmann and Matano Analysis of Interdiffusion Coefficient 76
3.2.3 Activity and Intrinsic Diffusivity 80
3.2.4 Kirkendall (Frenkel) Voiding Without Lattice Shift 84
3.3 Inverse Kirkendall Effect 84
3.3.1 Physical Meaning of Inverse Kirkendall Effect 86
3.3.2 Inverse Kirkendall Effect on the Instability of an Alloy Nanoshell 88
3.3.3 Inverse Kirkendall Effect on Segregation in a Regular Solution Nanoshell 90
3.4 Interaction Between Kirkendall Effect and Gibbs-Thomson Effect in the Formation of a Spherical Compound Nanoshell 93
References 97
Problems 97
CHAPTER 4 RIPENING AMONG NANOPRECIPITATES 99
4.1 Introduction 99
4.2 Ham's Model of Growth of a Spherical Precipitate (Cr is Constant) 101
4.3 Mean-Field Consideration 103
4.4 Gibbs-Thomson Potential 105
4.5 Growth and Dissolution of a Spherical Nanoprecipitate in a Mean Field 106
4.6 LSW Theory of Kinetics of Particle Ripening 108
4.7 Continuity Equation in Size Space 113
4.8 Size Distribution Function in Conservative Ripening 114
4.9 Further Developments of LSW Theory 115
References 115
Problems 116
CHAPTER 5 SPINODAL DECOMPOSITION 118
5.1 Introduction 118
5.2 Implication of Diffusion Equation in Homogenization and Decomposition 121
5.3 Spinodal Decomposition 123
5.3.1 Concentration Gradient in an Inhomogeneous Solid Solution 123
5.3.2 Energy of Mixing to Form a Homogeneous Solid Solution 124
5.3.3 Energy of Mixing to Form an Inhomogeneous Solid Solution 126
5.3.4 Chemical Potential in Inhomogeneous Solution 129
5.3.5 Coherent Strain Energy 131
5.3.6 Solution of the Diffusion Equation 134
References 136
Problems 136
CHAPTER 6 NUCLEATION EVENTS IN BULK MATERIALS, THIN FILMS, AND NANOWIRES 138
6.1 Introduction 138
6.2 Thermodynamics and Kinetics of Nucleation 140
6.2.1 Thermodynamics of Nucleation 140
6.2.2 Kinetics of Nucleation 143
6.3 Heterogeneous Nucleation in Grain Boundaries of Bulk Materials 148
6.3.1 Morphology of Grain Boundary Precipitates 150
6.3.2 Introducing an Epitaxial Interface to Heterogeneous Nucleation 151
6.3.3 Replacive Mechanism of a Grain Boundary 154
6.4 No Homogeneous Nucleation in Epitaxial Growth of Si Thin Film on Si Wafer 156
6.5 Repeating Homogeneous Nucleation of Silicide in Nanowires of Si 160
6.5.1 Point Contact Reactions in Nanowires 161
6.5.2 Homogeneous Nucleation of Epitaxial Silicide in Nanowires of Si 164
References 168
Problems 168
CHAPTER 7 CONTACT REACTIONS ON Si; PLANE, LINE, AND POINT CONTACT REACTIONS 170
7.1 Introduction 170
7.2 Bulk Cases 175
7.2.1 Kidson's Analysis of Diffusion-Controlled Planar Growth 175
7.2.2 Steady State Approximation in Layered Growth of Multiple Phases 178
7.2.3 Marker Analysis 179
7.2.4 Interdiffusion Coefficient in Intermetallic Compound 182
7.2.5 Wagner Diffusivity 186
7.3 Thin Film Cases 187
7.3.1 Diffusion-Controlled and Interfacial-Reaction-Controlled Growth 187
7.3.2 Kinetics of Interfacial-Reaction-Controlled Growth 188
7.3.3 Kinetics of Competitive Growth of Two-Layered Phases 193
7.3.4 First Phase in Silicide Formation 194
7.4 Nanowire Cases 196
7.4.1 Point Contact Reactions 197
7.4.2 Line Contact Reactions 202
7.4.3 Planar Contact Reactions 208
References 208
Problems 209
CHAPTER 8 GRAIN GROWTH IN MICRO AND NANOSCALE 211
8.1 Introduction 211
8.2 How to Generate a Polycrystalline Microstructure 213
8.3 Computer Simulation of Grain Growth 216
8.3.1 Atomistic Simulation Based on Monte Carlo Method 216
8.3.2 Phenomenological Simulations 217
8.4 Statistical Distribution Functions of Grain Size 219
8.5 Deterministic (Dynamic) Approach to Grain Growth 221
8.6 Coupling Between Grain Growth of a Central Grain and the Rest of Grains 225
8.7 Decoupling the Grain Growth of a Central Grain from the Rest of Grains in the Normalized Size Space 226
8.8 Grain Growth in 2D Case in the Normalized Size Space 229
8.9 Grain Rotation 231
8.9.1 Grain Rotation in Anisotropic Thin Films Under Electromigration 232
References 237
Problems 238
CHAPTER 9 SELF-SUSTAINED REACTIONS IN NANOSCALE MULTILAYERED THIN FILMS 240
9.1 Introduction 240
9.2 The Selection of a Pair of Metallic Thin Films for SHS 243
9.3 A Simple Model of Single-Phase Growth in Self-Sustained Reaction 245
9.4 A Simple Estimate of Flame Velocity in Steady State Heat Transfer 250
9.5 Comparison in Phase Formation by Annealing and by Explosive Reaction in Al/Ni 251
9.6 Self-Explosive Silicidation Reactions 251
References 255
Problems 256
CHAPTER 10 FORMATION AND TRANSFORMATIONS OF NANOTWINS IN COPPER 258
10.1 Introduction 258
10.2 Formation of Nanotwins in Cu 260
10.2.1 First Principle Calculation of Energy of Formation of Nanotwins 260
10.2.2 In Situ Measurement of Stress Evolution for Nanotwin Formation During Pulse Electrodeposition of Cu 264
10.2.3 Formation of Nanotwin Cu in Through-Silicon Vias 266
10.3 Formation and Transformation of Oriented Nanotwins in Cu 269
10.3.1 Formation of Oriented Nanotwins in Cu 270
10.3.2 Unidirectional Growth of Cu-Sn Intermetallic Compound on Oriented and Nanotwinned Cu 270
10.3.3 Transformation of (111) Oriented and Nanotwinned Cu to (100) Oriented Single Crystal of Cu 274
10.4 Potential Applications of Nanotwinned Cu 276
10.4.1 To Reduce Electromigration in Interconnect Technology 276
10.4.2 To Eliminate Kirkendall Voids in Microbump Packaging Technology 277
References 278
Problems 278
APPENDIX A LAPLACE PRESSURE IN NONSPHERICAL NANOPARTICLE 280
APPENDIX B INTERDIFFUSION COEFFICIENT ? D = CBMG'' 282
APPENDIX C NONEQUILIBRIUM VACANCIES AND CROSS-EFFECTS ON INTERDIFFUSION IN A PSEUDO-TERNARY ALLOY 285
APPENDIX D INTERACTION BETWEEN KIRKENDALL EFFECT AND GIBBS-THOMSON EFFECT IN THE FORMATION OF A SPHERICAL COMPOUND NANOSHELL 289
INDEX 293