Solder Joint Technology: Materials, Properties, and Reliability (Springer Series in Materials Science, 92) 0387388907, 9780387388908

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M AT E R I A L S S C I E N C E

King-Ning Tu

Solder Joint Technology Materials, Properties, and Reliability

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Springer Series in

M AT E R I A L S S C I E N C E

92

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Springer Series in

M AT E R I A L S S C I E N C E Editors: R. Hull R.M. Osgood, Jr. J. Parisi H. Warlimont The Springer Series in Materials Science covers the complete spectrum of materials physics, including fundamental principles, physical properties, materials theory and design. Recognizing the increasing importance of materials science in future device technologies, the book titles in this series ref lect the state-of-the-art in understanding and controlling the structure and properties of all important classes of materials. 78 Macromolecular Nanostructured Materials Editors: N. Ueyama and A. Harada

87 Micro- and Nanostructured Glasses By D. H¨ulsenberg and A. Harnisch

79 Magnetism and Structure in Functional Materials Editors: A. Planes, L. Ma˜nosa, and A. Saxena

88 Introduction to Wave Scattering, Localization and Mesoscopic Phenomena By P. Sheng

80 Micro- and Macro-Properties of Solids Thermal, Mechanical and Dielectric Properties By D.B. Sirdeshmukh, L. Sirdeshmukh, and K.G. Subhadra 81 Metallopolymer Nanocomposites By A.D. Pomogailo and V.N. Kestelman 82 Plastics for Corrosion Inhibition By V.A. Goldade, L.S. Pinchuk, A.V. Makarevich and V.N. Kestelman 83 Spectroscopic Properties of Rare Earths in Optical Materials Editors: G. Liu and B. Jacquier 84 Hartree–Fock–Slater Method for Materials Science The DV–X Alpha Method for Design and Characterization of Materials Editors: H. Adachi, T. Mukoyama, and J. Kawai 85 Lifetime Spectroscopy A Method of Defect Characterization in Silicon for Photovoltaic Applications By S. Rein 86 Wide-Gap Chalcopyrites Editors: S. Siebentritt and U. Rau

89 Magneto-Science Magnetic Field Effects on Materials: Fundamentals and Applications Editors: M. Yamaguchi and Y. Tanimoto 90 Internal Friction in Metallic Materials A Reference Book By M.S. Blanter, I.S. Golovin, H. Neuh¨auser, and H.-R. Sinning 91 Time-dependent Mechanical Properties of Solid Bodies By W. Gr¨afe 92 Solder Joint Technology Materials, Properties, and Reliability By K.-N. Tu 93 Materials for Tomorrow Theory, Experiments and Modelling Editors: S. Gemming, M. Schreiber and J.-B. Suck 94 Magnetic Nanostructures Editors: B. Aktas, L. Tagirov and F. Mikailov 95 Nanocrystals and Their Mesoscopic Organization By C.N.R. Rao, P.J. Thomas and G.U. Kulkarni

Volumes 30–77 are listed at the end of the book.

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King-Ning Tu

Solder Joint Technology Materials, Properties, and Reliability

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King-Ning Tu Department of Materials Science and Engineering University of California at Los Angeles, CA, USA 6532 Boelter Hall Los Angeles 90095–6595 Email, personal: [email protected]

Library of Congress Control Number: 2007921097 ISBN-10: 0-387-38890-7 ISBN-13: 978-0-387-38890-8

e-ISBN-10: 0-387-38892-3 e-ISBN-13: 978-0-387-38892-2

Printed on acid-free paper.  C

2007 Springer Science+Business Media, LLC All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. 9 8 7 6 5 4 3 2 1 springer.com

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Contents

1 Introduction 1.1 Introduction of Solder Joint................................................. 1.2 Lead-Free Solders............................................................... 1.2.1 Eutectic Pb-Free Solders.......................................... 1.2.2 High-Temperature Pb-Free Solders ............................ 1.3 Solder Joint Technology ...................................................... 1.3.1 Surface Mount Technology ....................................... 1.3.2 Pin-through-Hole Technology.................................... 1.3.3 C-4 Flip Chip Technology ....................................... 1.4 Reliability Problems in Solder Joint Technology...................... 1.4.1 Sn Whiskers........................................................... 1.4.2 Spalling of Interfacial Intermetallic Compounds in Direct Chip Attachment ......................................... 1.4.3 Thermal-Mechanical Stresses .................................... 1.4.4 Impact Fracture...................................................... 1.4.5 Electromigration and Thermomigration...................... 1.4.6 Reliability Science on the Basis of Nonequilibrium Thermodynamics .................................................... 1.5 Future Trends in Electronic Packaging .................................. 1.5.1 The Trend of Miniaturization ................................... 1.5.2 The Trend of Packaging Integration Evolution—SIP, SOP, and SOC ....................................................... 1.5.3 Chip–Packaging Interaction...................................... 1.5.4 Solderless Joints ..................................................... References.................................................................................

1 1 4 4 8 9 9 10 12 16 16 17 22 25 25 26 28 28 29 30 31 31

Part I Copper–Tin Reactions 2 Copper–Tin Reactions in Bulk Samples 2.1 Introduction...................................................................... 2.2 Wetting Reaction of Eutectic SnPb on Cu Foils......................

37 37 38

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2.2.1

Crystallographic Relationship between Cu6 Sn5 Scallop and Cu....................................................... 2.2.2 Rate of Consumption of Cu in Soldering Reaction with Eutectic SnPb................................................. 2.3 Wetting Reaction of SnPb on Cu Foil as a Function of Solder Composition ............................................................ 2.4 Wetting Reaction of Pure Sn on Cu Foils............................... 2.5 Ternary Phase Diagram of Sn-Pb-Cu .................................... 2.5.1 Ternary SnPbCu Phase Diagrams at 200 and 170◦ C .... 2.5.2 5Sn95Pb/Cu Reaction and Ternary SnPbCu Phase Diagrams at 350◦ C ........................................ 2.6 Solid-State Reaction of Eutectic SnPb on Cu Foils.................. 2.6.1 Formation of Cu3 Sn and Kirkendall Voids .................. 2.7 Comparison between Wetting and Solid-State Reactions .......... 2.7.1 Morphology of Wetting Reaction and Solid-State Aging.................................................... 2.7.2 Kinetics of Wetting Reaction and Solid-State Aging.................................................... 2.7.3 Reactions Controlled by Rate of Gibbs Free Energy Change....................................................... 2.8 Wetting Reaction of Pb-Free Eutectic Solders on Thick Cu UBM........................................................................... References................................................................................. 3 Copper–Tin Reactions in Thin-Film Samples 3.1 Introduction...................................................................... 3.2 Room-Temperature Reaction in a Bilayer Thin Film of Sn/Cu ......................................................................... 3.2.1 Phase Identification by Glancing Incidence X-ray Diffraction .................................................... 3.2.2 Growth Kinetics of Cu6 Sn5 and Cu3 Sn....................... 3.2.3 Copper Is the Dominant Diffusing Species .................. 3.2.4 Kinetic Analysis of Sequential Formation of Cu6 Sn5 and Cu3 Sn............................................................. 3.2.5 Atomistic Model of Interfacial-Reaction Coefficient ...... 3.2.6 Measurement of Strain in Cu and Sn Thin Films......... 3.3 Spalling in Wetting Reaction of Eutectic SnPb on Cu Thin Films........................................................................ 3.4 No Spalling in High-Pb Solder on Au/Cu/Cu-Cr Thin Films........................................................................ 3.5 Spalling in Eutectic SnPb Solder on Au/Cu/Cu-Cr Thin Films........................................................................ 3.6 No Spalling in Eutectic SnPb on Cu/Ni(V)/Al Thin Films........................................................................

43 48 48 52 53 56 57 58 58 60 60 64 67 68 70 73 73 74 74 75 80 81 89 92 93 97 100 100

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Spalling in Eutectic SnAgCu Solder on Cu/Ni(V)/Al Thin Films........................................................................ 3.8 Enhanced Spalling Due to Interaction across a Solder Joint....................................................................... 3.9 Wetting Tip Reaction on Thin-Film-Coated V-Grooves............ References.................................................................................

vii

3.7

4 Copper–Tin Reactions in Flip Chip Solder Joints 4.1 Introduction...................................................................... 4.2 Processing a Flip Chip Solder Joint and a Composite Solder Joint....................................................................... 4.3 Chemical Interaction across a Flip Chip Solder Joint............... 4.4 Enhanced Dissolution of Cu-Sn IMC by Electromigration......... 4.5 Enhanced Phase Separation in Solder Alloys by Electromigration and Thermomigration......................................................... 4.6 Thermal Stability of Bulk Diffusion Couples of SnPb Alloys ...................................................................... 4.7 Thermal Stress Due to Chip–Packaging Interaction ................. 4.8 Design and Materials Selection of a Flip Chip Solder Joint....................................................................... References................................................................................. 5 Kinetic Analysis of Flux-Driven Ripening of Copper–Tin Scallops 5.1 Introduction...................................................................... 5.2 Morphological Stability of Scallop-Type IMC Growth in Wetting Reactions.............................................................. 5.2.1 Analysis of Morphological Stability of Scallops in Wetting Reactions................................................... 5.3 A Simple Model for the Growth of Mono-Size Hemispheres...................................................................... 5.4 Theory of Nonconservative Ripening with a Constant Surface Area ..................................................................... 5.5 Size Distribution of Scallops ................................................ 5.5.1 Dependence of Cu6 Sn5 Morphology on Solder Composition................................................. 5.5.2 Size Distribution and Average Radius of Scallops ........ 5.6 Nano Channels between Scallops .......................................... References................................................................................. 6 Spontaneous Tin Whisker Growth: Mechanism and Prevention 6.1 Introduction...................................................................... 6.2 Morphology of Spontaneous Sn Whisker Growth.....................

101 104 105 108 111 111 113 116 117 119 123 124 124 125

127 127 128 131 135 139 142 143 147 150 150

153 153 154

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6.3

Stress Generation (Driving Force) in Sn Whisker Growth by Cu-Sn Reaction ................................................................ 6.4 Effect of Surface Sn Oxide on Stress Gradient Generation and Whisker Growth ................................................................ 6.5 Measurement of Stress Distribution by Synchrotron Radiation Micro-diffraction ................................................................ 6.6 Stress Relaxation (Kinetic Process) in Sn Whisker Growth by Creep: Broken Oxide Model ............................................ 6.7 Irreversible Processes.......................................................... 6.8 Kinetics of Grain Boundary Diffusion-Controlled Whisker Growth ................................................................ 6.9 Accelerated Test of Sn Whisker Growth ................................ 6.10 Prevention of Spontaneous Sn Whisker Growth ...................... References................................................................................. 7 Solder Reactions on Nickel, Palladium, and Gold 7.1 Introduction...................................................................... 7.2 Solder Reactions on Bulk and Thin-Film Ni........................... 7.2.1 Reaction between Eutectic SnPb and Electroless Ni(P) .................................................... 7.2.2 Reaction between Eutectic Pb-Free Solders and Electroless Ni(P) .................................................... 7.2.3 Formation of (Cu, Ni)6 Sn5 versus (Ni, Cu)3 Sn4 ............ 7.2.4 Formation of Kirkendall Voids .................................. 7.3 Solder Reactions on Bulk and Thin-Film Pd .......................... 7.3.1 Reaction between Eutectic SnPb and Pd Foil.............. 7.3.2 Reaction between Eutectic SnPb and Pd Thin Film.............................................................. 7.4 Solder Reactions on Bulk and Thin-Film Au .......................... 7.4.1 Reaction between Eutectic SnPb and Au Foil.............. 7.4.2 Reaction between Eutectic SnPb and Au Thin Film.............................................................. References.................................................................................

157 160 163 168 169 170 175 178 180 183 183 184 188 191 193 194 194 194 197 198 198 204 204

Part II Electromigration and Thermomigration 8 Fundamentals of Electromigration 8.1 Introduction...................................................................... 8.2 Electromigration in Metallic Interconnects ............................. 8.3 Electron Wind Force of Electromigration............................... 8.4 Calculation of the Effective Charge Number........................... 8.5 Effect of Back Stress on Electromigration and Vice Versa ........................................................................

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Measurement of Critical Length, Critical Product, Effective Charge Number .................................................... 8.7 Why Is There Back Stress in Electromigration? ...................... 8.8 Measurement of the Back Stress Induced by Electromigration............................................................ 8.9 Current Crowding and Current Density Gradient Force ........... 8.10 Electromigration in Anisotropic Conductor of Beta-Sn............. 8.11 Electromigration of a Grain Boundary in Anisotropic Conductor........................................................ 8.12 AC Electromigration .......................................................... References.................................................................................

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9 Electromigration in Flip Chip Solder Joints 9.1 Introduction...................................................................... 9.2 Unique Behaviors of Electromigration in Flip Chip Solder Joints ..................................................................... 9.2.1 Low Critical Product of Solder Alloys ........................ 9.2.2 Current Crowding in Flip Chip Solder Joints .............. 9.2.3 Phase Separation in Eutectic Solder Joints ................. 9.2.4 Narrow Range of Current Density ............................. 9.2.5 Effect of Under-Bump Metallization on Electromigration ................................................ 9.3 Failure Mode of Electromigration in Flip Chip Solder Joints ..................................................................... 9.4 Electromigration in Flip Chip Eutectic Solder Joints ............... 9.4.1 Electromigration in Eutectic SnPb Flip Chip Solder Joints .......................................................... 9.4.2 Electromigration in Eutectic SnAgCu Flip Chip Solder Joints .......................................................... 9.4.3 Marker Motion Analysis Using Area Array of Nano-indentations................................................... 9.4.4 Mean-Time-to-Failure of Flip Chip Solder Joints ......... 9.4.5 Comparison between Eutectic SnPb and SnAgCu Flip Chip Solder Joints............................................ 9.4.6 Kinetic Analysis of Pancake-Type Void Growth along the Contact Interface ...................................... 9.4.7 Time-Dependent Melting of Flip Chip Solder Joints..... 9.5 Electromigration in Flip Chip Composite Solder Joints............ 9.5.1 Thin-Film Cu UBM in Composite Solder Joints .......... 9.5.2 Thick Cu UBM in Composite Solder Joints................. 9.6 Effect of Thickness of Cu UBM on Current Crowding and Failure Mode..................................................................... 9.6.1 Cu Column Bumps ................................................. 9.6.2 The Design of a Near-Ideal Flip Chip Solder Joint .......

225 226 229 230 235 238 240 241 245 245 247 247 247 248 248 249 249 255 256 259 261 264 266 267 270 272 272 274 275 276 280

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9.7

Electromigration-Induced Phase Separation in Eutectic Two-Phase Solder Alloy ...................................................... 9.7.1 Electromigration-Induced Back Stress in Two-Phase Structure............................................... 9.7.2 Electromigration-Induced Kirkendall Shift in Two-Phase Structure............................................... 9.7.3 Stochastic Tendency in Electromigration in Two-Phase Structure............................................... References................................................................................. 10 Polarity Effect of Electromigration on Solder Reactions 10.1 Introduction...................................................................... 10.2 Preparation of V-Groove Samples......................................... 10.2.1 Electromigration of Eutectic SnPb as a Function of Temperature....................................................... 10.3 Polarity Effect on IMC Growth at the Anode......................... 10.3.1 IMC Growth without Electric Current ....................... 10.3.2 Growth of IMC at Anode and Cathode with Electric Current...................................................... 10.3.3 IMC Thickness Change with Current Density and Temperature .................................................... 10.3.4 Comparison among Electrodes of Cu, Ni, and Pd in V-Groove Samples............................................... 10.4 Polarity Effect on IMC Growth at the Cathode ...................... 10.4.1 Dynamic Equilibrium .............................................. 10.5 Effect of Electromigration on the Competing Growth of IMC.................................................................. References................................................................................. 11 Ductile–to-Brittle Transition of Solder Joints Affected by Copper–Tin Reaction and Electromigration 11.1 Introduction...................................................................... 11.2 Tensile Test Affected by Electromigration.............................. 11.3 Shear Test Affected by Electromigration................................ 11.4 Impact Test ...................................................................... 11.4.1 Charpy Test........................................................... 11.4.2 Mini Charpy Machine to Test Solder Joints ................ 11.5 Drop Test ......................................................................... 11.5.1 JEDEC-JESD22-B111 Standard of Drop Test ............. 11.5.2 Dropping of a Packaging Board Vertically and the Torque on Solder Balls ....................................... 11.6 Converting a Mini Charpy Impact Machine to Perform Drop Test ......................................................................... 11.6.1 Dropping of a Chip Size Package Horizontally in Mini Charpy Machine..............................................

281 283 285 286 287 289 289 289 291 293 294 294 295 297 297 299 301 302

305 305 306 309 311 311 314 316 316 320 322 323

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Dropping of a Chip Size Package Vertically in Mini Charpy Machine.............................................. 11.7 Creep and Electromigration................................................. References.................................................................................

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11.6.2

12 Thermomigration 12.1 Introduction...................................................................... 12.2 Thermomigration in Flip Chip Solder Joints of SnPb............... 12.2.1 Thermomigration in Unpowered Composite Solder Joints .......................................................... 12.2.2 In Situ Observation of Thermomigration .................... 12.2.3 Random States of Phase Separation in Eutectic Two-Phase Structures.............................................. 12.2.4 Thermomigration in Unpowered Eutectic SnPb Solder Joints .......................................................... 12.3 Fundamentals of Thermomigration ....................................... 12.3.1 Driving Force of Thermomigration ............................ 12.3.2 Entropy Production ................................................ 12.3.3 Effect of Concentration Gradient on Thermomigration ............................................... 12.3.4 The Critical Length below Which No Thermomigration Occurs in a Pure Metal............................................ 12.3.5 Thermomigration in a Eutectic Two-Phase Alloy......... 12.4 Thermomigration and DC Electromigration in Flip Chip Solder Joints ..................................................................... 12.5 Thermomigration and AC Electromigration in Flip Chip Solder Joints ..................................................................... 12.6 Thermomigration and Chemical Reaction in Solder Joints........ 12.7 Thermomigration and Creep in Solder Joints.......................... References.................................................................................

325 325 326 327 327 329 329 332 333 335 338 338 340 341 342 343 344 344 345 345 346

Appendix A: Diffusivity of Vacancy Mechanism of Diffusion in Solids

347

Appendix B: Growth and Ripening Equations of Precipitates

351

Appendix C: Derivation of Huntington’s Electron Wind Force

359

Subject Index .........................................................................

365

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Preface

The trend in consumer electronic products will be more and more wireless, portable, and handheld. To manufacture these multifunctional products, highdensity circuit interconnections between a Si chip and its substrate are needed. Flip chip solder joint technology, by which an area array of solder bumps is used to join a chip to its substrate, is growing rapidly in demand. Flip chip technology is the only technology that can provide a large number of such interconnections with reliability. Solder joints are ubiquitous in electronic products. Due to environmental concerns regarding the toxicity of Pb-based solders, the European Union Parliament issued a directive to ban the use of Pb-based solders in consumer products on July 1, 2006. The application of Pb-free solder joints to a wide range of devices is urgent, and R&D of Pb-free solders for electronic manufacturing is thus very active at the moment. While solder joint technology is mature, Pb-free solder technology is not, hence its reliability must be proven. For example, electrical shorting due to Sn whiskers, electrical opening due to electromigration, and joint fracture due to dropping of handheld devices to the ground are challenging reliability problems in the application of Pb-free solders. To solve these problems in a largely technology-based manufacturing industry, scientific understanding and solutions are required. The copper–tin reaction is essential in the formation of a solder joint and the failure of such joints is due to externally applied forces as in electromigration. A fundamental understanding of the copper–tin reaction and the effect of external forces on solder joint reliability is critical and is emphasized in this book. There are two themes in this book. The first is the copper–tin reaction as a function of time and temperature, and the second is the effect of external forces on the reaction. Actually the second theme also emphasizes phase transformations under an inhomogeneous boundary condition. Typically, metallurgical phase transformations occur under constant temperature and constant pressure so that Gibbs free energy is minimized. However, in thermomigration or stress migration (creep) of a solder joint, the temperature or the pressure is not constant because there exists a temperature gradient or a stress gradient

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to drive the phase change, so an equilibrium state with a minimum free energy will not be reached. In electromigration, a potential gradient exists across the sample too. These are irreversible processes. The contents of the book are divided into two parts. Part I, from Chapters 2 to 7, covers copper–tin reactions, and Part II, from Chapters 8 to 12, covers electromigration and thermomigration of solder joints. Chapter 1 is an overview of flip chip technology. Why it is important and the known reliability problems are explained. The future trend in electronic packaging technology and its effect on solder joint technology are covered. Chapter 2 concerns wetting reactions between molten eutectic solder and bulk Cu foils. The unique morphology of scallop-type Cu-Sn intermetallic compound formation is emphasized and analyzed. Chapter 3 considers about CuSn reactions in thin films. Thin-film reactions are important since most metallization on Si devices to be joined by solder is in thin film form. Spalling of thin-film intermetallic compounds is a unique reliability phenomenon. Chapter 4 covers solder reaction in a flip chip configuration in which the reaction occurs on two interfaces. The two interfacial reactions interact with each other and the interaction is a reliability issue. Chapter 5 presents a theoretical analysis of flux-driven ripening of scallop-type growth of Cu-Sn intermetallic compounds under the constraint of a constant surface area. Theoretically derived and experimentally measured distribution functions of scallops are compared. Chapter 6 examines spontaneous Sn whisker growth which is a creep phenomenon. The necessary and sufficient conditions of whisker growth are discussed, and how to conduct an accelerated test of Sn whisker growth and how to prevent its growth are presented. Chapter 7 discusses briefly solder reactions on nickel, palladium, and gold surfaces. In addition to copper, these metals are used as under-bump metallization in devices. Chapter 8 covers the fundamentals of electromigration and the differences between electromigration in solder alloys and in Al or Cu interconnects. Why electromigration in solder joints has only recently become a reliability problem is explained. Chapter 9 concerns the unique behavior of electromigration in flip chip solder joints, especially the effect of current crowding. It is a key chapter of the book. The unique failure model due to pancake-type void formation at the cathode contact interface is presented. Chapter 10 examines the interaction between electrical and chemical forces in solder joints. The polarity effect of electromigration on intermetallic compound formation at the cathode and the anode interfaces of a solder joint is presented. Chapter 11 describes the interaction between electrical and mechanical forces. An accidental drop to the ground is the most frequent cause of failure of portable devices. Impact test and drop test of solder joints are analyzed, and the effect of electromigration on these tests is discussed. Chapter 12 considers thermomigration in solder joints, and the interaction between electrical and thermal forces is analyzed. Microstructure instability in a eutectic two-phase structure driven by a temperature gradient is adressed.

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I started solder research in 1965, when I began my Ph.D. dissertation on cellular precipitation of Sn lamellae in SnPb alloys. However, the contents of this book are based on thirteen Ph.D. dissertations finished in the University of California at Los Angeles since 1996, supported by the National Science Foundation (Dr. Bruce MacDonald), Semiconductor Research Corporation (Dr. Harold Hosack), and several microelectronic companies (especially Dr. Paul A. Totta of IBM East Fishkill, NY, Dr. Fay Hua of Intel, Santa Clara, CA, Dr. Luu Nguyen at NSC, Santa Clara, CA, Dr. Darrel Frear at Freescale, Phoenix, AZ, and Dr. Yi-Shao Lai at ASE, Taiwan). The dissertations of H. K. Kim, Patrick Kim, Cheng-Yi Liu, Taek Yeong Lee, Woo-Jin Choi, Hua Gan, Albert T. Wu, Emily Shengquan Ou, Minyu Yan, Fei Ren, Jong-ook Suh, Annie Huang, and Tiffany Fan-Yi Ouyang are acknowledged. Also included are the work of several postdocs (Grant Pan, J. W. Jang, Everett C. C. Yeh, Kejun Zeng, J. W. Nah, and L. Y. Zhang) and M.Sc. students (Wang Yang, Ann A. Liu, Jessica P. Almaraz, Quyen Tang Huynh, Xu Gu, Rajat Agarwal, Joanne Huang, and Jackie Preciado). I acknowledge the generous support of these students and postdocs and thank them. It is their dedication and hard work that made this book possible. Many outstanding contributions to solder research have been made by other researchers. Since this book is an introduction to solder joint technology and covers only a small part of the literature on the subject, I was unable to include much of the published work on solder joints in the literature. I apologize to those colleagues whose work is not included here. Still I hope the book may serve as a steppingstone to reach out to a much broader field of solder and as a reference to future R&D in the field. Indeed, much work on the reliability of Pb-free solder joints remains undone. While this book is intended for engineers and scientists working on solder joint technology in the electronic manufacturing industry, it might be used as a reference book in a course on reliability science of electronic packaging technology for seniors and graduate students. Because very few textbooks on the subject of electronic packaging technology and reliability science are available, I include in the appendixes the derivations of the diffusion coefficient in vacancy mechanism of diffusion in a face-centered-cubic lattice, the growth and dissolution equation of a spherical particle in the ripening process, and Huntington’s electron wind force in electromigration. They are convenient references for analyzing the basic kinetic behaviors of solder joints discussed in this book. This derivation on electron wind force has been taken from the lecture notes of Professor A. M. Gusak at Cherkasy National University, Ukraine. He has been very helpful regarding the kinetic analyses presented in this book, for example, irreversible processes. I am also grateful to Dr. Yuhuan Xu at UCLA and Professor Yiping Wu at Huazhong University of Science and Technology, China, for helpful comments on the drop test in Chapter 11. I thank Professor Chih Chen, National Chiao Tung University, Hsinchu, Taiwan, ROC, and Professor Cheng-Yi Liu, National Central University, Chungli, Taiwan, ROC, for a critical review of the book, and Mr. Jong-ook Suh at UCLA for

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preparation of all the figures and Miss Fan-Yi Ouyang for revision corrections. Finally, I thank Professor Y. C. Chan of the Department of Electrical Engineering, City University of Hong Kong, and Professor Weijia Wen of the Department of Physics, Hong Kong University of Science and Technology, for hosting my two-month visit to Hong Kong so that I could concentrate on finishing the final version of the book. June 2006

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1 Introduction

1.1 Introduction of Solder Joint Solder has been used to join copper pipes for plumbing in every modern house and to join copper wires for circuitry connection in every electrical product. Solder joints are ubiquitous. The essential process in solder joining is the chemical reaction between copper and tin to form intermetallic compounds having a strong metallic bonding. After the iron–carbon (Fe-C) binary system, copper–tin (Cu-Sn) may be the second most important metallurgical binary system that has impacted human civilization, as suggested by the bronze (Cu-Sn alloy) age. Typically a solder alloy of lead (Pb) and tin is used to join copper parts; however, due to environmental concern of lead toxicity, the solder in plumbing is already Pb-free, and Pb-free solders are being introduced into electronic and electrical products. For example, there is a directive to ban Pb-based solders in consumer products by the European Congress on July 1, 2006. For a largescale application of Pb-free solders to electronic products, the reliability is of serious concern. Reliability of solder joint technology in the microelectronic packaging industry has been a concern for a long time, for example, the low cycle fatigue of tin–lead (SnPb) solder joints in flip chip technology due to the cyclic thermal stress between a Si chip and its substrate. At present, the risk of fatigue has been much reduced by the innovative application of underfill of epoxy between the chip and its substrate. On the other hand, to replace SnPb solders by Pb-free solders, new reliability issues have appeared, mostly because the Pb-free solders have a very high concentration of Sn. Furthermore, due to the demand of greater functionality in portable consumer electronic products, electromigration is now a serious reliability issue. This is because of the increase of current density to be carried by the power solder joints. This book is dedicated to the understanding of the fundamentals of solder joint reliability problems. The science of solder reaction and electromigration are emphasized, in particular. In this chapter, solder joint technology and related reliability problems will be briefly introduced. The rest of the chapters

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Chapter 1

will be divided into two parts. Part I will cover copper–tin reactions, while Part II will cover electromigration and thermomigration and related reliability issues in flip chip solder joints. The structure of a solder joint is unique in that it has two joint interfaces. Reliability failures tend to occur at these interfaces. While intermetallic compound formation at the interfaces is required for metallic bonding, the interfacial intermetallic has affected greatly the properties and reliability of the joint. Also, electromigration failure of a solder joint occurs typically at the cathode interfaces. Solder is preferred to have a eutectic composition. This is not only because the melting point of a eutectic alloy is lower than its two components, but more importantly because it has a single melting point. Therefore, the entire joint will melt when the temperature has reached its eutectic point so that both of its interfaces are joined at the same time. In the application of thousands of solder balls as input/output interconnections on a silicon chip, all of them must melt and join at the same time so that the very large number of solder joints between the chip and its substrate can be formed simultaneously by a very simple process of heating or “reflow.” To connect the large-scale integration of circuits on a Si chip to the circuits on its packaging substrate, flip chip technology (to be discussed later in this chapter and Chapter 4) provides the rare advantage that thousands of solder joints or electrical leads can be formed simultaneously by a low temperature heating process in forming gas. Since many of the solder joints can be placed near the center of a chip in order to avoid the voltage drop from an electrical lead which is located at the edge of the chip, it saves power too. The technology does require that all the joints melt or solidify at the same temperature, so a eutectic alloy is favored as solder. Solder is a low melting eutectic alloy. The eutectic tin–lead (SnPb) has a melting point of 183◦ C. To be able to form a metallic bond with Cu at such a low temperature is the key reason why SnPb solder joints have been used worldwide for so long. On the other hand, the typical temperature of solder joint application is either near room temperature or the device working temperature around 100◦ C. They are high-temperature applications of the solder alloy. Take the melting point of eutectic SnPb at 456 K as an example, room temperature and 100◦ C are respectively 0.66 and 0.82 of it. At such high homologous temperatures, thermally activated processes such as atomic diffusion cannot be ignored. The mechanical properties of solder joints or the measurement of the mechanical properties of solder joints at slow strain rates or the concern of reliability due to low cycle fatigue must take into account the contribution of thermally activated processes such as creep and recovery. To achieve a good solder joint, the wetting reaction between molten solder and solid Cu depends on chemical flux. A proper and fresh chemical flux is essential, so that flux is the most important factor in solder joint manufacturing. The flux is required in order to remove oxide on both the Cu surfaces

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and the solder surface so that the molten solder can wet the clean Cu surfaces to be joined. Solder reaction typically involves three chemical elements, e.g., a binary solder alloy of SnPb and a conductor of Cu. There are two kinds of solder reactions: the solder alloy can be in the liquid state or solid state. In a wetting reaction, the solder is in the liquid state and the conductor is in the solid state. Wetting reaction is often called “reflow” in electronic package manufacturing. In a “reflow,” the solder joint experiences a temperature cycle, in which part of the cycle must be above the melting point of the solder for half a minute or so. Since the manufacturing of a device needs to go through several reflows, the total period of wetting reaction for a solder joint in devices may add up to a few minutes. On the other hand, to meet the device reliability specification, the solder joint must be aged at 150◦ C for 1000 hr. In the aging test, while both the solder and conductor are in the solid state, chemical reaction does occur between them. The solid-state aging is of special interest in underthe-hood applications of automobiles where the temperature is quite high. In Chapters 3 and 6, it will be shown that solid-state reaction between solder and Cu occurs even at room temperature. In the solid state, a eutectic alloy is below the eutectic temperature. It has the unique thermodynamic property of a constant chemical potential independent of composition when the temperature is constant. The microstructure of the solid eutectic alloy is a two-phase mixture of two primary phases and they are at equilibrium with each other, independent of the amount of each phase. Therefore, in the two-phase microstructure, phase separation can occur without chemical potential change. Consequently, driven by an external force as in electromigration or in thermomigration, phase separation occurs readily in a eutectic solder, and the resulting microstructure change is quite unique, to be discussed in Chapters 9 and 12. In the eutectic SnPb alloy, Pb does not react with Cu to form any intermetallic compound. The binary Pb-Cu system is immiscible, so the solder reaction is between Sn and Cu. The purpose of alloying Pb with Sn is to lower the melting point, to soften the alloy or to enhance the ductility, and to provide a shiny appearance. Besides, eutectic SnPb is known to have no Sn whisker growth. Due to the environmental concerns of Pb, there are four anti-Pb bills pending in the U.S. Congress, including one from the Environmental Protection Agency. In the European Union, the WEEE (Waste from Electrical and Electronic Equipment) has issued a Directive which calls for a ban of Pb-containing solders in all electronic consumer products on July 1, 2006. At the moment, no chemical element has been found to replace Pb and to function as well as Pb. The most promising Pb-free solders which can replace the eutectic SnPb are the eutectic SnAgCu, eutectic SnAg, and eutectic SnCu. These Sn-based solders have a very high concentration of Sn, e.g., the eutectic SnCu has 99.3 wt% Sn and the eutectic SnAgCu has about 95 to 96 wt% of Sn. Hence, in essence the solder reaction between the Pb-free and Cu is the Cu-Sn reaction.

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In the following, the major solder joint technologies used in manufacturing of electronic devices will be described briefly. They are the surface mount technology, pin-through-hole technology, and flip chip technology [1, 2]. A clear picture of where and why solder is used in microelectronic devices is presented below in order to reveal the link to issues of reliability. Then the cause of reliability in these technologies will be addressed briefly, including Sn whisker growth, spalling of interfacial intermetallic compounds, low cycle fatigue, and electromigration and thermomigration in flip chip solder joints. Finally, the future trend in microelectronic packaging and the role of solder joint in the trend will be discussed. Because of the trend of miniaturization of devices and packaging technology, a continuing study of these reliability issues is needed in the near future. Since the topic of thermal stress-induced fatigue and creep has been well covered in many books, it will be briefly mentioned here. The two important contributors to solder joint reliability to be emphasized in this book are copper–tin reaction, and electromigration and thermomigration.

1.2 Lead-Free Solders 1.2.1 Eutectic Pb-Free Solders At present, nearly all the eutectic Pb-free solders are Sn-based. A special class of them are the eutectic alloys consisting of Sn and noble metals: Au, Ag, and Cu. Other elements to alloy with Sn such as Bi, In, Zn, Sb, and Ge have been considered. The eutectic points of the binary Pb-free solder systems are compared with that of eutectic SnPb in Table 1.1. It can be seen that there is a large temperature gap between the eutectic temperatures of SnZn (198.5◦ C) and SnBi (139◦ C), for which no known Pb-free solder system exists. Zinc (Zn) is cheap and readily available, but it quickly forms a stable oxide, resulting in excessive drossing during wave soldering, and more problematically, it shows very poor wetting behavior due to the stable oxide formation. Hence, a forming gas ambient is required. The eutectic SnZn has a melting point which is closest to that of eutectic SnPb among all the eutectic Pb-free solders and it has received much attention in Japan, especially. Bismuth (Bi) has very good wetting properties. The eutectic Sn-Bi solder has been used in pin-through-hole technology which will be discussed in the next section. However, the availability of Bi could be limited by the restrictions on Pb, because the primary source of Bi is a by-product in Pb refining. By restricting the use of Pb, much less Bi will be available. Antimony (Sb) has been identified as a harmful element by the United Nations Environment Program. Germanium (Ge) is used only as a minor alloying element of multicomponent solders due to its reactivity. Indium (In) is too scarce and too expensive to be considered for broad applications, besides it forms oxides very easily. A common characteristic of eutectic Sn-noble metal alloys is the high melting point and high concentration of Sn compared to that of eutectic SnPb.

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Ag3Sn

Cu6Sn5

100μm

Fig. 1.1. SEM image of Ag3 Sn platelet in SnAgCu solder joint.

Hence the corresponding reflow temperature will be higher, by about 40◦ C. It may increase the dissolution rate and solubility of Cu and Ni in the molten solder as well as the rate of intermetallic compound (IMC) formation with Cu and Ni under-bump metallization. If the surface and interfacial energies are considered, the surface energies of these Pb-free solders are higher than that of SnPb, so they form a larger wetting angle on Cu, about 35 to 40◦ . Concerning the microstructure of these eutectic solders, they are a mixture of Sn and IMC because of the high concentration of Sn, unlike that of eutectic SnPb which has no IMC. Since metallic Sn has the body-centered tetragonal lattice structure and tends to deform by twinning, its mechanical properties are anisotropic. The electrical conductivity of metallic Sn is also anisotropic. The mechanical and electrical properties of these eutectic solders will be anisotropic, thus the dispersion of the IMC may lead to the formation of inhomogeneous microstructures, especially in the case of Ag3 Sn. The image of Ag3 Sn appears to be long needlelike crystals in the eutectic SnAg on the cross-sectional image of a solder joint. But after the matrix of the solder is removed by deep etching, they turn out to be platelike, as shown in Fig. 1.1. If such Ag3 Sn crystals formed in a high-stress area, such as the corner of a solder bump, cracks can be initiated and can propagate along the interface between the Ag3 Sn and solder, leading to fracture failure as observed in Fig. 1.2. To avoid the formation of such large plate-type IMC, the Ag concentration in the solder should be less than 3%, below the eutectic composition of 3.5% as shown in Table 1.1. In the case of eutectic SnCu, it has only 0.7 wt% Cu, so the bulk of the solder is almost pure Sn. Then, the phenomenan of Sn whisker [3–5], Sn pest [6], and Sn cry [7] are of concern. Furthermore, if electroplating is used to prepare the solder, it is very difficult to have a controlled composition within 1%. In the case of Au-Sn solder, the formation of

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Fig. 1.2. SEM image of crack at the corner of SnAgCu solder joint.

Table 1.1. Binary Pb-free eutectic solders Systems Sn-Cu Sn-Ag Sn-Au Sn-Zn Sn-Pb Sn-Bi Sn-In

Eutectic temp. (◦ C)

Eutectic composition (wt%)

227 221 217 198.5 183 139 120

0.7 3.5 10 9 38.1 57 51

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Fig. 1.3. Eutectic ternary phase diagram showing the eutectic point of SnAgCu.

AuSn4 means that one Au atom will attract four Sn atoms. Hence, a small amount of Au can lead to the formation of a large amount of IMC. This is the origin of brittle “cold” joint when the content of Au is more than 5 wt% in a solder. Ternary and higher order solders are most likely based on the binary eutectic Sn-Ag, Sn-Cu, Sn-Zn, or Sn-Bi alloys. The most promising one is eutectic Sn-Ag-Cu. The eutectic Sn-Ag-Cu alloy forms good quality joints with copper. Its thermomechanical property is better than those of the conventional Sn-Pb solder. Its eutectic temperature has been determined to be about 217◦ C, but its eutectic composition has been a subject of controversy. Based on metallographic examination, differential scanning calorimetry measurements, and differential thermal analysis results, the eutectic composition was estimated at 3.5±0.3Ag, 0.9±0.2Cu (wt%) [8–10]. These data are plotted together with the thermodynamically calculated phase diagram in Fig. 1.3, where the equilibrium eutectic point is calculated to be Sn-3.38Ag-0.84Cu (wt%). While the accuracy of the eutectic point is of academic interest, it is an important issue in application. Due to the higher melting point, the reflow temperature will be around 240◦ C, which is higher than that of eutectic SnPb. It is a manufacturing issue, for the applications on those polymer substrates that have a low glass transition temperature as well as for the flux used in solder paste that has a high evaporation rate. Because the chemical composition of the flux for Pb-free solders is not as yet optimized, the reflow of Pb-free solder

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paste has produced many more residue voids in solder joints than the eutectic SnPb paste. The migration of these voids to contact interfaces can become a reliability issue. Both Cu and Ni thin films are used widely as on-chip under-bump metallization (UBM), but they can be reacted and dissolved away by molten solder during reflow, resulting in spalling of IMC, which is a subject of serious reliability concern to be discussed in Section 1.4.2. Hence, a solder of eutectic composition is undesirable when it is used with thin-film UBM. It must be supersaturated with excess Cu and/or Ni, about 1%, in order to reduce the dissolution. Therefore, the recommended composition for SnAgCu solder is about Sn-3Ag-3Cu. While it is off the eutectic composition and will not have a single melting point, the effect of the composition on melting temperature is very small and will not be an issue in manufacturing. 1.2.2 High-Temperature Pb-Free Solders At present, there is no high-temperature Pb-free solder to replace the 95Pb5Sn high-Pb solder, except the 70Au30Sn. A Sn-based solder of Sn-Ag or Sn-Cu having a higher Ag or Cu, respectively, than the eutectic composition has a large temperature gap between the liquidus and solidus points, hence it is undesirable as a solder due to partial or nonuniform melting when it goes through the large temperature gap. The 70Au30Sn alloy (at.%) has a eutectic point of 280◦ C, so it can be considered as a high temperature Pb-free solder, yet it is known to have a poor reflow behavior besides high cost. The binary system of Au-AuSb2 has a eutectic temperature at 360◦ C, yet its wetting property on Cu is unknown. Alloys of Sb-Sn have been considered as a high-temperature Pb-free solder, yet they have a large gap between the liquidus and solidus temperatures too. Sn-Zn alloys have the same problem. In the periodic table of chemical elements, Ge and Si belong to the same column as Sn and Pb, therefore, it is of interest to consider eutectic alloys of them with noble metals, such as Au-Ge which has a eutectic point at 356◦ C. Concerning their wetting behavior on Cu, an active flux must be available to prevent the oxidation of Ge or Si. However, these eutectic alloys undergo volume expansion upon solidification. In the molten state when Ge and Si are alloying with noble metals, their liquid structure is rather closely packed. But in solidification to form a two-phase eutectic structure, the Ge and Si have the diamond structure, which is quite open. Mechanical properties of these eutectic joints may be poor because Si and Ge are not metals. To overcome this problem, we may consider replacing Si or Ge by silicide or germanide phases. In other words, we consider the eutectic structures of silicide and noble or near-noble metals. The ternary system of Au-Ge-Co might be of interest since Au-Ge has a eutectic temperature of 356◦ C with a eutectic composition of Ge at 27 at.%. Also, Au-Co forms a eutectic system with a eutectic temperature at 996◦ C.

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Co and Ge form several germanides such as Co2 Ge, CoGe, and CoGe2 . It is unknown if a eutectic structure can be formed between Au and one of the germanides with a low eutectic temperature. However, the ternary phase diagram must be investigated first, the eutectic point of this ternary system must be calculated, and an active flux must be available. Owing to the trend of miniaturization, the size of flip chip solder joint will be below 50 μm in diameter, say 25 μm. For such a small solder joint, it can be transformed completely into intermetallic compound by solder reaction at the reflow temperature in 1 min or so. In Section 7.3, the rapid reaction between Pd and Sn to form Pd-Sn compounds will be discussed. Since the intermetallic compound has a high melting point, it will not melt at the reflow temperature after it is formed. Since it is Pb-free, it might serve as a high-temperature Pbfree solder joint.

1.3 Solder Joint Technology 1.3.1 Surface Mount Technology In most of the portable electronic consumer products, such as mobile handheld telephones, wire bonding technology is the most widely used method to connect the circuits on a Si chip to a leadframe substrate, which is then connected electrically to the outside via an antenna. Figure 1.4 shows wire bonding between a Si chip and a Cu leadframe. The legs of the leadframe are joined to bond pads on a packaging circuit board by using solder joints.

Si

Sealing glass

Leads Fig. 1.4. Schematic diagram of wire bonding between a Si chip and a leadframe.

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Cu Leadframe e-SnPb e-nAgCu

Surface Mount Solder Board Pad FR4 board Fig. 1.5. A schematic diagram of the solder joint between a leg and a substrate board.

These solder joints were fabricated by printing a pattern of mounts of solder paste on the bond pads and every leg is placed on a printed paste mount, then the assembly will be placed on a belt moving through a tube furnace in a forming gas ambient and heating to a temperature above the melting point of the solder paste to achieve joining. Figure 1.5 is a schematic diagram of the solder joint between a leg and a substrate board. The heating process is called “reflow,” and typically the temperature of reflow goes above the melting point of the solder by 30 to 40◦ C for half a minute or so. During this period the solder paste melts and reacts with the leadframe as well as the bond pad to form a metallic joint. To facilitate the joining of all the legs within the half-minute period, the leadframe is coated with a layer of eutectic SnPb. Owing to environmental concerns, the coating has been replaced with eutectic SnCu or pure Sn. However, spontaneous Sn whiskers are found to grow on these Pb-free coatings. The whiskers may become electrical shorts between the legs, and represent a reliability issue at the present time. Besides Sn whiskers, cracking may occur along the interface between the leg and the solder, mostly due to solder reaction induced void formation or impurity segregation. 1.3.2 Pin-through-Hole Technology The legs of the leadframe are typically bent into the shape of a pair of galewings or J-wings so that they can be placed on the solder paste mounts on the surface of a board for joining in surface mount technology. However, for devices in military applications, in order to enhance the mechanical reliability of the joints, the legs are straight so that they are like pins and they can be inserted into holes drilled in the board. The holes have been plated with Cu and immersion Sn, so that when the board with the inserted pins is guided over a fountain of molten solder, the molten solder touches the bottom surface of the board, wets the immersion Sn, and rises along the plated holes by the capillary force. Thus, the pins are soldered to the board through the holes. For

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Fig. 1.6. Cross-sectional image of through holes plated with Cu and immersion Sn.

this reason, it is also called pin-through-hole technology. Compared to surface mount technology, this technology has better mechanical reliability but also higher cost. The surface of the immersion Sn affects the capillary force and in turn controls the wetting action. If the plating bath contains impurity of S, the immersion Sn surface will appear gray and dull and cannot be wetted by the molten solder. The immersion Sn from a good plating bath should appear white and bright. Figure 1.6 is a cross-sectional image of the through holes plated with Cu and immersion Sn and part of the holes was not filled with solder. The incomplete filling was because of gray Sn [11]. The potential of the pin-through-hole technology is that it can be applied to the plating of macro-through-holes in Si. This will be clear after we have discussed the thermal stress issue in flip chip technology in the next section. The diameter of the through hole will be 10–100 μm, i.e., nearly the same diameter as flip chip solder balls. We can fill the macro-through-holes with solder or Cu and use the Si with plated-through-holes as packaging substrate for flip

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chip technology. When a Si chip is joined to a Si substrate, there will be no or very little thermal stress. 1.3.3 C-4 Flip Chip Technology In mainframe computers such as a server, the solder joints connecting Si chips to their substrate are more complicated. To see the complication, we begin with two simple facts about interconnection on a chip. Today’s aluminum or copper wiring on a very-large-scale-integration (VLSI) Si chip is 0.5 μm (or less) in width. Assuming the spacing between two parallel wires is also 0.5 μm, the pitch is 1 μm. Therefore, on a 1 cm2 chip area, we can have 104 wires, each being 1 cm in length. This means that in a single layer of wiring, the total length of the wire is 100 meters. Since six to seven layers of wiring are made on a chip and if we add the length of vias between the layers, we find that the interconnect wiring on a 1 cm2 chip is about 1 kilometer! We need this much wiring to connect millions of transistors on the chip in order for them to function together. This is the first fact. To provide external electrical leads to all these wires on the chip, we may need several thousands of input/output (I/O) pads on the chip surface of a logic chip. At present, the only practical way to provide such high density of I/O pads is to use area array of tiny solder balls. We can have 50-μm-diameter solder balls with a spacing of 50 μm between them, so the pitch is 100 μm. We place 100 of them along a length of 1 cm or 10,000 of them on an area of 1 cm2 . Thus, the second fact of interconnection between a chip and its substrate is that we can have about 10,000 I/Os or solder balls on a chip surface. Because of the expected use of solder balls of such small size and large number, the International Technology Roadmap for Semiconductors (ITRS) since 1999 has identified “solder joint in flip chip technology” to be an important subject of study concerning its yield in manufacturing and its reliability in use [12]. Actually, 25-μm-diameter solder balls are being developed. What is a flip chip? It refers to a method of achieving electrical connections between a Si chip and a ceramic module or a printed circuit board. The Si chip is flipped facing down so the circuit of very-large-scale integration faces the substrate. The electrical connection is achieved through an area array of solder bumps between the chip and its substrate. Unlike wire bonding, in which the wire connections are made at the periphery of the chip, flip chip connections are an area array of solder bumps covering all or a large part of the surface of the chip. Figure 1.4 is a schematic diagram of wire bonding of a Si chip to a leadframe. The leads (legs) of the leadframe are soldered to a circuit board by surface mount technology or by pin-through-hole technique. The VLSI side of the chip is upside-up in wire bonding. Because wire bonding requires ultrasonic vibration, the stress applied during the bonding process may damage the structure around and underneath the bonded area. Therefore, it must be done on the periphery of the chip, away from the active VLSI region in the

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Fig. 1.7. An area array of solder balls on a chip surface.

central area of the chip. Even if we can use 20-μm wire with 20-μm spacing, we can only have about 1000 I/Os on the periphery of a 1 cm2 chip, which is much less than the 10,000 solder balls that can be deposited or electroplated on the same chip area. Since the wire bondpads occupy the periphery of the chip, it wastes a large fraction of the chip surface too. In placing solder balls over the entire surface of a Si chip, it has been found that there is no stress problem when solder balls are placed directly over an active VLSI area. Figure 1.7 shows an area array of solder balls on a chip surface. To join the chip to a substrate, the chip will be flipped over, so it is a flip chip and the VLSI side of the chip is upside-down, facing the substrate. Generally speaking, the advantages of flip chip technology are smaller packaging size, large I/O lead count, and higher performance. In chip-size packaging, where the packaging is of nearly the same size as the chip, the small packaging size is achieved without the periphery bonding area. The larger I/O lead count is due to area array. The higher performance occurs because the bumps in the central part of the chip will allow the device to operate at lower voltage and higher speed. For devices that require these advantages such as handheld devices, flip chip is the only existing technology that can provide the reliability needed. The International Technology Roadmap for Semiconductors [12] has projected that Si technology will still be able to advance a new generation every two to three years in the foreseeable future, probably until 2015. To stay with the Si chip technology, the packaging technology must advance too. Thus,

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Chip

**out

Ceramic module

Eutectic solder

BGA

FR4 card

90%Pb/10% Sn ball

Fig. 1.8. Schematic diagram of cross section of a ceramic module joined to a large printed circuit board and resulting in the two-level packaging scheme for mainframe computers.

the circuit density and the number of I/Os on the packaging substrate must increase. For the projected technology, reliability issues need to be discussed. Flip chip technology has been used for over 30 years in mainframe computers. It originated from the “controlled collapse chip connection” or “C-4” technology in packaging chips on ceramic modules beginning in the 1960s [13, 14]. For a detailed discussion of C-4 technology and the history of its evolution, readers are referred to a recent review by Puttlitz and Totta [1]. When the VLSI chip technology was developed, a high density of wiring and interconnection was required for the packaging. This has led to the development of multilevel metal-ceramic modules and multichip modules for mainframe computers. In a multilevel metal-ceramic module, many levels of Mo wires were buried in the ceramic substrate. Each of these modules could carry up to a hundred chips. Several of these ceramic modules were joined to a large printed circuit board and resulted in the two-level packaging scheme for mainframe computers, shown in Fig. 1.8. It consisted of a first-level chipto-ceramic module packaging and a second-level ceramic module-to-polymer board packaging. In the first-level packaging, the on-chip under-bump metallization (UBM) is a trilayer thin film of Cr/Cu/Au. Actually, in the trilayer the Cr/Cu has a phased-in microstructure for the purpose of improving the adhesion between Cr and Cu and strengthening its resistance against solder reaction so that it can last several reflows. The bond pad on the ceramic surface is typically Ni/Au. The solder which joins the UBM and the bond pad is a high-Pb alloy such as 95Pb5Sn or 97Pb3Sn. A schematic diagram of the cross section of the joint is shown in Figure 1.9. The on-chip solder bumps

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Si Chip side

SiO2

Al Cr Cu Phased-in Au

Pb-Sn SOLDER 95

5

Mo

Au Ni Module side

MULTI-LAYERED CERAMICS

Fig. 1.9. Schematic diagram of the cross-section of the flip chip solder joint is shown.

were deposited by evaporation and patterned by lift-off, but now they are deposited by selective electroplating. The high-Pb bump has a melting point over 300◦ C. During the first reflow (around 350◦ C), a ball shape of the bump is obtained on the UBM. Since the surface of SiO2 cannot be wetted by molten solder, the base of the molten solder bump is defined by the contact opening of the UBM, thus the molten solder bump balls up on the UBM contact. Therefore, the UBM controls the dimensions (height and diameter) of the solder ball when its volume is given. Often, the UBM is called “ball-limiting metallization” (BLM). The BLM controls the height of the fixed volume of a solder ball when it melts; this is the control in “controlled collapse chip connection.” Without the control, the solder ball will spread and then the gap between the chip and the module is too small. To join the chips to a ceramic module, a second reflow is used. During the second reflow, the surface energy of the molten solder bumps provides a self-aligning force to position the chip on the module automatically. When the solder melts to join the chip to the module, the chip will drop slightly and rotate slightly. The drop and rotation are due to the reduction of surface tension of the molten solder ball, which achieve the alignment between the chip and its module, so it is a controlled collapse process. We note that the high-Pb solder is a high melting-point solder, yet both the chip and the ceramic module can withstand the high temperature of reflow without a problem. Additionally, the high-Pb solder reacts with Cu to form a layer-type Cu3 Sn, which can last several reflows without failure. We note that each of the metals in the trilayer of Cr/Cu/Au has been chosen for a particular reason. First, solder does not wet the Al wire, so Cu is selected for its reaction with Sn to form intermetallic compounds (IMC). Second, Cu does not adhere well to the dielectric surface of SiO2 , so Cr is selected as a glue layer for the adhesion of Cu to SiO2 . The phased-in Cu-Cr UBM was developed to improve the adhesion between Cu and Cr. Since Cr and Cu are immiscible, their grains form an interlocking microstructure when they are co-deposited.

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A discussion of the lattice image of the phased-in Cu-Cr microstructure will be given in Chapter 2. In such a phased-in microstructure, the Cu adheres better to the Cr and also it will be harder for Cu to be leached out to form IMC with Sn during reflow. Furthermore, the phased-in microstructure provides a mechanical locking of the IMC. Finally, Au is used as a surface passivation coating to prevent the oxidation or corrosion of Cu. It also serves as a surface finish to enhance solder wetting. In the second-level packaging of ceramic module to polymer board, i.e., to join the ceramic substrate to a printed polymer circuit board, another area array of solder joints is placed on the backside of the ceramic substrate. They are called ball-grid-array (BGA) solder balls which have a much large diameter than the C-4 solder balls. Typically the diameter is about 760 μm. They are eutectic SnPb solder with a lower melting point (183◦ C), which is reflowed around 220◦ C. Sometimes, composite solder balls of high-Pb and eutectic SnPb are used, with the high-Pb as the core of the ball. It is obvious that during this reflow (the third), the high-Pb solder joints in the first-level packaging will not melt. In summary, there are three steps in C-4 flip chip joints. The first is solder bumping on a chip surface by electroplating or by stencil printing of an area array of solder bumps, followed by a reflow to transform the bumps into balls. The second step is to bond the chip to its substrate in a flip chip configuration by a second reflow process. The substrate has an area array of bond pads to receive the balls. The third step is to underfill the gap between the chip and the substrate with epoxy. However, the BGA in the second level of packaging does not use underfill.

1.4 Reliability Problems in Solder Joint Technology 1.4.1 Sn Whiskers In May 1998, the Galaxy 4 satellite was killed in space by the growth of Sn whiskers; one of them bridged or shorted a pair of metal contacts in the satellite’s control processor [3–5]. The loss of the satellite was just one of the more visible examples of reliability problems caused by Sn whiskers in those electronic devices that require a long term and high degree of reliability. As eutectic SnPb solder is replaced by the Sn-based Pb-free solders, the whisker problem is of concern. Figure 1.10 shows an SEM image of whiskers on the legs of a leadframe, in which a very long whisker can be seen to have bridged a pair of the legs. The growth of whiskers on beta-tin (β-Sn) is a surface relief phenomenon of creep. It is driven by a compressive stress gradient and occurs at ambient. The whisker growth is spontaneous, indicating that the compressive stress is self-generated; no external applied stress is necessary. Otherwise, we expect a whisker to slow down and stop when the applied stress is exhausted, if

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Whisker

Fig. 1.10. SEM image of Sn whisker shorting two legs.

not applied continuously. Therefore, it is of interest to ask where is the selfgenerated driving force coming from? How can the driving force maintain itself to achieve the spontaneous and continuous whisker growth? Also, how large must the compressive stress be to grow a whisker? Spontaneous Sn whisker growth occurs readily on matte Sn finishes on Cu. Today, because of the wide application of Pb-free solders on Cu conductors used in the electronic packaging in consumer electronic products, Sn whisker growth has become a widely recognized reliability issue. When the solder finish on Cu leadframe is eutectic SnCu or matte Sn, whiskers are observed. We will show in Chapter 6 that the self-generated driving force is due to the room temperature reaction between Cu and Sn to form Cu6 Sn5 in the Pb-free finish on the Cu leadframe. Some whiskers can grow to several hundred micrometers, which are long enough to become electrical shorts between neighboring legs of a leadframe. As the dimension of packaging shrinks, shorter whiskers will cause problems. Hence, how to perform systematic studies of Sn whisker growth in order to understand the driving force, the kinetics, and the mechanism of growth, and how to suppress Sn whisker growth are challenging tasks in the electronic packaging industry today. 1.4.2 Spalling of Interfacial Intermetallic Compounds in Direct Chip Attachment In Section 1.3.3 on flip chip technology, we have shown a two-level packaging scheme which has worked well for mainframe computers, yet the ceramic module is too expensive for low-cost and large-volume production of consumer

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goods. To save cost, the electronic industry removes the ceramic module (or the first level packaging) so that chips can be attached directly to printed polymer circuit boards. This is so-called “direct chip attachment” or “flip chip on organic technology.” Since polymer substrates have a low glass transition temperature, the reflow temperature should be lower for flip chip on organic substrates, therefore the high-Pb solder cannot be used. Since the Cr/Cu/Au thin films have been successfully used as on-chip metallization in C-4 technology, one naturally attempts to transfer it to direct chip attachment, i.e., to join chips having the Cr/Cu/Au UBM to an organic substrate with eutectic SnPb solder. However, when eutectic SnPb is used to wet the Cr/Cu/Au or even the phased-in Cu-Cr, the joint fails in multiple reflows. The low-melting-point eutectic solder contains a high concentration of Sn (74 at.% Sn). It can consume all the Cu film very quickly (at a rate of about 1 μm/min at 200◦ C), resulting in spalling of the Cu-Sn compound [15–17]. Thus, the solder joint becomes mechanically weak because there is no adhesion between the solder and the remaining Cr. Figure 1.11 shows cross-sectional SEM images of the interface between eutectic SnPb and Au/Cu/Cu-Cr thinfilm UBM after a heat treatment at 200◦ C for (a) 1 min, (b) 1.5 min, and (c) 10 min. Many of the spherical grains in Fig. 1.11(c) have spalled (detached from the Cr/SiO2 surface) into the molten solder [16, 17]. The spalling phenomenon is extremely undesirable, because it leads to chemically and mechanically weak joints since the solder is now in contact with the unwettable Cr. Indeed, when we performed mechanical test of samples of solder balls sandwiched between two Si chips with Cu/Cr UBM, the load needed to fracture the joints decreased dramatically with increasing heat treatment time [18, 19]. In essence, if we replace the high-Pb solder joint as shown in Fig. 1.9 by the eutectic SnPb, the wetting reaction between molten eutectic SnPb and Au/Cu/Cr UBM becomes a problem. To solve this problem which is due to the reaction between a molten solder and a thin-film UBM, there are two general approaches: we can either improve the solder or improve the UBM. They are illustrated in Fig. 1.12(a) and (b). About the first approach, since we know that the phased-in Au/Cu/Cr works well with the high-Pb solder, we keep them as they are. But we will use a low-melting-point eutectic solder to join the high-Pb solder, this is the “composite solder” approach, as shown in Fig. 1.12(a). Detailed discussion about composite solder joints will be given in Section 4.2. The eutectic solder bump can be deposited on the organic substrate before joining. The key advantage is that the reflow temperature is low since it only needs to melt the low-melting-point solder which will wet the high-Pb solder. Nevertheless, we note that this approach has a potential problem. During reflow, the molten eutectic solder can migrate along the outer surface of the high-Pb solder bump to reach the circumference of the Au/Cu/Cr. Again, a certain amount of spalling of IMC occurs in the circumference of the UBM. More seriously, electromigration will drive the Sn from the substrate side to the chip side to replace the high-Pb when electrons flow from the chip to the substrate, to be discussed in Chapter 9.

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1 min

1.5 min

10 min

Fig. 1.11. (a) to (c) show cross-sectional SEM images of the interface between eutectic SnPb and Au/Cu/Cu-Cr thin film UBM after a heat treatment at 200◦ C for 1 min, 1.5 min, and 10 min, respectively.

In the second approach, a Ni-based UBM is used typically to replace the Cu-based UBM in order to slow down the solder reaction, as shown in Figure 1.12(b). We recall that Ni has been used in the bond pad on the ceramic module side, and indeed Ni has been found to have a much slower solder reaction rate with the eutectic SnPb (to be discussed in Chapter 7). However, evaporated or sputtered Ni films tend to have a high residue stress. The stress may crack the dielectric layer of SiO2 on the chip surface. That is why Ni has been used only on the module side where there is no active device. Two kinds of low-stress Ni-based UBMs are currently being used in wafer bumping. One is electroless Ni(P) UBM, which is quite thick, over 10 μm, and the other is a sputtered thin film Cu/Ni(V)/Al, in which the Ni(V) thin film is about 0.3 μm in thickness. We shall discuss their wetting reactions in Sections 3.6 and 3.7.

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(a)

(b)

Fig. 1.12. (a) Direct chip attachment by using a composite solder joint. (b) Direct chip attachment by using Ni-based UBM.

Besides Ni-based UBM, we can also use a very thick Cu UBM provided that stress is not an issue. A thick Cu UBM or a Cu column bump will survive several reflows without IMC spalling. As long as there remains free Cu in the UBM, the Cu6 Sn5 compound will stick to the free Cu and will not spall. All Pb-free solders, as far as we know today, are high-Sn solders. For example, the eutectic SnAg solder has about 96 at.% Sn. The problem of IMC spalling as we have discussed above is worse with these Pb-free solders due to the very high concentration of Sn. Solder reaction in flip chip technology has a dilemma. On the one hand, we require a very rapid solder reaction in order to achieve the joining of thousands of them simultaneously on a chip. On the other hand, we also want the solder reaction to stop right after the joining since the on-chip thin-film UBM is too thin to allow a prolonged reaction. Nevertheless, the manufacturing of a device requires these solder joints to survival several reflows, in which the total period of a solder bump in the molten state is several minutes. When the solder is Pb-free and has a high concentration of Sn, the Cu-Sn reaction rate is enhanced. Furthermore, the diffusion of Cu and Ni across a solder joint of diameter 100 μm is so fast during reflow or during solid-state aging that chip-to-packaging interaction takes place and affects solder joint reliability. This is illustrated below. Figure 1.13(a) is a schematic diagram depicting the metallurgical structures across a flip chip solder joint. The thin-film under-bump metallization (UBM) on the chip side consists of 300 nm of Cu/400 nm of Ni(V)/400 nm of Al. The thick metallic bond pad on the board side, across the solder bump, consists of 125 nm of Au/10 μm of Ni(P) on a very thick Cu trace. The Cu film and the Au film are respectively the surface metallization on the chip side and on the board side, and between them is the eutectic SnAgCu solder bump. Figure 1.13(b) shows the cross-sectional scanning electron microscopy image of such a solder joint which bonded a chip (the bottom) to a board

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Fig. 1.13. (a) A schematic diagram depicting the metallurgical structures across a real flip chip solder joint. The thin film under-bump metallization (UBM) on the chip-side consists of 300 nm of Cu/400 nm of Ni(V)/400 nm of Al. The thick metallic bond-pad on the board-side, across the solder bump, consists of 125 nm of Au/ 10 μm of Ni(P) on a very thick Cu pad. (b) The crosssectional scanning electron microscopy image of such a solder joint which bonded a chip (the bottom) to a board (the top). The formation of scallop-type IMC at the two solder interfaces can be seen. (c) The same image of the joint after 10 reflows. The IMC on the chipside has spalled into the solder.

(the top). The formation of scallop-type intermetallic compound (IMC) at the two solder interfaces can be seen. Figure 1.13(c) shows the same image of the joint after 10 reflows. The IMC on the chip side has spalled into the solder. In other words, the IMC has detached from the chip and moved into

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the solder. Consequently, there is very little adhesion at the interface between the solder and the chip. In other words, it is a weak interface chemically and mechanically. Therefore, the interest in solder reactions, especially the solder reaction on thin films, is to understand the problem of spalling of IMC and to prevent the latter from happening so that the solder joint is strong and can last a long time. The scallop-type morphology is itself of interest. Why IMC forms with such a morphology and why the morphology is stable (except ripening) under isothermal annealing at 200◦ C up to 40 min are intriguing. The electronic packaging industry would like to have flip chip solder joints that can last several reflows during manufacturing, and then in field use, they should possess the reliability to survive solid-state aging, thermal stress cycling, and electromigration. 1.4.3 Thermal-Mechanical Stresses The difference in coefficients of thermal expansion between a Si chip and its substrate is the cause of thermal-mechanical stress. Low cycle fatigue due to the thermal stress, or the Coffin–Manson mode of fatigue, has long been a reliability problem in the C-4 technology. To overcome the problem, a ceramic module which has nearly the same thermal expansion coefficient as Si was synthesized. Also, the technology of using a Si wafer as substrate for a Si chip was developed. Yet, for low-cost consumer products, the thermal stress in flip chip on organic substrates is very large, as shown in Figure 1.14(a). Due to the very large difference in coefficients of thermal expansion between Si (α = 2.6 ppm/◦ C) and the organic FR4 board (α = 18 ppm/◦ C), a very large shear strain exists in those bumps at the corners of a chip in direct chip attachment. When the solder is in the molten state [see Figure 1.14(b)], there is no thermal stress although the board has expanded much more than the chip. But upon cooling, when the solder solidifies, the thermal mismatch begins to interfere. We shall take the temperature difference to be that between room temperature and 183◦ C, which is the solidification temperature of eutectic SnPb solder. And we consider a bump at the corner of a chip of size 1 cm × 1 cm. The shear is equal to Δl/l = ΔαΔT. We obtain a value of Δl = 18 μm if we √ take l = ( 2)/2 cm, which is the distance of half diagonal of the chip. If we assume the chip to be rigid, the board will bend and the curvature is concave downward. This is because the solid bumps will prevent the upper surface of the board from shrinking, so the board bends when its lower part shrinks [see Fig. 1.14(c)]. Due to the bending and the fact that the solder joints and the chip are not rigid, the actual Δl will be less than the calculated value of 18 μm given in the last paragraph. Figure 1.15(a) shows the schematic diagram and diagonal cross-sectional SEM images of eutectic SnPb solder bumps between a flip chip and an FR4 board. Figure 1.15(b) shows the joints in the center part of the chip, where the alignment of the bump between the top UBM on the chip

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Solder ball Si chip

Organic module (FR4)

Δl

(a)

UBM

Δl

(b)

Δ l′

Δ l′

q

(c)

Fig. 1.14. (a) No thermal stress in flip chip on organic substrates before solder joining. (b) When the solder is in the molten state, there is no thermal stress although the board has expanded much more than the chip, so there is misalignment between the UBM and bond pad, (c) Upon cooling to room temperature, the board bent concave downward. This is because the solid bumps will prevent the upper surface of the board from shrinking, so the board bends when its lower part shrinks.

and the bottom bond pad on the board is good. Figure 1.15(c) shows the right-hand side corner of the chip, where we see that the bottom bond pad on the board has been displaced to the right by about 10 μm. Figure 1.15(d) shows the left-hand side corner of the chip, and the same displacement of the bond pad is to the left. The nominal shear strain is Δl/h = 10/60, where h = 60 μm is the gap between the chip and the board. In addition, the chip is bent and has a concave downward curvature of 57 cm. Clearly, the chip, the board, and the bumps are stressed. Besides the shear strain, there may be normal stresses in the solder joints, especially across those bumps in the center of the chip. During reflow, such thermal cycle is repeated. During normal device operation, the chip will experience a working temperature near 100◦ C due to joule heating, and produces a low cycle thermal stress between room temperature and 100◦ C to fatigue the solder joints. While the electronic industry has introduced epoxy underfill to redistribute the stresses, it remains a reliability issue.

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Si chip

Si chip

1 cm

1 cm

UBM Solder ball and UBM

Organic substrate

(a)

(b)

Center

Organic substrate

h

(c)

Right

Δx

(d) Left

Δx

100 μm

Fig. 1.15. (a) A schematic diagram and diagonal cross-sectional SEM images of eutectic SnPb solder bumps between a flip chip and a FR4 board, (b) SEM image of the joints in the center part of the chip, where the alignment of the bump between the top UBM on the chip and the bottom UBM on the board is good, (c) SEM image of the right-hand side corner of the chip, where we see that the bottom UBM on the board has been displaced to the right by about 10 μm, and (d) SEM image of the left-hand side corner of the chip, and the same displacement of the UBM is to the left.

If we introduce underfill in the configuration shown in Fig. 1.15(c), the solder joints have already been strained. Hence, it is better to apply underfill to unstrained solder joints. Assuming it can be done, we still cannot avoid the problem of thermal stress. This is because in subsequent solid-state aging, in thermal cycling, and in device operation, the stress returns. If the solder joint itself or its interface is weak, the stress can break it. It is worth noting that it is this large shear strain that limits the size of a Si chip in a flip chip manufacturing! Until we can solve the thermal stress issue, the chip size is limited to about 1 × 1 cm2 . Nevertheless, chips having a size of 2 × 2 cm2 are being made. In Fig. 1.15, it is obvious that if we keep the chip and the board to be the same and if we reduce the gap “h” between the chip and the board (or the diameter of the bump), the shear strain increases. What is not obvious is that if we keep the gap unchanged but increase the thickness of the UBM and bond pad, it reduces the actual thickness of solder in between them, and it will greatly increase the shear strain of the solder joint. This is clearly shown in Fig. 1.15(b) to (d), where the UBM and bond pad are quite thick, so the solder layer in between them is about 23 μm. Assuming that the UBM and bond pad are rigid and the solder takes all the shear, its shear strain will be Δl/h = 10/23, rather than Δl/h = 10/60 as given before. It is known that a tall solder joint suffers less thermal cycle fatigue, but the current trend is to use a smaller size solder bump and thicker UBM. In addition, a thick IMC formed between the UBM and solder will also further reduce the thickness of the unreacted solder and add to the shear

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strain. While the total thickness of IMC may be only a few micrometers, its thickness effect cannot be ignored if we use a small and thin solder joint. While a thick UBM such as a column of Cu can be used in order to overcome the problem of spalling of IMC and to increase the total height of a joint, it reduces the thickness of the solder and creates a new problem of large shear strain of the joint. This is especially serious when we deal with solder bumps that are less than 50 μm in diameter. We envisage the diameter of the solder bump in Figure 1.15(d) to be 50 μm and the thickness of the UBM and bond pad to remain the same, the solder layer in between them will be much thinner, and the shear strain will be much larger. The thickness of the intermetallic formed between the UBM and the solder cannot be reduced because the reaction temperature and time cannot be reduced. 1.4.4 Impact Fracture While epoxy underfill has been introduced to strengthen the bonding of C4 solder joints, no underfill is applied to assist the ball-grid array (BGA) of solder joints. Typically, the diameter of the solder ball in BGA is about 760 μm, so its volume or weight is three orders of magnitude larger than that of a C-4 solder bump 76 μm in diameter. Without underfill, the gravity of the very heavy solder ball itself can exert a very large force to break from its substrates during an impact or a shock. Consider that wireless, portable, and hand-held electronic consumer products are dropped accidentally to the ground very often. The impact of dropping may induce fracture of BGA solder joint interfaces, which is now one of the most serious failure modes of these devices. The high-speed shear stress in impact is as important as, if not more important than, the low cycle thermal stress discussed above from the point of view of reliability of consumer products. To characterize the toughness of a solder joint against impact, a mini Charpy impact test machine has been used to measure the impact toughness of solder joints and to study the ductileto-brittle transition in solder joints [20]. The transition occurs due to aging when either a large number of Kirkendall voids are formed at a solder joint interface or the segregation of a certain impurity occurs in the interface to cause brittleness. More discussion of the impact and drop tests will be given in Chapter 11. 1.4.5 Electromigration and Thermomigration The present packaging design rule is to distribute 1 ampere over five power solder bumps, or 0.2 ampere per bump. For a solder bump 100 μm in diameter, the current density will be about 2 × 103 A/cm2 . Since the contact area of the bump is much smaller than the cross section of the bump, the actual current density may be a factor of 2 higher at the solder bump contact where the current enters the bump. While this current density is about two orders of magnitude less than that in Al or Cu interconnect lines, electromigration

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in the solder bumps cannot be ignored [21–24]. This is because of the low melting point and high atomic diffusivity of solder alloys. For the eutectic SnPb solder with a melting point of 183◦ C, room temperature is about twothirds of its melting point on the absolute temperature scale. This is the same for Pb-free solders. The second reason is the low “critical product” of solder alloys, so that electromigration can occur in solder alloy under a very low current density, even as low as 5 × 103 A/cm2 . This point will be discussed in detail in Chapter 8. The third reason is the line-to-bump geometry, in which a large change of current density exists between the interconnect line and the solder bump. It leads to a unique current crowding at the line-tobump contact interface, where the current density is a factor of 10 to 20 higher than the average current density in the bump. Effect of the current crowding is the most serious reliability issue in flip chip solder joints from the point of view of electromigration failure [25]. The fourth reason is joule heating from the Al or Cu interconnect line contacting the bump. The joule heating not only will increase the temperature of the solder bump, which in turn will increase the rate of electromigration, but also may produce a small temperature difference across the solder bump to cause thermomigration. A temperature difference of 10◦ C across a solder bump 100 μm in diameter will give a temperature gradient of 1000◦ C/cm, which cannot be ignored [26]. Thermomigration will be covered in Chapter 12. Another very unique and important aspect electromigration behavior in solder joints is that it has two reactive interfaces. The polarity effect on IMC growth exists at the cathode and the anode. Electromigration drives atoms from the cathode to the anode. Therefore, it tends to dissolve or retard the growth of IMC at the cathode but build up or enhance the growth of IMC at the anode [27–29]. Figure 1.16 shows a SEM cross-sectional images of electromigration-induced failure at the cathode contact interface. The effect of current crowding can be recognized very clearly because the failure was initiated at the place where the current enters the solder bump. A detailed discussion will be given in Chapter 9. 1.4.6 Reliability Science on the Basis of Nonequilibrium Thermodynamics The examples of reliability problems given above indicate that the timedependent microstructure change or instability in solder joints is different from the phase transformations in conventional metallurgical systems. The latter occurs typically between two equilibrium end states, for example, in precipitation of GP zones or in martensitic transformation of a memory alloy [30–32]. The Gibbs free energy of the end states are defined when enthalpy and entropy at constant temperature and constant pressure are given. The time-dependent kinetic behavior can be represented by the temperature–time–transformation fraction (TTT) curve. However, in electronic reliability problems, it is the

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Fig. 1.16. A set of SEM images of electromigration failure caused by the dissolution of a thick Cu UBM of 14 μm due to current crowding at the cathode of a flip chip solder joint. The nominal current density was about 2 × 104 A/cm2 and the testing temperature was 100◦ C. The dissolution of Cu UBM and Cu conducting line at the upper left corner of the contact increases with time as shown from panel (a) to panel (c). Panel (d) shows a void formation in the Cu line. (Courtesy of Prof. C. R. Kao, National Taiwan University)

effect of external force in electromigration, for example, where the electrical potential is not constant, that leads to phase change, in turn an open in a circuit due to void formation at the cathode end or a short by extrusion at the anode end. Furthermore, in thermomigration, the phase change is due to a temperature gradient, so the temperature is not constant and no equilibrium state can be defined except a steady state. Stress-migration-induced void formation is a creep phenomenon under a stress or pressure gradient, so the pressure is not constant. Tin whisker growth at room temperature is a creep phenomenon too. Therefore, these microstructure failures or instability problems are driven by an external force; they do not have a uniform boundary condition such as constant temperature and constant pressure. They are irreversible processes in nonequilibrium thermodynamics. However, we should ask what is new in these irreversible processes? We mention three interesting features below.

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The first is the effect of interfaces where flux divergence occurs and the supersaturation of vacancies will lead to void nucleation and growth. The second is current crowding in interconnects and in flip chip solder joints (to be discussed in Chapters 8 and 9) so that even the driving force is not constant. The third is the eutectic system which has a two-phase microstructure so there are two fluxes interacting with each other (to be discussed in Chapters 9 and 12). However, there are phase changes in solder joint technology without an external force except temperature change as in wetting reaction and solid-state aging of solder joints. Therefore, the following chapters have been divided into two parts; Part I discusses Cu-Sn reactions and Part II discusses electromigration and thermomigration.

1.5 Future Trends in Electronic Packaging There are three trends in microelectronic technology that deserve our consideration; the trend of miniaturization, the trend of packaging integration evolution, and the trend of more serious chip–packaging interaction from the integration of Cu/ultralow k in interconnect technology. Another possible future trend is the use of fluxless and solderless joints. 1.5.1 The Trend of Miniaturization The trend of miniaturization of electronic devices may reach nanoscale dimension in the future. Today, the feature size of a field-effect transistor (FET) is already in the nanometer region, for example, the gate width is below 100 nm. Since ultrahigh density of Si memory technology is practical, the hard disk memory used in portable devices based on laser-drilling of holes on thin film disks will be replaced by flash memory sticks based on FET Si technology because of small size, no moving parts, and impact resistance. Therefore, it is possible to produce hand-held-size computers. To package nanoscale devices, it is likely that the dimensions of packaging structures will be scaled down by about two orders of magnitude, e.g., solder bumps 1 μm in diameter. While there is no challenge in producing such small solder bumps by lithographic technology and deposition, the standard solder reaction in reflow and solidstate aging, for example, at 150◦ C for 1000 hrs, will convert the entire bump into IMC. In other words, the entire joint becomes IMC, hence the physical properties of Cu-Sn IMC will be even more important in the future packaging technology. Even if we consider the shrinking of the diameter of a solder bump by a factor of 4, from 100 μm to 25 μm, the volume of the bump will be reduced by a factor of 64. Relatively speaking, the volume fraction of IMC in the smaller solder bump will increase 64 times. It will change the physical properties of the bump such as its mechanical strength drastically, and it will make the

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Cu-Sn reaction a much more serious reliability problem. This is because we are as yet unable to reduce the reaction temperature and reaction time in processing smaller solder joints. We have emphasized the reliability issues of flip chip solder joints when they are acted upon by chemical, mechanical, or electrical force individually. Due to the trend of miniaturization, these forces will be expected to combine together to make the reliability problems even more problematic. 1.5.2 The Trend of Packaging Integration Evolution—SIP, SOP, and SOC In packaging integration evolution, dramatic change is expected in portable consumer electronic products. The design of packaging and the effective use of limited space in hand-held devices will be the most challenging problems in packaging technology in the near future. There are system-in-packaging (SIP), system-on-packaging (SOP), system-on-chip (SOC), and other variations. The packaging technology is no longer about connecting a single chip to a single substrate or joining several of the same kind of chips and other discrete components to a module. SIP is the advanced multifunctional packaging. It is to integrate all kinds of components in and on a single package, mostly a laminated substrate. In other words, it is to take several differently packaged devices and components and assemble them on a substrate board, and the passive components are embedded in the substrate or surface mounted. It is a heterogeneous integration. Different components (logic IC, memory IC, passive components, etc.), different semiconductor chips (Si, SiGe, GaAs, GaN, etc.), and different technologies (electronics, optoelectronics, MEMS, biosensor, etc.) will be merged together on a high-density interconnected substrate. To do so, chip-size packaging becomes essential, in which the size of the packaging substrate is close to the size of the chip, so that each chip or device does not occupy extra space for cost-efficient assembly on the substrate. How to use the substrate space effectively in a handheld cellular phone, for example, is critical as the function of the device increases. The trend in chip-size packaging will lead to finer and finer pitch of solder bumps in flip chip technology. Besides chip-size packaging, chip on flexible substrate and stacking of various chips in three dimensions will be emphasized. In three-dimensional stacking of chips, a combination of wire bonding and solder bumping, or a multilevel soldering process or a high– low combination of two kinds of Pb-free solders will be needed. Eventually, a stacking of Si chips interconnected by via holes in the chips will be the most effective way of packaging. SIP will be the dominant technology for electronic consumer products in the near future. SOP is to integrate a system of various devices in the design stage on a module or board, so the integration will be more efficient than SIP which will just take individual components and interconnect them together on a substrate. The design in SOP is driven by system needs for specific applications,

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for example, microelectronic and optoelectronic devices can be integrated for mixed signal applications. The difference between SOP and SIP is small and will diminish in the future. SOC is to design and integrate a system on a single chip since chip manufacturing is becoming cheaper and cheaper. In other words, it is to integrate active devices such as memory and logic devices and some packaging components on a Si chip, so that the chip technology and chip-size-packaging technology may get closer and closer and merge together. It is more of a homogeneous integration. SIP starts from a concept based on packaging technology using a substrate to join multiple chips and components on it, and SOC starts from Si chip technology and uses a Si chip to build multiple functions and packaging components on the chip. The trend of miniaturization will drive SIP toward SOC eventually, as in the example of replacing hard disk memory by flash memory. 1.5.3 Chip–Packaging Interaction To reduce RC delay in a multilayered interconnect structure on a chip, ultralow-k materials with a value of dielectric constant approaching 2 are being developed and integrated with Cu conductors. The mechanical properties of ultralow-k materials are of concern owing to the thermal stress between Cu and ultralow-k due to their difference in thermal expansion coefficient, but a more serious thermal stress comes from chip–packaging interaction. The latter will be a major reliability issue in the future. In flip chip technology used in high-end devices such as a server, the Cu/ultralow-k multilayered structure will be joined to a packaging substrate by an area array of solder joints. In joining a chip to its packaging, there are under-bump metallization and the multilayered structure of Cu/ultralow-k on the chip side and there are bond pads on the substrate side, then in between the chip and the substrate there are solder bumps. In chip-join and in operation, thermal stress develops between the chip and the substrate, as discussed in Section 1.4.3. The thermal stress will affect not only the mechanical integrity of the solder bumps but also the Cu/ultralow-k multilayered structure. It has led to the well-known low cycle fatigue failure of solder joints, yet the effect of thermal stress on the Cu/ultralow-k structure due to chip–packaging interaction is unclear. The microelectronics industry has been able to live with the fatigue problem, especially with the help of underfill of epoxy between the chip and the substrate, otherwise our computers would not work today. This is because in the Al/SiO2 or Cu/low-k technology, the mechanical strength of the SiO2 and low k materials (which are carbon-doped SiO2 with a value of k slightly below 3) is quite strong, so the thermal stress affects mostly the solder bumps and its interfaces, but not the interlayer dielectrics. Yet this may not be true any more with the ultralow-k materials; at the least its weaker mechanical properties are of concern. Ultralow-k materials tend to be porous or a mixture with a certain amount of polymer, so they crack easily under stress. In the extreme,

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if we consider an array of flip chip solder bumps placed on a soft ultralow-k material, any displacement of the solder bumps will cause a strain in the soft ultralow-k material and also the Cu lines embedded in it. This will be a very serious reliability problem. To avoid the thermal stress from chip–packaging interaction, it seems that a Si substrate is better for Si chips since there will be no thermal stress between a Si chip and a Si substrate. 1.5.4 Solderless Joints In principle, we can have solderless joints. An example is the anisotropic conducting polymer, except that both its conduction and adhesion are not as yet good enough for high-end packaging technology. There are three basic criteria in solder joining reaction: it has to be low temperature, its electrical conduction should be metallic, and its interfacial adhesion or bonding strength should be as strong as atomic bonds in metals. As long as we can find an interfacial process that meets these criteria, we could have a replacement for solder joints, [33] provided that it can be applied over the active device area as in area array solder joints. Otherwise, we can use wire-bonding. We may consider the principle of wafer-bonding technique to develop solderless joints. The bonding of two Si wafers can occur at room temperature, without applying flux, and without applying heat and pressure. Flux has served as the poor-man’s vacuum to overcome the problem of surface oxide in interfacial bonding. Interfacial bonding without flux in ultrahigh vacuum and without interdiffusion and compound formation at room temperature can be achieved, provided that the two surfaces to be joined are atomically flat and clean as in wafer bonding. Without ultrahigh vacuum and without flux, we may consider using pure Au bumps or Cu bumps with a very thick Au coating. To achieve a direct Au-to-Au bonding, we should polish two Au bumps as flat as possible and bond them directly without chemical reaction at room temperature. To improve the hardness of Au for polishing, we could use very Au-rich alloys such as 18K gold or even Pt. However, the challenge is not to bond just one pair of Au bumps, but an area array of them between a chip and a substrate.

References 1. K. Puttlitz and P. Totta, “Area Array Technology Handbook for Microelectronic Packaging,” Kluwer Academic, Norwell, MA (2001). 2. J. H. Lau, “Flip Chip Technologies,” McGraw–Hill, New York (1996). 3. I. Amato, “Tin whiskers: The next Y2K problem?” Fortune Magazine, Vol. 151, Issue 1, p. 27 (2005). 4. B. Spiegel, “Threat of tin whiskers haunts rush to lead-free,” Electronic News, 03/17/2005. 5. http://www.nemi.org/projects/ese/tin whisker.html

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6. Y. Kariya, C. Gagg, and W. J. Plumbridge, “Tin pest in lead-free solders,” Sold. Surf. Mount Technol., 13, 39–40 (2001). 7. K. N. Tu and D. Turnbull, “Direct observation of twinning in tin lamellae,” Acta Metall., 18, 915 (1970). 8. C. M. Miller, I. E. Anderson, and J. F. Smith, “A viable Sn-Pb solder substitute: Sn-Ag-Cu,” J. Electron. Mater. 23, 595–601 (1994). 9. M. E. Loomans and M. E. Fine, “Tin-silver-copper eutectic temperature and composition,” Metall. Mater. Trans., 31A, 1155–1162 (2000). 10. K.-W. Moon, W. J. Boettinger, U. R. Kattner, F. S. Biancaniello, and C. A. Handwerker, “Experimental and thermodynamic assessment of SnAg-Cu solder alloys,” J. Electron. Mater., 29, 1122–1136 (2000). 11. Z. Kovac and K.N. Tu, “Immersion tin: its chemistry, metallurgy and application in electronic packaging technology,” IBM J. Res. Dev. 28, 726–734 (1984). 12. “1999 International Roadmap for Semiconductor Technology,” Semiconductor Industry Association, San Jose, CA (1999). See Website http://public.itrs.net/ 13. L. F. Miller, “Controlled collapse reflow chip joining,” IBM J. Res. Dev., 13, 239–250 (1969). 14. P. A. Totta and R. P. Sopher, “SLT device metallurgy and its monolithic extensions,” IBM J. Res. Dev., 13, 226–238 (1969). 15. B. S. Berry and I. Ames, “Studies of SLT chip terminal metallurgy,” IBM J. Res. Dev., 13, 286–296 (1969). 16. A. A. Liu, H. K. Kim, K. N. Tu, and P. A. Totta, “Spalling of Cu6 Sn5 spheroids in the soldering reaction of eutectic SnPb on Cr/Cu/Au thin films,” J. Appl. Phys., 80, 2774–2780 (1996). 17. H. K. Kim, K. N. Tu, and P. A. Totta, “Ripening-assisted asymmetric spalling of Cu-Sn compound spheroids in solder joints on Si wafers,” Appl. Phys. Lett., 68, 2204–2206 (1996). 18. C. Y. Liu, C. Chih, A. K. Mal, and K. N. Tu, “Direct correlation between mechanical failure and metallurgical reaction in flip chip solder joints,” J. Appl. Phys., 85, 3882–3886 (1999). 19. J. W. Jang, C. Y. Liu, P. G. Kim, K. N. Tu, A. K. Mal, and D. R. Frear, “Interfacial morphology and shear deformation of flip chip solder joints,” J. Mater. Res., 15, 1679–1687 (2000). 20. M. Date, T. Shoji, M. Fujiyoshi, K. Sato, and K. N. Tu, “Ductile-to-brittle transition in Sn-Zn solder joints measured by impact test,” Scr. Mater. 51, 641–645 (2004). 21. S. Brandenburg and S. Yeh, “Electromigration studies of flip chip bump solder joints,” in Proc. Surface Mount International Conference and Exposition, SMTA, Edina, MN, 1998, p. 337–344. 22. S.-W. Chen, C.-M. Chen, and W.-C. Liu, “Electric current effects upon the Sn/Cu and Sn/Ni interfacial reactions,” J. Electron. Mater., 27, 1193– 1197 (1998).

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23. C. Y. Liu, C. Chih, C. N. Liao, and K. N. Tu, “Microstructure– electromigration correlation in a thin stripe of eutectic SnPb solder stressed between Cu electrodes,” Appl. Phys. Lett., 75, 58–60 (1999). 24. T. Y. Lee, K. N. Tu, S. M. Kuo, and D. R. Frear, “Electromigration of eutectic SnPb solder interconnects for flip chip technology,” J. Appl. Phys., 89, 3189–3194 (2001). 25. E. C. C. Yeh, W. J. Choi, K. N. Tu, P. Elenius, and H. Balkan, “Current crowding induced electromigration failure in flip chip technology,” Appl. Phys. Lett., 80, 580–582 (2002). 26. A. T. Huang, A. M. Gusak, K. N. Tu, and Y.-S. Lai, “Thermomigration in SnPb composite flip chip solder joints,” Appl. Phys. Lett., 88, 141911 (2006). 27. Y. C. Hu, Y. L. Lin, C. R. Kao, and K. N. Tu, “Electromigration failure in flip chip solder joints due to rapid dissolution of Cu,” J. Mater. Res., 18, 2544–2548 (2003). 28. Y. H. Lin, C. M. Tsai, Y. C. Hu, Y. L. Lin, and C. R. Kao, “Electromigration induced failure in flip chip solder joints,” J. Electron. Mater., 34, 27–33 (2005). 29. H. Gan and K. N. Tu, “Polarity effect of electromigration on kinetics of intermetallic compound formation in Pb-free solder v-groove samples,” J. Appl. Phys., 97, 063514-1 to -10 (2005). 30. P. G. Shewmon, “Transformations in Metals,” Indo American Books, Delhi (2006). 31. D. A. Porter and K. E. Easterling, “Phase Transformation in Metals and Alloys,” Chapman & Hall, London (1992). 32. J. W. Christian, “The Theory of Transformations in Metals and Alloys; Part 1 Equilibrium and General Kinetic Theory,” 2nd ed., Pergamon Press, Oxford (1975). 33. Chin C. Lee and Ricky Chuang, “Fluxless non-eutectic joints Fabricated using Au-In multilayer composites,” IEEE Trans. Components and Packaging Technology, 26, 416–422 (2003).

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Copper–Tin Reactions

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2 Copper–Tin Reactions in Bulk Samples

2.1 Introduction Solder reaction is the wetting of a molten solder on a solid Cu surface. Typically, when a small drop of molten solder touches a large Cu surface, it spreads and forms a cap on the Cu surface. The cap has a stable wetting angle, which is defined usually by Young’s equation for a triple point. The wetting reaction forms Cu-Sn intermetallic compounds at the interface between the molten solder and Cu, and the interface achieves metallic bonding after cooling, hence two pieces of Cu can be joined by the solder in a solder joint. While the wetting reaction is important from the point of view of yield in manufacturing, we must also consider solid-state reaction between solid solder and Cu from 100◦ C to 150◦ C from the point of view of reliability. This is because the working temperature of Si devices is around 100◦ C and an aging at 150◦ C for 1000 hr is a required test in reliability specification. There are two intermetallic compounds of Cu and Sn; they are Cu6 Sn5 and Cu3 Sn, and they form during the wetting reaction as well as the solidstate reactions between Sn and Cu according to the binary phase diagram of Cu-Sn. A very interesting finding is that rates of the intermetallic compound formation are very different between wetting reaction and solid-state reaction; they differ by four orders of magnitude although the temperature of reaction differs by only 10◦ C or so between the two reactions. Since Pb does not react with Cu to form compounds, the intermetallic compound formation in the reaction between SnPb and Cu is similar to that between Sn and Cu. The effect of Pb on the Cu-Sn reaction can be examined by using the ternary phase diagrams of Sn-Pb-Cu at various temperatures. Below, we shall first discuss experimental studies of wetting reactions of eutectic SnPb on Cu foils followed by interpretation using their ternary phase diagrams. The morphology of scallop-type Cu6 Sn5 formation in the wetting reaction is unique that it is a supply-limited reaction, in contrast to the well-known diffusion-limited reaction or interfacial-reaction-limited reaction. Then solid-state reactions shall be discussed, in which a layer-type morphology of Cu6 Sn5 occurs and its growth obeys the diffusion-limited reaction.

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A comparison between the wetting reaction and solid-state reaction will be given [1]. While our interest in solder reactions concerns Pb-free solders, intermetallic compound formation between Pb-free solders and Cu is similar to the SnPb solder because the most important Pb-free solders are eutectic SnAgCu, eutectic SnAg, eutectic SnCu, or pure Sn [2]. Hence, Cu-Sn reaction is the key when these solders are joined to Cu. Since SnPb solder has been used on Cu for a long time and much study has been done on the ternary system of Sn-Pb-Cu, it is helpful to review the solder reactions of SnPb on Cu as the background references for Pb-free solders. Many useful references are listed in Refs. 1 and 2. In this chapter, thermodynamics and kinetics of Cu-Sn reaction will be emphasized.

2.2 Wetting Reaction of Eutectic SnPb on Cu Foils The samples of eutectic SnPb on Cu were prepared by melting a tiny bead of eutectic SnPb alloy (63Sn37Pb in wt%) on a Cu foil in mildly activated rosin flux (RMA). Solder beads 0.5 mm in diameter can be prepared by cutting tiny pieces of solder, about 2 mg each, from a roll of commercial solder wire and dropping the pieces into a disk containing RMA flux kept at 200◦ C on a hot plate. The pieces melt and form beads owing to balance of surface tension [3]. Removing the disk from the hot plate and cooling it to room temperature, the solid solder beads can be saved and stored in flux. Copper foils of 1 cm × 1 cm in area and 0.5 mm in thickness were polished and cleaned before one of the foils was fully immersed in the heated flux at 200◦ C with ± 3◦ C control. A solder bead was dropped on the Cu foil. The bead melted and spread out to form a cap on the Cu surface (see Fig. 2.1). After various periods of time from 0.5 min to 40 min on the hot plate, the solder cap sample was cooled to room temperature. To study the intermetallic compound (IMC) formation at the interface between the cap and Cu, the samples was cross-sectioned, polished, lightly etched, and examined by scanning electron microscopy (SEM) (see Fig. 2.2). The wetting angle, from a sideview of the sample, was measured as a function of wetting time. This is plotted in Fig. 2.3. The wetting angle of molten eutectic SnPb on Cu is stable at 11◦ . In Fig. 2.3, the wetting angles of pure Sn on Cu and SnBi on Cu, measured similarly, are shown too, and they are much larger than that of eutectic SnPb [4,5]. To observe the three-dimensional morphology of the interfacial IMC, a deep and selective Pb-etching was carried out. The etching removed the Pb and also the Sn above the IMC but did not etch the IMC. SEM of the IMC observed at a tilt angle reveals the three-dimensional scallop-type morphology of the IMC in Fig. 2.4(a) and (b), which show the same area of IMC scallops before and after the selective etching, and we can identify the same contour of the IMC in both figures. Figure 2.5 shows a set of SEM of the IMC scallops as a function of wetting time at 200◦ C. They were taken at the same magnification.

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Fig. 2.1. A solder bead melted and spread out to form a cap on the Cu surface.

Cu6 Sn5

Cross-sectional view(2D) Solder side Cu side

Cu3 Sn Cu

Solder

Cu

Fig. 2.2. Solder cap on Cu sample was cross-sectioned, polished, lightly etched, and examined by scanning electron microscopy (SEM) for the study of IMC formation at the interface between the cap and Cu.

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Wetting Angle (deg.)

35

SnBi/Cu 30 25 20 15 SnPb/Cu 10 0

10

20

30

40

Reflow Time (min)

Fig. 2.3. The wetting angle, from a side view of the sample, plotted as a function of reflow time. The wetting angle of molten eutectic SnPb on Cu is stable at 11◦ . The wetting angles of pure Sn and SnBi are shown too, and they are much larger than that of eutectic SnPb.

Fig. 2.4. The same area of IMC scallops (a) before and (b) after etching. We can identify the same contour of the IMC in both figures.

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Fig. 2.5. (a–d) Set of SEM images of IMC scallops as a function of reflow time.

We observe that the average size of the scallops increased with time. Since the scallops are very close to each other, the growth is a parasite reaction. It must have occurred by having the bigger ones grow at the expense of their smaller neighbors. In other words, it is a ripening reaction. But the ripening is nonconservative since the total volume of the scallops increases with time, accompanied by the Cu-Sn chemical reaction between the Cu from the foil and the Sn from the molten solder in order to grow the IMC. Kinetic analysis of the nonconservative ripening will be presented in Chapter 5. Since the manufacturing of a device involves several reflows, the total period of wetting reaction in an actual solder joint in devices may add up to a few minutes. Therefore, the study of wetting reaction up to 40 min is academic. In wetting reactions over a long period of time, the scallops were found to elongate, i.e., their height is much larger than their diameter. Often in crosssectional views of the solder joint, a few long and hollow Cu6 Sn5 tubes have been observed. Their formation is not due to the interfacial reaction, rather it has been attributed to the precipitation of supersaturated Cu from the molten solder upon solidification, especially if the surface of the solder bump solidifies before the Cu-Sn interface. These tubes were nucleated from the bump surface rather than from the bump interface. A more detailed discussion of the morphology, kinetics of growth, and crystallographic orientation relationship between the scallop and Cu will be given in Chapter 5.

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Fig. 2.6. SEM images of a halo.

A rather unique behavior of the wetting of eutectic SnPb on Cu is the side-band or halo formation on the Cu surface surrounding the solder cap. While the cap diameter is stable after a minute or so in wetting, the halo grows and enlarges its diameter with time. Figure 2.6 shows an SEM image of a halo. Figure 2.7 plots the growth rate of a halo at 200◦ C. While the cap

160 140 120 100 80 60 40 20 0

0

1

2

3

4

5

Fig. 2.7. Growth rate of halo at 200◦ C.

6

7

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diameter is stable in the initial period of halo formation, the halo may change the equilibrium condition of the wetting tip of the cap. It has been observed that after several minutes of halo growth, the solder cap becomes unstable and spreads out quickly to wet the entire area of the halo.

2.2.1 Crystallographic Relationship between Cu6 Sn5 Scallop and Cu Fig. 2.8 is a top-view image of Cu6 Sn5 scallops on a Cu substrate, and the crystallographic orientation relationship between the scallops and Cu has been determined. Samples were prepared by reacting small beads (∼0.5mg) of 55Sn45Pb (in wt. %) solder with a mirror-like polished copper foil in flux at 200◦ C with different reaction times from 30 sec to 8 min. The remaining solder was etched away to expose the scallops. The size of each scallop is about 1 to 3 μm as shown in Fig. 2.8, and each of them is a single crystal of Cu6 Sn5 . The grain sizes of Cu in the Cu foil were in mm scale. By scanning the micro x-ray beam in synchrotron radiation over an area of about 100 μm by 100 μm of the sample, the crystallographic information of several thousands of scallops and the Cu below them is obtained. The synchrotron radiation micro x-ray beam is capable of penetrating through the Cu6 Sn5 layer since it is thin. Laue patterns from both IMC scallops and Cu substrate can be obtained at the same time. Actually the strongest Laue spots were from the Cu, because the grain size of the Cu is much larger (mm scale) than the Cu6 Sn5 (1∼2 μm in size) and so the beam penetrated much deeper into the Cu. Grain orientation of Cu was analyzed first. After finishing the analysis of the Cu, Laue spots from the Cu were removed and the Laue pattern from the Cu6 Sn5 was analyzed.

Fig. 2.8. SEM image of top-view of Cu6Sn5 scallops on a Cu substrate.

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In the early stage of reaction, the spots from Cu3 Sn were not detected; either it did not form or its thickness was too thin to produce Laue spots strong enough to be detected. The crystal structure of η-Cu6 Sn5 has been thought to be hexagonal, but a recent study using electron diffraction showed that it is actually monoclinic (Space group = P21 /c, a = c = 9.83˚ A, b = 7.27 ˚ A, β = 62.5◦ ) [6]. From the Laue patterns, 3-dimensional computer models of crystal structures were simulated to determine the orientation relationships between the Cu and the monocline Cu6 Sn5 . Six types of preferred orientation relationships were found: (010)Cu6 Sn5 //(001)Cu (343)Cu6 Sn5 //(001)Cu (¯ 34¯ 3)Cu6 Sn5 //(001)Cu (101)Cu6 Sn5 //(001)Cu (141)Cu6 Sn5 //(001)Cu (¯ 14¯ 1)Cu6 Sn5 //(001)Cu

¯ Cu6 Sn5 //[110]Cu [101] [¯101]Cu6 Sn5 //[110]Cu [¯101]Cu6 Sn5 //[110]Cu

(2.1) (2.2)

[¯101]Cu6 Sn5 //[110]Cu ¯ Cu6 Sn5 //[110]Cu [101]

(2.4)

[¯101]Cu6 Sn5 //[110]Cu

(2.6)

(2.3) (2.5)

In every cases, the [¯ 101] direction of Cu6 Sn5 is aligned parallel to the [110] direction of Cu. Fig. 2.9 (a) is a map representing the angle between the [¯ 101] direction of Cu6 Sn5 and the [110] direction of Cu, after 4 minutes of wetting reaction. Scanned area was 100 μm × 100 μm, with a step size of 2 μm. Most of the spots have the angle close to 0◦ . Fig. 2.9 (b) is a histogram of orientation distribution corresponding to Fig 2.9 (a). The angle is close to zero for the majority of data points, indicating a very strong orientation correlation between Cu6 Sn5 and Cu. The orientation relationship (2.1) to (2.6)

Fig. 2.9. (a) Map representing the angle between the direction of Cu6 Sn5 and the [110] direction of Cu, after 4 minutes of wetting reaction. Most of the spots have the angle close to 0◦ . (b) Histogram of orientation distribution corresponding to Fig 2.9(a).

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Fig. 2.10. (a) Structure of Cu6 Sn5 projected along [−101] direction. Copper atoms in the Cu6 Sn5 are represented by circles. (b) Crystal planes for the six orientation relationships labeled with respect to the Cu atom hexagon

shown above can be classified into two groups. This is due to the strong pseudo-hexagonal symmetry around the Cu atoms in Cu6 Sn5 . Fig 2.10 (a) shows the structure of Cu6 Sn5 projected along the [¯101] direction. Copper atoms in the Cu6 Sn5 are represented by circles in hexagonal arrangement. In Fig. 2.10 (b), the crystal planes for the six relationships are labeled with respect to the Cu atom hexagon. Relationships involving planes (010), (343) and (¯ 34¯ 3) belong to the one group, and relationships with planes (101), (141) and (¯ 14¯ 1) belong to another group. The reason why the [¯ 101] direction of Cu6 Sn5 prefers to be parallel to the [110] direction of Cu is because of low misfit. Along the [¯101] direction of monoclinic Cu6 Sn5 , Cu atoms are located with intervals of 2.5573 ˚ A. Since the lattice constant of FCC Cu is a = 3.6078 ˚ A, the distance between two atoms along the diagonal of (001) plane is √

√ 2 2 aCu = × 3.6078 = 2.5511 ˚ A 2 2

Thus the misfit between Cu and Cu6 Sn5 is f=

|2.5511 − 2.5573| = 0.00244 = 0.24% 2.5511

The strong relation between the orientations of Cu6 Sn5 and Cu suggests that at the earliest stage of IMC formation, the Cu6 Sn5 forms prior to the Cu3 Sn. The lattice structure of Cu3 Sn is orthorhombic Cu3 Ti type [6], and it does not have any low index plane or direction which can have a small misfit with Cu or Cu6 Sn5 . If Cu3 Sn were formed first, before Cu6 Sn5 , it would have been impossible for Cu6 Sn5 to have such a strong orientation relationship with Cu. Since the low misfit directions between Cu6 Sn5 and Cu lie on (001) plane of Cu, (001) oriented single crystal Cu was used as substrate to verify the orientation relationship. Fig.2.11 is morphology of Cu6 Sn5 formed on (001)

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Fig. 2.11. Morphology of Cu6 Sn5 formed on (001) single crystal Cu.

single crystal Cu. It shows a dramatic change in morphology of Cu6 Sn5 on (001) Cu. The Cu6 Sn5 scallops were elongated along two perpendicular directions and showed a roof-top morphology. Electron back scattered diffraction (EBSD) analysis was performed on these scallops and the single crystal Cu substrate. From the EBSD analysis, it was confirmed that the elongation directions correspond to the two 110 directions on the (001) surface of Cu, which are the low-misfit directions for the Cu6 Sn5 . Fig. 2.12 shows the influence of the reflow or reaction time on the orientation relationship between the scallops and the Cu substrate shown in Fig. 2.8. The histograms of the angle between the [110] direction of Cu and the [001] direction of Cu6 Sn5 are given. We note that if the Cu6 Sn5 has a strong orientation relationship with the Cu, the majority of data will have a value close to 0◦ . At 30 sec which was the earliest reaction time of our measurement, the distribution shown in Fig. 2.12(a) is more random compared to longer annealing times. The distribution at 1 min (Fig. 2.12(b)) shows a strong relation between the Cu6 Sn5 scallops and the Cu grain. The correlation becomes very strong at 4 min (Fig. 2.12(c)), but weakens at 8 min (Fig. 2.12(d)). This change in distribution can be explained from the nucleation and growth of Cu6 Sn5 and Cu3 Sn. The Cu6 Sn5 scallops should nucleate first with a certain degree of randomness, resulting in a distribution such as that in Fig. 2.12(a). During the growth and ripening of Cu6 Sn5 scallops, scallops with bad orientation relationship will be consumed due to their larger interfacial energy with Cu. Hence, the fraction of scallops with good orientation relationship with Cu will increase. This explains why the distribution gradually moves toward 0◦ , as shown in Fig. 2.12(a) to 2.12(c). After a certain amount of reaction time, the orientation relationship between Cu6 Sn5 and Cu will be affected by the

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Copper–Tin Reactions in Bulk Samples (a)

(b)

140

# spots

47

300

120 100 80 40 40 20 0

250 200 150 100 50 0

(c)

20 40 60 Angle (degree)

80

0

0

20 40 60 Angle (degree)

0

20

(d)

80

# spots

600 800

500

600

400 300

400

200

200 0

100 0 0

20 40 60 Angle (degree)

80

40 60 Angle (degree)

80

Fig. 2.12. Influence of reflow or reaction time on the orientation relationship is shown by histograms of the angle between the [110] direction of Cu and the [001] direction of Cu6 Sn5 . (a) 30 min, (b) 1 min, (c) 4 min, and (d) 8 min.

nucleation and growth of Cu3 Sn between them. Formation of the Cu3 Sn by solid state reaction between Cu6 Sn5 and Cu may not be uniform. After a long reflow time, some of the Cu3 Sn grains will become thick and incoherent to both Cu6 Sn5 and Cu. The presence of incoherent grains of Cu3 Sn may rotate the Cu6 Sn5 scallops in order to release the misfit strain energy, so the orientation distribution of Cu6 Sn5 changes. The effect of reflow on the orientation of elongated scallops on (001) single crystal Co is much less. 2.2.2 Rate of Consumption of Cu in Soldering Reaction with Eutectic SnPb The rate of consumption of Cu in soldering reactions has been a critical question in electronic packaging technology. This is because the Cu thickness in most UBM is rather limited, except when a Cu column bump is used. The consumption of Cu in multiple reflows must be under control so that not all of the Cu will be consumed. Using cross-sectioned and top-polished samples, the total volume of Cu-Sn IMC formed between eutectic SnPb and Cu as a function of temperature from 200◦ C to 240◦ C and time up to 10 min has been determined [7]. The consumed thickness of Cu at the three temperatures is plotted in Fig. 2.13 versus time. From the slope of the curves, the

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Chapter 2 60

1.6 1.4

Δh (μm)

50

240 °C

Consumed Thickness

1.2

220 °C

1.0

40

200 °C

0.8

30

0.6

20

0.4

0.0

10

Consumption Rate

0.2 0

100

200

300

dh/dt×103 (μm/sec)

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500

600

0 700

Fig. 2.13. Consumed thickness of Cu at temperatures of 200, 220, and 240◦ C versus time.

consumption rate of Cu, dh/dt in μm/sec, was calculated for each temperature. The consumption rate of Cu is relatively high at the initial stage of wetting and decreases with time. After 1 min, the consumed Cu is about 0.36, 0.47, and 0.69 μm at 200, 200, and 240◦ C, respectively.

2.3 Wetting Reaction of SnPb on Cu Foil as a Function of Solder Composition To study the wetting behavior of SnPb solders on Cu as a function of composition, seven SnPb alloys (in wt%) were prepared: pure Pb, 5Sn95Pb, 10Sn90Pb, 40Sn60Pb, 63Sn37Pb, 80Sn20Pb, and pure Sn. Their melting temperatures are 327, 305, 299, 245, 183, 205, and 232◦ C, respectively [8, 9]. Beads of about 0.5 mm in diameter of these solder alloys were reflowed on Cu foils of 1 cm × 1 cm in area and 0.5 mm in thickness immersed in flux of mildly activated resin (RMA) in a shallow beaker heated on a hot plate to 10◦ C above the melting temperature of the solder alloy. After about 1 min when the solder cap was stable on the Cu surface, it was cooled and cleaned for wetting angle measurement. The side view of a set of solder caps as a function of SnPb composition is shown in Fig. 2.14. The wetting angles are plotted against composition in Fig. 2.15. Wetting angle has been defined by the classic Young’s equation, γsl = γvs + γlv cos θ,

(2.7)

where γ is the interfacial tension and the subscripts l, v, and s indicate the liquid flux, molten solder, and Cu substrate, respectively, as shown in Fig. 2.16. For the wetting of SnPb alloys on Cu, it is a reactive spreading process since intermetallic compound forms at the interface. According to previous studies of interfacial tension of molten SnPb solder in flux as a function of Sn

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Fig. 2.14. Side view of a set of solder caps as a function of SnPb composition. (a) Pb, (b) 5Sn95Pb, (c) 10Sn90Pb, (d) 40Sn60Pb, (e) 63Sn37Pb, (f) 80Sn20Pb, and (g) Pure Sn.

content, as redrawn in Fig. 2.17, the tension curve shows no minimum. The interfacial tension in the high-Pb region is constant and it increases with the Sn content. If we use this result and Young’s equation to calculate the wetting angle, we expect no minimum wetting angle, but a minimum was found as shown in Fig. 2.15. The disagreement indicates that if we consider only the balance of interfacial tensions, we cannot account for the measured wetting angle change of SnPb alloys as a function of composition. As seen in Fig. 2.15, the pure Pb has a very large wetting angle on Cu, yet by adding a small amount of Sn, the wetting angle is much reduced. On the other hand, the addition of a small amount of Sn into Pb does not change the interfacial tension as shown in Fig. 2.17. The strong effect of a small amount of Sn on decreasing the wetting angle comes from the Sn-Cu reaction to form interfacial intermetallic compound on Cu. The chemical reaction can provide an additional driving force to change the equilibrium condition of the wetting tip. To include the effect of the reaction on the wetting, Yost and Romig have

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Chapter 2 40 35

Wetting angle,

30 25 20 15 10 5 0 0

10

20

30

40

50

60

70

80

90

100

Pb content, wt%

Fig. 2.15. Wetting angle plotted as a function of composition.

estimated that [10, 11] 1 dE = σ + Γ(θ), 2πr dr

(2.8)

where σ corresponds to the driving force of compound formation and Γ(θ) is the driving force of imbalance of interfacial tensions. On the other hand, if we consider compound formation or chemical activity alone, it is difficult to explain why pure Sn has a larger wetting angle than some of the other SnPb solders, because pure Sn is expected to have a higher activity than other SnPb solders and has formed a thicker compound. The average thickness of scallop-type intermetallic compound formation, after 1 min at 10◦ C above the melting point, is plotted in Fig. 2.18. The average IMC formation of pure Sn γγlvlv

θ γsl

γvs

Fig. 2.16. Wetting tip configuration and Young’s equation, where γ is the interfacial tension and the subscripts l, v, and s indicate the liquid flux, molten solder, and Cu substrate, respectively.

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510

interfacial tension (mjm-2)

490 470 450 430 410 390 370 350 0

20

40

60

80

100

Sn content (weight percent)

Fig. 2.17. Interfacial tension of molten SnPb solder in flux plotted as a function of Sn content. The curve shows no minimum.

5

Total compound thickness (μm)

4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 0

10

20

30

40

50

60

70

80

90

100

Pb content, wt%

Fig. 2.18. Average thickness of scallop-type intermetallic compound formation, after 1 min at 10◦ C above the melting point, plotted as a function of solder alloy composition.

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is the largest among the SnPb solders. But the surface tension of pure Sn is also the largest as shown in Fig. 2.17. Combining the surface tension and IMC formation, we can explain the behavior of a minimum wetting angle as a function of alloy composition as shown in Fig. 2.15. However, it is difficult to analyze the spreading mechanism and determine the wetting angle at triple points without a thorough understanding of the driving force and kinetics of wetting. One important question is how much compound has formed during the wetting period, from the time the molten solder bead touches the Cu surface to the time it forms the cap. It is difficult to determine the interfacial reaction during the wetting period since it is a very short period; the spreading rate of a molten solder on a Cu surface is extremely high.

2.4 Wetting Reaction of Pure Sn on Cu Foils Since the Cu-Sn reaction is a central theme of this book, we shall discuss the reaction between molten Sn and Cu here. It is also crucial to the solder reaction of Pb-free solders because the latter are high-Sn solders. The reactions between thin-film Sn and thin-film Cu will be discussed in Chapter 3. Both Cu6 Sn5 and Cu3 Sn form in the reaction between molten Sn and Cu, and Cu6 Sn5 has the scallop-type morphology and Cu3 Sn has the layer-type morphology. This is similar to the molten reaction between eutectic SnPb and Cu. However, the scallop morphology of Cu6 Sn5 between pure Sn and Cu is quite different from that formed between eutectic SnPb and Cu [4, 12]. Figure 2.19(a) is an SEM image of the rounded scallops formed between 40Sn60Pb on Cu. The image was taken after the unreacted SnPb was etched away to expose the Cu6 Sn5 scallops. Figure 2.19(b) is an SEM image of the faceted scallops formed between Sn and Cu. While both kinds of scallops are Cu6 Sn5 , their morphology is very different. A rounded morphology occurs because the interfacial energy between molten SnPb and Cu6 Sn5 is isotropic, and the faceted morphology occurs because the interfacial energy between molten Sn and Cu6 Sn5 is highly anisotropic. The addition of Pb in the solder has affected the interfacial energy or the bonding energy. In the rounded scallops, the width-to-height ratio as measured from cross-sectional views can be approximated by hemispheres, but the faceted scallops have a larger widthto-height ratio. On the other hand, the growth kinetics of these two kinds of scallops is quite similar. Both obey t1/3 growth law. Figure 2.20 is a plot of the scallop growth versus annealing time. In the plot, the lateral width (from plan view images) and height (from cross-sectional views) were evaluated separately. After 4 min of reflow at 245◦ C, the layer-type Cu3 Sn has a thickness of about 300 nm and the scallops of Cu6 Sn5 have a height of about 1 to 2 μm. A fundamental parameter of the growth of scallops is the narrow channel between two of them. The channel will be analyzed in Chapter 5.

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Mean Grain Radius (μm)

Fig. 2.19. (a) SEM image of the rounded scallops formed between 40Sn60Pb on Cu. The image was taken after the unreacted SnPb was etched away to expose the Cu6 Sn5 scallops. (b) SEM image of the faceted scallops formed between Sn and Cu.

12 11 10 9 8 7 6 5 4 3 2 1 0

240 °C 220 °C 200 °C

0

2

4

6 8 10 Reflow Time (sec)1/3

12

14

Fig. 2.20. Plot of scallop growth versus annealing time.

53

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2.5 Ternary Phase Diagram of Sn-Pb-Cu Since a solder–metal reaction involves initially a solid–liquid reaction with a molten solder, followed by solidification and then a solid-state aging during reliability tests and device operation, it is necessary to have the phase diagram available in a wide temperature range, below and above the melting point of the solder. With computers, the CALPHAD (Calculation of Phase Diagram) technique has been developed to investigate the phase equilibrium of multicomponent systems [13]. In this technique, thermodynamic properties of a system are analyzed by using thermodynamic models for the Gibbs free energy of individual phases. The Gibbs free energy of the SnPbCu liquid phase in this formalism is ◦ liq ◦ liq ◦ liq Glid m = xCu GCu + xPb GPb + xSn GSn

+ RT (xCu ln xCu + xPb ln xPb + xSn ln xSn ) + E Gliq m,

(2.9)

where xi is the mole fraction of element i, ◦ Gliq i is the mole Gibbs energy of element i in the liquid state, and E Gliq is the excess Gibbs energy treated as m follows: E

liq liq liq liq Gliq m = xCu xPb LCu,Pb + xCu xSn LCu,Sn + xPb xSn LPb,Sn + xCu xPb xSn LCu,Pb,Sn , (2.10)

where Lliq i,j are the binary interaction parameters of the i–j system, which can be composition dependent and temperature dependent. The parameter Lliq Cu,Pb,Sn represents the ternary interaction, which is also composition dependent according to the expression 0 liq 1 liq 2 liq Lliq Cu,Pb,Sn = xCu LCu,Pb,Sn + xPb LCu,Pb,Sn + xSn LCu,Pb,Sn .

(2.11)

The coefficients n Lliq Cu,Pb,Sn can also be temperature dependent. Once the Gibbs free energy functions of all the phases in a system have been obtained, in principle any kind of phase diagrams and thermodynamic properties of interest may be calculated. When the experimental data needed to determine the ternary interaction parameters are not available, this technique enables us to extrapolate the thermodynamic description of a multicomponent system from those of the subsystems that have already been optimized. From Eq. (2.9) we see that when the content of any of the alloying elements is on the order of a few percent, the technique of thermodynamic extrapolation is a good approximation for a multicomponent system. Complete thermodynamic descriptions of the binary systems of Cu-Sn, Cu-Pb, and Sn-Pb have been assessed in the literature [14–16] By extrapolating them, i.e., by setting the ternary interaction parameter in Eq. (2.4) to zero, the ternary SnPbCu phase diagrams are calculated as shown in Fig. 2.21.

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Fig. 2.21. Ternary SnPbCu phase diagrams calculated for (a) 170, (b) 200 and (c) 350◦ C. (d) Enlarged SnPb side of the SnPbCu phase diagram at 200◦ C (Courtesy of Dr. Kejun Zeng, TI).

In the diagrams, L, η, and ε represent molten SnPb, Cu6 Sn5 , and Cu3 Sn, respectively. To verify the diagrams, we compare the calculated eutectic equilibrium temperature and composition of the SnPb binary eutectic at 181◦ C, 37.8 Pb, 62.12 Sn, and 0.08 Cu with the experimental data of Marcotte and Schroeder [16] at 182◦ C, 38.1 Pb, 61.72 Sn, and 0.18 Cu. An important assumption for interfacial reactions in bulk diffusion couples is the condition of local equilibrium at interphase interfaces. It assumes that every two neighboring phases (planar layers) are in equilibrium, which is represented by either a two-phase equilibrium region in a binary phase diagram or by a tie-line in an isothermal section of a ternary phase diagram at the temperature of interest. Since the assumption implies that the composition of the phases coexisting at the interface are those given by the equilibrium tie-line on the phase diagram, the effects of morphology and kinetics such as the interfacial curvature, capillary tension, precipitate size, metastable phase formation, stress gradient, and all external forces are totally neglected. Investigation of the theoretical nature of interfacial equilibrium has concluded that whereas the effect of interfacial curvature on equilibrium may be small, the

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effect of growth kinetics on interfacial equilibrium can be significant. As for strain, in the early stage of precipitate growth, the precipitates may possess a certain degree of coherency with the matrix, so the lattice strain must be included in the description of equilibrium at the phase interface. However, in the size scale of IMC growth in solder joints, the interfaces between molten solder and IMC scallops are incoherent and the interfacial equilibrium assumption tends to be valid. Currently, all data reported in the literature on solder reaction concerning the growth of IMC several tenths of a micrometer thick pertain to well-evolved microstructures. Thus, the assumption of local equilibrium can be applied to the molten solder/metal reactions, and the ternary phase diagrams can indeed provide a useful guide to the reactions. For example, the equilibrium phase diagram may enable us to predict whether Cu6 Sn5 or Cu3 Sn forms first in wetting reactions, which has been discussed in Section 2.2.1. However, we must combine the phase diagrams together with morphological and kinetic information in order to analyze the reactions at lower temperatures, e.g., thin film Cu-Sn reaction at room temperature to be considered in Chapter 3. In that case, the kinetic effect is more important. 2.5.1 Ternary SnPbCu Phase Diagrams at 200 and 170◦ C The ternary phase diagrams of SnPbCu at 200 and 170◦ C are shown in Fig. 2.21(b) and (a), respectively. The latter is for solid-state aging and the former is for wetting reaction between the eutectic SnPb and Cu. In the diagrams, L, η, and ε represent molten SnPb, Cu6 Sn5 , and Cu3 Sn, respectively. The eutectic composition is represented by the dot on the base connecting Sn and Pb. If we draw a line to connect the dot and the Cu apex, it is a tie line. The tie line cuts across several two-phase boundaries and three-phase zones in the phase diagram, and these are the phases which can form in the reactions. For the wetting reaction, we start from the eutectic dot in Fig. 2.21(b). The molten eutectic SnPb dissolves a very small amount of Cu before η formation [13]. Then the formation of η at the interface between the molten solder and Cu affects the solubility of Cu in the molten solder, because the molten solder is in contact with the η. However, the solubility may be modified by the morphology of the η phase, i.e., whether it is a layer-type or a scalloptype. The latter increases the solubility due to the curvature effect, but this information is unavailable from the phase diagram. The η formation depletes Sn (enriches Pb) in the boundary layer of molten solder next to the η. The depletion will stop at about 45 wt% Pb before the solid phase of α-Pb(Sn) forms [see Fig. 2.21(a)]. Since the η is thermodynamically unstable with Cu, the ε phase tends to form between them. Experimentally, both η and ε have been found. The latter is a very thin layer and it may have formed during cooling, but the former is a much thicker scallop-type layer. For the solid-state aging, we turn to Fig. 2.21(a). Again we start from the eutectic dot. A very small amount of dissolution of Cu into the solid solder

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occurs first and is followed by the formation of η. The solubility of Sn in Cu also will be modified by the formation and morphology of η. The depletion of Sn can lead to a very high concentration of Pb in the solder next to the η, up to about 85 wt% Pb. We note that it is not a solid solution of 85Pb15Sn (wt%), but a high-Pb eutectic phase. Again because η is unstable with Cu, the ε phase will form between them. Experimentally, both η and ε have been found. From the point of view of IMC formation, both the wetting reaction at 200◦ C and the solid-state aging at 170◦ C should have the same IMC products as indicated by the phase diagrams. Yet no information about the morphology of the IMC and their rate of formation is available from the phase diagrams. Besides, the only difference in these two phase diagrams is that the one at 200◦ C, Fig. 2.21(b), has the triangular zone of liquid solder and η. The significance of this zone on solder reaction is that it limits the amount of Sn to be depleted from the molten solder to form IMC. What effect this zone has on the wetting reaction as distinct from the solid-state aging is not obvious if we only examine the phase diagrams. We shall show later that the morphology and kinetics of reaction are actually very different between the wetting reaction and solid-state aging. 2.5.2 5Sn95Pb/Cu Reaction and Ternary SnPbCu Phase Diagrams at 350◦ C At 350◦ C, Cu6 Sn5 cannot form between Cu and the high Pb solder because the connection line between Cu and the solder crosses the liquidus line (Liq + ε) [see Fig. 2.21(c)]. Only ε-Cu3 Sn can form at 350◦ C at the solder/Cu interface. However, according to Fig. 2.21(c), η may form at 350◦ C if the solder is very rich in Sn. The availability or mass supply of the components that are involved in the interfacial reaction plays an important role in phase evolution after the first phase formation. In the SnPb/Cu system, if the solder volume is very small compared to that of Cu, e.g., the supply of Sn is limited or the supply of Cu is unlimited as in a Cu column bump, the Cu6 Sn5 layer that formed first will transform into Cu3 Sn. The transformation can lead to the formation of a large number of Kirkendall voids, which will be discussed in Section 2.6.1 and Chapter 9. On the other hand, if the Cu is thin as in a solder-Cu thin-film reaction, or the Cu supply is cut off, for instance by a crack between Cu and Cu3 Sn, the Cu3 Sn will be converted back to Cu6 Sn5 .

2.6 Solid-State Reaction of Eutectic SnPb on Cu Foils The wetting reaction of molten eutectic SnPb and Cu at temperatures above 200◦ C will be compared to the solid-state reaction of the same system below

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170◦ C [15–17]. Since several reflows will be needed in package manufacturing, solder is in molten state for several minutes. Therefore, the wetting reaction at 200◦ C for periods from 0.5 to 10 min will be studied. Solid-state reaction at 150◦ C for 1000 hr is a required reliability test. Thus, the solid-state reaction between eutectic SnPb and Cu in the temperature range from 120◦ C to 170◦ C up to 1000 hr will be studied. Another reliability test is thermal cycling between −40◦ C and 125◦ C up to a few thousand cycles. We note that while the temperature difference between wetting reaction and solid-state reaction is small, perhaps only 30◦ C, the reaction time differs by four orders of magnitude. Nevertheless, the very large difference in morphology and kinetics of intermetallic compound formation found between these two kinds of reactions will be emphasized. The rate of wetting reaction is four orders of magnitude faster than that in solid-state aging, although the temperature difference between them is only about 30◦ C. The Cu6 Sn5 formed in the wetting reaction has scallop-type morphology, but it becomes layer-type in the solid-state aging. In order to understand why the very large differences exist, we recall the thermodynamic calculation of the ternary phase diagrams of SnPbCu at 170◦ C and 200◦ C in Section 2.5.1. We shall conclude that the thermodynamic phase diagram cannot explain the difference, it is the morphology that affects the kinetics strongly. The wetting reaction is a high rate reaction because of its unique morphology. The reaction is controlled by the rate of free energy change rather than the free energy change.

2.6.1 Formation of Cu3 Sn and Kirkendall Voids In solid-state aging, it grows a thicker layer of Cu3 Sn. The formation of Cu3 Sn is accompanied by the formation of a large number of Kirkendall void in the layer and especially in the interface between Cu3 Sn and Cu. Figure 2.22 is a focused ion beam image of the cross section of eutectic SnPb solder on a Cu foil after aging at 150◦ C for 3 days. Many Kirkendall voids are found in the Cu3 Sn layer. Similar void formation has also been observed in aging of eutectic Pb-free solder on Cu foils. This is because Cu is the dominant diffusing species in the reaction, as identified by a marker motion experiment, which will be covered in Section 3.2.3. The competition in growth between Cu6 Sn5 and Cu3 Sn tends to favor the latter when the ratio of Cu to Sn is large in the sample, for example, in the case of a thin eutectic SnPb solder on a thick Cu column bump, which will be covered in Section 9.6.1. The transformation of 1 molecule of Cu6 Sn5 into 2 molecules of Cu3 Sn will leave behind 3 Sn atoms, which will attract 9 atoms of Cu to form 3 more molecules of Cu3 Sn. The vacancy flux needed to transport the Cu atoms will accumulate at the Cu/Cu3 Sn interface to form Kirkendall voids. Voids are undesirable in device applications, therefore it is of reliability interest to limit the growth of Cu3 Sn. The growth of Cu3 Sn is not only controlled by time, temperature, impurities,

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Fig. 2.22. Focused ion beam image of cross section of eutectic SnPb solder on a Cu foil after aging at 150◦ C for 3 days. Many Kirkendall voids are found in the Cu3 Sn layer. (Courtesy of Dr. Kejun Zeng, Texas Instruments.)

and the ratio of Cu/Sn in the sample, but also by external forces such as electromigration.

2.7 Comparison between Wetting and Solid-State Reactions To compare wetting and solid-state reactions, the samples were prepared by reflowing eutectic SnPb solder paste on a thick Cu under-bump metallization (UBM) that was electroplated on a Ti/W base [20] The size of the solder bump was 125 μm in diameter. The electroplated Cu UBM had a thickness of 20 μm. The samples were reflowed twice before the aging at 125, 150, and 170◦ C for 500, 1000, and 1500 hr in an air ambient. The total reaction product after two reflows is equivalent to a wetting reaction of 1 min at 200◦ C. Samples were cross-sectioned, polished, and lightly etched for optical and SEM observation both before and after aging. Wetting reaction and solid-state aging were studied on the same set of samples.

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Chapter 2 Fig. 2.23. Cross-sectional optical microscopic images of the solder bump and the Cu UBM after two reflows (a), two reflows followed by 500 (b), 1000 (c), and 1500 hr (d) at 170◦ C.

Figure 2.23 shows cross-sectional optical microscopic images of the solder bump and the Cu UBM after two reflows (a), two reflows followed by 500 (b), 1000 (c), and 1500 hr (d) at 170◦ C. Figure 2.24 shows enlarged images of the IMC in Fig. 2.23(a) to (c). The scallop-type Cu6 Sn5 IMC can be seen

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Fig. 2.24. Enlarged images of the IMC in Fig. 2.17(a) to (c).

in Figs. 2.23(a) and 2.24(a). The average diameter of the scallops is about 2 μm. In Figs. 2.23(b), 2.23(c), 2.23(d), 2.24(b), and 2.24(c), a thick layer of IMC, consisting of Cu6 Sn5 and Cu3 Sn, formed between the solder and the Cu in a smoother layerlike morphology. Although the interface between the solder and Cu6 Sn5 is not flat, there are no deep valleys between the scallops as shown in Figs. 2.23(a) and 2.24(a). The layer of Cu3 Sn is quite uniform and is as thick as the Cu6 Sn5 layer. An etching that preferentially removes Pb rendered a deep groove between the IMC and the solder. This indicates that the solder

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layer next to the IMC must contain a high concentration of Pb. In addition, extensive grain growth occurred in the solder. The total thickness of the IMC in Fig. 2.24( c) is only a few micrometers, which is not much bigger than the diameter of the scallops shown in Fig. 2.23(a). In addition, the thickness of Cu3 Sn after two reflows [as shown in Fig. 2.23(a)] is negligibly small, compared to that after aging [as shown in Fig. 2.23(c)]. The IMC formed during the solid-state aging can be determined by subtracting the amount of IMC formed during two reflows. The average thickness of IMC formed during two reflows was obtained by dividing the total cross-sectional area of the scallops by the total length. Figure 2.25 shows the IMC thickness measured at 500, 1000, and 1500 hr for the 125, 150, and 170◦ C aging, respectively. The growth is diffusion-controlled and the activation energy of the solid-state aging is found to be 0.94 eV/atom, as shown in Table 2.1. 2.7.1 Morphology of Wetting Reaction and Solid-State Aging In the classical analysis of solid-state interfacial reactions in a binary bulk diffusion couple, it is assumed that all the equilibrium IMCs form simultaneously in a layered morphology. The kinetics of growth of each layer can be diffusioncontrolled or interfacial-reaction-controlled. For a bulk diffusion couple of sufficient thickness at a high enough temperature, all the IMCs coexist and obey a diffusion-controlled growth, so the ratio of thickness among the layers is proportional to the ratio of the square root of the interdiffusion coefficient in each layer [21, 22] The analysis has no consideration of surface and interfacial energies, because the motion of a planar interface in a layered structure does not change energy. In wetting reaction between eutectic SnPb and Cu, the Cu6 Sn5 has a scallop-type morphology. Furthermore, the growth kinetics of the scallops has a t1/3 dependence on time, so it does not obey the diffusion-controlled or interfacial-reaction-controlled kinetics. The scallop-type morphology of IMC has also been observed in wetting reaction between eutectic SnPb and Ni, and between most of the Sn-based Pb-free solders and Cu [2]. The scallops grow bigger but fewer with time. This indicates a nonconservative ripening reaction among the scallop-type grains. In the morphology of solid-state aging as shown in Fig. 2.23(b), (c), and (d), since the samples were reflowed twice before aging, they must possess the scallops of Cu6 Sn5 before aging. Yet during the solid-state aging the morphology of Cu6 Sn5 has changed from scallop-type to layer-type. Why does it not keep the scallop-type growth in the solid-state reaction? More importantly, why has the change of morphology changed the kinetics of growth significantly? The scallop-type morphology has been found to be stable in wetting reaction, yet unstable in solid-state reactions. The issue of morphological stability will be discussed in Section 5.2. The scallop-type morphology

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5

Cu6Sn5 Cu3Sn Total IMC Consumed Cu

4 Thickness (μm)

Fig. 2.25. (a–c) IMC thickness measured at 500, 1000, and 1500 hr for the 125, 150, and 170◦ C aging, respectively.

63

3 2 1 0

0

1000

1500

2000

2500

Time1/2 (sec1/2)

(b) 10

Cu6Sn5 Cu3Sn Total IMC Consumed Cu

8 Thickness (μm)

500

6 4 2 0

0

500

1000

1500

2000

2500

Time1/2 (sec1/2)

Thickness (μm)

(c) 20 15

Cu6Sn5 Cu3Sn Total IMC Consumed Cu

10

5 0

0

500

1000

1500

2000 Time

1/2

2500 (sec1/2)

suggests that the scallops themselves are not a diffusion barrier to their own growth, unlike that of a layer-type growth! 2.7.2 Kinetics of Wetting Reaction and Solid-State Aging We will not review the kinetics of diffusion-controlled and interfacial-reactioncontrolled growth of layer-type IMC. Here we consider the scallop-type growth

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Chapter 2 Table 2.1. Activation energy of Cu consumption and compound growth. Consumed Cu

Cu3 Sn

Q (eV) D0 (cm2 /s) Q (eV) e-SnPb Sn–3.5Ag Sn–3.8Ag–0.7Cu Sn–0.7Cu

0.94 1.03 1.10 1.05

0.0149 0.115 0.0560 0.128

0.73 0.95 1.05 1.08

Total IMC

D0 (cm2 /s)

Q (eV)

D0 (cm2 /s)

1.85 × 10−5 0.00563 0.0595 0.109

1.25 1.19 0.94 1.00

59.59 6.64 9.56 × 10−3 0.109

in wetting reaction. A schematic diagram of the cross section of two of the scallops is shown in Fig. 2.26. For simplicity, we ignore the thin Cu3 Sn between the Cu6 Sn5 scallops and Cu. We assume that Cu will not diffuse through the bulk of Cu6 Sn5 , instead Cu diffuses through the valley between the two Cu6 Sn5 scallops in order to reach the molten solder. This Cu flux is represented by the vertical arrow. Once in the molten solder, the diffusivity of Cu is about 10−5 cm2 /sec, so it can quickly reach the front of the Cu6 Sn5 and react with Sn to grow the compound. At the same time, there is a ripening reaction among the scallops, so there is a Cu flux between the scallops, as represented by the horizontal arrow. By combining these two fluxes, the growth equation of a scallop has been given as [23, 24]   r3 =

 γΩ2 DC0 ρAΩυ(t) + dt, 3NA LRT 4πmNP (t) dr1

r1

At to

r2 Δ = Exposed area

Ti or Cr

dr2

Si Substrate

Fig. 2.26. Schematic diagram of cross section of two neighboring scallops.

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where r is the radius of a scallop, γ is the surface energy of the scallop, Ω is the average atomic volume, D is atomic diffusivity in the molten solder, C0 is the solubility of Cu in the molten solder, NA is Avogadro’s number, L is the numerical factor relating the mean separation between scallops and the mean scallop radius, RT has the usual thermodynamic meaning, ρ is the density of Cu, A is the total area of the solder/Cu interface, ν (=dh/dt, where h and t are thickness of Cu and time, respectively) is the consumption rate of Cu in the reaction, m is the atomic mass of Cu, and NP is the total number of scallops at the interface. We note that this growth model has included the surface energy γ of the scallops. But in a more detailed analysis to be presented in Chapter 5, the growth is independent of surface energy. In the equation, the first term on the right-hand side is the ripening term, and the second term is the interfacial reaction term. It was found that the flux of the first term (represented by the horizontal arrow in Fig. 2.26) is about 10 times greater than that of the second term (represented by the vertical arrow). Thus, the ripening process dominates the growth of Cu6 Sn5 . Since we have assumed that the diffusion of Cu in the molten solder is very fast, on the order of 10−5 cm2 /sec, and since the diffusion distance between neighboring scallops is very short, diffusion is not the rate-limiting step. However, the supply of Cu cannot come only from the regions just below the valleys, they must also come from the regions below the scallops or the base of a scallop, which requires a lateral diffusion of Cu along the interface between the scallop and Cu. We have to assume that this interfacial diffusion is very fast too. If this interfacial diffusion is rate-limiting, we should have observed a 1 t /2 dependence on time. On the other hand, we have assumed that scallops are hemispherical. Therefore, the scallop surface must be full of atomic steps, so we will not have an interfacial-reaction-controlled process. Since the growth of a hemisphere is a three-dimensional growth, the rate of growth depends on the supply of Cu through the channels to be discussed in Chapter 5, therefore it is a supply-limited growth of the scallops. We define it to be a supply-controlled growth, neither diffusion-controlled nor interfacial-reaction-controlled growth. What is amazing is that the activation energy of the growth was found to be about 0.2 to 0.3 eV/atom. It is a very low activation energy process, and is comparable to the activation energy of dissolution of Cu into molten Sn. We note that the activation energy of interfacial diffusion of Cu along the base of the scallops may be higher, yet it is not the rate-limiting step! In the solid-state aging of eutectic SnPb on Cu, we found that the morphology of IMC is layer-type. The activation energy of the growth of the layer-type Cu6 Sn5 , or Cu3 Sn (or both) is about 0.8 eV/atom. Thus, the solid-state aging is a much slower kinetic process. Another way to compare the kinetics is to compare the period of time needed to form the same amount of IMC. In the wetting reaction at 200◦ C, it took only a few minutes to form IMC a few micrometers thick, but in the solid-state aging at 170◦ C, it took 1000 hr. Thus, the wetting reaction is four orders of magnitude (in terms of time) faster than

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the solid-state aging, although the temperature difference between 200◦ C and 170◦ C is only 30◦ C. The basic reason for the difference is atomic diffusivity. In the liquid state it is about 10−5 cm2 /sec, but in a FCC solid near its melting point it is about 10−8 cm2 /sec. Thus, across the melting point there is a difference of three orders of magnitude in diffusivity. Specifically, for the solid-state aging at 170◦ C, if we assume the diffusion of Cu across the IMC has an activation energy of 0.8 eV/atom, the diffusivity is about 10−9 cm2 /cm. So there are four orders of magnitude of difference in diffusivity between the wetting reaction at 200◦ C and the solid-state aging at 170◦ C. This difference is correlated to the time difference found on the basis of the relation, x2 ≈ Dt. Knowing the activation energy of 0.8 eV/atom of the solid-state reaction, we ask the question: if the growth of Cu6 Sn5 compound during the wetting reaction at 200◦ C takes a layer-type morphology, what might happen? We shall consider the formation of a layer of 1-μm-thick Cu6 Sn5 by consuming about 0.5 μm of Cu. We find that it will take more than 1000 sec, this is because the Cu6 Sn5 would have become a diffusion barrier layer to its own growth. On the other hand, to consume 0.5 μm of Cu to form Cu6 Sn5 scallops in the wetting reaction, it actually takes less than 1 min. In other words, the rate of free energy gain in IMC formation will be much faster in the scalloptype growth than the layer-type growth. Since the rapid diffusion of Cu in the molten solder is not utilized in the layer-type growth, it becomes a slow growth. Therefore, it is the rate of free energy change, rather than the free energy change itself, which determines the morphology of scallop-type IMC growth. Clearly, the scallop-type morphology affects the kinetics strongly. The radius of the scallop cannot be constant because it must grow bigger with time. If the scallops do not grow in radius, they must grow longer and become a diffusion barrier layer because the valleys will be closed. However, not every scallop can grow in radius, so some of them must shrink. Hence, ripening occurs. But the ripening eventually must slow down as the scallops become bigger and bigger. This is because the bigger the scallops, the less the number of short circuit paths (the valleys) to reach the molten solder. It is of interest to determine the distribution of the size of the scallops, which will be discussed in Chapter 5. Whether it obeys the LSW theory of ripening [25–27] is of interest. Whether the distribution function is independent of time is unclear. In a typical wetting reaction in devices, the thickness of Cu consumed is less than 1 μm, so the scallops are not big at all. We should also question why the Cu6 Sn5 in solid-state aging does not keep the morphology of scallops. This is because scallops have a larger interfacial area than a flat interface. In the wetting reaction, the rapid gain in compound formation energy can compensate the interfacial energy spent in growing the scallops, but not in the solid-state reaction. In Chapter 5, we will show that the total surface area of scallops is unchanged in growth while the total volume of scallops increases. In solid-state aging, the rapid gain of free energy disappears,

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so the compound changes to a layer-type in order to reduce the interfacial energy. 2.7.3 Reactions Controlled by Rate of Gibbs Free Energy Change All chemical reactions at constant pressure and constant temperature occur with a negative Gibbs free energy change. In interfacial reactions forming IMCs, they should be governed by negative free energy change too. But in order to have the largest negative free energy change in a short period of time as in the wetting reaction, it is the rate of free energy change that is crucial. To obtain the largest free energy change during a short period of time, e.g., 1 min in a wetting reaction, we have [28]  ΔG = 0

τ

dG dt, dt

(2.12)

where dG/dt is the rate of free energy change of the reaction, and τ is a short. period. Thus, the system tends to choose the reaction path or product that can give the largest dG/dt during the period of τ, resulting in the largest gain of free energy change. Specifically, during a wetting reaction or reflow, a high rate of reaction is possible with the formation of scallop-type IMC. On the other hand, if we consider a reaction when τ is infinite, it is free energy change that is important, not the rate anymore. We have used the specific case of molten eutectic SnPb on Cu to illustrate the importance of a high rate reaction. Actually it is a general phenomenon. We have already mentioned that molten eutectic SnPb on Ni forms scalloptype Ni3 Sn4 . In the case of molten eutectic SnPb on Pd, the formation of PdSn3 has a lamellar-type morphology and has a growth rate over 1 μm/sec, which is most likely the fastest rate of intermetalllic growth by interfacial reaction, to be discussed in Chapter 7. The molten solder itself serves as a matrix for fast atomic transport for the growth of the lamellae. Among the Pd-Sn compounds, the formation energy of PdSn3 is much less than that of Pd2 Sn and Pd3 Sn. The latter do not form because the former has a much higher rate of growth. This is also true in the solid-phase amorphization in reactions in the binary systems of Rh-Si, Ti-Si, and Ni-Zr [29–31] It is because of the high rate of growth of the amorphous alloys that they can form first, before the formation of the equilibrium IMC phases in those binary systems.

2.8 Wetting Reaction of Pb-Free Eutectic Solders on Thick Cu UBM The reaction of four different eutectic solders, SnPb, SnAg, SnAgCu, and SnCu, on electroplated thick Cu UBM 15 μm in thickness were compared. A

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photo-resist was applied to the Cu to define the UBM contact area. Solder paste of the four eutectic solders was printed on the UBM and reflowed twice in a belt furnace. The temperature profile had a peak of 240◦ C, and the duration of time above the melting point of the solders is 60 sec. Following the reflows, solid-state aging was performed in a furnace under atmospheric ambient at three different temperatures of 125, 150, and 170◦ C for three different periods of 500, 1000, and 1500 hr. Figure 2.27 shows SEM images of the interface of the four solders on Cu after two reflows. All of them show scallop-type, rounded or faceted, morphology of Cu6 Sn5 . The scallops in the Pb-free solders are larger than those in the SnPb. The formation of Cu3 Sn is unclear because it is thin and below the resolution of the imaging technique used. In the SnAg and SnAgCu, some very large platelet-type Ag3 Sn IMC can be seen. Figure 2.28 shows optical microscopic images of the interface of the four solders on Cu after solid-state aging at 170◦ C for 1500 hr. The solid-state aging has changed the scallop-type morphology of Cu6 Sn5 into layer-type. Also, the formation of a layer of Cu3 Sn is clearly shown. In the SnPb solder, the matrix has extensive grain growth and a Pb-rich layer forms next to the Cu6 Sn5 . In the Pb-free solders, grain growth is not apparent. The thickness

Fig. 2.27. SEM images of the interface of four eutectic solders—(a) SnPb, (b) SnAg, (c) SnAgCu, and (d) SnCu—on Cu after two reflows.

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Fig. 2.28. Optical microscopic images of the interface of the four solders on Cu (Fig. 2.27) after solid-state aging at 170◦ C for 1500 hr.

of intermetallic compounds of Cu6 Sn5 and Cu3 Sn measured at 125, 150, and 170◦ C for 500, 1000, and 1500 hr has been reported in Ref. 20. The difference between SnPb and Pb-free solders in terms of IMC formation during solidstate aging is not large at all. From the IMC thickness, the consumption of Cu during the solid-state aging can be calculated. It is rather surprising to find that the amount of Cu consumed during solid-state aging for up to 1500 hr is of the same order of magnitude as the wetting reaction for a couple of minutes discussed in Section 2.7.1. If we just compare the amount of IMC formation in Figs. 2.27 and 2.28, they are of the same order of magnitude, yet the time difference between 2 min in reflow and 1500 hr (90,000 min) in aging is a difference of four orders of magnitude. In other words, the rate of IMC formation in wetting reaction is four orders of magnitude faster than that in solid-state aging. We note that thick Cu UBM is the trend in the electronic packaging industry. The reason will be made clear after we have discussed two issues; the first issue is the spalling of the scallop-type IMC in solder reaction on thin films of Cu to be discussed in Chapter 3, and the second issue is current crowding in electromigration in flip chip solder joints to be discussed in Chapter 9.

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References 1. K. N. Tu and K. Zeng, “Tin-lead (SnPb) solder reaction in flip chip technology,” Materials Science and Engineering Reports, R34, 1–58 (2001). (Review paper) 2. K. Zeng and K. N. Tu, “Six cases of reliability study of Pb-free solder joints in electron packaging technology,” Materials Science and Engineering Reports, R38, 55–105 (2002). (Review paper) 3. T. Young, Philos. Trans. R. Soc. London, 95, 65 (1805). 4. H. K. Kim, H. K. Liou, and K. N. Tu, “Morphology of instability of wetting tips of eutectic SnBi , eutectic SnPb, and pure Sn on Cu,” J. Mater. Res., 10, 497–504 (1995). 5. H. K. Kim, H. K. Liou, and K. N. Tu, “Three-dimension morphology of a very rough interface formed in the soldering reaction between eutectic SnPb and Cu,” Appl. Phys. Lett., 66, 2337–2339 (1995). 6. A. K. Larsson, L. Stenberg, and S. Liden, “Crystal structure modulation in η-Cu6 Sn5 ,” Z. Kristallogr., 210 (11), 832–837 (1995). 7. H. K. Kim and K. N. Tu, “Rate of consumption of Cu soldering accompanied by ripening,” Appl. Phys. Lett., 67, 2002–2004 (1995). 8. C. Y. Liu and K. N. Tu, “Morphology of wetting reactions of SnPb alloys on Cu as a function of alloy composition,” J. Mater. Res., 13, 37–44 (1998). 9. C. Y. Liu and K. N. Tu, “Reactive flow of molten Pb(Sn) alloys in Si grooves coated with Cu film,” Phys. Rev. E, 58, 6308–6311 (1998). 10. F. G. Yost and A. D. Romig, Jr., in “Electronic Packaging Materials Science III,” R. Jaccodine, K. A. Jackson, and R. C. Subdahl (Eds.), Materials Research Society Symp. Proc., 108, Pittsburgh, PA (1988). 11. W. J. Boettinger, C. A. Handwerker, and U. R. Kattner, “Reactive wetting and intermetallic formation,” in “The Mechanics of Solder Alloy Wetting and Spreading,” F. G. Yost, F. M. Hosking, and D. R. Frear (Eds.), Van Nostrand Reinhold, New York (1993). 12. J. Gorlich, G. Schmidt, and K. N. Tu, “On the mechanism of the binary Cu/Sn solder reaction,” Appl. Phys. Lett., 86, 053106–1 to –3 (2005). 13. L. Kaufman and H. Bernstein, “Computer Calculation of Phase Diagram,” Academic Press, New York (1970). 14. J.-H. Shim, C.-S. Oh, B.-J. Lee, and D. N. Lee, “Thermodynamic assessment of the Cu-Sn system,” Z. Metallkd., 87, 205–212 (1996). 15. A. Bolcavage, C. R. Kao, S. L. Chen, and Y. A. Chang, “Thermodynamic calculation of phase stability between copper and lead-indium solder,” in Proc. Applications of Thermodynamics in the Synthesis and Processing of Materials, Oct. 2–6, 1994, Rosemont, IL, P. Nash and B. Sundman (Eds.), TMS, Warrendale, PA, pp. 171–185 (1995). 16. V. C. Marcotte and K. Schroeder, “Cu-Sn-Pb phase diagram,” in Proc. Thirteenth North American Thermal Analysis Society, A. R. McGhie (Ed.), North American Thermal Analysis Society, 1984, pp. 294.

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17. H. Ohtani, K. Okuda, and K. Ishida, “Thermodynamic study of phase equilibria in the Pb-Sn-Sb system,” J. Phase Equil., 16, 416–429 (1995). 18. K. N. Tu, T. Y. Lee, J. W. Jang, L. Li, D. R. Frear, K. Zeng, and J. K. Kivilahti, “Wetting reaction vs. solid state aging of eutectic SnPb on Cu,” J. Appl. Phys. 89, 4843–4849 (2001). 19. K. N. Tu, F. Ku, and T. Y. Lee, “Morphological stability of solder reaction products in flip chip technology,” J. Electron. Mater., 30, 1129–1132 (2001). 20. T. Y. Lee, W. J. Choi, K. N. Tu, J. W. Jang, S. M. Kuo, J. K. Lin, D. R. Frear, K. Zeng, and J. K. Kivilahti, “Morphology, kinetics, and thermodynamics of solid state aging of eutectic SnPb and Pb-free solders (SnAg, SnAgCu, and SnCu) on Cu,” J. Mater. Res., 17, 291–301 (2002). 21. G. V. Kidson, “Some aspects of the growth of different layers in binary systems,” J. Nucl. Mater., 3, 21 (1961). 22. U. Gosele and K.N. Tu, “Growth kinetics of planar binary diffusion couples: Thin film case versus bulk cases,” J. Appl. Phys., 53, 3252 (1982). 23. H. K. Kim and K. N. Tu, “Kinetic analysis of the soldering reaction between eutectic SnPb alloy and Cu accompanied by ripening,” Phys. Rev. B, 53, 16027–16034 (1996). 24. A. M. Gusak and K. N. Tu, “Kinetic theory of flux driven ripening,” Phys. Rev. B, 66, 115403 (2002). 25. I. M. Lifshiz and V. V. Slezov, J. Phys. Chem. Solids, 19, 35 (1961). 26. C. Wagner, Z. Electrochem., 65, 581 (1961). 27. V. V. Slezov, “Theory of Diffusion Decomposition of Solid Solutions,” Harwood Academic Publishers, pp. 99–112 (1995). 28. D. Turnbull, “Metastable structures in metallurgy,” Metall. Trans. A, 12, 695–708 (1981). 29. S. Herd, K.N. Tu, and K.Y. Ahn, “Formation of an amorphous Rh-Si alloy by interfacial reaction between amorphous Si and crystalline Rh thin films,” Appl. Phys. Lett., 42, 597 (1983). 30. R. B. Schwarz and W. L. Johnson, Phys. Rev. Lett., 51, 415 (1983).

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3 Copper–Tin Reactions in Thin-Film Samples

3.1 Introduction On a silicon chip, thin-film under-bump metallization (UBM) is needed to join the solder bump to the Al or Cu wiring on the chip and also to control the size of the solder bump. This is because the oxide on a free Al surface prevents the wetting of molten solder. On the other hand, Cu reacts extremely fast with molten solder, therefore the Cu thin-film wiring cannot be wetted by molten solder. Control of the size of the solder bump makes use of the concept of ball-limiting metallization in C-4 technology; the so-called controlled-collapsechip-connection as discussed in Chapter 1. The most widely used thin-film UBM, between solder bump and Al or Cu interconnect wiring, is a trilayer film of Au/Cu/Cr or a trilayer film of Cu/Ni(V)/Al. In the trilayer thin film of Au/Cu/Cr, the Cr is needed for adhesion to dielectric surface and to Al wiring, the Cu is needed for soldering reaction, and the Au is needed for passivation to prevent surface oxidation. Therefore, how solder reacts with these thin films is crucial in device manufacturing, concerning both yield and reliability. In Chapter 1, we mentioned that several reflows are required in device manufacturing. In each reflow, every solder joint on the chip surface must be successfully joined and the UBM must survive several reflows, otherwise a very unique phenomenon of spalling of thin-film intermetallic compound (IMC) occurs, which is a major reliability subject to be covered in Sections 3.3 to 3.8. To discuss solder reaction on UBM thin films, we begin with the roomtemperature reaction between thin films of Cu and Sn. It is of interest for the following reasons. (1) The fast diffusion of noble metals in beta-Sn (white Sn) and Pb has been interpreted by the mechanism of interstitial diffusion. At 25◦ C, the diffusivity of Cu along the a- and c-axes of beta-Sn is about 0.5 × 10−8 and 2 × 10−6 cm2 /sec, respectively. This indicates that the mobility of Cu in Sn is high enough that the growth of Cu-Sn IMC can occur at room temperature. (2) Spontaneous Sn whisker is known to occur at room temperature on matte Sn plated Cu surfaces. In a spontaneous process, the

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driving force must come from within the system. If Cu and Sn react at room temperature, the free energy gain in interfacial chemical reaction might provide the driving force for whisker growth since the chemical energy per atom is four to five orders of magnitude higher than the elastic strain energy per atom. In other words, a chemical process can drive a mechanical process provided that it is a slow rate process such as creep, because the rate of solid state chemical reaction by interdiffusion is slow. (3) Thin-film samples allow the detection of the early stage of IMC formation. In this chapter, the kinetics of Cu-Sn reaction will be emphasized first.

3.2 Room-Temperature Reaction in a Bilayer Thin Film of Sn/Cu A bilayer of polycrystalline thin film of Cu and Sn has been used to study the room-temperature reaction. To detect the reaction in thin-film samples, high-resolution glancing incidence x-ray diffraction was used to analyze the interfacial IMC formation [1, 2]. The bilayer film was prepared by e-beam deposition of Cu followed by Sn on 1-inch-diameter and 1/8-inch-thick fused quartz disks kept at room temperature during the consecutive deposition in one run without breaking the vacuum at better than 2 × 10−7 torr. The deposition rate was about 0.5 nm/sec. Three sets of film having the followed thicknesses were prepared: 350 nm Sn/180 nm Cu/quartz, 350 nm Sn/600 nm Cu/quartz, and 2500 nm Sn/600 nm Cu/quartz. Since the thickness of the quartz disk was 1/8 inch, no bending of the sample can occur. A single layer of Sn film of thickness 350 nm and another one of 2500 nm were deposited on the same kind of fused quartz substrate at room temperature and kept at room temperature as references for lattice parameter measurements and for spontaneous Sn whisker growth (to be discussed in Chapter 6). Annealing of the bilayer films was carried out at four temperatures: −2◦ C (in a refrigerator), 20◦ C (air-conditioned room), 60◦ C and 100◦ C (vacuum furnace). Except for the room-temperature annealing where some temperature fluctuation may have occurred, the temperature was controlled to within ± 1◦ C. The annealing time was up to 1 year. 3.2.1 Phase Identification by Glancing Incidence X-ray Diffraction Structural change of the bilayer films as a function of annealing due to interdiffusion and reaction was investigated by x-ray diffraction using a glancing incidence Seeman-Bohlin diffractometer [1]. It has the sensitivity of detecting a polycrystalline Au film of 10 nm by resolving the 111, 200, 220, and 311 reflections of Au. Beta-Sn has a body-centered-tetragonal lattice with a = 0.58311 nm and c = 0.31817 nm. Copper has a face-centered-cubic lattice with lattice parameter of a = 0.36149 nm.

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Figure 3.1 shows four diffraction spectra of the set of 350 nm Sn on 600 nm of Cu on fused quartz. Figure 3.1(a) was obtained from the as-deposited state. It shows reflections of pure Cu and Sn, yet two reflections of Cu6 Sn5 (the η’ phase) were present, indicating that it forms during or right after the deposition of Sn on Cu. Figure 3.1(b) was obtained after 15 days at room temperature, and several more reflections of Cu6 Sn5 were detected. Comparing Fig. 3.1(a) and 3.1(b), they show that Cu reacts with Sn at room temperature based on the growth of Cu6 Sn5 at room temperature. Figure 3.1(c) was obtained after 1 year at room temperature. All reflections of Sn were gone. While there are reflections of Cu, all the other reflections can be identified to be those of Cu6 Sn5 . It is worthwhile noting that there is no reflection of Cu3 Sn, even though there was excess Cu in the sample. Figure 3.1(d) was obtained from a sample annealed at 100◦ C for 36 hr. The reflections of Cu6 Sn5 and Cu3 Sn were found, indicating the formation of both compounds. Figure 3.2(a) and (b) are respectively Seeman-Bohlin x-ray diffraction spectra from angles of 4θ from 40◦ to 190◦ taken from the sample annealed at room temperature for 1 year and the sample annealed at 100◦ C for 60 hr. In Fig. 3.2(a), only the reflections of Cu6 Sn5 can be detected, but reflections of both Cu6 Sn5 and Cu3 Sn are present in Fig. 3.2(b). It was concluded that Cu6 Sn5 , but not Cu3 Sn, forms at room temperature. The growth of Cu6 Sn5 was also detected in samples kept at −2◦ C. Both Cu6 Sn5 and Cu3 Sn were detected in sample kept at 60◦ C, indicating that Cu3 Sn forms at temperatures above 60◦ C. According to the binary phase diagram of Cu-Sn, the phase Cu6 Sn5 undergoes a phase transition of ordering around 170◦ C. The high-temperature phase has the ordered hexagonal NiAs structure with a = 0.420 nm and c = 0.509 nm. The low-temperature phase is a long-period superlattice with a period of 5 along both a- and c-directions. In Fig. 3.2(a), the superlattice reflections are indexed with *. While Sn forms surface oxide at room temperature, no oxide reflections were detected because the oxide was too thin. The reflections with * are from the superlattice, not from oxide. Table 3.1 lists the indexed reflections of Cu6 Sn5 shown in Fig. 3.2(a). The Cu3 Sn phase is ordered and has an orthorhombic lattice with a = 0.5516 nm, b = 0.3816 nm, and c = 0.4329 nm. It is a long-period superlattice of a smaller orthorhombic one with a = 0.5514 nm, b = 0.4765 nm, and c = 4329 nm. Table 3.2 lists the indexed reflections of Cu3 Sn shown in Fig. 3.2(b). 3.2.2 Growth Kinetics of Cu6 Sn5 and Cu3 Sn The kinetics of growth of Cu6 Sn5 and Cu3 Sn at and above room temperature is a reliability issue in solder joints because they consume Cu. Furthermore, the Cu3 Sn growth is accompanied by Kirkendall void formation. The rate of Cu consumption by solder reaction is of interest since the Cu thin-film layer in UBM is not very thick. To study the kinetics, thin-film bilayers of Sn/Cu were prepared on fused quartz substrate with the thickness of Cu at

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h¢ - Cu Sn 6 5 - Cu3Sn

∋

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d

Cu

h¢ Cu

∋

∋

230

213

222

h¢

Cu

∋

h¢

∋

h¢

∋

022 h¢

h¢ h¢ Cu

311

100°C 36 HOURS Cu h¢ 201

c Cu

COUNT (arbitrary units)

h¢ 112

h 300 212

h¢ 211

h¢ 202

Cu

h¢ h¢ 213 220 Cu

h¢ 203

h¢ 103

R.T. 1 YEAR Cu

Cu

h¢

b h¢

Sn

h¢

Sn Sn Sn

Sn

h¢

Sn

Cu

Sn

Sn

h¢

h¢ h¢

R.T. 15 DAYS Cu 220

a Cu 200

Sn 301

h¢ 100

110

Sn Sn 231 400 Sn 112 120

Sn 240

Cu 311 Sn 341

Sn Sn 141 132 h¢

130 140 150 160 NO HEAT TREATMENT

170

180

Cu Sn Sn 190

200

Fig. 3.1. Four diffraction spectra of the set of 350 nm Sn on 600 nm Cu. (a) The asdeposited state. It shows reflections of pure Cu and Sn, yet two reflections of Cu6 Sn5 (the

η  phase) are present, indicating that it forms during the deposition of Sn on Cu. (b) After

15 days at room temperature, several reflections of Cu6 Sn5 are detected. Comparing (a) and (b), they show the Cu and Sn reaction and the growth of Cu6 Sn5 at room temperature. (c) After 1 year at room temperature. All reflections of Sn are gone. While there are still reflections of Cu, all the other reflections can be identified as being those of Cu6 Sn5 . It is worth noting that there is no reflection of Cu3 Sn, even though there was excess Cu in the sample. (d) Annealed at 100◦ C for 36 hr. The reflections of Cu3 Sn and Cu6 Sn5 are found, indicating the formation of both compounds.

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77

Cu111

h′ 101

h′

110

' ∗

∗

'

'

011

∗

210

∗

'

002

h′

∗∗

'

'

60

'

50

h′

112

112

70

80

90

100

110

202

h′

h′

'

'

∗∗

40

h∗

h′

022

230 211

h′

202

213

'

h∗

h∗

Cu 200

'

200

Cu 220

201

h′

002

222

103

'

'

h∗101

'

COUNT (arbitrary units)

210

Cu 311 4q

311

120

130

100°C 60

140

150

160

170

180

190

HOURS

(b) h′

Cu 111

101

h′ COUNT (arbitrary units)

110

Sn200 Cu 200

h∗

h∗

40

50

h′

Cu 220

201

h∗

60

h∗ 70

h′

h∗ h∗ 80

h′

202

h′

h′

300

211

h′ 112

103

90 100 110 120 130 140 ROOM TEMPERATURE ONE YEAR

Cu 311

h′

4q

203 150

160

170

180

190

Fig. 3.2. Seeman-Bohlin x-ray diffraction spectra from angles of 4θ from 40◦ to 190◦ taken from (b) the sample annealed at room temperature for 1 year and (a) the sample annealed at 100◦ C for 60 hr. In (a), only the reflections of Cu6 Sn5 can be detected, but reflections of both Cu6 Sn5 and Cu3 Sn are present in (b). We conclude that Cu6 Sn5 , but not Cu3 Sn, can form at room temperature.

560 nm and that of Sn at either 200 or 500 nm. The bilayer thin films were deposited at liquid-nitrogen temperature in order to reduce as much as possible the interfacial reaction during deposition. The change of thickness of Cu6 Sn5 on room-temperature aging was measured by Rutherford backscattering. No formation of Cu3 Sn was detected on room-temperature aging [3]. In Fig. 3.3, three Rutherford backscattering spectra (RBS) of Sn/Cu samples are shown. The spectrum of curve (a) is that of a 200 nm Sn/560 nm

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Table 3.1. Reflections of Cu6 Sn5 found in bimetallic Cu-Sn thin films annealed at room temperature

4θ (deg.)

d ˚) (A

49.10 52.20 60.65 63.75 70.30 73.05 79.20 86.55 90.15 107.50 114.15 120.85 126.15 142.65 154.35 153.85

3.60 3.41 2.95 2.74 2.55 2.45 2.27 2.09 2.01 1.72 1.61 1.54 1.47 1.32 1.23 1.21

∗

Indexed as ordered NiAs structure with a = 4.19 ˚ A b = 5.09 ˚ A

101 002

110 201 112 103 202 211 203 300

Indexed as long period superlattice with a = 20.85 ˚ A b = 25.10 ˚ A 501∗ 503∗ 505 515∗ 0,0,10 525∗ 535∗ 550 554∗ 10,0,5 5,5,10 5,0,15 10,0,10 10,5,5 10,0,15 15,0,0

Long period superlattice line of η  .

Table 3.2. Reflections of Cu3 Sn found in bimetallic Cu-Sn thin films annealed at 100◦ C

4θ (deg.)

d ˚) (A

52.15 55.50 64.89 67.00 75.25 77.65 80.70 83.85 96.70 115.30 136.05 155.25 166.35 168.25

3.40 3.20 2.75 2.67 2.38 2.32 2.23 2.16 1.90 1.59 1.37 1.23 1.16 1.15

∗

and

‡

Indexed as ordered orthorhombic lattice with a = 5.514 ˚ A b = 4.765 ˚ A c = 4.329 ˚ A

Indexed as long period superlattice with a = 5.514 ˚ A b = 38.16 ˚ A c = 4.329 ˚ A

101∗ 011∗ 200

101 081 181 191‡ 280 290‡ 2,10,0‡ 002 182 0,16,2 2,24,0 283 2,16,2 381

indicates long period superlattice line.

210∗ 002∗ 112 022 230 213 222 311

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5 Cu

ARB. UNITS

4

Sn

a. As Dep.

Cu

Cu6 Sn5

b. Room Temp. 84 Days

Cu

Cu3Sn

c. 200° C - 10 min a

3 Cu

b Sn

2 c 1

0 200

300

400

CHANNEL NUMBER (5 keV/CHANNEL)

Fig. 3.3. Three Rutherford backscattering spectra (RBS) of Sn/Cu samples. The spectrum of curve (a) is that of 200 nm Sn/560 nm Cu right after the deposition at liquid-nitrogen temperature. The two arrows labeled Sn and Cu indicate the backscattered energy positions of Sn and Cu if they appear on the surface of the sample. As can be seen, the Cu spectrum has been displaced to lower energy due to the top Sn layer. Curve (b) is from the sample aged at room temperature for 84 days. The Sn sign has lowered and extended backward. The front part of the Cu spectrum has also lowered but extended forward. Together, they indicate a mixing of Sn and Cu.

Cu right after the deposition at liquid-nitrogen temperature. The two words labeled Sn and Cu indicate the backscattered energy positions of Sn and Cu if they were assumed to appear on the surface of the sample. As can be seen, the Cu spectrum has been displaced to lower energy due to the absorption of the top Sn layer. Curve (b) is from the sample aged at room temperature for 84 days. The Sn sign has lowered and extended backward. The front part of the Cu spectrum has also lowered but extended forward. Together, they indicate a mixing of Sn and Cu. The ratio of the height of Sn to that of Cu suggests a phase of Cu:Sn = 6:5, yet the confirmation of Cu6 Sn5 was obtained by x-ray diffraction. Curve (c) is from a sample annealed at 200◦ C for 10 min. The signal of Sn was reduced further, but that of Cu increased. Again the phase was confirmed by x-ray diffraction to be Cu3 Sn. During room-temperature aging, the measured thickness of Cu6 Sn5 is plotted against time in Fig. 3.4 for two sets of samples. Both the thicker and thinner Sn samples show a linear growth at a rate of 3.5 and 6 nm/day, respectively. When all the Sn was consumed by Cu6 Sn5 formation, the Cu6 Sn5 /Cu/SiO2 samples were annealed in the temperature range from 115◦ C to 150◦ C in a purified He furnace. The growth of Cu3 Sn between the Cu6 Sn5 and Cu was

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THICKNESS (× 10nm)

24 20 TOTALLY REACTED

2000 Å Sn/ 5600 Å Cu 16 12 8 4 0

5000 Å Sn/ 5600 Å Cu 0

5

10

15

20

25

30

35

40

45

TIME (DAYS)

Fig. 3.4. Measured thickness of Cu6 Sn5 plotted versus time for two sets of samples after room-temperature aging. Both the thicker and thinner Sn samples show linear growth at a rate of 3.5 and 6 nm/day, respectively.

measured from the reduction of Cu6 Sn5 by the Rutherford backscattering technique. The phase of Cu3 Sn was confirmed by glancing x-ray diffraction. Figure 3.5 plots the square of the measured remaining thickness of Cu6 Sn5 as a function of annealing time at temperatures of 115, 120, 130, 140, and 150◦ C. The linear relation indicates the reaction is diffusion-limited. The activation energy of reduction of Cu6 Sn5 was obtained by plotting the thickness of Cu6 Sn5 at a fixed annealing time on a logarithmic scale against inverse temperature, as shown in Fig. 3.6. The slope of the curve gives an activation energy of 0.99 eV/atom. 3.2.3 Copper Is the Dominant Diffusing Species To determine whether Cu or Sn is the dominant diffusing species during the room-temperature growth of Cu6 Sn5 , a flash of discontinuous W film about 1 nm thick was deposited between the Cu and Sn to serve as diffusion marker. The in-depth positions of the W film in the Sn/Cu sample before and after aging at room temperature for 60 hr were measured by Rutherford backscattering to determine the marker displacement. Figure 3.7 shows two RBS of the W marker signal and the bilayer thin films before and after the formation of Cu6 Sn5 . In Fig. 3.7(a), before reaction the signal of W overlaps that of Sn and appears as a small peak near the leading edge of the Sn signal. After reaction, the W signal overlaps the middle part of the Sn signal, as shown in Fig. 3.7(b). Together, they indicate that Cu is the dominant diffusing species. This is because as Cu atoms move forward, the W will be displaced backward, hence its signal will be shifted to lower energy. By simulation, the thickness of Cu6 Sn5 formed was about 245 nm and the position of the W marker in the sample was determined to be about 186 nm from the surface of the Cu6 Sn5 .

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5

(Cu6Sn5 THICKNESS)2 (× 106 Å)

4

3

Xo = 1500 Å 115°C

2 120°C 130°C 1 140°C 150°C 0 0 5 10 15 20 25 30

40

50

60

75

90

TIME (min)

Fig. 3.5. Square of the measured remaining thickness of Cu6 Sn5 plotted as a function of annealing time at temperatures of 115, 120, 130, 140, and 150◦ C. The linear relation indicates the reaction is diffusion-limited.

If we assume that the diffusion fluxes of Cu and Sn are equal, we expect the marker would locate roughly in the middle of the Cu6 Sn5 layer. It is actually much deeper into the Cu6 Sn5 layer, so the flux of Cu is larger than that of Sn. 3.2.4 Kinetic Analysis of Sequential Formation of Cu6 Sn5 and Cu3 Sn In the thin-film reactions between Sn and Cu, the formation of Cu6 Sn5 and Cu3 Sn is sequential, i.e., Cu6 Sn5 forms first and alone at room temperature, and Cu3 Sn will form only at temperatures above 60◦ C. We recall that in the wetting reaction which occurs between molten Sn and Cu at a much higher temperature, it seems that both Cu6 Sn5 and Cu3 Sn might

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150

140

130

120 115

9 8 lnt (sec)

7 6 5 4 2.3

2.4

2.5

2.6

1000/T (K−1)

Fig. 3.6. Activation energy of reduction of Cu6 Sn5 obtained by plotting the thickness of Cu6 Sn5 at a fixed annealing time on a logarithmic scale versus inverse temperature. The slope of the curve shows an activation energy of 0.99 eV/atom.

form simultaneously. However, using synchrotron radiation, a strong crystallographic orientation relationship between Cu6 Sn5 and Cu has been found on studying the wetting reaction from 30 sec to 4 min, indicating that Cu6 Sn5 should have nucleated on Cu directly without Cu3 Sn, as discussed in Section 2.2.1 After a longer wetting time of several minutes, the latter forms and coexists with Cu6 Sn5 , yet the orientation relationship between Cu6 Sn5 and Cu is affected by the growth of Cu3 Sn, as discussed in Section 2.2.1. If we consider the binary phase diagram of Sn-Cu, both intermetallic phases exist in the temperature range from room temperature to 250◦ C. Based on the phase diagram or thermodynamics, we cannot explain why at room temperature solid state reaction they form sequentially rather than simultaneously. Instead, we have to use kinetic reasoning to explain why Cu3 Sn does not form at room temperature. In view of kinetics, either Cu3 Sn cannot nucleate or it cannot grow even if it can nucleate. It cannot grow because it cannot compete with the faster growth of Cu6 Sn5 . Since both Cu6 Sn5 and Cu3 Sn can form together at temperatures above 60◦ C, Cu3 Sn must be able to nucleate above 60◦ C. Nucleation depends on undercooling. Because the nucleation at room temperature has a larger undercooling than the nucleation at 60◦ C, it will be difficult to use no nucleation at room temperature to explain the absence of Cu3 Sn. We shall consider that it cannot compete in growth against the rapid growth of Cu6 Sn5 . Sequential phase formation in thin film reactions has been studied in the reaction between Si and metallic films to form silicide IMC phases [4]. Single phase formation of a specific silicide on Si to serve as ohmic contacts and

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w

(a) 5600Å Cu

4

83

w

2000Å Sn

3 2

ARB. UNITS

1 0 5

(b)

4

w 1850 Å Cu6Sn5

4600 Å Cu

200-600 Å Cu6Sn5

w Cu

Sn

3 2 1

0

200

300

400

CHANNEL NUMBER (5 KeV/CHANNEL)

Fig. 3.7. Two Rutherford backscattering spectra of the W marker signal and the bilayer thin films of Sn/Cu before and after the formation of Cu6 Sn5 . (a) Before reaction, the signal of W overlaps that of Sn and appears as a small peak near the leading edge of the Sn signal. (b) After reaction, the W signal overlaps the middle part of the Sn signal. Together, they indicate that Cu is the dominant diffusing species.

gates in field-effect transistor devices has been a very important technological issue. There are millions or even billions of silicide contacts and gates on a Si chip having a very-large-scale integration of circuits. These contacts and gates must have the same physical properties. For example, we cannot have a contact that consists of a mixture of silicide phases. Therefore, the device application demands single phase formation, which in principle is contrary to thermodynamics. Thus, a kinetic rather than a thermodynamic reason has to be given. The kinetics of single phase growth has been analyzed by Gosele and Tu, assuming a layered model of competition of growth of coexisting phases by combining diffusion-controlled growth and interfacial-reaction-controlled growth [5].

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eq Cab

CA

Without with

interface reaction barriers

eq Cba Cbg

Cba

eq Cbg

AbB

AaB

Ag B eq Cgb

xb xbg

xab

x

Fig. 3.8. Schematic diagram depicting the growth of a layered intermetallic compound phase between two pure elements, for example, the growth of Cu6 Sn5 (Aβ B) between Cu (Aα B) and Sn (Aγ B). The concentration change of Cu across the interfaces is shown.

Figure 3.8 depicts the growth of a layered IMC phase between two pure elements, for example, the growth of Cu6 Sn5 between Cu and Sn. We represent Cu, Cu6 Sn5 , and Sn by Aα B, Aβ B, and Aγ B, respectively. The thickness of Cu6 Sn5 is xβ and the position of its interface with Cu and Sn is defined by xαβ and xβγ , respectively. Across the interfaces, there is an abrupt change in concentration. In Fig. 3.8, the concentration change of Cu across the interfaces is shown. In a diffusion-controlled growth of xβ , the concentrations at its interface are assumed to have the equilibrium values, represented by the broken curve in the xβ layer in Fig. 3.8. In an interfacial-reaction-controlled growth, the concentrations at its interface are assumed to be nonequilibrium, represented by the solid curve. To consider a diffusion-controlled growth of a layered phase of xβ in Fig. 3.8, we shall use Fick’s first law of diffusion in one dimension. The corresponding fluxes across the interface and in the layer are shown in Fig. 3.9. J = −D

dC dx

(3.1)

and also the flux equation of J = Cv,

(3.2)

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xab A Jab

85

A

A

Jbg

A

Jba

Jg b

A

Jb

xb

Fig. 3.9. Corresponding fluxes across the interface and in the layer of xβ .

where J is atomic flux (number of atoms/cm2 -sec), D is atomic diffusivity (cm2 /sec), C is concentration (number of atoms/cm3 ), x is length (cm), and v is the velocity of the moving interface (cm/sec). For example, v = dxαβ /dt of the interface xαβ . For the growth of this interface, by considering the conservation of flux that enters and leaves the interface, we have on the basis of Eqs. (3.2) and (3.1), (Cαβ − Cβα )

dxαβ ∂C ∂C = Jαβ − Jβα = −D |αβ + D |βα dt ∂x ∂x

(3.3)

Rearranging, we obtain the expression of velocity of the xαβ interface, dxαβ 1 = dt Cαβ − Cβα



∂C −D ∂x





αβ

∂C − −D ∂x





.

(3.4)

βα

To overcome the unknown of the concentration gradients in square brackets in the above equation, we have to make a transformation by combining the two √ variables of x and t into one, i.e., we consider C(x, t) = C(η), where η = x/ t, and so ∂C 1 dC =√ . ∂x t dη

(3.5)

The concentrations at the interface, i.e., Cαβ and Cβα , can be assumed to remain constant with respect to time and position, because we can take them as the equilibrium values under the assumption of a diffusion-controlled growth [6]. Hence, we have dC(η) = f (η), dη

(3.6)

where f (η) = constant if η is constant, independent of time and position, at the interfaces for a diffusion-controlled process. Therefore, the equation of

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velocity can be rewritten as       dxαβ ∂C 1 ∂C 1 √ . − D +D = dt Cαβ − Cβα ∂η αβ ∂η βα t

(3.7)

The quantity within square brackets is independent of time, after we take the factor of time out of the square brackets. Integration of the above equation gives √ xαβ = Aaβ t,

(3.8)

where   (DK)βα − (DK)αβ Aαβ = 2 , Cαβ − Cβα   dC Kij = . dη ij Following a similar approach, we can obtain at the other interface of xβγ , √ xβγ = Aβγ t.

(3.9)

By combining the two interfaces, we have the width of the β phase as √ √ Wβ = xβγ − xαβ = (Aβγ − Aαβ ) t = B t,

(3.10)

which shows that the β phase has a parabolic rate or diffusion-controlled growth. We note that the above is a very simple derivation of a diffusioncontrolled growth of a layered structure, or a relationship of x2 ∝ t for a layered growth with abrupt change of composition at its interfaces. A fundamental feature of a diffusion-controlled layer growth is that it will not disappear or cannot be consumed in competition of growth in a multilayered structure since its velocity of growth is inversely proportional to its thickness. As the thickness w approaches 0, lim

dw B = → ∞. dt w

(3.11)

The growth rate will approach infinity, or the chemical potential gradient to drive the growth will approach infinity. Therefore, in a multilayered structure, for example, Cu/Cu3 Sn/Cu6 Sn5 /Sn, when both Cu3 Sn and Cu6 Sn5 exist and have diffusion-controlled growth, they will coexist and grow together. For this reason, in a sequential growth of Cu6 Sn5 followed by Cu3 Sn, we cannot assume that both of them can nucleate and grow by a diffusion-controlled process, then they will coexist.

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Next we shall consider the interfacial-reaction-controlled growth in which the growth rate is linear with time, or the rate is constant and finite and independent of thickness. We note that the linear growth rate cannot continue forever; when the layer grows to a certain thickness, diffusion across the thick layer will be rate-limiting and the growth will change to diffusion-controlled or its time dependence will change from linear to parabolic [5]. In an interfacial-reaction-controlled growth, the concentration at the interface will be nonequilibrium as shown in Fig. 3.8. The flux in the β-phase will be given by eq Jβ = (Cβα − Cβα )Kβα ,

(3.12)

where Kβα is defined as the interfacial-reaction constant of the xαβ interface. It has the unit of velocity (cm/sec), and it infers the rate of removal of Cu atoms from the Aα B surface. We assume that there is a sluggishness in removing Cu atoms from the surface of Aα B so that the concentration Cβα is less than the equilibrium value. On the other hand, at the xβγ interface, there is sluggishness in accepting the incoming Cu atoms, so there is a buildup of Cu atoms and the concentration of Cβγ is greater than the equilibrium value. In Fig. 3.8, the broken curve in the β-phase represents the equilibrium concentration gradient, and the solid curve represents the nonequilibrium concentration gradient. The rate of growth of the β-phase does not depend on diffusion across itself, but rather it depends on the interfacial-reaction process at the two interfaces. Details of the kinetic analysis of such a layer can be found in the literature and will not be repeated here. The growth rate has been given as Gβ ΔCβ Kβeff Gβ ΔCβ Kβeff dxβ = , = x K eff dt 1 + xβ∗ 1 + xβ Dββ β where

1 Kβeff

=

1 Kβα

+

1 Kβγ

(3.13)

is the effective interfacial-reaction constant of the β-

phase, Kβγ is defined as the interfacial-reaction constant at the xβγ interface, Gβ is a constant, and ΔCβ is a concentration term, and Dβ is the interdiffusion coefficient in the β-phase. We define a “changeover” thickness of x∗β =

Dβ . Kβeff

(3.14)

For a large changeover thickness, or xβ /xβ ∗  1, i.e., under the condition that the interdiffusion coefficient is much larger than the effective interfacial-reaction coefficient, we obtain dxβ = Gβ ΔCβ Kβeff . dt

(3.15)

The process is interfacial-reaction-controlled, and the growth rate is constant.

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Chapter 3 Fig. 3.10. Schematic diagram depicting a four-layered thinfilm structure of Cu/Cu3 Sn/ Cu6 Sn5 /Sn.

CA

Aa B

AbB

Ag B

xb

xg

Ad B

x

To apply both diffusion-controlled growth and interfacial-reactioncontrolled growth to the thin-film Cu-Sn reaction, we depict in Fig. 3.10 a four-layered thin-film structure of Cu/Cu3 Sn/Cu6 Sn5 /Sn. We assume that the Cu3 Sn growth is interfacial-reaction-controlled and has velocity v1 , and the Cu6 Sn5 growth is diffusion-controlled and has velocity v2 . When their thickness is small, the magnitude of v2 can be quite large due to the inverse dependence on layer thickness, so we can assume v2  v1 and the rapid growth of Cu6 Sn5 can consume all of Cu3 Sn. We can also assume that both of them have an interfacial-reaction-controlled growth, with v2  v1 , again the growth of Cu6 Sn5 is dominant and we have a single phase growth. In Section 3.2.2 and Fig. 3.4, it was stated that Cu6 Sn5 has a linear growth at room temperature. Generally speaking, a drift velocity can be expressed as the product of driving force and mobility. In thin film reaction, the driving force is chemical affinity of IMC formation, e.g., the formation energy of Cu6 Sn5 . Then the physical meaning of the interfacial-reaction constant K (velocity) is that of interfacial mobility. An atomistic explanation of interfacial mobility will be presented in Section 3.2.5. Experimentally, it is of interest to prepare a bilayer of Cu/Sn thinfilm sample and age at 100◦ C for a short time to form a structure of Cu/Cu3 Sn/Cu6 Sn5 /Sn, and then follow with a long aging at room temperature to learn whether the Cu3 Sn will grow thicker or will be consumed by the growth of Cu6 Sn5 . The aging at 100◦ C must be short so that both Cu3 Sn and Cu6 Sn5 will not be too thick to have achieved diffusion-controlled growth. If the room-temperature aging consumes the existing Cu3 Sn, it indicates that even if Cu3 Sn can nucleate at room temperature, it cannot grow side-by-side with Cu6 Sn5 , so the single phase formation of Cu6 Sn5 at room temperature is due to growth selection. On the other hand, if existing Cu3 Sn can grow or can coexist with Cu6 Sn5 , the finding of no Cu3 Sn on room-temperature reaction between Cu and Sn means that it cannot nucleate.

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3.2.5 Atomistic Model of Interfacial-Reaction Coefficient In the kinetic analysis discussed in the last section, the two most important kinetic parameters are atomic diffusivity and interfacial-reaction-controlled coefficient. Atomistic diffusion in face-centered-cubic metals via vacancy mechanism has been well developed and presented in textbooks (see Appendix A). For example, the diffusivity can be expressed as 

ΔGf D = f nυ0 λ exp − kT 2





ΔGm exp − kT





ΔH = D0 exp − kT

 ,

(3.16)

where the prefactor  2

D0 = f nυ0 λ exp

ΔSf + ΔSm k

 (3.17)

and the activation enthalpy ΔH = ΔHf + ΔHm

(3.18)

and f is the correlation factor, n is the number of nearest neighbors and n = 12 in face-centered-cubic lattices, υ0 is the Debye frequency of vibration, λ is the atomic jump distance between an atom and its nearest neighbor vacancy, ΔGm and ΔGf are the free energy of motion and formation of a vacancy, respectively, and kT has the usual meaning of thermal energy. The physical meaning of exp (−ΔGf /kT ) is the probability of having a vacancy next to the jumping atom. The physical meaning of exp (−ΔGm /kT ) is the probability of a successful exchange jump between an atom and a nearest neighbor vacancy. Concerning the correlation factor, we note that f = 0.87 for vacancy mechanism in face-centered-cubic lattices. For comparison, we present below a similar expression of the interfacialreaction-controlled coefficient. In Fig. 3.11, the energy of activation processes F′

(Sn)

ΔGf

n + ΔGm n−

(Cu6Sn5)

λ Fig. 3.11. The energy of activation processes across the Cu6 Sn5 /Sn interface, where ΔGm is the activation energy of motion across the interface and ΔG is the gain of free energy (driving force) in the reaction or the growth of the compound per atom of the Cu6 Sn5 molecule, and δ is the width of the interface.

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across the Cu6 Sn5 /Sn interface is depicted, where ΔGm is the activation energy of motion across the interface and ΔG is the gain of free energy (driving force) in the reaction or the growth of the compound per atom of the Cu6 Sn5 molecule, and δ is the width of the interface. If we consider a one-dimensional growth and assume a unit area of the interface advancing a distance of dx, or a volume of dx times 1, the number of atoms in the volume is dx/Ω and Ω is atomic volume. The total free energy gained is ΔG(dx/Ω) and should equal the work done, dx = pdV = pdx, Ω ΔG p= . Ω

ΔG

(3.19) (3.20)

p is pressure. To examine ΔG, we consider the chemical reaction of 6Cu + 5Sn → Cu6 Sn5 . We have the chemical affinity A = μη − 6μCu − 5μSn ,

(3.21)

where μη is the chemical potential of the Cu6 Sn5 compound molecule and μCu and μSn are the chemical potential of the unreacted Cu and Sn atom, respectively. The Gibbs free energy change of the reaction is dG = −SdT + V dp − Adn,

(3.22)

where n is the extent of the reaction (units of moles or molecules), and S, T , V , and p have their usual meaning in thermodynamics. At a constant temperature and constant ambient pressure, the free energy gain of the reaction is ΔG = AΔn.

(3.23)

To relate the driving force to the kinetics of interfacial reaction, we consider the atomic flux of Sn jumping from the Sn grain, across the interface, to the Cu6 Sn5 grain, and we have [7] 

J1→2

ΔGm = A2 n1 υ1 exp − kT

 ,

(3.24)

where A2 is the probability of accommodation of the atom per unit area on the surface of Cu6 Sn5 , i.e., the probability of an atom that can attach to the grain of Cu6 Sn5 , n1 is the number of atoms per unit area on the Sn grain

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ready to make a jump across the interface, and υ1 is the vibration frequency. The reverse flux from the Cu6 Sn5 to the Sn is   ΔGm + ΔG J2→1 = A1 n2 υ2 exp − . kT

(3.25)

If ΔG = 0, the two sides are at equilibrium; it means the growth stops. There is no net motion, so the fluxes are equal. Thus, we have A2 n1 υ1 = A1 n2 υ2 .

(3.26)

With ΔG < 0, we have a net motion of growth, 

Jnet

   ΔGm ΔG = A2 n1 υ1 exp − 1 − exp − kT kT   ΔGm ΔG = A2 n1 υ1 exp − . kT kT

(3.27)

The linearization process assumes ΔG  kT . The velocity of growth is   ΔGm ΔG ΔG A2 n 1 υ 1 Ω 2 v = Jnet Ω = exp − =M , kT kT Ω Ω

(3.28)

where M is the mobility, and ΔG/Ω = p as shown in Eq. (3.20).   A2 n1 υ1 Ω2 ΔGm M= exp − . kT kT

(3.29)

To check the units of M , we note that on the basis of Einstein’s relationship, M = D/kT , where D is diffusivity and has units of cm2 /sec. Since the units of A2 n1 Ω2 and υ1 are cm2 and sec−1 , respectively, it is correct. For comparison, we take the diffusivity, 

ΔGm D = A2 n1 υ1 Ω exp − kT 2

 ,

(3.30)

and compare it to the diffusivity of atomic diffusion via vacancy mechanism in a face-centered-cubic lattice, for which we have 

ΔGf D = f nυ0 λ exp − kT 2





ΔGm exp − kT





ΔH = D0 exp − kT

 .

(3.31)

The physical meaning of exp(−ΔGf /kT ) is the probability of having a vacancy next to the jumping atom, so it is similar to the meaning of A2 in Eq. (3.24),

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which is the probability of a site on the Cu6 Sn5 surface which is available to accept a Cu atom or a Sn atom. If A2 = 1, the interfacial kinetic process is fast, so the growth will be diffusion-controlled. If A2 < 1, the interfacial kinetic process will be sluggish, so the growth will be interfacial-reaction-controlled. Concerning the correlation factor, we note that f = 0.87 for vacancy mechanism in face-centered-cubic lattices, but we can take f ∼ 1 in the reactive growth since the probability of reverse jump or dissociation jump of an atom from the compound during the growth is small. In the above, we have considered the growth atom by atom. Since there are Cu atoms and Sn atoms, we should consider the growth per molecule, but it will involve 6 Cu atoms and 5 Sn atoms. This is unlikely because the interfacial reaction process will be extremely slow. On the other hand, when we assume the growth occurs atom by atom, the gain in free energy per atom is less than A/11, where A is chemical affinity of the formation of a molecule of Cu6 Sn5 . This is because only when a molecule of Cu6 Sn5 is formed do we gain the energy of A. If it is only partially formed, the average energy per atom should be higher than A/11.

3.2.6 Measurement of Strain in Cu and Sn Thin Films In Section 3.2.1, we discussed using the Seeman-Bohlin diffractometer to measure the lattice parameter of a thin film and to identify the phase. The direction of the reciprocal lattice vector of each reflection in this diffractometer makes a different inclination angle ϕ(= θ − γ) with respect to the normal of the film surface, where θ is the Bragg angle and γ is the fixed incidence angle of the x-ray beam. The x-ray measures the interplanar spacing, or strain, in the direction of the reciprocal lattice vector. By extrapolation to ϕ = 90◦ , the strain in the direction of the principal stress, in the direction parallel to the surface plane of the film, can be obtained [1]. The following reflections of 220, 311, 331, and 420 of Cu, and reflections of 400, 231, 420, 411, 440, 123, 303, 233, and 143 of Sn were used in the extrapolations. Since the lattice of beta-Sn is body-centered tetragonal, the extrapolation to obtain both lattice parameters a and c was carried out by successive iterations. It was found that the remaining Cu film in the trilayer Cu/Cu6 Sn5 /Sn films when annealed at room temperature was under tension and the remaining Sn film was under compression. Table 3.3 lists the extrapolated lattice parameters, i.e., the lattice parameter along the direction parallel to the film surface of Cu and Sn annealed at room temperature. The lattice parameters of the single layer of Sn deposited and annealed at room temperature on fused quartz are also listed for reference. The strain in the Cu film in the direction parallel to the film surface was found to be about +0.06% with uncertainty of ± 50%. The strain in the Sn film along the same direction is about −0.16%, which is below the elastic limit of 0.2%. The compressive stress will be related to spontaneous Sn whisker growth to be discussed in Chapter 6.

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Table 3.3. Extrapolated lattice parameters of Cu and Sn after room-temperature annealing

Specimen Sn/Cu

Annealing time

Lattice parameter of Cu (= 0.0010) (˚ A)

Lattice parameter of Sn (= 0.0020) (˚ A)

3.6162

a = 5.8132 c = 3.1701 a = 5.8144 c = 3.1706 a = 5.8063 c = 3.1692

Right after deposition 15 days

3.6181

30 days

3.6176

1 yr

3.6180

Sn(3500 ˚ A)

a = 5.8205 c = 3.1747

3.3 Spalling in Wetting Reaction of Eutectic SnPb on Cu Thin Films When a thick Cu foil is replaced by a thin Cu film, a dramatic change in the IMC morphology occurs in solder wetting reaction on the thin film. Figure 3.12 shows the cross-sectional SEM image of eutectic SnPb solder on an 870 nm Cu thin film deposited on a 100 nm Ti film on an oxidized Si wafer after wetting reaction for 10 min at 200◦ C. The scallop-type Cu6 Sn5 IMC no longer exist, rather the IMC have become spheroids and some of them have left the substrate and spalled into the molten solder [8–11]. This may be unexpected because when the Cu film is completely consumed by the solder, we expect that the interfacial reaction should stop since there is no more Cu. Yet the ripening reaction among the scallops continues and transforms the hemispherical scallops into spheroids. The spheroids have a 180◦ wetting angle on the Ti surface. There is no adhesion between them, so the spheroids can detach easily from the Ti surface and spall into the molten solder. In the molten

Fig. 3.12. Cross-sectional SEM image of eutectic SnPb solder on an 870 nm Cu thin film deposited on a 100 nm Ti film on an oxidized Si wafer after annealing for 10 min at 200◦ C. The scallop-type Cu6 Sn5 IMC no longer exist; rather the IMC have become spheroids and some of them have left the substrate and spalled into the molten solder.

1μm

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Fig. 3.13. Cross-sectional SEM image of a piece of eutectic SnPb solder sandwiched between two Si chips having Au/Cu/Cr trilayer films. After 20 min at 200◦ C, the Cu6 Sn5 spheroids have departed from the bottom surface (b) and moved to the upper surface (a), assisted by gravity force. This is the phenomenon of “spalling” of IMC.

state of the solder, this can be illustrated with the help of gravity because the density of the molten solder is greater than that of the Cu6 Sn5 compound. Figure 3.13 shows the cross-sectional SEM image of a piece of eutectic SnPb solder sandwiched between two Si chips having the Au/Cu/Cr trilayer films. After 20 min at 200◦ C, the Cu6 Sn5 spheroids have departed from the bottom surface and moved to the upper surface. This is the phenomenon of “spalling” of IMC. When it takes place, the solder is in direct contact with the unwetted substrate and dewetting occurs. Figure 3.14 shows spalling of IMC in a solder cap on Au/Cu/Cr trilayer thin films. Figure 3.15 shows an SEM image of a dewetted surface after spalling. Figure 3.16 is a set of schematic diagrams of the sequence of ripening, spalling, and dewetting in a molten solder–thin film reaction. To explain the morphological transformation, we recall that Fig. 2.26 depicts the conservative or constant volume ripening between two neighboring scallops and the opening of a large gap between them. When all of the Cu

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Fig. 3.14. Cross-sectional SEM images of a eutectic SnPb solder cap on Au/Cu/Cr trilayer films. (a) Low-magnification image of the cap. (b)–(e) High-magnification images of various cross sections showing the spalling of IMC.

thin film has been reacted, the ripening among Cu6 Sn5 scallops becomes conservative. The gap allows the molten solder to be in direct contact with the Ti surface, which is unwetted by the molten solder. Figure 3.17 depicts the transformation from a hemispherical-type scallop to a sphere driven by

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Fig. 3.15. SEM image of a dewetted surface after spalling.

the lowering of the sum of surface and interfacial energies in a conservative ripening. In the following, we shall review a sequence of reactions between molten solder and different thin-film under-bump metallizations in electronic packaging technology, and we shall see that the spalling is a recurring phenomenon and remains a very challenging reliability issue for Pb-free solders.

(a)

Flux ripening Cu

Sn

Cr

Cu-Sn compound

Si (b)

Sn

Flux

spalling Cu Cr

Si

γSn/Flux (c)

γCr/Flux θ

Flux

γCr/Sn Si

Sn

dewetting Cu Cr

Fig. 3.16. Schematic diagrams of the sequence of ripening, spalling, and dewetting in a solder–thin film reaction.

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Molten Solder

rs rh

Soild

Soild

Cr

Cr

Hemispherical Cu6Sn5

Cu6Sn5 Spheroid

γCu6Sn5/Cr is very large Interfacial energy change for a fixed volume

πrh2γCu6Sn5/Cr + 2πrh2γsolder/Cu6Sn5 > πrh2γCr/solder + 4πrs2γsolder/Cu6Sn5 Fig. 3.17. Schematic diagram depicting the transformation from a hemispherical-type particle to a sphere driven by lowering of the sum of surface and interfacial energies in a conservative ripening.

3.4 No Spalling in High-Pb Solder on Au/Cu/Cu-Cr Thin Films First, we review the controlled-collapse-chip-connection (C-4) solder joint used in mainframe computers [12]. Figure 1.9 is a schematic diagram of a 95Pb5Sn solder ball joining a thin-film metallization which consists of 100 nm Au/ 500 nm Cu/ 300 nm co-deposited Cu-Cr to a ceramic module. Since Cu and Cr have poor adhesion to each other, the co-deposited Cu-Cr or phased-in Cu-Cr was developed to improve the adhesion between them. This is because Cr and Cu are immiscible, so their grains form an interlocking microstructure when they are co-deposited. Figure 3.18 shows a selected area electron diffraction pattern of a phase-in Cu-Cr thin film, in which the diffraction rings from Cu and Cr can be identified. Figure 3.19 shows a bright-field cross-sectional transmission electron microscopy (TEM) image of the trilayer thin-film structure [13]. A selected area diffraction pattern of the Cu-Cr layer can be indexed as a mixture of reflection rings of Cu and Cr. A high-resolution TEM image of the mixed Cu and Cr layer is shown in Fig. 3.20, in which the lattice of Cu or Cr can be identified. When a molten high-Pb solder of 95Pb5Sn wets this trilayer thin-film metallization, it dissolves the Au, forms AuSn4 compound particles in the solder, and forms Cu3 Sn compound on the Cu-Cr layer, but there is no Cu6 Sn5 formation. This is in agreement with the Sn-Pb-Cu phase diagram at 350◦ C, as discussed in Chapter 2. What is rather surprising is that there has been no spalling of Cu3 Sn reported until recently [14]. The phase-in Cu-Cr

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Fig. 3.18. Selected area electron diffraction pattern of a phase-in Cu-Cr. The diffraction rings of Cu and Cr are identified.

200 nm

Fig. 3.19. Bright-field cross-sectional transmission electron microscopy (TEM) image of the trilayer thin-film structure.

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Fig. 3.20. High-resolution TEM image of the mixed Cu and Cr layer. The lattice of Cu or Cr can be identified. (Courtesy of Prof. Ning Wang, Hong Kong University of Science and Technology.)

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thin film is quite stable with the high-Pb solder. Since the phase-in Cr-Cu was developed not only to improve the adhesion between Cr and Cu, but also to resist spalling, it indicates that spalling of Cu3 Sn might have occurred if a layered structure of Cu/Cr is used instead of the phased-in Cu-Cr/Cr. It is likely that the spalling of Cu3 Sn has been retarded by the interlocking microstructure in the phase-in Cu-Cr.

3.5 Spalling in Eutectic SnPb Solder on Au/Cu/Cu-Cr Thin Films Due to the need for more functions in consumer electronic products and in turn the need for more input/output (I/O) interconnections on a chip surface, flip chip technology has gained wider application in electronic manufacturing. In consumer products, chips are joined to polymer boards and cards to lower the cost. The low-melting eutectic SnPb which can be reflowed at 220◦ C is more suitable than the high-Pb solder in C-4 technology. When the eutectic SnPb solder reacts with Cu at 220◦ C, the reaction product is Cu6 Sn5 rather than Cu3 Sn. This is in agreement with the ternary phase diagrams of Sn-PbCu shown in Fig. 2.21. The Cu6 Sn5 , however, is morphologically unstable on the Cu-Cr surface, leading to spalling [8–11]. Figure 3.13 showed the crosssectional SEM image of a eutectic SnPb solder bump sandwiched between two Si chips having the Au/Cu/Cu-Cr films. After 20 min at 200◦ C, the Cu6 Sn5 spheroids have spalled.

3.6 No Spalling in Eutectic SnPb on Cu/Ni(V)/Al Thin Films Owing to the spalling behavior of eutectic SnPb on Au/Cu/Cu-Cr UBM discussed above, the Cu/Ni(V)/Al thin-film UBM was investigated for eutectic SnPb solder bumping. Figure 3.21(a) shows a cross-sectional TEM image of the solder–thin film interface after 1 reflow; the Si, SiO2 , a bilayer of Al and Ni(V), and Cu6 Sn5 are seen [15]. Within the Cu6 Sn5 layer, isolated regions of unreacted Cu surrounded by a cluster of small Cu3 Sn grains are found. Between the Cu3 Sn and Cu, there are Kirkendall voids. Figure 3.21(b) shows a cross-sectional TEM image of the interface after an additional annealing of 5 min at 200◦ C. Neither Kirkendall voids nor Cu3 Sn grains can be found any more. The Cu6 Sn5 showed some grain growth but it attached very well to the Ni(V). Even after 20 to 40 min annealing at 220◦ C, very little change was found, and the Cu6 Sn5 and Ni(V) layers were stable. Figure 3.21(c) is a higher magnification image of the Ni(V) layer and its interface with the Cu6 Sn5 layer. When Ni contains more than 7 wt% V, it is diamagnetic and can be sputtered at a high rate. The V seems to have lowered the stacking fault energy of Ni, so a large number of twin boundaries in the Ni are seen in Fig. 3.21(c). Why does the Cu6 Sn5 not transform into spheroids and spall

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(a)

Cu3Sn Ni(V)

Cu6Sn5 Al

Al SiO2 Si

1μm (b)

Cu6Sn5 Ni(V) Al SiO2 Si

1μm

Fig. 3.21. (a) Cross-sectional TEM image of the solder–thin film interface after 1 reflow; the Si, SiO2 , a bilayer of Al and Ni(V), and Cu6 Sn5 are seen. Within the Cu6 Sn5 layer, isolated regions of uneacted Cu surrounded by a cluster of small Cu3 Sn grains are found. Between the Cu3 Sn and Cu, there are Kirkendall voids. (b) Crosssectional TEM image of the interface after an additional annealing of 5 min at 200◦ C. Neither Kirkendall voids nor Cu3 Sn grains are seen. The Cu6 Sn5 showed some grain growth but it attached very well to the Ni(V). (c) High-magnification image of the Ni(V) layer and its interface with the Cu6 Sn5 layer.

into the solder? A plausible answer is that the interface between Cu6 Sn5 and Ni(V) is a very low energy interface, hence it is stable against morphological transformation.

3.7 Spalling in Eutectic SnAgCu Solder on Cu/Ni(V)/Al Thin Films Since the Cu/Ni(V)/Al UBM is stable with eutectic SnPb, it has been extended to Pb-free solder [16]. Figure 3.22 shows SEM backscattering images

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solder

(Cu,Ni)6Sn5

solder

Cu6Sn5

(a)

(b)

solder

(Cu,Ni)6Sn5

(c)

(Cu,Ni)6Sn5

(d)

Fig. 3.22. SEM backscattering images of cross sections of samples of eutectic SnAgCu solder on Al/Ni(V)/Cu thin films after (a) 1 (i.e., the as-bonded condition), (b) 5, (c) 10, and (d) 20 reflows.

of cross sections of samples of eutectic SnAgCu solder on Al/Ni(V)/Cu thin films after 1 (i.e., the as-bonded condition), 5, 10, and 20 reflows. Two types of IMC, Cu6 Sn5 (also (Cu,Ni)6 Sn5 )) and Ag3 Sn, were found in the solder bump after these reflows. The Cu6 Sn5 was present mainly at the interface, although some large Cu6 Sn5 also existed inside the solder. After 1 reflow, the Cu layer was consumed and converted to Cu6 Sn5 , while the Ni(V) layer was intact as shown in Fig. 3.23(a). After 5 reflows, the morphology of the IMC changed from a rounded scallop shape to an elongated scallop or rod shape with an increase in the aspect ratio. The IMC was faceted and some of them had broken away from the UBM. Since the 300 nm Cu layer in UBM has been consumed after 1 reflow (the as-bumped condition), the volume of the Cu6 Sn5 IMC should not increase during the subsequent reflows. However, the cross-sectional SEM image in Fig. 3.23(b) indicates that the IMC volume does increase with the number of reflows, owing to the alloying of Ni in the Cu6 Sn5 and its transformation to (Cu,Ni)6 Sn5 . EDX analyses have confirmed the transformation. White patches were seen in the Ni(V)

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solder

solder Cu6Sn5

(Cu,Ni)6Sn5

Ni

(a)

(b)

(Cu,Ni)6Sn5

Ni

Sn

solder

solder

(c)

103

(Cu,Ni)6Sn5

Sn

Ni

(d)

Sn

Fig. 3.23. (a) After 1 reflow, the Cu layer was consumed and converted to Cu6 Sn5 , while the Ni(V) layer was intact. (b) After 5 reflows, the cross-sectional SEM image indicates that the IMC volume does increase with the number of reflows, owing to the alloying of Ni in the Cu6 Sn5 and its transformation to (Cu,Ni)6 Sn5 . EDX analyses have confirmed the transformation. White patches were seen in the Ni(V) layer, and the patches were confirmed by EDX as mainly containing Sn and V. (c) After 10 reflows, the white patches dominated the Ni(V) layer. (d) After 20 reflows, the Ni(V) layer disappeared and a layer of Sn separated the IMC from the Al layer. It is Sn rather than Ni-Sn IMC that is found in place of the original Ni(V) layer. Some of the intermetallic rods detached from the UBM and spalled into the solder.

layer shown in Fig. 3.23(b). The patches were confirmed by EDX as mainly containing Sn and V. With the number of reflows increased to 10, the white patches dominated the Ni(V) layer as shown in Fig. 3.23(c). After 20 reflows, the Ni(V) layer disappeared and a layer of Sn separated the IMC from the Al layer [Fig. 3.23(d)]. It is Sn rather than Ni-Sn IMC that is found to have replaced the original Ni(V) layer. Some of the intermetallic rods detached from the UBM and spalled into the solder. Clearly, the Cu/Ni(V)/Al UBM becomes unstable with eutectic SnAgCu in multiple reflows. The dissolution of Ni(V) by the molten Pb-free solder is nonuniform and seems to have initiated on certain weak spots on the Ni(V) surface and spread

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(Cu,Ni)6Sn5

Sn

Ni

(a)

Fig. 3.24. SEM backscattering images of the eutectic SnAgCu solder on Al/Ni(V)/ Cu thin films annealed at 260◦ C for (a) 5 min, (b) 10 min, and (c) 20 min. The nonuniform dissolution of the Ni(V) layer and the formation of white patches in the layer increased with annealing time.

(Cu,Ni)6Sn5

(b)

Ni

Sn

(Cu,Ni)6Sn5

(c)

Sn

laterally to form patches. SEM backscattering images of the eutectic SnAgCu solder on Al/Ni(V)/Cu thin films annealed at 260◦ C for 5, 10, and 20 min are shown in Fig. 3.24(a) to (c), respectively. The nonuniform dissolution of the Ni(V) layer and the formation of white patches in the layer increased with annealing time.

3.8 Enhanced Spalling Due to Interaction across a Solder Joint The (Cu,Ni)6 Sn5 particles from the Cu/Ni(V)/Al thin-film UBM, as discussed in the last section, can be induced to spall quickly by the interaction of the metallization on the other interface of the solder joint. Figure 3.24 has already shown such a case. Without metallization on the other side of a solder joint, i.e., if we have just a bump of eutectic SnCuAg on Cu/Ni(V)/Al, spalling

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was observed after 20 reflows. With a metallization of Au/Ni(P) joined to the other side of the bump, the spalling occurs after 5 reflows. Both SnPb and Pb-free solder joints were studied and similar results were obtained. In the molten solder, atomic diffusivity is about 10−5 cm2 /sec, hence it takes only 10 sec for atoms to diffuse across a molten solder joint 100 μm in diameter. Since there are Au, Ni, and P on the other side of the solder joint, one of them could have enhanced the spalling. It turns out that if we replace Au/Ni(P) by a piece of pure Ni on the other side of the solder joint, the enhanced spalling of IMC occurs. The dissolution of pure Ni into the molten solder enhances the dissolution of Cu6 Sn5 compound and exposes the Ni(V) layer to the molten solder. The enhanced dissolution of Cu6 Sn5 is due to the formation of (Cu,Ni)6 Sn5 . The increase in volume leads to a large compressive stain.

3.9 Wetting Tip Reaction on Thin-Film-Coated V-Grooves The classic Young’s equation of an equilibrium wetting tip was derived by minimizing the total surface and interfacial energies involved, but no free energy of formation of interfacial IMC was included. The wetting angle is defined by the equilibrium condition among the surface and interfacial energies at the wetting tip. Assuming that the wetting tip (or a wetting cap) configuration is achieved instantaneously, the free energy of IMC formation may be ignored if the rate of formation of the interfacial IMC is much slower than the spreading rate for a drop of molten solder on a metal surface. Here we shall present two phenomena in solder reactions wherein the wetting tip is unstable. The first one is the wetting of molten SnPb on Pd and Au. They show no stable wetting angle. Details of these wetting reactions will be given in Chapter 7. In the case of eutectic SnPb on Pd, the tip advances on the Pd surface unceasingly until the solder is consumed entirely [17]. In the case of 95Pb5Sn solder on Au, the molten solder has a sunken interface into Au which deepens with time [18]. In both cases, the wetting angle and the tip configuration change with time. In the SnPb/Pd case, it is because of rapid reaction to form IMC, and in the SnPb/Au case, it is because of rapid dissolution of Au into the molten solder. The second one concerns the wetting of molten eutectic SnPb cap on Cu. While there is a stable wetting angle, the tip is unstable in the sense that it grows a halo. The halo spreads out unceasingly due to the formation of a very thin layer of IMC below the halo. The halo has also been found in front of a molten tip of eutectic SnPb on Ni. To study the effect of IMC formation on a reactive wetting tip, we must study the very early stage of wetting reaction. It is possible to do so in thin-film-coated V-grooves etched on a Si wafer surface. Using lithographic

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Fig. 3.25. (a) Schematic diagram of the cross section of a V-groove and (b) corresponding TEM image. (Courtesy of Prof. Ning Wang, Hong Kong University of Science and Technology.)

technique, etched V-grooves along [110] direction on (001) surface of Si wafers and coated with a bilayer of Cu/Cr film have been made. A schematic diagram of the cross section of a V-groove and a corresponding TEM image are shown in Fig. 3.25(a) and (b), respectively. Molten pure Pb will not run into the V-groove, but the molten Pb(Sn) alloy having only 1 to 5% Sn will run into it, driven by the horizontal capillary force, as shown in the lower part of Fig. 3.26. The more Sn is present in the molten solder, the longer the length of the run (or the faster the run). The length of the run shows a direct correspondence to the wetting angle on Cu as a function of the Sn concentration

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Fig. 3.26. SEM images show that molten pure Pb will not run into the V-groove, but the molten Pb(Sn) alloy having only 1 to 5% Sn will run into it, driven by the horizontal capillary force.

in the molten solder; see the SEM images in the upper part of Fig. 3.26. While pure Pb unwets Cu, the Pb(Sn) alloy wets Cu and the wetting angle decreases with increasing amount of Sn in Pb [19, 20]. Since the addition of a few percent of Sn does not change the surface energy of the molten solder [21], no change of wetting angle is expected on the basis of Young’s equation. Hence, the change is due to Cu-Sn interfacial reaction in forming IMC. How

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to calculate the change of wetting angle and in turn the wetting rate as a function of solder composition is challenging. The wetting rate has been given by the Washburn equation and can be measured using a CCD camera [22]. Knowing the rate, it is possible to estimate the rate of IMC formation in the very early stage of the wetting reaction. However, for the melting solder to run along the V-groove, the V-groove is typically kept at a temperature slightly higher than the melting point of the solder. Then, it will take some time to cool it to room temperature to measure the amount of IMC formation. Yet during the cooling period, plenty of IMC can be formed at the wetting tip! We cannot use the measured IMC to estimate how much IMC forms during the initial wetting reaction because the cooling time is much longer than the time of instantaneous wetting. However, it is difficult to run the molten solder in a horizontal V-groove kept at room temperature. On the other hand, it can be done if a room-temperature piece of Si with a coated V-groove is dipped vertically into a pool of molten solder and the molten solder is allowed to rise along the V-groove; after the piece touches the pool, it should be removed from the pool quickly.

References 1. K. N. Tu, “Interdiffusion and reaction in bimetallic Cu-Sn thin films,” Acta Metall., 21, 347 (1973). 2. J. W. Mayer, J. M. Poate, and K. N. Tu, “Thin films and solid-phase reactions,” Science, 190, 228-234 (1975). J. M. Poate and K. N. Tu, “Thin film and interfacial analysis,” Physics Today, May (1980), p.34. 3. K. N. Tu and R. D. Thompson, “Kinetics of interfacial reaction in bimetallic Cu-Sn thin films,” Acta Metall., 30, 947 (1982). 4. K. N. Tu and J. W. Mayer, “Silicide formation,” in Thin Films—Interdiffusion and Reactions, J.M. Poate, K.N. Tu, and J.W. Mayer (Eds.), John Wiley, New York (1978). 5. U. Gosele and K.N. Tu, “Growth kinetics of planar binary diffusion couples: Thin film case versus bulk cases,” J. Appl. Phys., 53, 3252 (1982). 6. G. V. Kidson, “Some aspects of the growth of different layers in binary systems,” J. Nucl. Mater., 3, 21 (1961). 7. D. A. Porter and K. E. Easterling, “Phase Transformation in Metals and Alloys,” Chapman & Hall, London (1992). 8. A. A. Liu, H. K. Kim, K. N. Tu, and P. A. Totta, “Spalling of Cu6Sn5 spheroids in the soldering reaction of eutectic SnPb on Cr/Cu/Au thin films,” J. Appl. Phys., 80, 2774–2780 (1996). 9. C. Y. Liu, H. K. Kim, K. N. Tu, and P. A. Totta, “Dewetting of molten Sn on Au/Cu/Cr thin film metallization,” Appl. Phys. Lett., 69, 4014–4016 (1996). 10. D. W. Zheng, Z. Y. Jia, C. Y. Liu, W. Wen, and K. N. Tu, “Size dependent dewetting and sideband reaction of eutectic SnPb on Au/Cu/Cr thin film,” J. Mater. Res., 13, 1103–1106 (1998).

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11. D. W. Zheng, W. Wen, K. N. Tu, and P. A. Totta, “In-situ scanning electron microscopy study of eutectic SnPb and pure Sn wetting on Au/Cu/Cr multilayered thin films,” J. Mater. Res., 14, 745–749 (1999). 12. K. Puttlitz and P. Totta, “Area Array Technology Handbook for Microelectronic Packaging,” Kluwer Academic, Norwell, MA (2001). 13. G. Z. Pan, A. A. Liu, H. K. Kim, K. N. Tu, and P. A. Totta, “Microstructure of phased-in Cr-Cu/Cu/Au bump-limiting-metallization and its soldering behavior with high Pb and eutectic SnPb solders,” Appl. Phys. Lett., 71, 2946–2948 (1997). 14. J. W. Jang, L. N. Ramanathan, J. K. Lin, and D. R. Frear, “Spalling of Cu3Sn intermetallics in high-Pb 95Pb5Sn solder bumps on Cu underbump-metallization during solid-state annealing,” J. Appl. Phys., 95, 8286–8289 (2004). 15. C. Y. Liu, K. N. Tu, T. T. Sheng, C. H. Tung, D. R. Frear, and P. Elenius, “Electron microscopy study of interfacial reaction between eutectic SnPb and Cu/Ni(V)/Al thin film metallization,” J. Appl. Phys., 87, 750–754 (2000). 16. M. Li, F. Zhang, W. T. Chen, K. Zeng, K. N. Tu, H. Balkan, and P. Elenius, ”Interfacial microstructure evolution between eutectic SnAgCu solder and Al/Ni(V)/Cu thin films,” J. Mater. Res., 17, 1612–1621 (2002). 17. Y. Wang and K. N. Tu, “Ultra-fast intermetallic compound formation between eutectic SnPb and Pd where the intermetallic is not a diffusion barrier,” Appl. Phys. Lett., 67, 1069–1071 (1995). 18. P. G. Kim and K. N. Tu, “Morphology of wetting reaction of eutectic SnPb solder on Au foils,” J. Appl. Phys., 80, 3822–3827 (1996). 19. C. Y. Liu and K. N. Tu, “Morphology of wetting reactions of SnPb alloys on Cu as a function of alloy composition,” J. Mater. Res., 13, 37–44 (1998). 20. C. Y. Liu and K. N. Tu, “Reactive flow of molten Pb(Sn) alloys in Si grooves coated with Cu film,” Phys. Rev. E, 58, 6308–6311 (1998). 21. F. H. Howie and E. D. Hondros, J. Mater. Sci., 17, 1434 (1982). 22. J. A. Mann, Jr., L. Romero, R. R. Rye, and F. G. Yost, “Flow of simple liquids down narrow V- grooves,” Phys. Rev. E, 52, 3967–3972 (1995).

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4 Copper–Tin Reactions in Flip Chip Solder Joints

4.1 Introduction In Chapters 2 and 3, we discussed solder reactions on bulk and thin-film Cu, respectively. In those reactions, there is only one interface between the solder and the Cu. However, in a solder joint there are two interfaces. Typically a solder joint joins two pieces of Cu tube together as in plumbing, or it joins two metallic contacts as in Si devices. These two interfaces in a flip chip solder joint are not independent of each other from the point of view of interfacial reactions. In a flip chip solder joint, the solder bump joins a thin-film under-bump metallization (UBM) on the Si chip side and a metallic bond-pad on the substrate side. A schematic diagram of the cross section of a flip chip solder joint was shown in Fig. 3.19. On the Si chip side, circuit lines are made of Al or Cu interconnects. Between the interconnect line and solder bump, there is a trilayer of Au/Cu/Cu-Cr thin films, and the contact area between the trilayer thin film and the solder bump is defined by an opening in a dielectric film of SiO2 . The trilayer film is called under-bump metallization (UBM). The shape of the contact area between the UBM and solder bump is close to an octagon rather than a circle because it is difficult to pattern a circle using lithographic technique. On the substrate side, the circuit is typically made of Cu traces. Between the Cu trace and solder bump, there is a bond pad, e.g., a very thick Cu or electroless Ni(P) 10 to 20 μm in thickness and covered with a plated Au layer. A solder mask is used to pattern the bond pad, which has a contact area to the solder bump much larger than the contact area of the UBM on the Si chip. In this chapter, we introduce the concept that the reactions on the two sides of a solder bump can influence each other. We shall illustrate that these two interfaces, one between UBM and solder and the other between solder and bond pad, are not independent of each other. This is because the chemical diffusion of noble and near-noble metal atoms such as Cu or Ni in a molten

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solder as well as in a solid-state solder are very fast. For example, it takes just a few seconds for Cu atoms to diffuse from one side of a molten solder joint to the other side of the joint, in other words, it is within the period of a single reflow. Furthermore, in joining the chip to the substrate, thermal stress is developed and then the joint will carry electric current in device operation, so the effects of stress migration and electromigration will enhance the interaction between the two interfaces across the solder joint. These effects have become serious reliability issues, especially when they are combined, to be discussed in later chapters. When a temperature gradient exists across a solder joint due to joule heating, thermomigration tends to occur too. In this chapter, the effect of interaction of Cu-Sn reactions across a solder joint on its reliability will be emphasized. Besides the two interfaces, the bulk of the solder bump is involved in the interaction too. Eutectic solder in the solid state has a lamellar two-phase microstructure. The two-phase eutectic structure has a very unique property, namely, that the two phases are in equilibrium with each other independent of their volume fraction. For example, the lamellar spacing in a eutectic structure is undefined. Thus, the lamellar spacing of each phase, or the volume fraction of each phase, or the local composition of the eutectic solder, can be changed without affecting the chemical potential of the eutectic structure. In a eutectic two-phase mixture, a change of composition does not mean any change of chemical potentials; it means instead just a change of local volume fractions of the two phases. Thus, if we induce phase segregation in the eutectic solder by an external driving force, for example, in thermomigration or electromigration, it means a change of the gradient of volume fractions, not a gradient of chemical potentials. Gradient of volume fractions is not a driving force. Therefore, the segregation in two-phase mixtures such as eutectic SnPb can be enormous, because there is no resistance to the change since there is no change in chemical potential. Thus, when an external force is applied to a solder joint, there is a microstructure instability in the bulk of the solder. Typically, Pb is driven to the anode and Sn is driven to the cathode in electromigration. Consequently, the Cu-Sn reaction at the cathode is enhanced because of the continuing arrival of Sn. We shall emphasize this unique reliability issue in Sections 4.4 and 4.5. We note that in eutectic SnPb solder, the eutectic structure consists of Sn and Pb. But in Pb-free solders, Sn and Cu6 Sn5 as well as Sn and Ni3 Sn4 also form eutectic structures too, so the segregation of Cu6 Sn5 and/or Ni3 Sn4 in a Sn-based Pb-free solder can be enormous. Concerning the instability in the reactions, there is no doubt that the design of the dimensions of UBM, solder bump, and bond pad and the selection of materials are very important in manufacturing flip chip technology. This is not only because of the chip-to-substrate solder joint reaction to be discussed here, but also because the design and the selection will affect electric current distribution in the joint, and in turn, will affect joule heating and electromigration and thermomigration. Hence, reliability concerns must be taken

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into account in the design stage of the device. However, the optimal design of a flip chip solder joint and intelligent selection of materials are beyond the scope of this book. Nevertheless, a brief discussion will be given in Sections 4.8 and 9.6.2.

4.2 Processing a Flip Chip Solder Joint and a Composite Solder Joint The processing of flip chip solder joints starts with depositing the UBM followed by electroplating a thick solder bump on the UBM. Figure 4.1 depicts the steps (steps 1 to 9) of depositing and patterning the UBM and the plating (steps 10 to 12) of a solder bump on a UBM and reflowing the cylindrical bump to form a solder ball. We note that there is a TiW thin film below the trilayer UBM. The continuous TiW film serves as electrodes during the electroplating of the solder bump. After plating of the solder bump and removal of the photoresist, the part of TiW which is uncovered by the plated solder is etched away using the solder itself as etching mask so that the bumps are insulated from each other electrically after the etching. We also note that electroplating the solder bump requires a very thick photoresist of at least 50 μm. Since a thick photoresist is used to produce micro-electro-mechanical systems (MEMS) devices on Si, it is available in many research laboratories. After etching of the photo resist and the TiW, a first reflow will change the plated cylindrical bump to a round solder ball. In the next steps the chip having an array of solder balls is joined to a printed circuit board with an array of bond pads by a second reflow, thus producing the flip chip samples. The alignment between the array of solder balls on the chip and the array of bond pads on the substrate is crucial. Typically a flip chip bonder is used. However, the second reflow process has a built-in tolerance of misalignment. When the solder ball melts, its liquid surface tension will pull and twist the chip to achieve a near-perfect alignment in order to reduce the surface tension. This is a unique feature in “control-collapse-chip-connection” or C-4 process. If the substrate is a ceramic module, the solder can be high-Pb having a high melting point above 300◦ C so that a high reflow temperature is needed. On the other hand, if the substrate is polymer-based such as FR4 board, we have to use eutectic SnPb or Pb-free solder. Since eutectic solder will cause spalling of intermetallic compound from thin-film UBM as discussed in Chapter 3, either a thick UBM or a composite solder joint must be used in order to overcome the spalling problem. In a composite solder joint, the Au/Cu/Cu-Cr UBM and the high-Pb solder are kept on the chip side, but a eutectic solder will be deposited on the bond pad on the polymer-based substrate before joining the chip to the substrate. In Fig. 4.2, the processing steps of a eutectic solder on the bond pad by stencil printing are shown. After the reflow step to from a eutectic solder ball on all the bond pads, a step of

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Fig. 4.1. The steps (steps 1 to 9) of depositing and patterning the UBM and plating (steps 10 to 12) of a solder bump on a UBM and reflowing the bump to form a solder ball. (Courtesy of Dr. J. W. Nah, UCLA.)

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Fig. 4.2. The processing steps of a eutectic solder on the bond pad by stencil printing and caking.

caking will be followed. In caking, the eutectic solder balls will be pressed to render a flat top surface. Then a flip chip bonder will be used to align the chip and the substrate so that the high-Pb solder balls will sit on top of the flattened eutectic solder plateaus; next, a low-temperature reflow will be able to join the two solders together to form a composite solder joint. A schematic diagram of the cross section of a pair of flip chip composite solder joint is shown in Fig. 4.3. The chip with 97Pb3Sn solder balls was flipped and assembled on the substrate with 37Pb63Sn solder plateaus. The UBM on the chip side was

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Fig. 4.3. Schematic diagram of the cross section of a pair of flip chip composite solder joint.

sputtered TiW (0.2 μm)/Cu (0.4 μm)/electroplated Cu (5.4 μm) and the bond pad on the substrate side was electroless Ni(P) (5 μm)/Au (0.1 μm). The thickness of the Al metal line on the chip side was 1 μm and that of the Cu metal line on the substrate side was 18 μm. For the flip chip assembly, the typical reflow condition of 37Pb63Sn solder was applied with a peak temperature of 220◦ and a dwell time of 90 sec in nitrogen atmosphere. The composite solder joint was achieved by having the molten 37Pb63Sn solder wet and coat the entire surface of the solid 97Pb3Sn solder ball. In Fig. 4.3, a round coating of the eutectic on the high-Pb solder ball is depicted.

4.3 Chemical Interaction across A Flip Chip Solder Joint Typically, the Cu-Sn reaction on the Si chip side belongs to the class of solder reactions with a thin film of Cu, as discussed in Chapter 3. But the Cu-Sn reaction on the substrate side belongs to the class of solder reactions with a bulk Cu, as discussed in Chapter 2. In flip chip solder joints, these two kinds of reaction occur on the two sides of the joints, and they are about 100 μm apart. However, these reactions are not independent of each other. This is because Cu and other noble and near-noble metals such as Au and Ni can diffuse across a solder joint having a thickness of about 100 μm in a very short time. For example, if we take the atomic diffusion in molten solder to be 10−5 cm2 /sec, we find that it will take only 10 sec for Cu atoms to diffuse across the bump. In the reflow, the period within which the solder is in the molten state is about 0.5 min, hence there is plenty of time for the Cu on both sides of the solder bump to communicate with each other and can actually affect each side’s reaction. In the solid state, noble and near-noble metal atoms diffuse

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interstitially in Sn and Pb, with a diffusivity close to 10−8 cm2 /sec around room temperature. Then it will take less than several hours for these atoms to diffuse across a solder bump 100 μm in thickness. Yet the required reliability test of solid state aging is 1000 hr at 150◦ C. Due to these fast diffusions in the molten state as well as in the solid state, we cannot ignore the interaction across a solder bump. Enhanced spalling of ternary intermetallic compound of (Cu, Ni)6 Sn5 or (Ni, Cu)3 Sn4 occurs as shown in Fig. 1.13 and discussed in Section 3.8.

4.4 Enhanced Dissolution of Cu-Sn IMC by Electromigration More serious interaction across a flip chip solder joint will come from electromigration. In a flip chip solder joint, electric current must go through the chip and its packaging substrate; the contact of the UBM on the chip side and the contact of the bond pad on the substrate side become respectively the cathode and the anode, or vice versa, across a solder joint. Electromigration will dissolve Cu from the UBM and the Cu-Sn IMC at the cathode and transport the dissolved Cu atoms to the anode and form Cu-Sn IMC at the anode, or vice versa. Therefore, electromigration in the solder bump affects chip–packaging interaction. In Fig. 4.4, a set of five SEM images of the cathode contact in a composite solder joint before and after electromigration are shown [1]. Figure 4.4(a) is the image before electromigration, showing the TiW, Cu3 Sn and the matrix of the high-Pb solder joint. The Cu3 Sn is found to be stable with the high-Pb solder matrix in thermal aging without electric current stressing. However, when a current density of 2.25 × 104 A/cm2 was applied and the direction of electron current flow was from the chip side at the upper left corner into the solder joint, some Cu6 Sn5 was formed below the Cu3 Sn after 3 hr, and at the same time, some Cu above the Cu3 Sn was consumed and also in the solder matrix, more Sn was found to have diffused from the anode side to the cathode side [see Fig. 4.4(b)]. After 12 hr, more reaction has occurred at the upper left corner and the Cu above the Cu3 Sn is completely gone and a much thicker Cu6 Sn5 was formed below the Cu3 Sn [see Fig. 4.4(c)]. A small void was found to have formed near the Cu6 Sn5 and Cu3 Sn interface. After 18 and 20 hr, a large void formed and it had extended all the way to the TiW layer and the device failed with a very large increase in resistance [see Fig. 4.4(d) and (e), respectively]. Clearly, the chemical reaction at the cathode was affected by electromigration. It is worth noting that at the upper right corner of the contact in Fig. 4.4(d) and (e), neither dissolution of Cu nor phase transformation similar to that at the upper left corner was found. What is significant in the above observation is that a stable layered structure became unstable under electromigration. Typically, a layered morphology

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e -Cu

(b)

(a)

Cu3Sn

e-

Sn (d)

Cu

e-

(e)

e-

Sn

A

A,

Cu6Sn5

Cu

Cu3Sn

Cu3Sn Cu6Sn5

Cu3Sn

Cu6Sn5

10 μm

(c)

Cu

Cu6Sn5

Sn

Cu

Cu3Sn Sn

Fig. 4.4. A set of five SEM images of the cathode contact in a composite solder joint before and after electromigration. (a) The image before electromigration, showing the TiW, Cu3 Sn, and high-Pb solder joint matrix.

formed in a diffusion couple, for example, is stable in constant-temperature annealing. The layers may grow or shrink upon annealing, but the layered morphology is maintained. Any perturbation on a flat interface is in principle unstable and will be removed by ripening. On the other hand, such a layered structure may become unstable under electromigration, particularly when current crowding exists. The instability leads to the dissolution of the Cu UBM as shown in Fig. 4.4 and in turn the failure of the solder joint. In Chapters 8 and 9 we shall introduce the subject of electromigration, the unique behavior of electromigraiton in flip chip solder joints, and the interaction between chemical and electrical forces.

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4.5 Enhanced Phase Separation in Solder Alloys by Electromigration and Thermomigration

Temperature (°C)

The so-called Soret effect refers to when a homogeneous single-phase alloy becomes inhomogeneous under a temperature gradient [2]. We describe here a similar but different effect in which a homogeneous eutectic two-phase alloy becomes inhomogeneous under a temperature gradient, i.e., thermomigration. The difference is that in the Soret effect the inhomogeneous alloy has created a chemical potential gradient to resist the effect. But in a eutectic alloy under thermomigration, there is no chemical potential gradient to resist phase separation or redistribution of composition in the eutectic two-phase alloy. We refer to this as the “eutectic effect on phase separation” induced by thermomigration or by electromigration. The subject of thermomigration will be covered in Chapter 12. Compositionally, what is unique in a eutectic system is that there is no chemical potential gradient as a function of composition below the eutectic temperature. In other words, the chemical potential is uniform and does not depend on composition. For example, a schematic phase diagram of Sn-Pb is shown in Fig. 4.5, and we consider a diffusion couple of 70Pb30Sn and

A

B

Fig. 4.5. Schematic phase diagram of a binary eutectic system of SnPb shows that below the eutectic temperature, it will phase-separate into two primary phases having a lamellar microstructure. The two lamellar phases are at equilibrium with each other, independent of the lamellar spacing or their volume fraction. If we consider a diffusion couple of “A” and “B” at 150◦ C, each of them has phase-separated into two lamellar phases. Since they are at equilibrium, there is no chemical potential difference to drive them to intermix under isothermal annealing at 150◦ C.

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30Pb70Sn alloys annealed at 150◦ C. These two alloys are represented by the two dots, A and B, on the constant-temperature line, the thick line, drawn in Fig. 4.5. At ambient pressure and 150◦ C, it is a constant-pressure and -temperature process, hence any composition along the broken line will decompose into the two end-phases of α and β at the two points indicated by the arrows. Composition of each phase is determined by thermodynamic equilibrium between them and is known from the phase diagram; they are the primary or end phases. These two end phases are at equilibrium with each other, independent of the amount of each phase. In the next section, it will be shown that there is neither interdiffusion nor homogenization between the diffusion couple annealed at ambient pressure and 150◦ C, except a minute amount of ripening. This is because at 150◦ C, these two alloys in the diffusion couple will phase-separate into the same two primary phases of Sn and Pb, except that the amount of the two primary phases is different, which obeys the level rule. They have the lamellar microstructure. However, the lamellar spacing or lamellar thickness is not defined. In other words, the lamellar thickness, or the amount of each phase, or the composition, can be changed without affecting the equilibrium condition. To be precise, there is a change of total lamellar interfacial energy. Since these two primary phases are at equilibrium with each other, independent of their amount, there is no driving force to homogenization upon aging at a constant temperature, say 150◦ C. However, if an external driving force is applied, such as a temperature gradient in thermomigration or an electric field in electromigration, to a homogeneous two-phase eutectic alloy below the eutectic temperature, a very large degree of phase separation or composition redistribution can be induced because there will be no chemical potential change in phase separation, so there is no chemical potential gradient to oppose the applied driving force as in the Soret effect. In a eutectic two-phase mixture a change of concentration does not mean any change of chemical potentials, but rather just a change of local volume fractions of the two phases. Thus, if some segregation in solder is induced by thermomigration or electromigration, it means a change of the gradient of volume fractions, not of chemical potentials. Gradient of volume fractions is not a driving force. Therefore, the segregation in two-phase mixtures such as eutectic SnPb can be enormous, compared with a single-phase alloy such as PbIn, in which a change of composition will cause a counteracting force due to concentration gradient. In principle, after a sufficiently long duration of thermomigration or electromigration, the eutectic solder sample could have achieved a complete phase separation into two parts. Actually this has been observed in electromigration in flip chip solder joint of eutectic SnPb. Figure 4.6(a) and (b) show respectively SEM images of the cross section of a eutectic SnPb solder joint before and after electromigration at 5 × 103 A/cm2 at 160◦ C for 82 hr, and Sn has segregated to the anode side and Pb to the cathode side. More discussion of the subject will be given in Chapter 9. However, we note that when a large amount of Sn is driven to the

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Pb

e-

Sn

Fig. 4.6. SEM images of the cross section of a eutectic SnPb solder joint before (a) and after (b) electromigration at 5 × 103 A/cm2 at 160◦ C for 82 hr. Sn has segregated to the anode side and Pb to the cathode side. (Courtesy of Dr. Yi-Shao Lai, ASE, Taiwan, ROC.)

cathode or the anode, it will react with Cu to form a large amount of IMC, as shown in Fig. 4.4. If we examine the binary phase diagram of Sn-Cu or Sn-Ni, we find that Sn and Cu6 Sn5 as well as Sn and Ni3 Sn4 form eutectic couples. This means that below their eutectic temperature, a large amount of these compounds can be formed in a matrix of Sn, and the compounds will be in equilibrium with the matrix. Indeed this has been observed in electromigration in solder joints, as shown in Fig. 1.16. Since both Cu and Ni are being used as UBM in solder joints, they can be dissolved by electromigration into the solder joint and form a large amount of intermetallic compounds (IMC) near the anode, especially the Pb-free solders which are Sn-based.

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Chapter 4 Fig. 4.7. SEM images of the interface of the bulk couple before and after annealing.

Before aging

After one week aging

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4.6 Thermal Stability of Bulk Diffusion Couples of SnPb Alloys Experimentally, a bulk diffusion couple of alloys of 70Pb30Sn and 30Pb70Sn was annealed at 150◦ C for 5 weeks. SEM images of the interface of the couple before and after the annealing are shown in Fig. 4.7. Composition distribution curves across the interface measured by electron micro-probe before and after the annealing are shown in Fig. 4.8. Assuming an interdiffusion coefficient of 1 × 10−8 cm2 /sec, we expect to detect an interdiffusion zone 5 μm wide after 5 weeks. The detected width of the interface is much less than that, indicating almost no interdiffusion. Experimentally, in a composite solder joint consisting of 5Sn95Pb and 63Sn37Pb (eutectic), no interdiffusion or mixing of composition was found after aging at 150◦ C at ambient pressure for several days. Figure 4.9 shows

Sn concentration (wt %)

Sn (wt %) composition distribution curves 100 80 60 40 20

Before Aging After 5 weeks aging

0 0

500

1000

1500

2000

Distance starts from the middle of Pb-rich bulk sample to the middle of Sn-rich bulk sample (μm)

Fig. 4.8. Composition distribution curves across the interface of the diffusion couple measured by electron micro-probe before and after annealing.

a)

b)

Fig. 4.9. SEM images of the cross sections of the 5Sn95Pb and eutectic SnPb composite solder joint before (a) and after (b) aging. No substantial interdiffusion can be detected.

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SEM images of the cross sections of the composite solder joint before and after aging. No substantial interdiffusion can be detected [3]. The results shown above are not unexpected. They were experiments under constant temperature and constant pressure. When the Gibbs free energy is minimized, the two phases have equal chemical potential, so there was no driving force to homogenize them. Only when an electric current or a temperature gradient is applied to the diffusion couple can interdiffusion occur and lead to a change of volume fraction of the two phases.

4.7 Thermal Stress Due to Chip–Packaging Interaction To reduce resistance–capacitance delay in multilayered interconnect structure, ultralow-k materials with a value of k approaching 2 are being developed for the integration with Cu conductors. The weak mechanical properties of ultralow-k materials are of concern owing to thermal stress. The thermal stress exists between Cu and ultralow k due to their difference in thermal expansion coefficient, but also due to chip-to-packaging interaction. This is a relatively new reliability issue. In Section 1.4.2, we discussed thermal-mechanical stress across a flip chip due to the difference in thermal expansion coefficients of Si and FR4 polymer substrate board. In flip chip technology, the Cu/ultralow-k multilayered structure on a Si chip will be joined to a packaging substrate by an area array of solder joints. Around the device operation temperature of 100◦ C, a thermal stress is developed between the Si chip and the substrate, whether the latter is ceramic or polymer. The thermal stress will affect the mechanical integrity of the solder bumps as well as the Cu/ultralow-k multilayered structure. When SiO2 was used as the interlayer dielectric, since SiO2 is mechanically rather strong, the load from the chip-to-packaging interaction will be taken up by the solder bump which is softer. The thermal stress has led to the well-known low cycle fatigue failure of flip chip solder bumps in device applications. In the past, the microelectronics industry invented the epoxy underfill to redistribute the thermal stress and reduce its effect on solder joint failure. Moire interferometry has been developed to analyze the thermal stress distribution in the flip chip solder joints [5–7]. However, when ultralow k is used as interlayer dielectric, the thermal stress induced by the chip-to-packaging interaction will be shared between the solder bump and the multilayer structure of Cu/ultralow k. The thermal stress may crack the dielectric in the Cu/ultralow-k multilayered structure.

4.8 Design and Materials Selection of a Flip Chip Solder Joint In Chapter 3, Sections 3.3 to 3.7 presented a sequence of events of the selection of UBM with respect to the change of solder alloy. Spalling of IMC has been

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the issue. To overcome the spalling problem, very thick Cu UBM such as Cu column bump has been studied, to be discussed in Section 9.6. Clearly, it is better to take into account the reliability issues in the design stage of a device. The design of the dimensions of a flip chip solder joint and the selection of materials to form the joint depends on the application of the device and the specifications from the device designer. For example, from the point of view of electromigration, it is important to know the current carrying capacity of a joint as required by the designer, then the current density distribution in the circuit of the joint must be considered. Today, very powerful threedimensional simulation is capable of revealing any current crowding in the circuit since it causes local joule heating and enhances electromigration. In addition, the related temperature distribution due to joule heating and even stress distribution can be obtained too. Nevertheless, the challenge to the design is that reliability is a time-dependent event. The microstructure of a joint will change in field use, so the current distribution will change with time. Reliability is a dynamic problem! Furthermore, up to now there has been no industrial standard of electromigration test of a flip chip solder joint. It will help greatly if a standard is available. It is beyond the scope of this book to cover the details of the design and selection rules of a flip chip solder joint. What is done here is to offer some basic understanding of the reliability problems of solder joints, so that designers may be aware of them in their circuit design.

References 1. J. W. Nah, K. W. Paik, J. O. Suh, and K. N. Tu, ”Mechanism of electromigration induced failure in the 97Pb-3Sn and 37Pb-63Sn composite solder joints,”J. Appl. Phys., 94, 7560–7566 (2003). 2. D. V. Ragone, “Thermodynamics of Materials,” Volume II, Chapter 8, John Wiley, New York (1995). 3. A. Huang, Ph.D. dissertation, UCLA (2006). 4. J. W. Nah, UCLA, Personal communication. 5. Y. Gao, C. K. Liu, W. T. Chen, and C. G. Woychik, “Solder ball connect assembles under thermal loading: 1. Deformation measurement via Moire interferometry, and its interpretation,” IBM J. Res. Dev., 37, 635– 648 (1993). 6. D. Post, B. Han, and P. Ifju, “High Sensitivity Moire: Experimental Analysis for Mechanics and Materials,” Springer, Berlin (1994). 7. Z. Liu, H. Xie, D. Fang, H. Shang, and F. Dai, “A novel nano-Moire method with scanning tunneling microscope,” J. Mater. Process. Technol., 148, 77– 82 (2004).

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5 Kinetic Analysis of Flux-Driven Ripening of Copper–Tin Scallops

5.1 Introduction In Chapter 2, we demonstrated that in the wetting reaction of a cap of molten eutectic SnPb solder on a bulk Cu foil, the intermetallic compound formation of Cu6 Sn5 takes a unique morphology of closely distributed scallops. Morphology controls kinetics. The kinetics of growth of the scallops is a supply-controlled reaction, rather than diffusion-controlled or interfacialreaction-controlled. The scallops appear to have touched each other side-by-side and cover the entire interface between the molten solder cap and the Cu. When the time of wetting reaction is extended, the diameter of the cap does not increase, except for the growth of a halo around the cap. Thus, the interfacial area between the cap and Cu does not change. However, within the cap, the interfacial reaction between the molten SnPb and Cu continues and the scallop grows, so the average diameter of the scallop increases with time. Since the scallops are touching each other, the growth of any one in diameter is a parasitic reaction; it grows at the expense of its nearest neighbors, so the neighboring scallops shrink. It is a ripening process. Figure 2.5 showed that on a fixed interfacial area, while the average size of scallops has increased with time, the number of scallops decreases with time. The ripening process is nonconservative, meaning that the total volume of the scallops increases with time. The volume increase is due to Cu-Sn reaction which grows the Cu6 Sn5 scallops by the diffusion of Cu into the molten solder. A very unique kinetic behavior of the scallop-type morphology is that the scallop does not seem to become a diffusion barrier to its own growth, unlike the growth of a layer-type intermetallic compound. In a layered growth, it obeys a diffusion-controlled growth; typically the thicker the layer, the better diffusion barrier it is to its own growth. The layer thickness should have a square root dependence on time, as discussed in Chapter 3. In scallop growth, the diameter of the scallop was measured to have a cubic root dependence on time, quite similar

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to a conservative ripening described by the LSW theory [1–3]. However, in the classic ripening process described by the LSW theory, it is diffusion-controlled. While the total volume of all the scallops increases with time, the base area or the interfacial area between the scallops (or the cap) and the Cu is fixed. This is a major constraint of the reaction; a constraint of constant interfacial or base area. It is very interesting to note that if the scallops are assumed to be hemispheres, it follows that the total surface area of the hemispherical scallops is also fixed at twice the base area, independent of the size distribution of the hemispheres. Therefore, we have a ripening process which has a constant-surface area, rather than a constant volume. In the classic LSW ripening, it proceeds under a constant-volume constraint and is driven by the reduction of the total surface area. The scallop-type ripening proceeds under a constant-surface-area constraint and is driven by the increase of the total volume of the scallops, in other words, by the gain in the formation energy of intermetallic compound. In the scallop-type ripening process, there are two important constraints. The first is that the reaction interface or the total surface of scallops is constant. The second is conservation of mass, in which all the flux of Cu diffusing into the molten solder is consumed by scallop growth to increase the average diameter of scallops, but at the same time it will reduce the number of channels between scallops under the first constraint. This is the reason for supply-controlled reaction or flux-driven ripening since the reaction rate depends on the supply of the Cu flux. Here we define the “channel” between two neighboring scallops to be a gap, not a grain boundary. In other words, the width of the gap is several nanometers, not 0.5 nm of a grain boundary in the solid state. A reduction of the number of channels will reduce the flux of Cu needed for the growth. In experiments, scallops of Cu6 Sn5 were observed to elongate in the growth direction after approximately 10 min of reaction between molten eutectic SnPb and Cu at 200◦ C. In the following, we shall first consider the stability of scallop-type morphology in wetting reactions before we present a kinetic analysis of the distribution and growth of scallops. On kinetics, first a simple model of growth of mono-size scallops is presented to illustrate the basic idea. Second, a general model of the distributional growth of different sized scallops in ripening will be analyzed.

5.2 Morphological Stability of Scallop-Type IMC Growth in Wetting Reactions Why is morphology important in phase transformations? It affects the kinetic path in the transformation. In wetting reactions of molten solder on Cu films, it is the morphological change that leads to “spalling” of IMC, as discussed in Chapter 3. In wetting tip reactions, when surface energy or

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interfacial energy is considered, morphological stability or equilibrium of the triple point at the wetting tip is conserved. Only when we are sure that the scallop-type morphology is stable in wetting reactions will the kinetic analysis of its ripening make sense [4]. In the following, we shall compare the morphology and the kinetics of solid-state reactions to those of wetting reactions. In solid-state reactions, a layer-type rather than a scallop-type morphology is stable and kinetic analysis of the layer-type growth will be reviewed briefly below [5]. In the classical analysis of solid-state interfacial reactions in a binary bulk diffusion couple, the kinetics of growth of each IMC layer can be diffusioncontrolled or interfacial-reaction-controlled, as discussed in Chapter 3. For a bulk diffusion couple of sufficient thickness at a high enough temperature and after a very long time, we can have all the layered IMCs coexisting with diffusion-controlled growth. The ratio of thickness among the layers is proportional to the ratio of the square root of the interdiffusion coefficient in the layers. The analysis of reaction in bulk diffusion couples has been extended to reactions between two metallic thin films and between a metallic thin film and a silicon wafer. With the availability of modern analytical techniques, which can detect IMC formation with atomic resolution, it was found that not all the equilibrium IMCs would form in thin-film reactions [6, 7]. Actually, only one of them forms if the reaction takes place at a low temperature. In the case of a Ni film on a silicon wafer at 200◦ C, the phase of Ni2 Si will form alone [8, 9]. When it consumes all the Ni, then NiSi will form in between the Ni2 Si and Si. After the growth of NiSi has consumed all the Ni2 Si, the phase NiSi2 will form in between the NiSi and Si, and the growth of NiSi2 will consume all the NiSi finally. The reaction ends with a film of NiSi2 on Si. It is a sequential formation of silicide phases; they form one-by-one. Using a model of competing growth between two thin layers, e.g., Ni2 Si and NiSi between Ni and Si, and employing both diffusion-controlled and interfacial-reaction-controlled kinetics, Gosele and Tu were able to explain the phenomenon of “single phase growth” in thin film reactions [10]. Their model defines a critical thickness or a thin film thickness below which only one IMC can form. To verify the singlephase growth phenomenon, a Ni film was evaporated on NiSi/Si to obtain a sample of Ni/NiSi/Si and the sample was annealed. Instead of the growth of NiSi, the Ni was found to react with NiSi to form Ni2 Si. The latter grew and consumed all the NiSi and only after that was the sequential growth as stated above repeated. How to predict which of the IMCs will be the first phase to form, i.e., the Ni2 Si in the Ni/Si reaction, and what is the sequence of the ensuing phase formations have been actively studied. Many models exist to predict the first phase formation of solid-state interfacial reactions in thin films. Actually they are quite successful in predicting the phase using equilibrium phase diagrams and applying the criterion of the largest Gibbs free energy change or the largest driving force in IMC formation. However, a metastable phase, such as an amorphous alloy, which does

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not exist in equilibrium phase diagrams, can be the first phase formation, as in Rh/Si and Nb/Zr reactions [11, 12]. The metastable phase has a relatively small Gibbs free energy of formation compared to that of the equilibrium IMCs, so amorphous phase formation does not have the largest gain in Gibbs free energy. Also, the first phase formation tends to depend on temperature. For example, an amorphous phase cannot be the first phase formation if the formation temperature is very high. At the moment, a plausible explanation of the metastable phase formation or the selection of the first phase formation and its temperature dependence is that it has the highest “rate” of Gibbs free energy change [13]. It is the largest Gibbs free energy change in a short time or the fastest rate of growth that determines the first phase formation. Or, the phase which has the largest flux of interdiffusion tends to become the first phase of formation. In other words, the first phase selection is based on kinetics, not thermodynamics. However, we need kinetic data in order to predict which phase has the highest rate of growth, but unfortunately kinetic data are not available for most reactions. In wetting reaction between eutectic SnPb and Cu, the morphology of the Cu6 Sn5 is not layer-type, rather it has a scallop-type morphology. The scallop-type morphology is stable as long as there is unreacted Cu. When the thickness of Cu changes from a foil to a thin film, the nonconservative ripening changes to a conservative ripening after the Cu film is completely consumed. It becomes unstable and leads to spalling of IMC as we have discussed in Section 3.3. Now we turn to solid-state aging of the same system. Figure 2.23 showed four SEM images of eutectic SnPb on a thick Cu substrate before and after aging at 170◦ C for 500, 1000, and 1500 hr. These samples were reflowed twice at 200◦ C before the solid-state aging. In these figures, we observed that both Cu6 Sn5 and Cu3 Sn compounds have layer-type morphology; their interfaces are rather flat. Specifically, the Cu6 Sn5 no longer has the channels in the scallop-type morphology and the Cu3 Sn is very thick. Since the samples were reflowed twice before aging, they must possess the scallops of Cu6 Sn5 in the initial stage of aging. Yet during the solid-state aging the morphology of Cu6 Sn5 has changed from the scallop-type to layer-type. Naturally, we ask why it does not maintain the scallop-type growth in the solid-state aging. Figure 5.1 shows a top view of the surface of Cu6 Sn5 of a sample of eutectic SnPb on Cu aged at 150◦ C for 2 months. The solder over the IMC was etched away. The Cu6 Sn5 has a rather flat surface, and grain boundaries were formed between grains. Interestingly, if we wet the layered IMC by molten eutectic SnPb solder, the scallop-type morphology of Cu6 Sn5 returns. Figure 5.2(a) shows a SEM image of the cross section of a sample of eutectic SnPb on a Cu foil aged at 170◦ C for 960 hr. In the layered IMC, a few of the grains with vertical and flat grain boundaries are seen, and a rather thick layer of Cu3 Sn formed below the Cu6 Sn5 . Figure 5.2(b) shows a cross section of the sample after it was reflowed at 200◦ C for 40 min. The scallop-type grains of Cu6 Sn5 reappeared

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Fig. 5.1. SEM image of the top view of the surface of Cu6 Sn5 of a sample of eutectic SnPb on Cu aged at 150◦ C for 2 months. The solder over the IMC was etched away. The Cu6 Sn5 has a rather flat surface, and grain boundaries were formed between grains. (Courtesy of Jong-ook Suh, UCLA.)

with a curved surface. In Fig. 5.3(a), the morphology of a layer-type IMC of another sample after a solid-state aging at 130◦ C for 480 hr is shown. While its top surface is rough, the grains are columnar, not scallop-type, and no channels exist between the grains. When this sample was reflowed at 200◦ C for only 1 min, the columnar grains transformed back to scallops, as shown in Fig. 5.3(b). Both Figs. 5.2 and 5.3 reveal that the scallop-type grains are stable in contact with molten solder, but the layer-type grains are stable in contact with solid solder.

5.2.1 Analysis of Morphological Stability of Scallops in Wetting Reactions The formation of layer-type IMC in solid-state reactions is common. What is uncommon here is why the layer-type IMC transforms to scallop-type IMC when it is wetted by molten solder. The transformation indicates that the scallop-type morphology is thermodynamically stable in wetting reactions. We consider such a transformation in Fig. 5.4, where the solid lines represent a schematic diagram of the cross section of a layer-type Cu6 Sn5 . The broken lines represent the wetting of the top surface and grain boundaries of Cu6 Sn5 grains by molten solder. The change in interfacial and grain boundary energies

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Chapter 5 Fig. 5.2. (a) SEM image of the cross section of a sample of eutectic SnPb on a Cu foil aged at 170◦ C for 960 hr. In the layered IMC, a few of the grains with vertical and flat grain boundaries are shown, and a rather thick layer of Cu3 Sn formed below the Cu6 Sn5 . (b) Crosssectional image of the sample after reflowing at 200◦ C for 40 min. The scallop-type grains of Cu6 Sn5 reappeared and the IMC grains had a curved surface.

(a)

(b)

is given as 1 2πrhσGB + πr2 σSS ≥ 2πrhσLS + πr2 σLS , 2 where σGB , σSS , and σLS represent grain boundary energy in Cu6 Sn5 , interfacial energy between solid solder and Cu6 Sn5 , and interfacial energy between molten solder and Cu6 Sn5 , respectively, and r and h are respectively the radius and height of the solid Cu6 Sn5 grains. The factor 1/2 appears in the first term on the left-hand side of the inequality equation because a grain boundary is shared by two grains. The sum of energies on the left-hand side of the equation is greater than that on the right-hand side. We compare morphological stability in wetting reaction to that in solidstate aging. In wetting reaction, Fig. 5.5(a), we represent the stable scalloptype morphology by the solid lines and the unstable layer-type morphology by the broken lines, and we have 2πR2 σLS ≤

1 2πrhσGB + πr2 σLS , 2

where R is the radius of the scallop. For the hemispherical scallop, we assume

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Fig. 5.3. (a) The morphology of a layer-type IMC of a eutectic SnPb on a Cu foil after solid-state aging at 130◦ C for 480 hr. The grains are not scallop-type and no channels between the grains can be found. (b) When this sample was reflowed at 200◦ C for only 1 min, the grains transformed back to scallops.

that the interfacial energy σLS is isotropic. In solid-state aging, Fig. 5.5(b), we represent the stable layer-type morphology by the solid lines and the unstable scallop-type morphology by the broken lines and we have 2πR2 σSS ≥

1 2πrhσGB + πr2 σSS . 2 Molten Solder

sSS

sLS

Cu6Sn5

Cu6Sn5

sGB

Fig. 5.4. Schematic diagram of the transformation of a layer to a scallop-type Cu6 Sn5 . The cross section of a layer-type Cu6 Sn5 is depicted by the solid lines. The broken lines represent the wetting of the top surface and grain boundaries of Cu6 Sn5 grains by molten solder.

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Chapter 5 sLS

(a)

R

sGB

h r

sSS

(b) R

sGB

h

Fig. 5.5. (a) In wetting reaction, the transformation of a layered to a scalloped IMC. The stable scallop-type morphology is represented by the solid lines and the unstable layer-type morphology by the broken lines. (b) In solidstate aging, the transformation of a scalloped to a layered IMC. The stable layer-type morphology is represented by the solid lines and the unstable scallop-type morphology by the broken lines.

r

In the above two inequalities, we have assumed a constant-volume transformation between a cylindrical grain and a hemispherical grain, so that we need not consider volume energy but only interfacial and grain boundary energies. To simplify all of the above inequality equations, we assume that the radius of the cylindrical grain is equal to the radius of the hemispherical grain (i.e., r = R). Alternatively, we can also assume that the height of the cylindrical grain is equal to its radius, r = h, and the result is similar. We obtain h=

2 r. 3

Substituting this relation into the last three inequality equations, we have the following two inequalities: 7 σLS , 6 2 ≥ σGB ≥ σLS . 3

σSS ≥ σSS

The first inequality equation shows that the interfacial energy between a molten solder and Cu6 Sn5 is less than that between a solid solder and Cu6 Sn5 . The second inequality equation implies that the energy of large-angle grain boundaries in Cu6 Sn5 must be quite high. When a molten solder reacts with the layer-type Cu6 Sn5 , the reaction wets the large-angle grain boundaries in the layer-type Cu6 Sn5 , as depicted in Fig. 5.4. The interfaces between the solid solder and Cu6 Sn5 and the grain boundaries in Cu6 Sn5 can be replaced by the low-energy interfaces of the molten solder and Cu6 Sn5 . Therefore, the scalloptype morphology persists in wetting reactions and the layer-type morphology persists in solid-state aging.

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The stability is due to minimization of interfacial and grain boundary energies. The interfacial energy between a molten solder and Cu6 Sn5 is less than that between a solid solder and Cu6 Sn5 , so the scallop-type morphology of grains persists in wetting reactions and the layer-type morphology persists in solid-state aging. When the molten solder reacts with the layer-type Cu6 Sn5 and transforms it back to scallop-type Cu6 Sn5 , the reaction must begin by wetting the large-angle grain boundaries in the layer-type Cu6 Sn5 , as depicted in Fig. 5.4. It implies that the energy of large-angle grain boundaries in Cu6 Sn5 must be quite high, so they can be replaced by the low-energy interfaces of the molten solder and Cu6 Sn5 . During the wetting reaction, the neighboring scallops will not join together to form grain boundaries. Therefore, they can only grow bigger by ripening. In ripening, the total surface area of the hemispherical scallops is conserved. On the other hand, the scallops cannot keep on growing to become very big. This is because the bigger the scallops, the fewer the channels in between them. Since channels are the short circuit paths for Cu to reach the molten solder, the scallop-type growth has to slow down when the channels are reduced. In order to keep the channels, the scallops will elongate, and very long scallops have been observed in extended wetting reactions.

5.3 A Simple Model for the Growth of Mono-Size Hemispheres Figure 5.6(a) is a schematic diagram of the cross section of an array of hemispherical Cu6 Sn5 scallops grown on Cu, represented by the solid curves. The following assumptions are made to analyze the kinetics of scallop growth [14– 16]. (a) The presence of Cu3 Sn and Pb in the reaction is ignored for convenience. (b) A liquid channel exists between two scallops, the depth of which reaches the Cu surface. The width of the channel “δ” is assumed to be small compared to the radius of scallops. The morphology of scallops and channels is assumed to be thermodynamically stable in the presence of molten solder. The channels serve as rapid diffusion paths for Cu to go into the molten solder to grow the scallops. Although the scallops are separated by channels, they remain in close contact with each other. Figure 5.6(b) is a cross-sectional transmission electron microscopic image of Cu6 Sn5 scallops, channels, and a thin layer of Cu3 Sn on Cu. The channel, as indicated by an arrow, has a width less than 50 nm. (c) The shape of the scallops is represented by hemispheres. On a given interfacial area of “S total ” between the scallops and the Cu, the total surface area between all hemispherical scallops and molten solder is just twice “S total .” In Fig. 5.6(a), if we represent the cross section of a single large hemispherical scallop by the broken half circle, its surface is 2 S total ,

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Chapter 5

(a) R

Jout

Jin R2

R1

R3

2πR2 ≅

N

Σ 2πRi2 ≅ i=1

R4

2Stotal

(b)

1 μm Fig. 5.6. (a) Schematic diagram of the cross section of an array of hemispherical Cu6 Sn5 scallops grown on Cu, represented by the solid curves. (b) Cross-sectional transmission electron microscopic image of Cu6 Sn5 scallops, channels, and a thin layer of Cu3 Sn on Cu. The channel, indicated by the arrow, has a width less than 50 nm.

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the same as the sum of the surfaces of the smaller scallops represented by the solid curves. Hence, while the growth increases the total volume, it does not change the total surface area of the scallops. (d) By conservation of mass, all the influx of Cu from the Cu substrate is consumed by the growth of the scallops. Hence, the outflux of Cu from the ripening zone into the bulk of the molten solder is assumed to be negligible. In this ripening process, there are two important constraints. The first constraint is that the interface of reaction is constant. When the scallops are assumed to be hemispherical, it also means that the total surface area of scallops is constant. Therefore, we have a ripening process which proceeds under constant surface with increasing volume. The second constraint is conservation of mass, in which all the influx of Cu is consumed by scallop growth. In the classical LSW ripening, the process proceeds under almost a constant volume, so the decrease of surface (and surface energy) provides the driving force. Strictly speaking, mono-size distribution (size distribution as Dirac’s δ-function) is not compatible with scallop growth since scallop growth is parasitic and dependent upon the shrinkage of neighboring smaller scallops. It is an unrealistic model and at the best, it approximates a narrow distribution function of scallops. The big advantage of this model is that we change a many-body problem to a one-body problem. We shall show below that the mono-size approximation is good for a rough estimate of average values of the kinetics. According to the first constraint that the interface between the scallops and Cu is occupied completely by scallops except the thin channels, we have N πR2 ∼ = S total = const,

(5.1)

where N is the number of scallops and R is radius. The free surface (the cross-sectional area of channels at the bottom) for the supply of Cu from the substrate is S free = N 2πR

δ δ = S total , 2 R

(5.2)

where δ is the channel width. Thus, the free surface decreases during the scallop growth as 1/R. The volume of the reaction product of IMC scallops is equal to Vi = N

2π 3 2 R = S total R. 3 3

(5.3)

According to the second constraint that all influx of Cu atoms diffusing into the molten solder from the substrate is consumed by the growth of IMC

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Chapter 5 Fig. 5.7. The meaning of C e and C b in Eq. (5.5).

scallops due to conservation of mass, we have ni Ci

dVi = J in S free . dt

(5.4)

Here ni is atomic density in IMC, i.e., number of atoms per unit volume, and Ci is atomic fraction of Cu in IMC, which is 6/11 in Cu6 Sn5 . The influx is taken approximately as  J in = −nD

Ce +

α R



− Cb

R

,

(5.5)

where α = (2γΩ/RG T )C e , γ is isotropic surface tension at IMC/melt interface, Ω is molar volume, RG is gas constant, and T is temperature. The meaning of C e and C b is defined in Fig. 5.7. In our case α ∼ = 4.4 × 10−7 cm. First, we consider the case α/R  C b − C e , so that Cb − Ce J in ∼ , = nD R

(5.6)

where n is atomic density or number of atoms per unit volume in the melt or molten solder. Then, substituting Eqs. (5.6), (5.2), and (5.3) into the balance Eq. (5.4), we obtain 2 dR Cb − C ni Ci S total = nD 3 dt R

e



 δ total , S R

(5.7)

which immediately gives R3 = kt, 9 n D(C b − C e )δ k= . 2 ni Ci

(5.8a) (5.8b)

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Note that the surface tension is absent in the expression for the rate constant, despite the “ripening-like” time law. If we take n/ni ≈ 1, Ci = 6/11, D ≈ 10−5 cm2 /sec, δ ≈ 5 ∗ 10−6 cm, C b − e C ≈ 0.001, where the concentration C b is taken for equilibrium of melt with the Cu3 Sn phase, the rate constant k ≈ 4 ∗ 10−13 cm3 /sec. For example, for annealing time t = 300 sec, it gives R ≈ 5 ∗ 10−4 cm, which agrees very well with experimental data.

5.4 Theory of Nonconservative Ripening with a Constant Surface Area For scallops having a distribution of size, we let f (t, R) be the size distribution function of scallops, so that the total number of scallops is equal to [15] ∞ N (t) =

f (t, R)dR,

(5.9)

0

and the average values are = N

∞ Rm f (t, R)dR.

(5.10)

0

The first constraint of constant interface takes the form ∞

πR2 f (t, R)dR = S total − S free ∼ = S total = const.

(5.11)

0

The cross-sectional area of all channels for copper supply is ∞ S

free

=

δ 2πRf (t, R)dR. 2

(5.12)

0

The total volume of the growing scallops is ∞ Vi =

2 3 πR f (t, R)dR. 3

(5.13)

0

According to the second constraint, we have ni Ci

dVi = J in S free . dt

(5.14)

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Chapter 5

Here ni is atomic density in IMC, i.e., number of atoms per unit volume, and Ci is atomic fraction of Cu in IMC, which is 6/11 in Cu6 Sn5 . The influx is taken approximately as  J

in

= −nD

Ce +

α R



− Cb

R

,

(5.15)

where n is atomic density in solder, α = (2γΩ/kG T )C e , γ is isotropic surface tension at IMC/melt interface, Ω is molar volume, kG is Boltzmann’s constant, and T is temperature. C e and C b are defined as the equilibrium concentration (the atomic fraction of Cu in molten solder) on a flat surface and concentration at the entrance of the channels (corresponding to the concentration of Cu in the molten solder on the substrate surface). Since scallops must grow and shrink atom by atom, the distribution function should satisfy the usual continuity equation in the size space: ∂f ∂ =− (f uR ), ∂t ∂R

(5.16)

where the velocity in the size space, uR , is simply the growth rate of scallops with radius R and is determined by the flux density, j(R), on each individual scallop. The expression for j(R) is usually found as a quasi-stationary solution of diffusion problem in infinite space around a spherical grain with fixed supersaturation < C > −C e at infinity. Then uR =

j(R) dR n D < C > −(C e + α/R) =− . = dt ni Ci ni Ci R

(5.17)

While this expression is good for LSW theory, it is not good for the present case because the scallops are on an interface and the diffusion distance between them is of the same order of magnitude of the size of scallops. On the other hand, the diffusion in the melt is very fast, so we suggest that the expression of j(R) can be obtained by assuming that the flux on (or out of) each individual scallop should be proportional to the difference between the average chemical potential of copper μ in reaction zone (we take it to be the same everywhere— mean-field approximation) and the chemical potential at the curved scallop– β melt interface, μ∞ + R , and β = 2γΩ:   β −j(R) = L μ − μ∞ − , R

dR L = dt ni Ci

 μ − μ∞ −

β R

 ,

(5.18)

where the parameters L, β, μ − μ∞ are determined self-consistently from the above-mentioned two constraints of constant surface, Eq. (5.1), and mass

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conservation, Eq. (5.4). We obtain dR k 1 uR = = dt 9 < R2 > − < R >2 9 n k= D(C b − C e )δ. 2 ni Ci



1− R

 ,

(5.19) (5.20)

During the nonconservative flux-driven ripening, the rate of growth/shrinkage of each scallop is determined not only by diffusivity and the average size of all scallops, < R >, but also by the capacity of channels to supply Cu for the reaction. Thus, in the mean-field approximation, the basic equation for the distribution function has the following form: ∂f ∂ k

=− ∂t 9 < R2 > − < R >2 ∂R

  f

1 1 − R

 ,

(5.21)

where the rate coefficient k is determined by the incoming flux conditions, which in turn are determined by the channels. The formal solution of the distribution function is ⎧ ⎫ 1/3 R/(bt) ⎪ ⎪  ⎨ ⎬ B R 3 − 4ξ f (t, R) = exp dξ 2 1/3 ⎪ bt (bt) ξ − 3ξ + 9/4 ⎪ ⎩ ⎭ 0

B R ϕ(η), τ = bt, η = , 1/3 τ (bt) S total B = ∞ . π ξ 2 ϕ(η)dη =

(5.22) (5.23)

0

The parameter b should be found self-consistently. A standard integration gives ϕ(η) = 0, η > ϕ(η) =  3 2

  3 , 2

    3 3 · exp − . , 0 < η < 4 3 2 −η 2 −η η

(5.24)

A plot of ϕ(η) versus η is shown in Fig. 5.8. Thus, we have a unique asymptotic solution which satisfies the universal scaling expression in Eq. (5.15). Also we have < η 2 > − < η >2 ∼ = 0.0615, < η > = 3/4, < η 3 > ∼ = 0.5535.

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Chapter 5

. . . . . . . . . .

ϕ (η )versus h .

Fig. 5.8. Plot of ϕ(η) versus η. k ∼ k ∼ k The parameter b = 9(− 2 ) = 0.5535 = . Hence, average cube of grain size is equal to

< R3 >=< ξ 3 > bt ∼ = kt. The averaged size will be 1/3

< R > = < ξ > (bt)

3 ∼ = 4



k t 0.5535

1/3

1/3 ∼ = 0.913 (kt) .

(5.25)

If we take n/ni ≈ 1, Ci = 6/11, D ≈ 10−5 cm2 /sec, δ ≈ 5 ∗ 10−6 cm, C b − C e ≈ 0.001, where the concentration C b is taken for equilibrium of melt with the Cu3 Sn phase, the rate constant k ≈ 4 ∗ 10−13 cm3 /sec. For example, for annealing time t = 300 sec, it gives R ≈ 5 ∗ 10−4 cm, which agrees very well with experimental data. Rate of ripening and growth of R is determined by the incoming flux condition.

5.5 Size Distribution of Scallops The morphology of Cu6 Sn5 IMC was found to be highly faceted when the solder is pure tin, and rounded when the solder has a composition near

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the eutectic. The dependence of IMC morphology on solder composition and reaction temperature has been investigated systematically, prior to measurement of size distribution and growth rate according to reaction time. This is because morphology of IMC will affect the kinetic path of ripening among IMC scallops, and the FDR theory assumed that IMC scallop shape is hemispherical. To investigate the morphology of IMC formation in SnPb/Cu reactions, samples with different solder composition were prepared: pure Sn, 90Sn10Pb, 80Sn20Pb, 70Sn30Pb, 60Sn40Pb, 50Sn50Pb, 40Sn60Pb, 30Sn70Pb, and 20Sn80Pb [17]. Solder with Pb concentration higher than 90 wt% Pb was not investigated since Cu3 Sn will form instead of Cu6 Sn5 . These solder alloys were cut into small pieces weighing about 0.5 mg, and melted in mildly activated flux (197 RMA) to form a spherical bead. Cu foil (99.999%) was cut into 1 cm × 1 cm square pieces, 1 mm thick. Each Cu piece was mechanically polished down to colloidal silica to reduce surface roughness, cleaned ultrasonically with acetone, followed by methanol and DI water to remove organic contaminants on the surface, etched with 5% HNO3 +95% H2 O for 15 seconds to remove native oxide, and rinsed with DI water and followed by drying with nitrogen gas. Then these Cu pieces were quickly immersed into hot 197 RMA flux. Solder wetting on Cu was prepared by dropping the small solder bead on the polished Cu foil at 20 ◦ C above melting temperature of each alloy for 2 min. The 55Sn45Pb solder was selected for measurement of size distribution and growth rate of IMC for 30 sec, 1 min, 2 min, 4 min, and 8 min, at 200◦ C. Reaction time over 10 min was not investigated because of elongation of scallops. To observe IMC scallops in plan view, the unreacted solder was removed by mechanical polishing, followed by selective chemical etching. The selective etching was performed by using 1 part nitric acid, 1 part acetic acid, and 4 parts glycerol at 80◦ C. Since overetching or underetching of solder can change the IMC morphology, different etching times were applied repeatedly to confirm the correct morphology. 5.5.1 Dependence of Cu6 Sn5 Morphology on Solder Composition Figure 5.9 shows the change of IMC morphology as a result of reaction between copper and SnPb solder of different compositions. The observed Cu6 Sn5 IMC morphology is summarized in Table 5.1. When the Pb content of SnPb solder composition was higher than 70 wt%, faceted scallops were observed all over the sample together with some round scallops. When the Pb concentration of solder was within the range from 60 wt% to eutectic composition (34 wt%), only round scallops were observed. When the Pb concentration was further decreased down below 30 wt%, again faceted scallops were observed together with some round scallops. Finally, when the solder became pure tin, only faceted IMC was observed.

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Chapter 5

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Fig. 5.9. SEM images of Cu6 Sn5 IMC formed by wetting reaction with copper and solders having compositions of (a) 20Sn80Pb, (b) 30Sn70Pb, (c) 40Sn60Pb, (d) 50Sn50Pb, (e) 70Sn30Pb, (f) 80Sn20Pb, (g) 90Sn10Pb, and (h) pure Sn.

For eutectic SnPb solder, some samples showed only round scallops. But in other samples, clusters of faceted scallops were observed at the center of solder cap. This also took place when the solder composition was 60Sn40Pb. When a small piece (0.5 mg) was taken from a solder chunk (∼3 g), small inhomogeneity of the solder chunk may cause a 1–2 wt% change of composition in the small piece, in extreme cases. Since the eutectic SnPb solder cap on Cu has a wetting angle of 11o , the amount of solder covering IMC is much thinner at the edge. At the edge of solder cap, the consumption of Sn from the molten solder due to IMC growth will result in higher concentration of Pb. This effect may change IMC morphology across the solder cap, from the center to the edge. To accurately determine the IMC morphology of eutectic SnPb solder, solders with different compositions near the eutectic temperature were melted to control the liquidus phase composition of solder. Solders of 80Sn20Pb, 50Sn50Pb, 30Sn70Pb, and eutectic (63Sn37Pb) composition were reacted with copper at 0.5◦ C above eutectic temperature (183.5◦ C). The temperature control was within ±1◦ C. The solders went through partial melting, and the composition of liquidus phase became very close to the eutectic composition. As

295 Facet

Morphology

Facet

275 Round

255 Round

235 Round

200

Round

200

Facet

210

Facet

225

Facet

240

Facet

250

20Sn80Pb 30Sn70Pb 40Sn60Pb 50Sn50Pb 60Sn40Pb 63Sn37Pb 70Sn30Pb 80Sn20Pb 90Sn10Pb 100Sn

Reaction Temperature (◦ C)

Solder Composition

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Table 5.1. Summary of the observed Cu6 Sn5 IMC morphology.

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Chapter 5 (a)

(b)

(c)

(d)

Fig. 5.10. SEM images of Cu6 Sn5 IMC formed by wetting reaction between copper and solders of (a) 80Sn20Pb, (b) 63Sn37Pb, (c) 50Sn50Pb, and (d) 30Sn70Pb composition at 0.5◦ C above eutectic temperature (183.5◦ C). The temperature control was within ±1◦ C. The solders went through partial melting, and the composition of liquidus phase came very close to the eutectic composition.

shown in Fig. 5.10, the morphology of scallops had round shape, regardless of solder composition. Thus the true morphology of Cu6 Sn5 when SnPb solder composition is eutectic is smooth round morphology. The general idea of classic theories on the formation of faceted or rounded liquid-solid interface is that if the interface is faceted, the adatoms at the surface of solid phase tend to fill nearly all the available surface sites before advancing to the next atomic layer, resulting in atomically flat interface with small number of kink sites. [18, 19] If the crystal surface is round, the interface is more or less atomically rough, possessing a large number of kink sites. To have round shaped scallops, they should have many atomic steps and kinks at the surface. Since step and kink have many broken bonds, scallops tend to have more of them at the surface when the broken bond energy is low. The broken bond energy is low when the IMC/solder interfacial energy is low. The IMC/solder interfacial energy can be estimated by considering the wetting angle between solder and copper. When solder wets copper, copper surface is replaced by IMC/solder interface. Thus IMC/solder interfacial energy is low when solder/copper wetting angle is low, because the molten solder will prefer to spread out to increase the IMC/solder interfacial area. C.Y. Liu investigated effect of SnPb solder composition on the wetting angle of molten SnPb on Cu and found the lowest

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Fig. 5.11. Plot of ln(mean height (μm)) versus ln(time (sec)) along with ln(mean radius) versus ln(time).

wetting angle when solder composition was somewhat higher in Pb than the eutectic composition (around 55 wt% Pb). [20] This is in agreement with the finding shown in Table 1 that scallops had round shape near the eutectic composition. 5.5.2 Size Distribution and Average Radius of Scallops Since scallop morphology showed a dependence on solder composition, the solder with 55Sn45Pb composition was selected to ensure round morphology of scallops for size distribution analysis. The plot of the data of radius versus time to check the agreement with Eq. (5.25) is shown in Fig. 5.11. The growth exponent was found to be 0.35 to 0.33, which is close to 1/3. The magnitude of k in Eq. (5.25) was found to be 1.65 × 10−2 μm3 /sec. The particle size distribution (PSD) is shown in Fig. 5.12. The theoretical curve is the curve of f (r/ < r >), where < r > is average radius, normalized to f (y)dy = 1. The heights of histogram bars were also normalized for comparison with the theoretical curve. The height indicates frequency density, and the total area of bars is 1. The experimental data showed a much better agreement with FDR theory than LSW theory [see Fig. 5.12(a)]. The widths and peak positions of bars are in good agreement with the theoretical curve from FDR theory, but heights are slightly lower than expected, which is found quite often when experimental data are compared to theoretical curves. In the very early stage of the wetting reaction, nucleation of scallops will have a greater effect on the size distribution. Thus, the PSD of short reaction

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Fig. 5.12. Normalized particle size distributions of Cu6 Sn5 scallops. The reaction time is shown in each histogram. Theoretical curves from LSW theory and FDR theory are shown in (a) for comparison.

time was expected to be less ideal. However, the size distribution of 30 sec of reaction already showed very good agreement with the FDR theory [see Fig. 5.12(a)]. Thus, 30 sec is enough time for scallops to reach statistically stable size distribution, and ripening is already dominant over nucleation and growth. The standard deviations of PSD showed very little variation with reaction time (around 0.4). The average scallop height was also measured from cross-sectional SEM images, as shown in Fig. 5.13. The growth exponent of the height was 0.35 and k was 2.40 × 10−2 μm3 /sec. Because cross-sectional images were used to measure the height of scallops, the number of scallops measured is much less than the previous case of measuring the radius of scallops from top-view images. Thus, height measurement is not statistically as reliable as radius measurement, although the growth exponent of height versus time was also close to

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Fig. 5.13. Morphology of cross-sectional scallop at the interface between 55Sn45Pb and Cu.

1/3. The aspect ratio between height and radius remained almost constant. The average value of aspect ratio was 1.05. The constant k in Eq. (5.25) is composed of several thermodynamic parameters. k is given as k=

9 n D(C b − C e )δ , 2 ni Ci

where Ci is Cu concentration in the IMC scallop, C e is Cu concentration in solder melt with stable equilibrium with planar Cu6 Sn5 , and C b is Cu quasi-equilibrium concentration in the vicinity of substrate. n is atomic density in molten solder, ni is atomic density in IMC, and D is diffusivity of Cu in molten solder. We take Ci ≈ 6/11, C b − C e ≈ 0.001, n/ni ≈ 1, D ≈ 10−5 cm2 /sec. Since k = 2.10 × 10−14 cm3 /sec, the channel width is calculated to be δ = 2.54 nm. Since FDR assumed hemispherical scallops, it is of interest to see if there is any change of ripening behavior when scallop morphology deviates a lot from hemispherical shape. Ghosh investigated Ni3 Sn4 formation by the reaction between various eutectic solders and Cu/Ni/Pd metallization [21]. Ni3 Sn4 scallops had extremely faceted morphology, and their size distribution deviated a lot from the FDR theoretical curve. But their growth rate also followed t1/3 . G¨ orlich et al. investigated ripening of Cu6 Sn5 when pure Sn reacted with

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Cu [22]. As mentioned in the last section, the Cu6 Sn5 formed by reaction between pure Sn and Cu has faceted morphology. However, the faceted scallops in top-view micrographs of G¨orlich’s work do not reveal edges as sharp as those in Fig. 5.9. This could be due to the use of too strong metallographic etchant. The fit of size distribution of the faceted Cu6 Sn5 scallops with the FDR theoretical curve is not as good as for the round scallops, but still a moderately good agreement is obtained [22]. The growth exponent was 0.34 for scallop diameter and 0.40 for height. This deviation from the theory can be examined in terms of geometric height-to-radius aspect ratio (height/(width/2)). In G¨ orlich’s work, the scallop aspect ratio was about 0.71 when pure Sn reacted with Cu, and 1.67 for eutectic PbSn reacted with Cu.

5.6 Nano Channels between Scallops One of the most important kinetic parameters in the FDR theory of interfacial ripening is width of the channel between scallops. In the analysis presented in the last section, the channel width was calculated to be about 2.54 nm. The width is much larger than the effective width of a large-angle grain boundary in metals and alloys. The channel is assumed to be wetted by molten solder during the reactive ripening. The experimental value of the width and whether the width can be measured in situ during the reactive ripening are of interest.

References 1. I. M. Lifshiz and V. V. Slezov, “The kinetics of precipitation from supersaturated solid solutions,” J. Phys. Chem. Solids, 19 (1/2), 35–50 (1961). 2. C. Wagner, Z. Electrochem., 65, 581 (1961). 3. V. V. Slezov, “Theory of Diffusion Decomposition of Solid Solution,” Harwood Academic Publishers, Newark, NJ, pp. 99–112 (1995). 4. K. N. Tu, F. Ku, and T. Y. Lee, “Morphology stability of solder reaction products in flip chip technology,” J. Electron. Mater., 30, 1129–1132 (2001). 5. K. N. Tu, T. Y. Lee, J. W. Jang, L. Li, D. R. Frear, K. Zeng, and J. K. Kivilahti, “Wetting reaction vs. solid state aging of eutectic SnPb on Cu,” J. Appl. Phys., 89, 4843–4849 (2001). 6. H. Foell, P. S. Ho, and K. N. Tu, “Cross-sectional TEM of silicon-silicide interfaces,” J. Appl. Phys, 52, 250 (1981). 7. H. Foell, P. S. Ho, and K. N. Tu, “Transmission electron microscopy of the formation of nickel silicides,” Philos. Mag. A, 45, 32 (1982). 8. K. N. Tu, W. K. Chu, and J. W. Mayer, “Structure and growth kinetics of Ni2 Si on Si,” Thin Solid Films, 25, 403 (1975). 9. K.N. Tu, “Selective growth of metal-rich silicide of near noble metals,” Appl. Phys. Lett., 27, 221 (1975).

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10. U. Gosele and K. N. Tu, “Growth kinetics of planar binary diffusion couples: Thin film case versus bulk cases,” J. Appl. Phys., 53, 3252 (1982). 11. S. Herd, K. N. Tu, and K. Y. Ahn, “Formation of an amorphous Rh-Si alloy by interfacial reaction between amorphous Si and crystalline Rh thin films,” Appl. Phys. Lett., 42, 597 (1983). 12. S. Newcomb and K. N. Tu, “TEM study of formation of amorphous NiZr alloy by solid state reaction,” Appl. Phys. Lett., 48, 1436–1438 (1986). 13. D. Turnbull, “Meta-stable structure in metallurgy,” Metall. Trans. A, 12, 695–708 (1981). 14. H. K. Kim and K. N. Tu, “Kinetic analysis of the soldering reaction between eutectic SnPb alloy and Cu accompanied by ripening,” Phys. Rev. B, 53, 16027–16034 (1996). 15. A. M. Gusak and K. N. Tu, “Kinetic theory of flux-driven ripening,” Phys. Rev. B, 66, 115403-1 to -14 (2002). 16. K. N. Tu, A. M. Gusak, and M. Li, “Physics and materials challenges for Pb-free solders,” J. Appl. Phys., 93, 1335–1353 (2003). (Review paper) 17. J. O. Suh, Ph.D. dissertation, UCLA (2006). 18. K. A. Jackson, “Current concepts in crystal growth from the melt,” in “Progress in Solid State Chemistry,” H. Reiss (Ed.), Pergamon Press, New York, pp. 53–80 (1967). 19. D. P. Woodruff, “The Solid–Liquid Interface,” Cambridge University Press, London (1973). 20. C. Y. Liu and K. N. Tu, “Morphology of wetting reactions of SnPb alloys on Cu as a function of alloy composition,” J. Mater. Res., 13, 37–44 (1998). 21. G. Ghosh, “Coarsening kinetics of Ni3 Sn4 scallops during interfacial reaction between liquid eutectic solders and Cu/Ni/Pd metallization,” J. Appl. Phys., 88, 6887–6896 (2000). 22. J. G¨ orlich, G. Schmitz, and K. N. Tu, “On the mechanism of the binary Cu/Sn solder reaction,” Appl. Phys. Lett., 86, 053106 (2005).

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6 Spontaneous Tin Whisker Growth: Mechanism and Prevention

6.1 Introduction Whisker growth on beta-tin (β-Sn) is a surface relief phenomenon of creep [1–16]. It is driven by a compressive stress gradient and occurs at room temperature. Spontaneous Sn whiskers are known to grow on matte Sn finish on Cu. Today, due to the wide application of Pb-free solders on Cu conductors used in the packaging of consumer electronic products, Sn whisker growth has become a serious reliability issue because the Sn-based Pb-free solders are very rich in Sn. The matrix of most Sn-based Pb-free solders is almost pure Sn. The well-known phenomena of tin such as tin-cry, tin-pest, and tin-whisker are receiving attention again. The Cu leadframes in surface mount technology of electronic packaging are finished with a layer of solder for surface passivation and for enhancing wetting during the joining of the leadframes to printed circuit boards. When the solder finish is eutectic SnCu or matte Sn, whiskers are often observed. Some whiskers can grow to several hundred micrometers in length, which are long enough to become electrical shorts between neighboring legs of a leadframe. The trend in consumer electronic products is to integrate systems in packaging, so that elements of devices and parts of components are getting closer and closer together and the probability of shorting by whiskers is becoming much greater. A broken whisker can fall between two electrodes and become a short. How to suppress Sn whisker growth, and how to perform systematic tests of Sn whisker growth in order to understand the driving force, the kinetics, and the mechanism of growth are challenging tasks for the electronic packaging industry today. Due to the very limited temperature range of Sn whisker growth, from room temperature to about 60◦ C, accelerated tests are difficult. This is because if the temperature is lower, the kinetics is insufficient due to slow atomic diffusion, and if the temperature is higher, the driving force is insufficient because of stress relief by lattice diffusion owing to the high homologous temperature of Sn.

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The whisker growth is spontaneous, indicating that the compressive stress needed for the growth is self-generated; no externally applied stress is required. Otherwise, we expect the growth to slow down and stop when the applied stress is exhausted, if it is not applied continuously. Therefore, it is of interest to ask where is the self-generated compressive stress coming from, how can the driving force maintain itself to sustain the spontaneous whisker growth, and also how large must the compressive stress gradient be to grow a whisker? Spontaneous whisker growth is a unique process of creep in which both stress generation and stress relaxation occur simultaneously at room temperature. The three indispensable conditions of Sn whisker growth are: (1) the fast room-temperature diffusion in Sn, (2) the room-temperature reaction between Sn and Cu or another element to form IMC which generates the compressive stress in Sn, and (3) the breaking of the protective surface oxide on Sn. The last condition is needed in order to produce a compressive stress gradient for creep. When the oxide is broken at a weak spot, the exposed free surface is stress-free, so a compressive stress gradient is developed, and creep or the growth of a whisker can occur to relax the stress. While whisker growth occurs at a constant temperature, it does not occur under a constant pressure, therefore we cannot use minimum Gibbs free energy change to describe the growth. Rather an irreversible process of whisker growth will be presented in Section 6.7. Cross-sectional scanning and transmission electron microscopy have been used to examine Sn whiskers, with samples prepared by focused ion beam thinning [14]. Also, x-ray micro-diffraction in synchrotron radiation has been used to study the structure and stress distribution around the root and vicinity of a whisker grown on eutectic SnCu [15]. The growth of Sn whiskers is from the bottom, not from the top, since the morphology of the tip does not change with whisker growth. Many Sn whiskers are long enough to short two neighboring legs of the leadframe shown in Fig. 1.10. It is possible that when there is a high electrical field across the narrow gap between the tip of a whisker and the point of contact on the other leg, just before the tip of the whisker touches the other leg, a spark may cause a fire. The fire may result in failure of the device or a satellite [17–20].

6.2 Morphology of Spontaneous Sn Whisker Growth In Fig. 6.1(a), an enlarged SEM image of a long whisker on the eutectic SnCu finish is shown. The whisker in Fig. 6.1(a) is straight and its surface is fluted. The crystal structure of Sn is body-centered tetragonal with the lattice constant “a” = 0.58311 nm and “c” = 0.31817 nm. The whisker growth direction, or the axis along the length of the whisker, has been found mostly to be the “c” axis, but growth along other axes such as [100] and [311] has also been found.

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(a)

10 μm

(b)

10 μm Fig. 6.1. (a) Enlarged SEM image of a long whisker on the eutectic SnCu finish. (b) Short whiskers or hillocks observed on the pure or matte Sn finish surface.

On the pure or matte Sn finish surface, short whiskers or hillocks were observed as shown in Fig. 6.1(b). The surface of the whisker in Fig. 6.1(b) is faceted. Besides the difference in morphology, the rate of whisker growth on the pure Sn finish is much slower than that on the SnCu finish. The direction of growth is more random too. Comparing the whiskers formed on eutectic SnCu and pure Sn, it seems that the Cu in eutectic SnCu enhances Sn whisker growth. Although the composition of eutectic SnCu consists of 98.7 at % Sn and 1.3 at % Cu, the small amount of Cu seems to have a very large effect on whisker growth on the eutectic SnCu finish. In Fig. 6.2(a), a cross-sectional SEM image of a leadframe leg with SnCu finish is shown. The rectangular core of Cu leadframe is surrounded by an approximately 15-μm-thick SnCu finish. A higher-magnification image of the interface between the SnCu and the Cu, prepared by focused ion beam, is shown in Fig. 6.2(b). An irregular layer of Cu6 Sn5 compound can be seen between the Cu and SnCu. No Cu3 Sn was detected at the interface. The grain size in the SnCu finish is about several micrometers. More importantly, there are Cu6 Sn5 precipitates in the grain boundaries of SnCu. The grain boundary

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(a)

Cu

SnCu

(b) (c)

Fig. 6.2. (a) Cross-sectional SEM image of a leadframe leg with SnCu finish. The rectangular core of Cu is surrounded by an approximately 15-μm-thick SnCu finish. (b) Higher-magnification image of the interface between the SnCu and Cu layers, prepared by focused ion beam. An irregular layer of Cu6 Sn5 compound can be seen between the Cu and SnCu. No Cu3 Sn was detected at the interface. The grain size in the SnCu finish is about several micrometers. More importantly, there are Cu6 Sn5 precipitates in the grain boundaries of SnCu. (c) Cross-sectional SEM image, prepared by focused ion beam, of matte Sn finish on Cu leadframe. While the layer of Cu6 Sn5 compound can be seen between the Cu and Sn, there is much less Cu6 Sn5 precipitate in the grain boundaries of Sn.

precipitation of Cu6 Sn5 is the source of stress generation in the CuSn finish. It provides the driving force of spontaneous Sn whisker growth. We shall address this critical issue of stress generation later. In Fig. 6.2(c), a cross-sectional SEM image of matte Sn finish on Cu leadframe is shown, prepared by focused ion beam. While the layer of Cu6 Sn5 compound can be seen between the Cu and the Sn, there is much less Cu6 Sn5 precipitate in the grain boundaries of Sn. The grain size in the Sn finish is also about several micrometers. The lack of grain boundary Cu6 Sn5 precipitates

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Fig. 6.3. TEM images of the crosssection of whiskers, normal to their length, together with [001] electron diffraction patterns.

is the most important difference between the eutectic SnCu and the pure Sn finish with respect to whisker growth. TEM images of the cross section of whiskers, normal to their length, are shown in Fig. 6.3(a) and (b) together with electron diffraction patterns. The growth direction is the c-axis. There are a few spots in the images which might be dislocations.

6.3 Stress Generation (Driving Force) in Sn Whisker Growth by Cu-Sn Reaction The origin of the compressive stress can be mechanical, thermal, and chemical. The mechanical and thermal stresses tend to be finite in magnitude, so they cannot sustain a spontaneous or continuous growth of whiskers for a

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Sn Whisker Sn Oxide

Crack

σ

(321)

(321)

(210)

(321)

Sn

(321)

(321)

σ

Cu6Sn5 Cu

Fig. 6.4. A fixed volume “V ” in the Sn finish is indicated by the dotted square. It contains an IMC precipitate, and the growth of the precipitate due to the diffusion of a Cu atom into this volume to react with Sn will produce a compressive stress in the volume.

long time. The chemical force is essential for spontaneous Sn whisker growth, but not obvious. The chemical force is due to the room-temperature reaction between Sn and Cu to form the intermetallic compound (IMC) of Cu6 Sn5 . The chemical reaction provides a sustained driving force for spontaneous growth of whiskers as long as the reaction continues with unreacted Sn and Cu [13]. Compressive stress is generated by interstitial diffusion of Cu into Sn and the formation of Cu6 Sn5 in the grain boundary of Sn. When the Cu atoms from the leadframe diffuse into the finish to grow the grain boundary Cu6 Sn5 , as shown in Fig. 6.2(b), the volume increase due to the IMC growth will exert a compressive stress to the grains on both sides of the grain boundary. In Fig. 6.4, we consider a fixed volume “V ” in the Sn finish that contains an IMC precipitate, as shown by the dotted square. The growth of the IMC due to the diffusion of a Cu atom into this volume to react with Sn will produce a stress, σ = −B

Ω , V

(6.1)

where σ is the stress produced, B is the bulk modulus, and Ω is the partial molecular volume of a Cu atom in Cu6 Sn5 (we ignore the molar volume change of Sn atoms in the reaction for simplicity). The negative sign indicates that the stress is compressive. In other words, we are adding an atomic volume into the fixed volume. The assumption of a fixed volume means the constraint of a constant volume. If the fixed volume cannot expand, a compressive stress will occur within the volume. When more and more Cu atoms, say “n” Cu atoms,

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diffuse into the volume, V, to form Cu6 Sn5 , the stress in the above equation increases by changing Ω to n Ω. In diffusional processes, such as the classic Kirkendall effect of interdiffusion in a bulk couple of A and B, the atomic flux of A diffusing into B is not equal to the opposite flux of B diffusing into A. If we assume that A diffuses into B faster than B diffuses into A, we might expect that there will be a compressive stress in B since there are more A atoms diffusing into it than B atoms diffusing out of it. However, in Darken’s analysis of interdiffusion, there is no stress generated in either A or B or no consideration of stress was given. Why? Darken made a key assumption that vacancy concentration is in equilibrium everywhere in the sample [21, 22]. To achieve vacancy equilibrium, we must assume that vacancies (or vacant lattice sites) can be created and/or annihilated in both A and B as needed. Hence, provided that the lattice sites in B can be added to accommodate the incoming A atoms, there is no stress. The addition of a large number of lattice sites implies an increase in lattice planes if we assume that the mechanism of vacancy creation and/or annihilation is by dislocation climb mechanism. It further implies that lattice plane can migrate, which means “Kirkendall shift,” in turn implying marker motion if markers are embedded in the moving lattice planes in the sample. Hence, we have the marker motion equation in Darken’s analysis. However, we must recall that in some cases of interdiffusion in bulk diffusion couples, vacancy may not be in equilibrium everywhere in the sample, so very often Kirkendall void formation has been found due to the existence of excess vacancies [23]. To absorb the added atomic volume by the fixed volume of V in the finish due to the in-diffusion of Cu as considered in Fig. 6.4, we must add lattice sites in the fixed volume. Furthermore, we must allow Kirkendall shift or allow the added lattice plane to migrate, otherwise compressive stress will be generated. Since Sn has a native and protective oxide on the surface, the interface between the oxide and Sn is a poor source and sink for vacancies. Furthermore, the protective oxide ties down the lattice planes in Sn and prevents them from moving. This is the basic mechanism of stress generation in spontaneous Sn whisker growth. For the oxide to be effective in tying down lattice plane migration, the finish cannot be too thick. In a very thick finish, say over 100 μm, there are more sinks in the bulk of the finish to absorb the added volume of Cu. We note that a whisker is a surface relieve phenomenon. When bulk relaxation mechanism occurs, whiskers will not grow. There is a dependence of whisker formation on the thickness of finish. Since the average diameter of whiskers is about a few micrometers, whiskers will grow more frequently on a finish having a thickness of a few micrometers to a few times its diameter. Sometimes it is puzzling to find that Sn whiskers seem to grow on a tensile region of a Sn finish. For example, when a Cu leadframe surface was plated with SnCu, the initial stress state of the SnCu layer right after plating was tensile, yet whisker growth was observed. If we consider the cross section of a

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Cu leadframe leg coated with a layer of Sn as shown in Fig. 6.2(a), the leadframe experienced a heat treatment of reflow from room temperature to 250◦ C and back to room temperature. Since Sn has a higher thermal expansion coefficient than Cu, the Sn should be under tension at room temperature after the reflow cycle. Yet with time, a Sn whisker grows, so it seems that a Sn whisker grows under tension. Furthermore, if a leg is bent, one side of it will be in tension and the other side in compression. It is surprising to find that whiskers grow on both sides, whether the side is under compression or tension. These phenomena are hard to understand until we recognize that the thermal stress or the mechanical stress, whether it is tensile or compressive, is finite. It can be relaxed or overcome quickly by atomic diffusion at room temperature. After that, the continuing chemical reaction will develop the compressive stress needed to grow whiskers. So the chemical force is dominant and persistent. When we consider the driving force of spontaneous whisker growth on Sn or SnCu solder finish on Cu, the compressive stress induced by chemical reaction at room temperature is essential. Room-temperature reaction between Sn and Cu was studied by using thin film samples; see Chapter 3. The idea of compressive stress induced by the growth of a grain boundary precipitate of Cu6 Sn5 has a few variations. One is the wedge model proposed by Lee and Lee [24] that the Cu6 Sn5 phase between the Cu and Sn has a wedge shape in growing into the grain boundaries of Sn. The growth of the wedge will exert a compressive stress to the two neighboring Sn grains, same as splitting a piece of wood with a wedge. So far, very few wedge-shaped IMCs have been observed in XTEM; for example, see Fig. 6.2(b).

6.4 Effect of Surface Sn Oxide on Stress Gradient Generation and Whisker Growth To discuss the effect of surface oxide on Sn whisker growth, we shall refer to the effect on Al hillock growth. In an ultrahigh vacuum, no surface hillocks were found on Al surfaces under compression [25]. Hillocks grow on Al surfaces only when the Al surface is oxidized, and Al surface oxide is known to be protective. Without surface oxide in an ultrahigh vacuum, the free surface of Al is a good source and sink of vacancies, so a compressive stress can be relieved uniformly on the entire surface or on the surface of every grain of the Al based on the Nabarro–Herring model of lattice creep or Coble model of grain boundary creep. To apply these models to a Sn finish without oxide, as depicted in the top diagram in Fig. 6.5, the relaxation can occur in each of the grains by diffusion to the free surface of each grain since there is a stress gradient. The free surfaces are stress-free and are effective source and sink of vacancies. Therefore, the relaxation is uniform over the entire Sn film surface; all the grains just become slightly thicker. Consequently, no localized growth of hillocks or whiskers will take place.

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Vacancy flow

161

Surface with no oxide Uniform relaxation No hillocks No whiskers

Fig. 6.5. Nabarro–Herring model of lattice creep or Coble model of grain boundary creep in a Sn layer without surface oxide. The schematic diagram shows that when the surface has no oxide, relaxation of stress can occur in each of the grains by atomic diffusion to the free surface of each grain.

We note that a whisker or hillock is a localized growth on a surface. To have a localized growth, the surface cannot be free of oxide, and the oxide must be a protective oxide so that it effectively blocks all the vacancy sources and sinks on the surface. Furthermore, a protective oxide also means that it pins down the lattice planes in the matrix of Sn (or Al), so that no lattice plane migration can occur to relax the stress in the volume, V, considered in Fig. 6.4. Only those metals which grow protective oxides, such as Al and Sn, are known to have serious hillock or whisker growth. When they are in thin film or thin layer form, the surface oxide can pin down the lattice planes near the surface easily. On the other hand, it is obvious that if the surface oxide is very thick, it will physically block the growth of any hillock and whisker. No hillocks or whiskers can penetrate a very thick oxide or a thick coating. No break means no free surface and no stress gradient. Thus, a necessary condition of whisker growth is that the protective surface oxide must not be too thick so that it can be broken at certain weak spots on the surface to form free surfaces, and from these spots whiskers grow to relieve the stress. In Fig. 6.6(a), a focused ion beam image of a group of whiskers on the SnCu finish is shown. In Fig. 6.6(b), the oxide on a rectangular area of the surface of the finish was sputtered away by using a glancing incidence ion beam to expose the microstructure beneath the oxide. In Fig. 6.6(c), a higher-magnification image of the sputtered area is shown, in which the microstructure of Sn grains and grain boundary precipitates of Cu6 Sn5 are clear. Due to the ion channeling effect, some of the Sn grains appear darker than the others. The Cu6 Sn5 particles distribute mainly along grain boundaries in the Sn matrix, and they are brighter than the Sn grains due to less ion channeling. The diameter of the whiskers is about a few micrometers, comparable to the grain size in the SnCu finish. In ambient, we assume that the surface of the finish and the surface of every whisker are covered with oxide. The growth of a hillock or whisker is an eruption from the oxidized surface. It has to break the oxide. When the Sn matrix is under compression, its oxide is under tension, so the oxide breaks under tension. The stress that is needed to break the oxide may be the

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Fig. 6.6. (a) Focused ion beam image of a group of whiskers on the SnCu finish. (b) The oxide on a rectangular area of the surface of the finish was sputtered away by using a glancing incidence ion beam to expose the microstructure beneath the oxide. (c) Higher-magnification image of the sputtered area, in which the microstructure of Sn grains and grain boundary precipitates of Cu6 Sn5 are clear.

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minimum stress needed to grow whiskers. It seems that the easiest place to break the oxide is at the base of the whisker. Then to maintain the growth, the break must remain open so that it behaves like a stress-free free surface and vacancies can be supplied continuously from the break and can diffuse into the Sn layer to sustain the long-range diffusion of the Sn atoms needed to grow the whisker. In case a part of the break is healed by oxide, the growth of the whisker will lead to a turn in whisker growth direction toward the healed side, and as a consequence, a bent whisker is formed. In Fig. 6.4, we have depicted that the surface of the whisker is oxidized, except for the base. The surface oxide of the whisker serves the very important purpose of confinement so that the whisker growth is essentially a one-dimensional growth. The surface oxide of the whisker prevents it from growing in the lateral direction, thus it grows with a constant cross section and has the shape of a pencil. Also, the oxidized surface may explain why the diameter of a Sn whisker is just a few micrometers. This is because the gain in strain energy reduction in whisker growth is balanced by formation of the surface of the whisker. By balancing the strain energy against the surface energy in a unit length of the whisker, πR2 ε = 2πRγ, we find that R=

2γ , ε

(6.2)

where R is radius of the whisker, γ is surface energy per unit area, and ε is strain energy per unit volume. Since strain energy per atom is about four to five orders of magnitude smaller than the chemical bond energy or surface energy per atom of the oxide, the diameter of a whisker is found to be several micrometers, which is about four orders of magnitude larger than the atomic diameter of Sn. For this reason, it is very difficult to have spontaneous growth of nano-diameter Sn whiskers. The broken oxide at the base is a key assumption in the model of spontaneous Sn whisker growth to be discussed in Section 6.6. The free surface exposed by the broken oxide produces the stress gradient to drive the whisker growth.

6.5 Measurement of Stress Distribution by Synchrotron Radiation Micro-diffraction The micro-diffraction apparatus in the Advanced Light Source (ALS), at Lawrence Berkeley National Laboratory, was used to study Sn whiskers grown on SnCu finish on Cu leadframe at room temperature [15]. The white radiation beam was 0.8 to 1 μm in diameter and the beam step-scanned over an area of 100 μm by 100 μm in steps of 1 μm. Several areas of the SnCu finish were scanned and those areas were chosen so that in each of them there was a whisker, especially the areas that contained the root of a whisker. During

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Fig. 6.7. Low-magnification SEM image of an area of finish in which a whisker is circled and scanned.

the scan, the whisker, and each grain in the scanned area, can be treated as a single crystal to the beam. This is because the grain size is larger than the beam diameter. At each step of the scan, a Laue pattern of a single crystal is obtained. The crystal orientation and the lattice parameters of the Sn whisker and the grains in the SnCu matrix surrounding the root of the whisker were measured by the Laue patterns. The software in ALS is capable of determining the orientation of each of the grains, and displaying the distribution of the major axis of these grains. Using the lattice parameters of the whisker as stress-free internal reference, the strain or stress in the grains in the SnCu matrix can be determined and displayed. Figure 6.7 shows a low-magnification picture of an area of finish wherein a whisker is circled and scanned. Figure 6.8 shows an in-plane orientation map of the angle between the (100) axis of Sn grains and the x-axis of the laboratory frame. An image of the whisker is seen. The x-ray micro-diffraction study shows that in a local area of 100 μm × 100 μm the stress is highly inhomogeneous with variations from grain to grain. The finish is therefore under a biaxial stress only on the average. This is because each whisker has relaxed the stress in the region surrounding it. But the stress gradient around the root of a whisker does not have a radial symmetry. The numerical value, and the distribution of stress, are shown in Fig. 6.9, where the root of the whisker is at the coordinates of x = −0.8415 and y = −0.5475 as shown in Fig. 6.8. Overall, the compressive stress is quite low, of the order of several mega pascals, but we can still see the slight stress gradient going from the whisker root area to the surroundings. This means that the stress level just below the whisker is slightly less compressive than the surrounding area. This is because the stress near the whisker has been

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In-plane Orientation Map [Angle between (100) and X] 90.00 85.50 81.00 76.50 72.00 67.50 63.00 58.50 54.00 49.50 45.00 40.50 36.00 31.50 27.00 22.50 18.00 13.50 9.000 4.500 0

X (mm)

-0.82

-0.84

-0.86

-0.88

-0.90 -0.60 -0.58 -0.56 -0.54 -0.52 -0.50

Y (mm) Fig. 6.8. Plot of in-plane orientation map of the angle between the (100) axis of Sn grains surrounding the whisker (shown in Fig. 6.7) and the x-axis of laboratory reference frame.

-0.830

35.00 32.38 29.75 27.13 24.50 21.88 19.25 16.63 14.00 11.38 8.750 6.125 3.500 0.8750 -1.750 -4.375 -7.000 -9.625 -12.25 -14.88 -17.50

X (mm)

-0.835 -0.840 -0.845 -0.850 -0.855

-0.56

- 0.55

-0.54

Y (mm) Fig. 6.9. Stress distribution around the root of a whisker, which is at the coordinates of x = −0.8415 and y = −0.5475.

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(Unit : Mpa) -0.5400

-0.5415

-0.5430

-0.5445

-0.5460

-0.5475

-0.5490

-0.5505

-0.5520

-0.5535

-0.5550 -0.03

-0.8340

-2.82

-3.21

-2.26

0.93

0.93

-0.23

-8.17

2.22

1.49

1.6

-0.8355

-2.26

-2.64

-2.64

-1.04

1.37

1.37

-1.31

0.87

0.87

0.87

-0.7

-0.8370

-2.53

-3.21

-3.21

-2.64

-1.04

3.61

0.75

0.87

0.7

0.7

-0.19

-0.8385

-7.37

-9.62

-6.57

-2.64

3.61

4.52

3.61

0.29

-1.31

0

-4.79

-0.8400

-7.37

-8.22

-6.57

-1.18

0.75

4.23

0.75

-2.25

-2.27

-2.91

-6.91

-0.8415

-4.17

-4.84

-4.17

-1.81

-0.67

.000

-1.96

-1.96

-3.74

-5.08

-5.08

-0.8430

-4.17

-4.17

-3.63

-1.81

-1.81

-2.29

-2.29

-1.96

-1.96

-3.27

-3.27

-0.8445

-4.14

-4.17

-3.86

-3.63

-2.79

-4.64

-4.78

-0.84

-1.4

-1.49

-3.27

-0.8460

-3.14

-3.63

-3.86

-3.63

-3.13

-4.78

-4.78

0.04

0.04

-1.41

-2.33

-0.8475

-4.14

-4.49

-4.49

-4.64

-3.86

-6.64

-1.72

3.55

3.55

-0.41

-2.33

-0.8490

-3.33

-5.67

-6.20

-6.29

-2.66

-2.08

-1.72

-1.79

0

-1.79

-3.73

Whisker Fig. 6.10. Plot of −σzz , which is the deviatoric component of the stress along the surface normal. The total strain tensor is equal to the sum of the deviatoric strain tensor and the dilatational strain tensor. In the figure, the whisker part is removed in order to observe the stress around the whisker root more clearly. The absolute value of stress in the whisker is higher than that in the surrounding grains. If we assume the whisker to be stress-free, the surface of SnCu finish is under compressive stress.

relaxed by whisker growth. In Fig. 6.10 the light-colored arrows indicate the directions of local stress gradient. Some circles next to each other in Fig. 6.10 show a similar stress level, which most likely means that they belong to the same grain. Figure 6.10 shows a plot of −σzz , which is the deviatoric component of the stress along the surface normal. The total strain tensor is equal to the sum of the deviatoric strain tensor and the dilatational strain tensor. The latter is measured from energy of Laue spot using monochromatic beam and the former is measured from deviation in crystal Laue pattern using white radiation beam. εij = εdeviatoric + εdilatational      ε11 ε12 ε13   δ     =  ε21 ε22 ε23  +  0  ε ε32 ε33   0 31

0 δ 0

 0  0  , δ

(6.3)

where the dilatational strain δ = 13 (ε11 + ε22 + ε33 ) and εii = εii + δ. We explain in the following the measurements of these two strain tensors. The deviatoric strain tensor is calculated from the deviation of spot positions

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in the Laue pattern with respect to their “unstrained” positions. The latter is obtained from an “unstrained” reference. By assuming that the whisker is strain-free, we used the Sn whisker itself as the unstrained reference and calibrated the sample–detector distance and the tilt of detector with respect to the beam. The geometry is fixed. From the Laue spot positions of the strained sample, we can then measure any deviation of their positions from the calculated positions if the sample has zero strain. The transformation matrix which relates the unstrained to the strained Laue spot positions is then calculated and the rotational part is taken out. The deviatoric strain can then be computed from this transformation matrix. The more spots we have in the Laue pattern, the more accurate will be the deviatoric strain tensor determined. We note that the deviatoric strain is related to the change in the shape of the unit cell, but the unit cell volume is assumed to be constant and it consists of five independent components. The sum of the three diagonal components should be equal to zero. To obtain the total strain tensor, we must add the dilatational strain tensor to the deviatoric strain tensor. The dilatational component is related to the change in volume of the unit cell and it consists of a single component of expansion or shrinkage, δ, in the last equation. In principle, if the deviatoric strain tensor is known, only one additional measurement is needed, i.e., the energy of a single reflection is required to obtain this single dilatational component. We can use the monochromatic beam to do so. From the orientation of the crystal and the deviatoric strain we can calculate for each reflection what the energy of E0 for zero dilatational strain would be. We scan the energy by rotating the monochromator around this energy E0 and watch the intensity of the peak of interest on the CCD camera. The energy which maximizes the intensity of the reflection is the actual energy of the reflection. The difference in the observed energy and the E0 gives the dilatational strain. Since σxx + σyy + σzz = 0 by definition, −σ zz is a measure of the in-plane stress (note that for a blanket film, with free or passivated surface, on the average the total normal stress σzz = 0), from that σb (biaxial stress) = (σxx + σyy )/2 = (σxx + σyy )/2 − σzz = −3σzz /2 . This relation is always true on the average. A positive value of −σzz indicates an overall tensile stress whereas a negative value indicates an overall compressive stress. However, the measured stress values, corresponding to a strain of less than 0.01%, are only slightly larger than the strain/stress sensitivity of the white beam Laue technique (sensitivity of the technique is 0.005% strain). No very long range stress gradient has been observed around the root of a whisker, indicating that the growth of a whisker has released most of the local compressive stress in the distance of several surrounding grains. In Fig. 6.9, the whisker part is removed in order to observe the stress around the whisker root more clearly. The absolute value of stress in the whisker is higher than that in the surrounding grains. If we assume the whisker to be stress-free, the surface of SnCu finish is under compressive stress.

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6.6 Stress Relaxation (Kinetic Process) in Sn Whisker Growth by Creep: Broken Oxide Model Whisker growth is a unique creep phenomenon in which stress generation and stress relaxation occur simultaneously. Therefore, we must consider two kinetic processes of stress generation and stress relaxation and their coupling by irreversible processes [13]. About the two processes in whisker growth, the first is the diffusion of Cu from the leadframe into the Sn finish to form grain boundary precipitates of Cu6 Sn5 . This kinetic process generates the compressive stress in the finish. The second is the diffusion of Sn from the stressed region to the stress-free region at the root of a whisker to relieve the stress. The distance of diffusion in the second process is much longer than the first and also the diffusivity in the second process is slower too, so the second process tends to control the rate in the growth of whiskers. Since the reaction of Sn and Cu occurs at room temperature, the reaction continues as long as there are unreacted Sn and Cu. The stress in the Sn will increase with the growth of Cu6 Sn5 in it. Yet the stress cannot build up forever; it must be relaxed. Either the added lattice planes in the volume, V, in Fig. 6.4 must migrate out of the volume, or some Sn atoms will have to diffuse out from the volume to a stress-free region. Room temperature is a relatively high homologous temperature for Sn, which melts at 232◦ C, hence the self–diffusion of Sn along Sn grain boundaries is fast at room temperature. Therefore, the compressive stress in the Sn induced by the chemical reaction at room temperature can also be relaxed at room temperature by atomic rearrangement via self grain boundary diffusion. The relaxation occurs by the removal of atomic layers of Sn normal to the stress, and these Sn atoms can diffuse along grain boundaries to the root of a stress-free whisker to feed its growth. This is a creep process driven by a stress gradient. It is worth noting that creep at a slow rate is driven by a stress gradient, not by a stress. Typically creep is defined as a time-dependent deformation under a constant load. If we take a rectangular bar and apply a constant load or stress at its two ends, it will creep. However, in the normal direction of the free surface of the four sides of the bar, there is no stress. Hence, there is a stress gradient between the end surfaces and the side surfaces. The driving force of atomic migration in creep is stress gradient as given in the Nabarro–Herring model. Under a hydrostatic tension or compression, there may be random walk of atoms, but no creep. The diffusion of Cu into the Sn finish generates a compressive stress. However, a uniform compressive stress will not cause creep; we need a mechanism to produce a compressive stress gradient in the Sn finish. In Section 6.4, we discussed that a broken surface oxide can produce a free surface which is stress-free by definition. Hence, a stress gradient is developed in the broken oxide model and creep or whisker growth can occur.

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Furthermore, because of the stress gradient, creep is a process which does not occur under the condition of constant pressure, therefore we cannot minimize Gibbs free energy change to describe the creep process. It is an irreversible process.

6.7 Irreversible Processes To formulate the irreversible process, we have the linear phenomenological relation between the fluxes Ji and the forces Xj ,  Ji = Lij Xj , j

where Lij are the phenomenological coefficients. In pairing the forces of chemical reaction and stress, the fluxes of Cu and Sn atoms can be given as J1 = L11 X1 + L12 X2 , J2 = L21 X1 + L22 X2 ,

(6.4)

where J1 = JCu is atomic flux of Cu in units of atoms/cm2 sec, J2 = JSn is atomic flux of Sn in units of atoms/cm2 sec, X1 = −∇μ1 is chemical potential gradient, and X2 = −∇μ2 is stress potential gradient. We note that stress potential is a chemical potential too. To examine X1 , we consider the chemical reaction of 6Cu + 5Sn → Cu6 Sn5 We have the chemical affinity as given in Section 3.2.5, A = μη − 6 μCu − 5 μSn

(6.5)

where μη is the chemical potential of the Cu6 Sn5 compound molecule and μCu and μSn are the chemical potentials of the unreacted Cu and Sn, respectively. X1 = −∇G |T,p = A∇n

(6.6)

under constant temperature and pressure, where n is number of moles or molecules of Cu6 Sn5 formed. Since our model of the growth of Cu6 Sn5 is by interstitial diffusion of Cu into the finish and reaction with Sn at the interface of Cu6 Sn5 and Sn, we assume it is an interfacial-reaction-controlled reaction. We recall that in Section 3.2.2, the growth of Cu6 Sn5 at room temperature was measured to be linear with time. On X2 , we recall that the stress induced by the diffusion of Cu into Sn can be represented by σ = −B(Ω/V ), so the stress is assumed to be hydrostatic.

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Since the stressed region is near a free surface, the stress state may not be isotropic, nevertheless it is a vector. We define X2 = −∇σΩ,

(6.7)

where σ and Ω are the stress and atomic volume (or partial molar volume in a binary system), respectively. The driving force is the stress gradient. We emphasize that J1 , J2 , X1 , and X2 are vectors, so Lij are tensors. The pair of flux equations is Cu Cu Dij Dij (A∇n)i + CCu (−∇σΩ)i , kT kT Sn Dij (−∇σΩ)i . = CSn M21 (A∇n)i + CSn kT

JiCu = CCu JiSn

(6.8)

In the second equation of Eq. (6.4), the meaning of the first term after the equals sign, i.e., the L21 X1 term, is to describe the flux of Sn driven by chemical reaction to form Cu6 Sn5 . Because we are considering the formation of Cu6 Sn5 within Sn, so Sn is everywhere and no long-distance diffusion of Sn is needed in the formation of Cu6 Sn5 . Actually, we have assumed that the reaction occurs by interstitial diffusion of Cu to a grain boundary precipitate of Cu6 Sn5 and by the reaction with Sn at the interface of the Cu6 Sn5 precipitate. We assume that the growth of the precipitate is interfacial-reaction-controlled. Hence, we have L21 X1 = CSn K21 = CSn M21 X1 = CSn M21 (A∇n)i ,

(6.9)

where K21 = M21 X1 is the interfacial reaction constant and it has the dimension of velocity, and M21 is the mobility of the interface between Cu6 Sn5 and Sn. The choice of M21 must fulfill Onsager’s reciprocity relation of L12 = L21 . How to choose M21 requires an analysis of the interfacial reaction process, which has been discussed in Section 3.2.5. On the other cross term or the last term in the first equation of Eq. (6.4), it means the Cu flux in the Sn finish driven by stress gradient. Since the chemical potential is much larger than the stress potential, this cross term is negligible. Therefore, in modeling the growth of a Sn whisker in the next section, we shall assume a very simple model of creep.

6.8 Kinetics of Grain Boundary Diffusion-Controlled Whisker Growth When the surface oxide is broken around a grain whose surface normal is near a close-packed direction and surrounded by high angle grain boundaries, this grain can be pushed out by pressure in the Sn layer. If the deposited Sn finish has a texture, this grain should not be a part of the texture because it should

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be surrounded by high-angle boundaries to facilitate pressure transmission through the grain boundary structure. This may explain why there are only a few places from where whiskers nucleate and grow. The growth of a whisker occurs at the root; it is being pushing out. What is the growth mechanism? When Sn atoms diffuse to the root of a whisker, how can they be incorporated into the root of a whisker? The growth can be regarded as grain growth because the whisker is a single crystal and it grows longer with time. In the classical model of normal grain growth, the basic process is grain boundary migration against its curvature by atoms jumping from one grain across a grain boundary to the grain on the other side of the grain boundary. Yet in whisker growth, it is unclear if there is grain boundary migration at the root. Using a series of cross-sectional SEM images, the microstructure of the root of a whisker and its surrounding grains have been observed [15]. It suggests that most likely there is no migration of the grain boundaries between the whisker and the surrounding grains during the growth of the whisker. Whisker growth is a grain growth with very little grain boundary migration at the root of the whisker. It seems that Sn atoms arrive at the root region along grain boundaries and they can be incorporated into the root of a whisker without jump across a grain boundary as in normal grain growth. This is because the Sn atoms are already diffusing in grain boundaries. Hence, no grain boundary migration is needed. The atomistic model of incorporation of atoms into the whisker for its growth requires more study; it may take place at the kink sites on the bottom side of the whisker, similar to stepwise growth on a free crystal surface in epitaxial growth of thin films. We must mention that there are vacancies coming in from the surface crack at the root area to assist the growth. To study the grain boundary structure around the root of a whisker, crosssectional TEM samples for direct observation of the root of a whisker were prepared. Figure 6.11 is a SEM image of the preparation of cross-sectional TEM samples by focused ion beam etching. Focused ion beam (FIB) was used to etch two rectangular holes into the finish separated by a thin wall as shown in Fig. 6.11. The location of the two holes was selected to have a whisker on top of the wall between them. After etching, the thickness of the wall is less than 100 nm so that it is transparent to 100-keV electrons. The thin wall contains a thin vertical section of the whisker, the root of the whisker, and a couple of grains surrounding the whisker. Figure 6.12 is a FIB image and the corresponding bright-field TEM image of the thin slice. Figure 6.13 is a higher-magnification bright-field TEM image of a grain boundary between a whisker and a neighboring grain in the root region of the whisker. The grain boundary plane appears straight. Sometimes the surface of a whisker along its length has the appearance of very fine sawtooth steps. It indicates that the growth of the whisker may have the ratcheted motion instead of a smooth motion. The ratcheted motion may be due to a repetitive breaking of the oxide at the root of the whisker. The growth of the whisker has to break the oxide and expose a free surface.

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Fig. 6.11. SEM image of the preparation of cross-sectional TEM samples by focused ion beam etching. Focused ion beam was used to etch two rectangular holes into the finish separated by a thin wall. The thin wall will be cut out and examined by TEM.

Yet the free surface in ambient will form oxide right away, so the oxide has to be broken repetitively and may be in ratcheted steps. The atomistic mechanism of the growth of a whisker will require more experimental study and analysis.

Fig. 6.12. FIB image and the corresponding bright-field TEM image of the thin wall containing the crosssection of a whisker and grains around its root.

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Fig. 6.13. Bright-field cross-sectional TEM image of a grain boundary between a Sn whisker and a neighboring grain in the root region of the whisker. The grain boundary plane appears straight.

To analyze the growth kinetics of a whisker, we assume a two-dimensional model in cylindrical coordination. The distribution of whiskers is assumed to have a regular arrangement so that each occupies a diffusional field of diameter of 2b, as shown in Fig. 6.14. We assume that the whisker has a constant diameter of 2a and a separation of 2b and it has a steady-state growth in the diffusional field which can be described by a two-dimensional continuity equation in cylindrical coordinates. We recall that stress can be regarded as an energy density and a density function obeys the continuity equation [13, 26]. ∇2 σ =

∂ 2 σ 1 ∂σ = 0. + ∂r2 r ∂r

(6.10)

The boundary conditions are σ = σ0

at r = b, σ = 0 at r = a.

The solution is σ = Bσ0 ln(r/a), where B = [ln(b/a)]−1 and σ0 is the stress

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Fig. 6.14. The whiskers are assumed to have a regular arrangement so that each occupies a diffusional field of diameter of 2b.

in the Sn film. Knowing the stress distribution, we can evaluate the stress gradient, Xr = −

∂σΩ . ∂r

(6.11)

Then the flux to grow the whisker is calculated at r = a, J =C

D Bσ0 D Xr = . kT kT a

(6.12)

We note that in a pure metal, C = 1/Ω. The volume of materials transported to the root of the whisker in a period of dt is JAdtΩ = πa2 dh,

(6.13)

where A = 2πas is the peripheral area of the growth step at the root, s is the step height, and dh is the increment of height of the whisker in dt. Therefore, the growth rate of the whisker is dh 2 σ0 ΩsD . = dt ln(b/a) kT a2

(6.14)

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To evaluate the whisker growth rate, we need to know the self-diffusivity of Sn. The self-lattice diffusivities in the direction parallel and normal to the c-axis are slightly different and are given as D// = 7.7 × exp(−25.6 kcal/RT ) cm2 /sec, D⊥ = 10.7 × exp(−25.2 kcal/RT ) cm2 /sec. The lattice diffusivities at room temperature are about 10−17 cm2 /sec. This means that in 1 year, or t = 108 sec, the diffusion distance calculated by using x2 ∼ = Dt is about 1 μm. Thus, the lattice diffusivities are too slow to be responsible for whisker growth at room temperature. Self-grain-boundary diffusion of Sn has not been determined. If we assume that the large-angle grain boundary diffusivity requires one-half of the activation energy of lattice diffusion given above, we obtain a self-grain-boundary diffusivity of about 10−8 cm2 /sec. Using a = 3 μm, b = 0.1 mm, σ0 Ω = 0.01 eV (at σ0 = 0.7 × 109 dyne/cm2 ), kT = 0.025 eV at room temperature, s = 0.3 nm, and D = 10−8 cm2 /sec (the self-grain-boundary diffusivity of Sn at room temperature), we obtain a growth rate of 0.1 × 10−8 cm/sec. At this rate, we expect a whisker of 0.3 mm after 1 year, which agrees well with the observed result. Since we assume grain boundary diffusion, we note that there are only several grain boundaries connecting the base of a whisker to the rest of the Sn matrix. Hence, in taking the total atomic flux which supplies the growth of a whisker to be JAdtΩ, where A = 2πas, we have assumed that the flux goes to the entire periphery of the whisker “2πa” but only for a step height of “s” for its growth. The values of b and σ0 used in the above calculation were taken from Ref. 12. These values differ from what we found in Ref. 15, where the stress is about 10 MPa or 108 dyne/cm2 but the diffusion distance is only a few grain diameters. Using the latter values, the calculated growth rate is about the same.

6.9 Accelerated Test of Sn Whisker Growth One of the most annoying behaviors of a Sn whisker is that it does not grow when we want it to grow, yet it grows when we do not want it to . The growth of just one whisker is a threat of reliability. In order to predict the lifetime of Pbfree solder finish without whisker growth, we should conduct accelerated tests as in most reliability problems. An accelerated test can be conducted at larger driving force or faster kinetics, provided that the mechanism of failure remains the same. Typically, tests at higher temperatures are performed to obtain the activation energy of the rate controlling process, which then enables us to extrapolate the lifetime at the device operation temperature. For Sn whisker growth, while it is possible to conduct the tests up to 60◦ C, the rate of whisker growth is still quite slow due to slow atomic diffusion. When the temperature

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approaches 100◦ C, the diffusion is fast enough to relieve the stress. Hence, we encounter a situation of competition between driving force and kinetics. Although we can add Cu to Sn to have a faster whisker growth as in eutectic SnCu solder, the rate is still not fast enough. Besides, we need to isolate the effect of Cu on whisker growth. We consider here the use of electromigration to conduct accelerated tests of whisker growth. The subject of electromigration will be covered in Chapter 8. In the classic Blech test structure of electromigration in Al short strips, atoms of Al are being driven from the cathode to the anode and a compressive stress is built up at the anode end of a stripe and hillocks grow there. The advantage of using electromigration to study whisker growth is that not only can we vary the applied current density (larger driving force), we can also use higher temperatures (faster kinetics). Hence, we can control both the driving force as well as the kinetics. Figure 6.15 shows the growth of a Sn whisker at the anode of a test sample of pure Sn under electromigration [27, 28]. Measuring the growth rate and the diameter of the whisker, we obtain the volume change per unit time of the whisker, V = JAdtΩ, where J is the electromigration flux in units of number

Fig. 6.15. The sequential growth of a Sn whisker at the anode of a test sample of pure Sn under electromigration.

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of atoms/cm2 -sec, A is the cross-section of the whisker, dt is unit time, and Ω is atomic volume. Knowing J, we have D J =C kT



 dσΩ ∗ + Z ejρ dx

(6.15)

where C = 1/Ω in pure Sn, D is diffusivity, kT is thermal energy, σ is stress at the anode and we may assume the stress at the cathode is zero, dσ/dx is the stress gradient along the short stripe of Sn of length dx, Z ∗ is the effective charge number of the diffusing Sn atoms in electromigration, e is electron charge, j is current density, and ρ is resistivity of Sn at the test temperature. We can determine σ from the last equation. To determine the stress gradient for the whisker growth, we note that the electrons flow out of the stripe at the bottom corner of the anode. It has the highest stress since Sn atoms are being pushed to this point. When the oxide on the upper corner of the anode is broken, a vertical stress gradient is generated and it is this stress gradient which drives whisker or hillock growth at the anode end. Figure 6.16 shows a SEM image of whiskers at the anode end of a set of stripes of eutectic SnPb driven by electromimgration. The stripes were cut by focused ion beam, and it was found that whiskers grow at the anode ends.

Fig. 6.16. SEM image of whiskers at the anode end of a set of stripes of eutectic SnPb driven by electromigration. (Courtesy of Prof. Chih Chen, National Chiao Tung University.)

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If we keep the stripe dimension and the applied current density unchanged, we may determine the activation energy of whisker growth when the growth as a function of temperature is obtained. However, the accelerated test may not be meaningful until we can confirm that the whisker driven by electromigration has the same growth behavior and mechanism as the whisker grown spontaneously on the Pb-free finish.

6.10 Prevention of Spontaneous Sn Whisker Growth On the basis of the analysis presented in this chapter, we have three indispensable conditions of spontaneous whisker growth: (1) the room-temperature grain boundary diffusion of Sn in Sn, (2) the room-temperature reaction between Sn and Cu to form Cu6 Sn5 , which provides the compressive stress or the driving force for whisker growth, and (3) the breaking of the protective surface Sn oxide. If we remove any one of them, we will have in principle no whisker growth. However, we have found from the synchrotron radiation study that it takes only a very small stress gradient to grow Sn whiskers, hence it is difficult to prevent whisker growth. National Electronics Manufacturing Initiative (NEMI) has recommended a solution to remove condition (2) by introducing a diffusion barrier of Ni between the Cu leadframe and the Pb-free finish to prevent Cu from reacting with Sn. To remove condition (3) is unrealistic since we must have no oxide on the finish, and to do so we must keep the sample in ultrahigh vacuum. We propose here to remove condition (1) by blocking the grain boundary diffusion of Sn. Furthermore, if we can remove both conditions (1) and (2), it is even better. Since Sn whisker growth is an irreversible process which couples stress generation and stress relaxation, it is essential to uncouple them in order to prevent Sn whisker growth. In other words, we must remove both stress generation and stress relaxation. Stress generation can be removed by using a diffusion barrier to block the diffusion of Cu into Sn. Besides Ni, we can also use Cu3 Sn intermetallic compound. In Chapter 3, we have shown that above 60◦ C, Cu3 Sn will form between Cu and Sn. A heat treatment of the finish on Cu leadframe above 60◦ C will form Cu6 Sn5 and Cu3 Sn between them to serve as diffusion barrier. Up to now, no solution to remove stress relaxation has been given. In other words, how to prevent the creep process or the diffusion of Sn atoms to the whiskers is unknown. We can do so by using another diffusion barrier. Since we have to block the diffusion of Sn atoms from every grain of Sn in the finish, it is nontrivial. We may succeed by adding several percent of Cu or another element into the matte Sn or the eutectic SnCu solder. We recall that the Cu concentration in the eutectic SnCu is only 1.3 at.% or 0.7 wt%. We shall add about several (3 to 7) wt% of Cu. The reason for doing so is to have enough precipitation of Cu6 Sn5 in all the grain boundaries in the finish, so that every grain of Sn in the finish will be coated by a grain boundary layer of Cu6 Sn5 .

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Fig. 6.17. A layered structure of a Sn-Cu finish on a Ni diffusion barrier on a Cu leadframe. Each of the Sn grains is surrounded by Sn-Cu precipitates.

Thus, the grain boundary coating becomes a diffusion barrier to prevent the Sn atoms from leaving each of the grains in the Sn. When there is no diffusion of Sn, there is no growth of Sn whisker since the supply of Sn is cut. Figure 6.17 depicts a layered structure of a Sn-Cu finish on a Ni diffusion barrier on a Cu leadframe. The optimal concentration of Cu in the finish requires more study. Cross-sectional SEM and FIB images of the samples should be obtained to investigate the microstructure of electroplated Sn-Cu finish, having a high concentration of Cu. There are two key reasons for the selection of Cu (or another element) to form grain boundary precipitate in Sn. The first is that when the Sn has so much supersaturated Cu, it will not take more Cu from the leadframe. The second is that the addition of Cu will not affect strongly the wetting property of the surface of the finish. Without a good property of wetting, it cannot be used as finish on the leadframe since the most important property of a surface finish is that it should be wetted easily by molten solder with the help of flux. For low-reliability devices, it will be sufficient to plate the Sn-3 to 7 wt% Cu finish directly on Cu leadframe without the Ni diffusion barrier. As previously mentioned, when the Sn is supersaturated with Cu, it will not take more Cu from the leadframe. The advantage is that it is a low-cost process without the additional deposition of Ni. For high-reliability devices, we should keep the Ni diffusion barrier and deposit the Sn-Cu finish on the Ni. The combination has diffusion barriers to prevent the diffusion of both Cu and Sn. It will be much more effective than just using one of them. Whether the addition of several percent of Cu is effective or not may depend or how the Cu is added, e.g., by using nanosize Cu particles. Whether there are other problems must be studied, such as the brittleness of the grain boundary precipitates. Whether there are other elements better than Cu for the purpose of whisker prevention also remains to be studied. It is known that the addition of several percent of Pb will prevent Sn whisker growth since Pb is soft and it tends to reduce the local stress gradients in Sn. Also, because Sn-Pb is a eutectic system, the eutectic microstructure consists of two separated and intermixing phases, and they block each other in terms of long-range diffusion. Thus, adding several percent of the other soft elements

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that have eutectic phase diagram with Sn, such as Bi, In, and Zn, may be a good choice. If there is no Sn diffusion, we expect no Sn whisker growth. Finally, the simplest method to avoid whisker problem may be to spray the entire packaging structure with a thick coating.

References 1. 2. 3. 4. 5. 6.

7. 8. 9. 10. 11.

12. 13.

14.

15.

16.

17.

C. Herring and J. K. Galt, Phys. Rev. 85, 1060 (1952). J. D. Eshelby, Phys. Rev., 91, 755 (1953). F. C. Frank, Philos. Mag., 44, 854 (1953). G. W. Sears, Acta Metall., 3, 367 (1955). S. Amelinckx, W. Bontinck, W. Dekeyser, and F. Seitz, Philos. Mag., 2, 355 (1957). W. C. Ellis, D. F. Gibbons, and R. C. Treuting, “Growth of metal whiskers from the solid,” in “Growth and Perfection of Crystals,” R. H. Doremus, B. W. Roberts, and D. Turnbull (Eds.), John Wiley, New York, pp. 102– 120 (1958). A. P. Levitt, in “Whisker Technology,” Wiley–Interscience, New York (1970). U. Lindborg, “Observations on the growth of whisker crystals from zinc electroplate,” Metall. Trans. A, 6, 1581–1586 (1975). I. A. Blech, P. M. Petroff, K. L. Tai, and V. Kumar, “Whisker growth in Al thin-films,” J. Cryst. Growth, 32, 161–169 (1975). N. Furuta and K. Hamamura, “Growth mechanism of proper tin-whisker,” Jpn. J. Appl. Phys., 8, 1404–1410 (1969). R. Kawanaka, K. Fujiwara, S. Nango, and T. Hasegawa, “Influence of impurities on the growth of tin whiskers,” Jpn. J. Appl. Phys. Part I, 22, 917–922 (1983). K. N. Tu, “Interdiffusion and reaction in bimetallic Cu-Sn thin films,” Acta Metall., 21, 347–354 (1973). K. N. Tu, “Irreversible processes of spontaneous whisker growth in bimetallic Cu-Sn thin film reactions,” Phys. Rev. B, 49, 2030–2034 (1994). G. T. T. Sheng, C. F. Hu, W. J. Choi, K. N. Tu, Y. Y. Bong, and L. Nguyen,“Tin whiskers studied by focused ion beam imaging and transmission electron microscopy,” J. Appl. Phys., 92, 64–69 (2002). W. J. Choi, T. Y. Lee, K. N. Tu, N. Tamura, R. S. Celestre, A. A. MacDowell, Y. Y. Bong, and L. Nguyen, “Tin whiskers studied by synchrotron radiation micro-diffraction,” Acta Mater., 51, 6253–6261 (2003). W.J. Boettinger, C.E. Johnson, L. A. Bendersky, K.-W. Moon, M.E. Williams, and G.R. Stafford, Whisker and hillock formation in Sn, SnCu, and Sn-Pb lectrodeposists; Acta Mater., 53, 5033–5050 (2005). I. Amato, “Tin whiskers: The next Y2K problem?” Fortune magazine, vol. 151, issue 1, p.27 (2005).

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18. R. Spiegel, “Threat of tin whiskers haunts rush to lead-free,” Electronic News, 03/17/2005. 19. http://www.nemi.org/projects/ese/tin whisker.html 20. W. J. Choi, G. Galyon, K. N. Tu, and T. Y. Lee, “The structure and kinetics of tin whisker formation and growth on high tin content finishes,” in “Handbook of Lead-Free Solder Technology for Microelectronic Assemblies,” K. J. Puttlitz and K. A. Stalter (Eds.), Marcel Dekker, New York (2004). 21. P. G. Shewmon, “Diffusion in Solids,” McGraw–Hill, New York (1963). 22. D. A Porter and K. E. Easterling, “Phase Transformations in Metals and Alloys,“ Chapman & Hall, London (1992). 23. K. Zeng, R. Stierman, T.-C. Chiu, D. Edwards, K. Ano, and K. N. Tu, “Kirkendall void formation in SnPb solder joints on bare Cu and its effect on joint reliability,” J. Appl. Phys., 97, 024508–1 to –8 (2005). 24. B.-Z. Lee and D. N. Lee, “Spontaneous growth mechanism of tin whiskers,” Acta Mater., 46, 3701–3714 (1998). 25. C. Y. Chang and R. W. Vook, “The effect of surface aluminum oxide film on thermally induced hillock formation,” Thin Solid Films, 228, 205–209 (1993). 26. K. N. Tu and J. C. M. Li, “Spontaneous whisker growth on lead-free solder finishes,” Mater. Sci. and Eng. A, 409, 131–139 (2005). 27. C. Y. Liu, C. Chen, and K. N. Tu, “Electromigration of thin stripes of SnPb solder as a function of composition,” J. Appl. Phys., 80, 5703–5709 (2000). 28. S. H. Liu, C. Chen, P. C. Liu, and T. Chou, “Tin whisker growth driven by electrical currents,” J. Appl. Phys., 95, 7742 (2004).

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7 Solder Reactions on Nickel, Palladium, and Gold

7.1 Introduction In this chapter we shall discuss solder reaction with Ni, Pd, and Au. These metals and Cu are being used in under-bump metallization (UBM) or in bond pad, yet the role of Cu and Ni differs from that of Pd and Au. For Cu and Ni, the formation of intermetallic compound (IMC) of Cu-Sn or Ni-Sn is chosen so as to achieve metallic bonds in a solder joint. For Pd and Au, they have been used as surface coating to passivate the surface of Cu and Ni as well as to enhance wetting reaction. Typically, the surface of Cu is protected by a thin film of Au and that of Ni is protected by a film of Pd. Often Au is used on Ni too. The reaction between solder and Ni has received much attention because the reaction rate is about two orders of magnitude slower than that of Cu, so the effect of spalling of IMC on thin film Ni is less serious and Ni can also serve as a diffusion barrier of Cu, as discussed in Section 6.10. Why the reaction rate between Ni and solder is much slower than that between Cu and solder has been an interesting kinetic question. The answer is unclear at the moment; mostly it is because the supply of Ni to the reaction may be much slower than Cu. The supply may depend on the diffusion of Ni along the interface between Ni3 Sn4 and Ni and also on the solubility of Ni in the molten solder [1–3]. The reaction between Au and Sn forms Sn4 Au and consumes a large fraction of the solder and it is well-known that if a solder joint has more than 5% Au, it will have the problem of “cold joint” or brittle joint due to the presence of a large volume fraction, over 25%, of the Sn4 Au intermetallic in the joint. The reaction between Pd and eutectic SnPb solder has the fastest rate of IMC formation in wetting reaction as well as in solid-state aging. The growth rate is about 1 μm/sec in the wetting reaction, so the reaction can consume an entire solder joint in 1 minute when the joint diameter is below 50 μm. This fast reaction has the potential to transform a solder joint completely into

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an intermetallic joint. This will become a critical issue in flip chip technology when the solder bump size is below 25 μm. A common nature of reactions of molten solder on Pd and Au is the very fast rate of IMC formation. It is due to the effect of IMC morphology on the kinetics of growth. In the following, we shall discuss solder reaction with Ni first, followed by the reactions with Au and Pd.

7.2 Solder Reactions on Bulk and Thin-Film Ni The reaction rate of molten eutectic SnPb on Ni is about 100 times slower than that of molten eutectic SnPb on Cu [1–32]. The growth of Ni3 Sn4 between the molten solder and Ni has the scallop-type morphology, and the diffusivity of Ni in molten solder should be nearly the same as that of Cu. But why the formation rate is slow is unclear. Because of this slow wetting reaction, electronic packaging companies have attempted to replace Cu-based thin-film UBM by Ni-based thin-film UBM. Ghosh [7, 8] has recently optimized the thermodynamic descriptions of the Ni-Sn and Ni-Pb binary systems and calculated several isothermal sections of the Ni-Sn-Pb ternary phase diagram by extrapolation. The calculation obtained phase diagrams of SnPbNi at 170◦ C, and 240◦ C in weight percentage [see Fig. 7.1(a) and (b)]. They are rather similar to each other except the zones of the liquid solder + Ni3 Sn4 and liquid solder + Ni3 Sn4 + (Pb) in the diagram at 240◦ C. The solubility of Ni in the molten solder is expected to be higher than that in the solid solder. The first compound to form in the wetting reaction will be Ni3 Sn4 , and the molten solder that is in equilibrium with the compound may contain up to 65 wt% Pb, but the solid solder may contain up to 88 wt% Pb. Since Ni3 Sn4 is unstable on Ni, the other compounds such as Ni3 Sn2 and Ni2 Sn may form between them, provided that temperature is high enough and time is long enough. Figure 7.2(a) to (c) show SEM images of the three-dimensional morphology of Ni3 Sn4 formation between eutectic SnPb and Ni at 240◦ C for 1, 10 and 40 min, respectively. It is a tilt view of the interface after a preferential etching of Pb. The scallops of Ni3 Sn4 can be seen. The rate of consumption of Ni by the wetting reaction in the temperature range of 200 to 240◦ C is shown in Fig. 7.3. Compared it to the rate of consumption of Cu by the same solder as shown in Fig. 2.13, the Ni is much slower. For example, after 40 min at 240◦ C, the size (linear dimension) of the Ni3 Sn4 scallops is about 2 μm. In Fig. 2.5, the size of Cu6 Sn5 scallops after 40 min at 200◦ C is already 10 μm, so in three-dimensional growth, the latter is at least 100 times faster. The slow reaction rate of Ni with molten eutectic SnPb solder has been of keen interest in UBM applications. Nevertheless, when a Ni/Ti thin film was reacted by the molten solder, the spalling phenomenon was observed. Figure 7.4(a) to (c) show cross-sectional SEM images of eutectic SnPb on 200 nm Ni/50 nm Ti at 220◦ C for 1, 5, and 40 min, respectively. The absence

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Fig. 7.1. Calculated phase diagrams of SnPbNi at 170◦ C (a), 240◦ C (b), 400◦ (c), and enlargement of the phase diagram near the SnPb eutectic point (d) in weight percentage. (Courtesy of Dr. K. Zeng, TI.)

of Ni3 Sn4 at the interface can be seen in Fig. 7.4(b) and (c). Although the spalling process is slower than that of Cu6 Sn5 , it does occur. The above discussions are for the wetting reaction when solder is in the molten state. When solder is in the solid state, the dissolution of Ni into the solder should result in the formation of Ni3 Sn4 [see Fig. 7.1(a)]. However, if the temperature is too low ( 10−5

(e.g., liquid nitrogen temperature), electromigration cannot occur because there is no atomic mobility of diffusion, even though there is a driving force. The contribution of thermal effect can be recognized by the fact that electromigration in a bulk eutectic solder bump occurs at about three-quarters of its melting point in absolute temperature, electromigration in a polycrystalline Al thin-film line occurs at less than one-half of its melting point in absolute temperature, and electromigration in a Cu thin-film line having bamboo-type grain structure occurs at about one-quarter of its melting point in absolute temperature. At these homologous temperatures, there are atoms which undergo random walks in the bulk of the solder bump, in the grain boundaries of the Al thin-film line, and on the free surface of Cu damascene interconnect, respectively, and these are the atoms which take part in electromigration under the applied current. Indeed, we assume the Si device working temperature to be 100◦ C, which is about three-quarters of the melting point of solders, about slightly less than half of the melting point of Al, and about one-quarter of the melting point of Cu. In this homologous temperature scale, lattice diffusion, grain boundary diffusion, and surface diffusion occur predominantly at threequarters, one-half, and one-quarter of the absolute temperature of a metal, respectively. [16] Table 8.1 lists the melting points and diffusivities which are relevant to the electromigration behaviors in Cu, Al, and eutectic SnPb. The diffusivities for Cu and Al were calculated on the basis of the following equations from the master log D versus Tm /T plot for face-centered cubic metals (see Fig. 15 in Ref. 26): Dl = 0.5 exp(−34Tm /RT ), Dgb = 0.3 exp(−17.8Tm /RT ), Ds = 0.014 exp(−13Tm /RT ),

(8.1)

where Dl , Dgb , and Ds are respectively lattice diffusivity, grain boundary

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diffusivity, and surface diffusivity [25–27]. Tm is the melting point, and the units of 34 Tm , 17.8 Tm , and 13 Tm are in cal/mole. As shown in Table 8.1, at 100◦ C the lattice diffusivity of Cu and Al are insignificantly small, and the grain boundary diffusivity of Cu is three orders of magnitude smaller than the surface diffusivity of Cu. At 350◦ C the difference between surface diffusivity and grain boundary diffusivity of Cu is much less, indicating that we cannot ignore the latter. The lattice diffusivity of eutectic SnPb (not a face-centered cubic metal) at 100◦ C given in Table 8.1 is an average value of tracer diffusivity of Pb and Sn in the alloy [29]. It depends strongly on the lamellar microstructure of the eutectic sample. Since a solder joint 100 μm in diameter has typically a few large grains, the smaller diffusivity is better for our consideration. The surface diffusivity of Cu, grain boundary diffusivity of Al, and lattice diffusivity of the solder are actually rather close at 100◦ C. To compare atomic fluxes transported by these three kinds of diffusion in a metal, we should have multiplied the diffusivity by their corresponding crosssectional area of path of diffusion. But the outcome is the same. Table 8.1 also shows the homologous temperature of Cu, Al, and solder at the device operation temperature of 100◦ C; they are 0.25, 0.5, and 0.82, respectively. The homologous temperature of solder is very high. It means that the application of solder joint in devices will be affected by the hightemperature properties of the solder, or controlled by thermally activated processes such as diffusion. For example, the mechanical properties of solder joints will be influenced greatly by creep. This is a very important point to remember when we study the mechanical properties of solder joints. In face-centered cubic metals such as Al and Cu, atomic diffusion is mediated by vacancies. A flux of Al atoms driven by electromigration to go to the anode, requires a flux of vacancies to go to the cathode in the opposite direction. If we can stop the vacancy flux, we stop electromigration. To maintain a vacancy flux we must supply vacancies continuously. Hence, we can stop a vacancy flux by removing the sources or supplies of vacancies. Within a metal interconnect, dislocations and grain boundaries are sources of vacancies, but the free surface is generally the most important and effective source of vacancies. For Al, its native oxide is protective, which means that the interface between the metal and its oxide is not a good source or sink of vacancies. This is also true for Sn. When vacancies are removed without replenishment or to be added without an effective sink, equilibrium vacancy concentration cannot be maintained, so back stress will be generated. This topic is discussed in Section 8.5. If the atomic or vacancy flux is continuous in the interconnect, i.e., the anode can supply vacancies and the cathode can accept them continuously, and if there is no flux divergence in between, vacancy concentration is in equilibrium everywhere, then there will be no electromigration-induced damage such as void and extrusion formation. In other words, without mass flux divergence no electromigration damage will occur in an interconnect when fluxes of atoms and vacancies can pass through it uniformly. Hence, atomic or mass

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flux divergence is a necessary condition concerning electromigration failure in real devices. The most common mass flux divergences are the triple points of grain boundaries and interfaces between dissimilar materials. Since a solder joint has two interfaces, one at the cathode and one at the anode, they are the common failure sites, especially the cathode interface where accumulation of vacancies to form voids occurs. In summary, electromigration involves both atomic and electron fluxes. Their distribution in interconnects is the most important concern in electromigration damage. In a region where both distributions are uniform, there will be electromigration, but no electromigration-induced damage because of lack of flux divergence. Concerning atomic or vacancy fluxes, the most important factor is the temperature scale shown in Table 8.1. Atomic diffusion must be thermally activated. The second is the design and processing of the interconnect structure. Nonuniform distribution or divergence in interconnects occurs at microstructure irregularities such as grain boundary triple points and interphase interfaces, and they are the sites of failure initiation. In the following sections, the effects of microstructure, solute, and stress on electromigration in solder joints will be discussed in turn. The mean-time-to-failure analysis on the basis of void and hillock formation due to flux divergence will also be discussed. Concerning the electron flux, the current density must be high enough for electromigration to occur. Because transistors in devices are turned on by pulsed direct current, for transistor based devices such as computers we consider only electromigration under direct current. A brief review of electromigration by pulsed direct current can be found in Ref. 18. While a uniform current distribution is expected in straight lines, nonuniform current distribution occurs at corners where a conducting line turns, at interfaces where conductivity changes, and also around voids or precipitates in a matrix. One of the most important factors that affects electromigration in a flip chip solder joint is the unique line-to-bump geometry, where a very large change of current density takes place from the line to the bump, which in turn leads to a large current crowding at the contact between the line and the bump. The effect of current crowding on electromigration-induced damage in the solder bump will be discussed below. Furthermore, because of current crowding and rectified interfaces, AC electromigration can occur in flip chip solder joints. In a uniform current distribution region, only DC electromigration occurs, but in a nonuniform current distribution region, both DC and AC electromigration may occur.

8.3 Electron Wind Force of Electromigration The electrical force acting on a diffusing atom (ion) proposed by Huntington and Grone is taken to be [1] ∗ Fem = Z ∗ eE = (Zel∗ + Zwd )eE,

(8.2)

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(b)

electron flow Fig. 8.4. Schematic diagram of electromigration of a diffusing atom (a) before, and (b) at the activated state, where it possesses a very large scattering cross section.

where e is the charge of an electron and E is the electric field (E = ρj, where ρ is resistivity and j is current density) and Z ∗ is the effective charge number of electromigration. Zel∗ can be regarded as the nominal valence of the diffusing ion in the metal when the dynamic screening effect is ignored; it is responsible ∗ for the field effect and Z∗el eE is called the direct force. Zwd is an assumed charge number representing the momentum exchange effect between electrons ∗ and the diffusing ion, and Zwd eE is called the electron wind force, and it is generally found to be of the order of 10 for a good conductor, so the electron wind force is much greater than the direct force for electromigration in metals. Hence, in electromigration, the enhanced flux of atomic diffusion is in the same direction as electron flux. To appreciate the electron wind force, we depict in Fig. 8.4(a) the configuration of a shaded Al atom and a neighboring vacancy in a face-centered cubic lattice structure before they exchange position along a direction. They have four nearest neighbors in common, including the two shown by the broken circles, one on top and one on the bottom of the close-packed atomic plane. When the shaded atom is diffusing halfway toward the vacancy as depicted in Fig. 8.4(b), it is at the activated state, sitting at a saddle point while displacing the four nearest-neighbor atom. Since the saddle point is not part of the lattice periodicity, the atom at the saddle position is out of its equilibrium position and will make a much larger contribution to the resistance to electrical current than a normal lattice atom. In other words, it experiences a greater electron scattering and hence a greater electron wind force which will push it to an equilibrium position, the vacant site. The diffusion of the atom is enhanced in the direction of the electron flow. We note that the diffusing atom will experience the electron wind force, not just at the saddle point, but all the way from the beginning to the end in the entire jumping path of the diffusion. To estimate the electron wind force, the ballistic approach to the scattering process was developed by Huntington and Grone [1]. The model postulates a transition probability of free electrons per unit time from one free electron state to another free electron state due to the scattering by the diffusing atom.

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The force, the momentum transfer per unit time, is calculated by summing over the initial and final states of the scattered electrons. The step-by-step derivation of the model is presented in Appendix C. Below, a simple derivation is given. During elastic scattering of electrons by a diffusing atom, the system momentum is conserved. The average change in electron momentum in the transport direction is equal to 2me < υ >, where me is the electron mass and < υ > is the mean velocity of electrons in the direction of current flow. The force on the ion induced by the scattering is −→ 2me < υ > Fwd = , τcol

(8.3)

where τcol is the mean time interval between two successive collisions. The net momentum lost per second per unit volume of electrons to the diffusing ions is then 2nme < υ > /τcol , and the force on a single diffusing ion is −→ 2nme < υ > Fwd = , τcol Nd

(8.4)

where n is the electron density and Nd is the density of diffusing ions. The electron current density can be written as j = −ne < υ > .

(8.5)

Substituting < υ > in Eq. (8.5) into Eq. (8.4), we obtain 2me j −→ Fwd = − eτcol Nd    n ρd =− eE, Nd ρ

(8.6)

where ρ = E/j is the total resistivity of a conductor, ρd = m/ne2 τcol is the metal resistivity due to the diffusing atoms, and E is the applied electrical field. Aside from the electron “wind” force, the electric field E will produce a direct force on the diffusing ion to be given by − → Fd = Zel∗ eE,

(8.7)

where Zel∗ can be regarded as the nominal valance of the metal ion when the dynamical scattering effect around the ion is ignored. Thus, the total force

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will be      N ρd −−→ FEM = Zel∗ − Z eE, Nd ρ

(8.8)

where N is the atomic density of the conductor and n = N Z is used. Equation (8.8) can be written as −−→ FEM = Z ∗ eE

(8.9)

     N ρd Z ∗ = Zel∗ − Z . Nd ρ

(8.10)

and

Z ∗ is called the effective charge number of the ion in electromigration. Electromigration model based on the ballistic scattering of electrons is the first and simplest model of the phenomenon of electromigration. Theoretical understanding is further developed by contributions of numerous researchers to date. In spite of these theoretical developments, the model developed by Huntington and Grone, especially the drift velocity of electromigration, is employed as the theoretical basis in nearly all experimental studies of electromigration. For example, the drift velocity is taken as vd = M F =

D ∗ Z ejρ. kT

(8.11)

This indicates that if we measure the drift velocity using short stripes (to be discussed in Sections 8.5 and 8.6) and know the diffusivity, D, we will be able to calculate Z ∗ . The above model shows that the effective charge number can be given in terms of specific resistivities of a diffusing atom and a normal lattice atom,

∗ Zwd

ρd N d m0 = −Z ρ , m∗ N

(8.12)

where ρ = m0 /ne2 τ and ρd = m∗ /ne2 τd are the resistivity of the equilibrium lattice atoms and the diffusing atoms, respectively. m0 and m∗ are the free electron mass and effective electron mass, respectively, and we can assume that they are equal, and τ and τd are relaxation times. In an fcc lattice, there are 12 equivalent jump paths along the < 110 > directions. For a given current direction, the average specific resistivity of a diffusing atom must be corrected

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by a factor of one-half. By rewriting Eq. (8.10), we have ⎡ ⎢1 Z ∗ = −Z ⎣ 2

⎤ ρd ⎥ N d m0 ρ m∗ − 1 ⎦ , N

(8.13)

where Zel has been taken as Z, the nominal valence of the metal atom. This is the equation of Huntington and Grone for the effective charge number of electromigration. To calculate Z ∗ , we need to know the specific resistivity of a diffusing atom, or its ratio to that of a lattice atom.

8.4 Calculation of the Effective Charge Number If the specific resistivity of an atom in a metal is assumed to be proportional to the elastic cross section of scattering, which in turn is assumed to be proportional to the average square displacement from equilibrium, or < x2 >, the cross section of a normal lattice atom can be estimated from the Einstein model of atomic vibration in which the energy of each mode is 1 1 mω 2 < x2 >= kT, 2 2

(8.14)

where the product m ω2 is the force constant of the vibration, and m and ω are atomic mass and angular vibrational frequency, respectively. To obtain the cross section of scattering of a diffusing atom, < x2d >, we assume that the atom and its surrounding as shown in Fig. 8.4(b) have acquired the motion energy of diffusion, ΔHm , which is independent of temperature, 1 mω 2 < x2d >= ΔHm . 2

(8.15)

Then, the ratio of the last two equations gives the ratio of cross section of scattering, < x2d > 2ΔHm = . < x2 > kT

(8.16)

This shows that the ratio varies inversely with temperature. This dependence comes from the well-known fact that the resistivity of normal metals varies linearly with temperature above the Debye temperature. Substituting the last equation into the equation of Z*, we obtain [9] Z ∗ = −Z



 ΔHm m0 − 1 . kT m∗

(8.17)

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Chapter 8 Table 8.2. Comparison of the measured and calculated values of Z* Measured Z ∗

Temp (◦ C)

ΔHm (eV)b

Monovalent Au Ag Cu

−9.5 to −7.5 −8.3 ± 1.8 −4.8 ± 1.5

850 to 1000 795 to 900 870 to 1005

0.83 0.66 0.71

−7.6 to −6.6 −6.2 to −5.5 −6.3 to −5.4

Trivalent Al

−30 to −12

480 to 640

0.62

−25.6 to −20.6

−47

250

0.54

−44

Metal

Quadrivalent Pb

a

c

Calculated Z ∗

a

Data of measured Z* taken from Huntington (1974), where the correlation factor is ignored. Data of ΔHm taken from Table 3.1. c Data of calculated Z* are obtained by using Eq. (14.12). b

In the above equation, the numerical factor of 1/2 is canceled when the probability of averaging jumps in a given direction (i.e., the direction of electron flow) from among the 12 paths in an fcc metal is taken into account. Now the value of Z* can be calculated at a given temperature by using the last equation. The calculated values of Z* agree quite well with those measured for Au, Ag, Cu, Al, and Pb (see Table 8.2). For example, at 480◦ C, the measured and calculated Z* for Al (taking ΔHm = 0.62 eV/atom) are about −30 and −26, respectively. The temperature dependence of Z* calculated for Au is also found to agree well with the measured values (see Fig. 8.5). Roughly speaking, we can see from Fig. 8.4(b) that the diffusing atom at the activated state possesses a scattering cross section of about 10 atoms, therefore its effective charge number will be roughly equal to 10Z, where Z is its nominal valence number, so we have the order of magnitude of Z* of −10, −30, and −40 for Cu (noble metal), Al, and Pb (or Sn), respectively.

8.5 Effect of Back Stress on Electromigration and Vice Versa Figure 8.6 is a schematic diagram of a short Al strip patterned on a baseline of TiN. In electromigration, a high current density of electrons moves from left to right and it transports Al atoms from the cathode to the anode, leading to depletion or void formation at the cathode and pileup or hillock formation at the anode. Hence, the damage of electromigration can be recognized directly. The depletion rate at the cathode can be measured and the drift velocity of electromigration can be deduced. Furthermore, it was found that the longer the strip, the more the depletion at the cathode side in electromigration.

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Fig. 8.5. The temperature dependence of Z* calculated for Au is found to agree well with the measured values.

But below a “critical length,” there was no observable depletion as shown in Fig. 8.1. The dependence of depletion on strip length was explained by the effect of back stress. In essence, when electromigration transports Al atoms in a strip from cathode to anode, the latter will be in compression and the former in tension. On the basis of the Nabarro–Herring model of equilibrium vacancy concentration in a stressed solid, the tensile region has more and the compressive region has less vacancies than the unstressed region, so there is a vacancy concentration gradient decreasing from the cathode to the anode.

Fig. 8.6. Schematic diagram of a set of short Al strips patterned on a baseline of TiN.

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The gradient induces an atomic flux of Al diffusing from the anode to the cathode, and it opposes the Al flux driven by electromigration from the cathode to the anode. The vacancy concentration gradient depends on the length of the strip; the shorter the strip, the greater the gradient. At a certain short length defined as the “critical length,” the gradient is large enough to balance electromigration so no depletion at the cathode and no extrusion at the anode occur [10–13]. In analyzing this stress effect, irreversible processes have been proposed by combining electrical and mechanical forces on atomic diffusion. The electrical force proposed by Huntington and Grone is taken to be Fem = Z ∗ eE.

(8.2)

The mechanical force is taken as the gradient of chemical potential in a stressed solid, Fme = −∇μ = −

dσΩ , dx

(8.18)

where σ is hydrostatic stress in the metal and Ω is atomic volume. In essence, it is a creep process, driven by a stress gradient. Thus, we have a pair of phenomenological equations for atomic flux and electron flux [9]: D dσΩ D ∗ +C Z eE, kT dx kT dσΩ Je = −L21 + nμe eE, dx

Jem = −C

(8.19a) (8.19b)

where Jem is atomic flux in units of atoms/cm2 -sec, and Je is electron flux in units of coulomb/cm2 -sec. C is the concentration of atoms per unit volume, and n is the concentration of conduction electrons per unit volume. D/kT is atomic mobility and μe is electron mobility. L21 is the phenomenological coefficient of irreversible processes and it contains the deformation potential. In Eq. (8.19a), if we take Jem = 0, there is no net electromigration flux or no damage. In other words, it reaches a steady state in an irreversible process. The expression for the “critical length” is obtained as Δx =

ΔσΩ . Z ∗ eE

(8.20)

Since the resistance of the conductor can be taken to be constant at a constant temperature, we have instead the “critical product” or “threshold product” of “jΔx” by rearranging the current density from the right-hand side to the

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left-hand side of the equation: jΔx =

ΔσΩ . Z ∗ eρ

(8.21)

Under a constant applied current density, a bigger value of critical product in Eq. (8.21) means a longer critical length, in turn a larger back stress in Eq. (8.20). For Al and Cu interconnects, we take j = 106 A/cm2 and Δx = 10 μm, and we have a typical value of critical product about 1000 A/cm. We note that while the back stress in the above is induced by electromigration, the interaction between an applied stress and electromigration is the same; for example, an applied compressive stress at the anode will retard electromigration. If we consider a short strip deposited on an insulating substrate and take Je = 0 in Eq. (8.19b), we have N∗ = −



1

dφ

at Je = 0, Ω dσ

(8.22)

where dφ/dσ is deformation potential defined as the electrical potential per unit stress difference at zero current. By using Onsager’s reciprocity relation, L12 = L21 , we obtain dφ Z ∗ Dρe =− . dσ kT The dimensions of dφ/dσ and N * are cm3 /C and C

(8.23) −1

, respectively.

8.6 Measurement of Critical Length, Critical Product, Effective Charge Number To calculate the critical length in Eq. (8.20) for Al strips, we take the stress at the elastic limit of Al, σ = −1.2 × 109 dyn/cm2 ; Ω = 16 × 10−24 cm3 ; e = 1.6 × 10−19 C; Ex = jρ = 1.54 V/cm, where j = 3.7 × 105 A/cm2 and ρ = 4.15 × 10−6 Ω cm at 350◦ C. Substituting these values into Eq. (8.20), we obtain ΔxAl =

−78μm . Z∗

By taking Z ∗ = −26 for bulk Al, we have the critical length of 3 μm, which is of the right order of magnitude, but shorter than the experimental value found in between 10 and 20 μm. Since the Al strips are polycrystalline thin films, grain boundary diffusion might have played a dominant role in electromigration, and Z* for atomic diffusion in grain boundaries might be smaller than in the bulk. Note that the critical length can be measured experimentally in a long strip

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by extending the time of electromigration to a sufficiently long period until the mass transport or depression at the cathode end ceases. The temperature dependence of the critical length can be examined by substituting Z* into Eq. (8.20), obtaining Δx =

ΔσΩ  . ΔHm m0 −Z − 1 ejρ kT m∗ 

(8.24)

For normal metals whose electrical resistivity increases linearly with temperature above the Debye temperature, the last equation shows that the critical length is rather insensitive to temperature, provided that ΔHm  kT so that the unity in the denominator can be dropped. To calculate the critical product in Eq. (8.21), we take j = 106 A/cm2 and Δx = 10 μm for Al stripes, and we have a typical value of critical product of about 1000 A/cm. To calculate the effective charge number, we can use Eq. (8.20) provided that we have measured Δx and Δσ. On the other hand, if we use a very long strip and ignore the back stress effect and measure the drift velocity, we have  D ∗ D0 Q vd = M F = (8.25) Z ejρ = exp − Z ∗ ejρ. kT kT kT This indicates that if we know the diffusivity, D, we will be able to calculate Z*. Furthermore, if we measured the drift velocity at several temperatures, we can take the natural logarithm of the last equation and obtain  D0 ∗ Q ln(vd T ) = ln eZ jρ − . (8.26) k kT Thus, by plotting ln (vd T ) versus 1/kT , we can determine the activation energy of the diffusion process in electromigration.

8.7 Why Is There Back Stress in Electromigration? Although the Blech structure has been used very often in experimental studies of electromigration in Al strips, there has been a question about the origin of the back stress. If we confine a short strip by rigid walls as shown in Fig. 8.7,

Fig. 8.7. A short strip confined by rigid walls.

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we can envisage easily the compressive stress at the anode induced by electromigration. In a fixed or constant volume of V at the anode, the stress change in the volume by adding atoms or adding ΔV into it by electromigration is Δσ = −B

ΔV ΔV ΔC = −B VΩ − B , V C Ω

(8.27)

where B is bulk modulus and Ω is atomic volume. The negative sign indicates that the stress is compressive. In other words, we are adding atomic volume into the fixed volume. If the fixed volume cannot expand, a compressive stress will occur. Theoretically, a fixed volume means the constraint of a constant volume. Thus, the implicit assumption in the origin of back stress is the assumption of a constant volume constraint. Why we can have such a constraint in Al short strips will be explained below. In a fixed volume confined within rigid walls, the compressive stress increases with the addition of atoms. However, in short strip experiments, there are no rigid walls to cover the Al strips, except native oxide. How can the back stress build up at the anode if the native oxide is not a rigid wall? In Section 6.3, we mentioned that in diffusional processes, such as the classic Kirkendall effect of interdiffusion in a bulk diffusion couple of A and B, while the atomic flux of A is not equal to the opposite flux of B, no stress was assumed in the analysis of Darken’s model of interdiffsuion. If it is assumed that more A atoms are diffusing into B, we might expect that there will be a compressive stress in B, on the basis of the argument given above. However, Darken has made a key assumption that vacancy concentration is in equilibrium everywhere, hence vacancies (or lattice sites) can be created and/or annihilated as needed in the sample. Hence, there is no compressive stress in B, provided that the lattice sites in B can be added readily to accommodate the incoming A atoms. The addition of a large number of lattice sites implies an increase in lattice planes and an expansion in volume if we assume that the mechanism of vacancy creation and/or annihilation is by dislocation climb mechanism. However, if we assume a constraint of constant volume, we must allow the excess lattice planes to migrate in the reverse direction and out of the volume, in turn implying marker motion if markers are embedded in the frame of the moving lattice in the sample. Therefore, in the ideal case of Darken’s model of interdiffusion, lattice shift occurs due to an effective vacancy generation and annihilation under the constant volume constraint. If not, strain or stress will be generated. Thus, a plausible explanation of the back stress in Al short strips is that the Al native oxide has removed the sources and sinks of vacancies from the surface, therefore when electromigration drives atoms into the anode region, the out-diffusion of vacancies will reduce the vacancy concentration in the anode region if there is no source to replenish it. Furthermore, we must allow

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the added lattice planes to move, otherwise a compressive stress will be generated. Since the Al thin film has a native and protective oxide on the surface, the oxide tends to tie down the lattice planes in Al and prevent them from moving. The oxide is effectively tying down the lattice planes because the film is thin. This is the basic mechanism of back stress generation in Al interconnects. In Chapter 6, we discussed spontaneous Sn whisker growth at room temperature; the mechanism of compressive stress generation is similar to that presented in the above since Sn also has a protective native oxide. However, since Sn has a low melting point, no spontaneous whisker growth occurs near or above 100◦ C because of fast stress relaxation. For the same reason, back stress induced by electromigration in solder joints is not as strong as that in Al because of the high homologous temperature of solder. The back stress can be relaxed quickly over a certain distance from the anode. On the basis of the above discussion, it is clear that the origin of back stress, in turn the existence of a critical product or critical length of electromigration in Al short strips, depends on the effectiveness of sources and sinks of vacancies in the samples. If the sources and sinks are as effective as in the assumption of Darken’s model of interdiffusion, there will be no back stress, no critical product, and no threshold current density of electromigration. Electron wind force can be regarded as a driving force of atomic diffusion, and the latter is a thermally activated process. Theoretically, even at 1 K, atomic diffusion can take place except that the probability or the frequency of exchange jumps will be infinitely small, so as electromigration. However, in real devices, it is not electromigration itself but rather electromigration-induced damage that is of concern, and the damage should not occur within the lifetime of the device. The Blech short strip structure has enabled us to see electromigration induced damage of void formation at the cathode and hillock formation at the anode very conveniently. Indeed there is a threshold current density, a back stress, and a critical length of Al short strip, but they are unique because of the surface oxide on the thin-film Al short strips. For Cu interconnect, the situation is different since it has no protective oxide. The time dependence of stress buildup in a short strip by electromigration can be obtained by solving the continuity equation since stress is energy density and a density function obeys the continuity equation, and we can convert ΔC to Δσ from the last equation [11, 12]: C ∂σ D D ∂2σ − =− 2 B ∂t kT ∂x BkT



∂σ ∂x

2 −

CDZ∗ eE ∂σ . BkT ∂x

(8.28)

The solution for a finite line and the manner of stress buildup as a function of time is shown in Fig. 8.8. Clearly, in the beginning of electromigration the back stress is nonlinear along the length of the stripe, represented by the curved lines. In reality, the buildup is asymmetrical since the hydrostatic tensile stress at the cathode can hardly be developed.

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600

STRESS (MPa)

400 200 0 –200 –400 –600

0.0

0.2 0.4 0.6 0.8 REDUCED DISTANCE (x/L)

1.0

Fig. 8.8. The solution for a finite line and the manner of stress buildup as a function of time.

8.8 Measurement of the Back Stress Induced by Electromigration A serious effort has been dedicated to measuring the back stress in Al strips during electromigration. It is not an easy task since the strip is thin and narrow; typically it is only a few hundred nanometers thick and a few micrometers wide, so a very high intensity and focused x-ray beam is needed in order to determine the strain in Al grains by precision lattice parameter measurement. Micro-diffraction x-ray beams using synchrotron radiation have been employed to study the back stress. White x-rays of 10μm × 10μm beam from the National Synchrotron Light Source (NSLS) at Brookhaven National Laboratory were used to study electromigration-induced stress distribution in pure Al lines [13]. The line was 200 μm long, 10 μm wide, and 0.5 μm thick with 1.5 μm SiO2 passivation layer on top, 10 nm Ti/60 nm TiN shunt layer at the bottom, and 0.2-μm-thick W pads at both ends which connect the line to contact pads. The electromigration tests were performed at 260◦ C. Results of the steady-state rate of resistance increase, δ(ΔR/R)/δt, and the electromigration-induced steady-state compressive stress gradient, δσEM /δx, versus current density are shown in Fig. 8.9. No electromigration occurred below the threshold current density “jth ” of 1.6 × 105 A/cm2 . Below the threshold current density, the electromigration-induced steady-state stress gradient increased linearly with current density, wherein the electron wind force was counterbalanced by the mechanical force, so no electromigration drift was observed. However, the basic reason for the existence of the threshold stress is unclear.

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2

0.005

1

0

2.0×105

Fig. 8.9. Steady-state rate of resistance increase, δ(ΔR/R)/ δt, and electromigrationinduced steady-state compressive stress gradient, δσEM /δx, plotted versus current density. (Courtesy of Prof. G. S. Cargill, Lehigh University.)

0.000

jth 0.0

d(ΔR/R)/dt [hr-1]

dsEM /dx [MPa/μm]

0.010

4.0×105

6.0×105

Current density [A/cm2]

The x-ray micro-diffraction apparatus at the Advanced Light Source (ALS) of Lawrence Berkeley National Laboratory is capable of delivering white xray beams (6–15 keV) focused to 0.8 to 1 μm by a pair of elliptically bent Kirkpatrick–Baez mirrors [34, 35]. In the apparatus, the beam can be scanned over an area of 100 μm by 100 μm in steps of 1 μm. Since the diameter of the grains in the strip is about 1 μm, each grain can be treated as a single crystal with respect to the micro-beam. Structural information such as stress/strain and orientation can be obtained by using white beam Laue diffraction. Laue patterns were collected with a large-area (9 × 9 cm2 ) charge-coupled device (CCD) detector with an exposure time of 1 sec or longer, from which the orientation and strain tensor of each illuminated grain can be deduced and displayed by software. The resolution of the white beam Laue technique is 0.005% strain. In addition, a four-crystal monochromator can be inserted into the beam to produce monochromatic light for diffraction. The combined white and monochromatic beam diffractions are capable of determining the total strainstress tensor in each grain. The technique and applications of Scanning X-ray Microdiffraction (μSXRD) have been described by MacDowell et al. [30, 31]. Whether back stress exists in electromigration in Cu damascene structure at the device working temperature has not been confirmed. If electromigration occurs by surface diffusion in a Cu damascene structure, we need a mechanism of back stress generation in the bulk of the structure induced by surface diffusion. Without a protective surface oxide, surface diffusion occurs, and thus the surface is a good source and sink of vacancies.

8.9 Current Crowding and Current Density Gradient Force Interconnect in VLSI technology is a three-dimensional multilevel structure. When electrical current turns or converges, e.g., at vias in the 3D structure, where the current passes from one level of interconnect to another level,

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eAI

(a) Cathode

Anode

TiN

(b)

106

0.6

105

0.4

104

0.2

Cathode

103 0.0

(c) Cathode

0.5

1.0

AI

1.5

0.0 2.0 μm

Anode

TiN

Fig. 8.10. Sketch of the cross section of the well-known Blech–Herring short strip test structure of electromigration. (b) Simulation of the current crowding picture. (c) If a void nucleates and grows in the high current density region, it will not be able to deplete the cathode completely.

current crowding occurs and affects electromigration significantly. We postulate that defects such as vacancies and solute atoms will have a higher potential in the high current density region than in the low current density region. The potential gradient in the current crowding area provides a driving force to push these defects from the high current density region to the low current density region. As a consequence, the voids tend to form in the low current density region rather than in the high current density region. In other words, failure tends to occur in a low current density region in 3D interconnects [32, 33]. Figure 8.10(a) is a sketch of the crosssection of the well-known Blech short strip test structure of electromigration. We assume electrons go from the left (cathode) to the right (anode). The W baseline has a higher resistance than the short Al strip so the electrons will make a detour from the W into the Al because the latter is a better conductor. In the region where the current enters the Al, current crowding occurs. The current crowding has been simulated and shown in Fig. 8.10(b), where the arrow indicates that the upper left corner and its neighborhood are the low current density region. Clearly, the lower left corner of Al/TiN interface, where current crowding occurs, is the high current density region [34–36].

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e-

Over-hang

AI Cathode

AI

W

via

W

Anode

AI

Fig. 8.11. Sketch of the cross section of a two-level Al interconnect structure connected by W vias. One way to delay the wear-out failure is to add an overhang of the Al interconnect above the W via, as shown by the dotted line.

Many SEM images have shown that void formation occurs at the cathode of the strip as a result of electromigration. If a void nucleates and grows in the high current density region, as depicted in Fig. 8.10(c), it will not be able to extend to the low current density region in the upper corner because the void is an open, and the current will be pushed back toward the anode. In order to deplete the entire cathode, the vacancies must go to the low current density region, so the void must start from the upper left corner of the left end of the strip. Figure 8.11 is a sketch of the crosssection of a two-level Al interconnect structure connected by W vias. Again it is assumed that electrons go from left to right and current crowding occurs in passing through the vias. We consider the via on the left and indicate by an arrow that the upper left corner and its neighborhood over-hang region are the low current regions where a void tends to form first. Since atomic diffusion in W is much slower than that in Al, the W/Al interface is a flux divergence plane of diffusion, where more Al atoms are leaving. The reverse flux of vacancies would lead to vacancy condensation near the interface. But the void formation will not begin at the right-hand edge of the W/Al interface where the current density is the highest; rather it tends to occur at the upper left corner or the neighboring regions. As the void grows, it leads to circuit failure when it covers the entire via so the via is open. In the microelectronic industry, this has been called the wear-out mechanism of failure. One way to delay the wear-out failure is to add an overhang of the Al interconnect above the W via, as shown by the dotted line in Fig. 8.11. The overhang provides an additional volume or reservoir for void growth, so it can lengthen the mean time to failure. However, it is implicitly assumed in this remedy that vacancies will go to the low current density region of the overhang. Often it is assumed that there is a stress gradient to drive the vacancies to the low current density region. A stress gradient is developed after a void is formed because of its free surface. The nucleation of a void requires supersaturation of vacancies, hence vacancies have to diffuse to the low current density region first before the void formation. Following the electron wind

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force, we expect vacancies to go to the high current density region, in turn void formation there, but this is not true since void formation occurs in the low current density region. To envisage the driving force that enables vacancies to go from the high current density region to the low current density region, we consider a singlecrystal Al strip and assume that a vacancy in the Al crystalline lattice has a specific resistivity of ρv . The specific resistivity may depend on current density due to joule heating since resistivity depends on temperature. However, for simplicity, we ignore the temperature effect here and assume that it is independent of current density for the simple analysis to be given below. Since vacancy is a lattice defect, we can regard its specific resistivity as the excess resistivity over that of a lattice atom. Under electromigration in a current density of je , a voltage drop of je ρv occurs around the vacancy. From the energetic viewpoint, we can regard that the vacancy has a potential of je ρv above the surrounding lattice atoms. Knowing the charge of the vacancy, we have the potential energy of the vacancy in the current density of je . Let the charge of the vacancy be Z ∗∗ e, where Z ∗∗ is the effective charge number of the vacancy and e is the charge of an electron, we have the potential energy of Pv = Z ∗∗ eje ρv for a vacancy stressed by the current density je . If we assume the equilibrium vacancy concentration in the crystal without any electrical current (je = 0) to be Cv , Cv = C0 exp (−ΔGf /kT ),

(8.29)

where C0 is the atomic concentration of the crystal and ΔGf is the formation energy of a vacancy. When we stress the crystal by a current density of je , the vacancy concentration will be reduced to Cve = C0 exp − (ΔGf + Z ∗∗ eje ρv )/kT.

(8.30)

Under a uniform high current density, the equilibrium vacancy concentration in the crystal decreases. In other words, the electric current dislikes any excess high-resistance obstacles (or defects) and prefers to get rid of them until the equilibrium is reached. When there exists a current density gradient as in current crowding, a driving force exists to do so, F = −dPv /dx.

(8.31)

This force drives the excess vacancies to diffuse in the direction normal to the direction of current flow. Now if we go back to Fig. 8.10(a) and consider the electromigration flux in the short strip, in the middle section of the strip, the current density is constant so there is a constant flux of Al atoms moving from left to right and a balance flux of vacancies moving from right to left. A few of the vacancies near the surface or the substrate may escape to the surface or the substrate interface, but the concentration as given by Eq. (8.30)

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is maintained. When the vacancy flux approaches the cathode and enters the current crowding region, most of them become excess and a force to divert them to the low current density region comes into play. Consequently, a component of the vacancy flux is moving in the direction normal to the current flow, Jcc = Cve (Dv /kT )(−dPv /dx)

(8.32)

where Dv /kT is the mobility and Dv is the diffusivity of vacancies in the crystal. Since a constant flux of vacancies keeps moving from anode to cathode due to electromigration, the total flux of vacancies moving toward the cathode is given by the sum of two components, Jsum = Jem + Jcc = Cve (Dv /kT )(−Z ∗ eE − dPv /dx),

(8.33)

where the first term is due to electromigration driven by the current density (electron wind force) and the second term is due to current crowding driven by the current density gradient. In the first term, Z ∗ is the effective charge number of the diffusing Al atom, and E = je ρ (where ρ is the resistivity of the Al). We note here that we assume the vacancy flux is opposite but equal to the Al flux. Also, it is important to note that the sum in brackets is a vector sum; the first term is directed along the current and the second term is directed normal to the current. In other words, the vacancies are driven by two forces in the current crowding region. They are depicted in Fig. 8.12. Since the current turns in the current crowding region, the direction of Jsum changes with position. Clearly, a detailed simulation is needed in order to unravel the magnitude and distribution of the forces in the current crowding region. How large is the gradient force is of interest. If we apply a current density of 105 A/cm2 through the strip and assume that the current density will drop to zero across the thickness of the strip of 1 μm, the gradient can be as high as 109 A/cm3 . The gradient force is of the same magnitude as the electron wind force. Under such a large gradient, high-order effect might exist, but we will ignore it at this moment. Current crowding in flip chip solder joints and its effect on electromigration-induced failure will be presented in Section 9.3.

AI Cathode

TiN Fig. 8.12. The vacancies are driven by two forces in the current crowding region.

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8.10 Electromigration in Anisotropic Conductor of Beta-Sn White tin (or beta-Sn) has a body-centered tetragonal crystal structure, and its lattice parameters are a = b = 0.583 nm and c = 0.318 nm. Its electrical conductivity is anisotropic; the resistivity along the a and b axes is 13.25 μΩcm and that along the c-axis is 20.27 μΩ-cm. In electromigration under an applied current density of 6.25 × 103 A/cm2 at 150◦ C for 1 day, the beta-Sn stripes were found to show a voltage drop of up to 10%, reported by Lloyd [37]. The electromigration in white tin (Tm = 232◦ C) is of interest because most of the Pb-free solders are Sn-based and the electromigration at the device working temperature occurs primarily by lattice diffusion which may lead to a noticeable microstructural change affected by its anisotropic conductivity. Figure 8.13 shows SEM images of the top view of a Sn strip before (a) and after (b) electromigration at 2 × 104 A/cm2 at 100◦ C for 500 hr. The lower image shows that a few of the grains rotated after electromigration. In Fig. 8.14, the cross section of a beta-Sn grain is shown. It has a bodycentered tetragonal structure and we assume that its c-axis is making an angle (a) 0 h

(b) 500 h Fig. 8.13. (a) SEM images of the top view of a Sn strip before and (b) after electromigration at 2 × 104 A/cm2 at 100◦ C for 500 hr. The lower image shows that a few of the grains rotated after electromigration. (Courtesy of Professor C. R. Kao, National Central University, Jhongli, Taiwan, ROC.)

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Chapter 8 Fig. 8.14. Cross section of a beta-Sn grain. E versus j.

θ with the x-axis, its a-axis is on the plane of the figure and is making an angle of (90◦ − θ) with the x-axis, and its b-axes is normal to the plane of the figure. The applied current density of electrons, j, is from left to right, along the x-axis. The resistivity along the a- and b-axis is the same and smaller than that along the c-axis. Due to the anisotropy of resistivity, the electrical field, E, can be written in two components, Ea and Ec , along the aand c-axes, respectively. The electrical field along the a-axis is Ea = ρa ja ; the field along the c-axis is Ea = ρc jc , where ja and jc are respectively the two components of the electrical (electron) current density, j, along the a- and c-axes. In isotropic materials, such as Cu or Al, they have the same resistivity along all the axes; therefore, the magnitude of ρc jc is the same as ρa ja . This also means Ea = Ec , the overall electrical field within the grain will coincide with the current flow direction, j. However, due to the difference of the magnitude between Ea and Ec in anisotropic materials, such as beta-Sn, there will be an angle ϕ, as shown in Fig. 8.14, between the combined electric field E and the direction of j inside the grain. This is a unique property of anisotropic conducting material, and it is important to examine analytically how the angle ϕ would affect the interaction between the electrical current and the electrical force exerted on the grain [38]. In Fig. 8.14, the two components of current density j along the a- and c-axes would be ja = j sin θ,

jc = j cos θ.

(8.34)

Therefore, the resulting electrical fields along these two axes are Ea = ρa j sin θ,

Ec = ρc j cos θ.

(8.35)

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The combined electrical field, E, would be E=

 Ea2 + Ec2 =

2

2



(ρa j sin θ) + (ρc j cos θ) = j

2

2

(ρa sin θ) + (ρc cos θ) . (8.36)

To evaluate the magnitude of the angle ϕ, we consider the components of E, Ea and Ec , on the y-axis. From Fig. 8.14, E sin ϕ = Ec sin θ − Ea cos θ.

(8.37)

By rearrangement, we have sin ϕ =

Ec sin θ − Ea cos θ (ρc j cos θ) sin θ − (ρa j sin θ) cos θ = . E E

(8.38)

By substituting E from Eq. (8.36), we have sin ϕ =

j[(ρc cos θ) sin θ − (ρa sin θ) cos θ]  . 2 2 j (ρa sin θ) + (ρc cos θ)

(8.39)

The current term, j, can be canceled out and by substituting 2 sin θ cos θ = sin 2θ, the last equation becomes (ρc − ρa ) sin 2θ sin ϕ =  . 2 2 2 (ρa sin θ) + (ρc cos θ)

(8.40)

Similarly, if we consider the components of E, Ea and Ec , on the x-axis, we obtain cos ϕ = 

ρc cos2 θ + ρa sin2 θ 2

2

.

(8.41)

(ρa sin θ) + (ρc cos θ)

Either Eq. (8.40) or (8.41) defines the magnitude of the angle ϕ between the electrical-field and the applied current density from the data of resistivity and the orientation of the grain. Equation (8.40) shows that if θ = 0◦ and θ = 90◦ , then ϕ = 0◦ or in these cases E will be parallel to j, which will be considered later. Since the direction of the electrical field deviates from that of the current density, it follows that the force originating from this field will also deviate from the current flow direction. The effect on force can have two significant consequences. The first is a torque and the second is that the force has a component parallel to the grain boundary plane or the y-axis as shown in Fig. 8.14. It can be seen that the force generated from momentum exchange

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between electrons and atoms exerted on the boundaries of the grain is also making an angle to the current density. The existence of a pair of totally opposite forces provides a torque. Note that the boundaries need not be all grain boundaries, they could also be the interface between the sample and the substrate.

8.11 Electromigration of a Grain Boundary in Anisotropic Conductor We consider electromigration of a grain boundary. The electron flux is normal to the plane of the grain boundary. In the case of grain boundaries in Al thin films, electromigration-induced migration of the grain boundaries has been observed. We shall consider a grain boundary in beta-Sn, which is an anisotropic conductor, and we shall demonstrate that electromigraion will lead to an atomic flux along the plane of the grain boundary. In other words, the induced atomic flux along the grain boundary is moving in a direction normal to the electron flux or the electron wind force [39]. In Fig. 8.15, a simple and geometrically ideal situation of a grain boundary between two beta-Sn grains is depicted; grain 3 on the right and grain 2 on the left of the grain boundary. We assume that grain 2, on the left, has its crystallographic c-axis directed along the flow direction of electron current, j, which is directed from left to right as indicated by a long arrow. We further assume that grain 3, on the right, has its crystallographic a-axis also directed along the current flow direction. Since both resistivity and diffusivity along a- and c-axes in beta Sn are different, the electron wind force and the corresponding vacancy fluxes in the c-axis (grain 2) and a-axis (grain 3) grains will

e-

δ

Grain 1

c

jv

d

Grain 2

V More Compressive

Grain Boundary I

a

jv

Grain 3

More Tensile

V

c

h

jv

Grain Boundary II

Fig. 8.15. Schematic diagram of a simple and geometrically ideal situation of a sandwiched grain structure.

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be different: Jvc =

Cvbulk Dvc,bulk ∗ c Z eρ j, kT

Jva =

Cvbulk Dva,bulk ∗ a Z eρ j. kT

(8.42)

Jvc and Jva are the vacancy fluxes in grain 2 along the c-axis and in grain 1 along the a-axis, respectively. We have the reference data below for the diffusivity and resistivity of Sn atoms along these two directions: Dc = 5.0 × 10−13 cm2 /sec, ρc = 20.3 × 10−6 Ω-cm; Da = 1.3 × 10−12 cm2 /sec, ρa = 13.3 × 10−6 Ω-cm. The atomic flux under electromigration should be in the same direction of electron flow. Therefore, a counterflux of vacancy flows from right to left, as indicated by the two short arrows. The effective charge, Z ∗ , is considered to be the same in both directions. Since Dc ρc < Da ρa , from Eq. (8.42), we find a larger vacancy flux reaches the grain boundary from grain 3 to grain 2, yet a smaller vacancy flux leaves the grain boundary going into grain 2. In grain 2, supersaturation of vacancies occurs at the grain boundary and a corresponding tensile stress occurs near the grain boundary. If we consider a small volume within the grain boundary of d × h × δ, where d is the width of the grain, h is the height of the grain, and δ is the effective grain boundary width, we have in the steady state, the balance of the flux or conservation of mass, Cvbulk Z ∗ ej a,bulk a C ∞ − CvL ρ − Dvc,bulk ρc ) × d × h ∼ (Dv × d × δ. = DvGB v kT h

(8.43)

The first term of this equation states the difference of the flux through bulk diffusion; the second term means that the difference of the vacancy flux goes to the surface via grain boundary diffusion, since the surface is a good sink/source of vacancy. From Eq. (8.43), the difference of vacancy concentrations can be evaluated as ΔCv ∼ Cvbulk Z ∗ ej a,bulk a (Dv ρ − Dvc,bulk ρc ) × h, = h kT δDvGB

(8.44)

where ΔCv = Cv∞ − CvL , where Cv∞ is the equilibrium vacancy concentration of the free surface and CvL is the vacancy concentration in the grain boundary. Thus, we have obtained a flux of vacancies (or atoms) along the grain boundary, provided that a sink for vacancies exists at the end of the grain boundary, which can be a free surface or a void. Again we note that this flux is moving in a direction normal to the electron flux. We recall that this

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is the second case where atomic or vacancy flux is moving normal to electron flux, and the first case is due to current density gradient presented in Section 8.9. If we extend the above analysis to a three-grain structure of one c-axis grain sandwiched between two a-axis grains, it will lead to grain rotation of the c-axis grain in the sandwiched structure, as shown in Fig. 8.15 [39]. Furthermore, the analysis presented above can also be applied to interphase interfaces. For example, if we consider the interface between solder and Cu6 Sn5 in a flip chip solder joint, since the resistivity and diffusivity in these two phases are different, there will be a vacancy flux along the interface under electromigration with electron flow normal to the plane of the interface. This interfacial flux could lead to void formation and morphological change of the interface, to be discussed in Section 9.4.6.

8.12 AC Electromigration Electromigration in interconnects is commonly a DC behavior. In devices based on field-effect transistors used in computers, such as dynamic random assess memory (DRAM) devices, the gate of the transistor is turned on and off by pulsed DC current. On the other hand, in most communication devices, AC current is used. Especially in power switching devices, and radio frequency and audio power amplifiers, a large AC swing occurs during operation. The question whether AC can induce electromigration is often asked. Typically it is believed that AC has no effect on electromigration. We follow Huntington and Grone’s model that the driving force of electromigration is due to momentum exchange in the scattering of electrons by diffusing atoms. A diffusing atom will not be in equilibrium and will have a large scattering cross section. If we consider AC of frequency 60 Hz or 60 cycles/sec, it means in a period of 1/120 sec, the scattering will be reversed once. For lattice diffusion in Pb assuming a vacancy mechanism of diffusion at 100◦ C, the fraction of equilibrium vacancy in 1 cm3 of Pb is given by  nV ΔGf = exp − , n kT where ΔGf is the formation free energy of a lattice vacancy. Taking ΔGf = 0.55 eV/atom, we have nV /n = 10−7 . If we take n = 1022 atoms/cm3 , we have nV = 1015 vacancies/cm3 , meaning that these many vacancies are attempting to jump. The successive jumps are limited by the frequency factor 

ΔGm υ = υ0 exp − kT

,

where υ0 is the Debye frequency or attempt frequency of jumping of the diffusing atom and is about 1013 Hz for metals above their Debye temperature.

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Taking ΔGm = 0.55 eV/atom, which is assumed to be the motion free energy of a vacancy in Pb, we obtain υ = 106 jumps/sec. Then in 1/120 sec, there are about 104 successive jumps of each of the 1015 vacancies/cm3 . Implicitly, we have assumed that the lifetime of the transition state or the activated state is very short. In other words, in each cycle of the 60 Hz AC, a large number of vacancies (or atoms) jump in one direction in the first half cycle driven by electromigration and then an equal number of vacancies will jump in the opposite direction in the second half cycle. They cancel out each other statistically, so there is no net atomic flux driven by AC current. Nevertheless, AC will generate joule heating and joule heating may develop a temperature gradient that induces atomic diffusion. In the above analysis, an implicit assumption is that the electric field or electric current is uniform. However, when the current distribution is nonuniform, it is unclear whether AC electromigration can occur or not. Nonuniform current distribution occurs when electric current turns as in a flip chip solder joint, or in a metal interconnect between a Cu line and via, or in a two-phase alloy where a precipitate and its matrix have different resistivities, or at a reactive interphase interface such as Sn/Cu. In the last case, if the interface is not at equilibrium, the atomic jumps across the interface in one direction are not the same as the jumps in the reverse direction. Since it is irreversible, the AC effect of electromigration may enhance the jumping in one direction. At a Schottky barrier across a metal/n-type semiconductor interface, the carrier flow is oneway from the semiconductor to the metal, so a high current density of AC may enhance the diffusion of the semiconductor into the metal.

References 1. H. B. Huntington and A. R. Grone, “Current-induced marker motion in gold wires,” J. Phys. Chem. Solids, 20, 76 (1961). 2. H. B. Huntington, in “Diffusion,” H. I. Aaronson (Ed.), American Society for Metals, Metals Park, OH, p. 155 (1973). 3. H. B. Huntington, in “Diffusion in Solids: Recent Development,” A. S. Nowick and J. J. Burton (Eds.), Academic Press, New York, p. 303 (1974). 4. I. Ames, F. M. d’Heurle, and R. Horstman, IBM J. Res. Dev., 4, 461 (1970). 5. I. A. Blech, “Electromigration in thin aluminum films on titanium nitride,” J. Appl. Phys., 47, 1203–1208 (1976). 6. I. A. Blech and C. Herring, “Stress generation by electromigration,” Appl. Phys. Lett., 29, 131–133 (1976). 7. F. M. d’Heurle and P. S. Ho, in “Thin Films: Interdiffusion and Reactions,” J. M. Poate, K. N. Tu, and J. W. Mayer (eds.), Wiley–Interscience, New York, p. 243 (1978). 8. P. S. Ho and T. Kwok, Rep. Prog. Phys., 52, 301 (1989). 9. K. N. Tu, “Electromigration in stressed thin films,” Phys. Rev. B, 45, 1409–1413 (1992).

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10. R. Kircheim, Acta Metall. Mater., 40, 309 (1992). 11. M. A. Korhonen, P. Borgesen, K. N. Tu, and C. Y. Li, J. Appl. Phys., 73, 3790 (1993). 12. J. J. Clement and C. V. Thompson, J. Appl. Phys., 78, 900 (1995). 13. P. C. Wang, G. S. Cargill III, I. C. Noyan, and C. K. Hu, Appl. Phys. Lett., 72, 1296 (1998). 14. K. L. Lee, C. K. Hu, and K. N. Tu, J. Appl. Phys., 78, 4428 (1995). 15. R. S. Sorbello, in “Solid State Physics,” H. Ehrenreich and F. Spaepen (Eds.), Academic Press, New York, Vol. 51, pp. 159–231 (1997). 16. C. K. Hu and J. M. E. Harper, Mater. Chem. Phys., 52, 5 (1998). 17. R. Rosenberg, D. C. Edelstein, C. K. Hu, and K. P. Rodbell, Annu. Rev. Mater. Sci., 30, 229 (2000). 18. E. T. Ogawa, K. D. Li, V. A. Blaschke, and P. S. Ho, IEEE Trans. Reliab., 51, 403 (2002). 19. K. N. Tu, “Recent advances on electromigration in very-large-scaleintegration of interconnects,” J. Appl. Phys., 94, 5451–5473 (2003). 20. C. L. Gan, C. V. Thompson, K. L. Pey, W. K. Choi, H. L. Tay, B. Yu, and M. K. Radhakrishnan, Appl. Phys. Lett., 79, 4592 (2001). 21. A. V. Vairagar, S. G. Mhaisalkar, A. Krishnamoorthy, K.N. Tu, A.M. Gusak, M. A. Mayer, and E. Zschech, “In-situ observation of electromigration induced void migration in dual-damascene Cu interconnect structures,” Appl. Phys. Lett., 85, 2502–2504 (2004). 22. A. V. Vairagar, S. G. Mhaisalkar, M. A. Meyer, E. Zschech, A. Krishnamoorthy, K. N. Tu, and A. M. Gusak, “Direct evidence of electromigration failure mechanism in dual-damascene Cu interconnect tree structures,” Appl. Phys. Lett., 87, 081909 (2005). 23. M. Y. Yan, J. O. Suh, F. Ren, K. N. Tu, A. V. Vairagar, S. G. Mhaisalkar, and A. Krishnamoorthy, “Effect of Cu3 Sn coatings on electromigration lifetime improvement of Cu dual-damascene interconnects,” Appl. Phys. Lett., 87, 211103 (2005). 24. M. Y. Yan, K. N. Tu, A. V. Vairagar, S. G. Mhaisalkar, and A. Krishnamoorthy, “Confinement of electromigration induced void propagation in Cu interconnect by a buried Ta diffusion barrier layer,” Appl. Phys. Lett., 87, 261906 (2005). 25. T. V. Zaporozhets, A. M. Gusak, K. N. Tu, and S. G. Mhaisalkar, “Threedimensional simulation of void migration at the interface between thin metallic film and dielectric under electromigration,” J. Appl. Phys., 98, 103508 (2005). 26. P. G. Shewman, “Diffusion in Solids,” 2nd ed., The Minerals, Metals, and Materials Society, Warrendale, PA (1989). 27. N. A. Gjostein, in “Diffusion,” H. I. Aaronson (Ed.), American Society for Metals, Metals Park, OH, p. 241 (1973). 28. P. Wynblatt and N. A. Gjostein, Surf. Sci., 12, 109 (1968). 29. D. Gupta, K. Vieregge, and W. Gust, Acta Mater., 47, 5 (1999).

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30. A. A. MacDowell, R. S. Celestre, N. Tamura, R. Spolenak, B. Valek, W. L. Brown, J. C. Bravman, H. A. Padmore, B. W. Batterman, and J. R. Patel, Nucl. Instrum. Methods., A 467, 936 (2001). 31. N. Tamura, A. A. MacDowell, R. S. Celestre, H. A. Padmore, B. Valek, J. C. Bravman, R. Spolenak, , W. L. Brown, T. Marieb, H. Fujimoto, B. W. Batterman, and J. R. Patel, Appl. Phys. Lett., 80, 3724 (2002). 32. H. Okabayashi, H. Kitamura, M. Komatsu, and H. Mori, AIP Conf. Proc., 373, 214 (1996). (See Figs. 2 and 4) 33. S. Shingubara, T. Osaka, S. Abdeslam, H. Sakue, and T. Takahagi, AIP Conf. Proc., 418, 159 (1998). (See Table I). 34. K. N. Tu, C. C. Yeh, C. Y. Liu, and C. Chen, “Effect of current crowding on vacancy diffusion and void formation in electromigration,” Appl. Phys. Lett., 76, 988–990 (2000). 35. C. C. Yeh and K. N. Tu, “Numerical simulation of current crowding phenomena and their effects on electromigration in VLSI interconnects,” J. Appl. Phys., 88, 5680–5686 (2000). 36. E. C. C. Yeh and K. N. Tu, J. Appl. Phys., 89, 3203 (2001). 37. J. Lloyld, J. Appl. Phys., 94, 6483 (2003). 38. A. T. Wu, K. N. Tu, J. R. Lloyd, N. Tamura, B. C. Valek, and C. R. Kao, “Electromigration induced microstructure evolution in tin studied by synchrotron x-ray microdiffraction,” Appl. Phys. Lett., 85, 2490–2492(2004). 39. A. T. Wu, A. M. Gusak, K. N. Tu, and C. R. Kao, “Electromigration induced grain rotation in anisotropic conduction beta-Sn,” Appl. Phys. Lett., 86, 241902(2005).

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9 Electromigration in Flip Chip Solder Joints

9.1 Introduction In 1998, Brandenburg and Yeh reported electromigration failure in flip chip eutectic SnPb solder joints [1]. Using a current density of 8 × 103 A/cm2 at 150◦ C for about 100 hr, they detected failure by the formation of a pancake type of void across the entire cathode contact to the Si chip. In addition, a significant amount of phase separation in the bulk of the eutectic solder bump was observed; the Pb has moved to the anode side and the Sn to the cathode side. On the other hand, in the pair of bumps tested, while the one in which electrons flowed from the Si to the substrate failed as described by the pancake-type void formation, the other one in which electrons flowed from the substrate to the Si did not fail. On the basis of their data, an attempt was made by using Black’s equation of mean-time-to-failure to extrapolate lifetime of flip chip solder joint. Taking the exponential factor of current density n = 1.8 and activation energy of diffusion Q = 0.8 eV, they showed that electromigration in flip chip solder joint would become a serious reliability issue in flip chip technology. Since then, the subject has been included in the International Technological Roadmap for Semiconductors for study. The four interesting findings in their work are (1) the low current density, which is about two orders of magnitude less than that required to cause electromigration failure in Al or Cu interconnects, (2) the failure mode of pancake-type void formation, (3) the failure mode is asymmetrical in the pair of bumps tested; the failure occurs only in the one bump with the cathode contact to the Si side, and (4) the redistribution of Pb and Sn; they moved in opposite directions. Since Sn moves against the electron flow, it might mean that the effective charge of Sn is positive, which is unreasonable. It is generally accepted that the basic mechanism of electromigration in solder is the same as that in Al or Cu, and the basic concept of electromigration in a metallic conductor remains true that it enhances atomic diffusion in the electron flow direction by electron wind force. Hence, there is no reason to expect that Pb and Sn behave differently in electromigration.

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Furthermore, in eutectic SnPb solder joints, it is found that at temperatures above 100◦ C, while atoms of Pb move in the same direction as electrons, Sn atoms move in the opposite direction. However, in electromigration in eutectic SnPb conducted at room temperature, Sn and Pb reversed their diffusion direction. On the other hand, in pure Sn or Pb-free solders, Sn moves in the same direction as electrons, evidenced by the growth of Sn hillocks and whiskers at the anode [2–6]. An attempt to explain this behavior of reverse flow of Sn by the constraint of constant volume will be presented in Section 9.7. Flip chip solder joint technology was discussed in Section 1.3.3. A schematic diagram of the cross section of such a joint was depicted in Fig. 1.9. In today’s circuit design, each power solder joint in a flip chip may carry 0.2 A and it will be doubled in the near future. At present, the diameter of a solder joint is about 100 μm and it will be reduced to 50 μm and even 25 μm soon. If the diameter of solder bumps and the spacing between them is 50 μm, we can place 100 × 100 = 10, 000 solder joints on a 1 cm × 1 cm chip surface. In the most advanced devices today, there are already over 7000 solder joints on a chip. When a current of 0.2 A is applied to a bump, the average current density in a 50-μm solder bump is about 104 A/cm2 . This current density is about two orders of magnitude smaller than that in Al and Cu interconnects. Nevertheless, electromigration does occur in flip chip solder joints at such low current density, and it occurs by lattice diffusion. Often the easy electromigration in solder joints is explained by the low melting point of solder or fast atomic diffusion in solder. However, Table 8.1 shows that at the device working temperature of 100◦ C, lattice diffusion in solder is not much slower than grain boundary diffusion in Al, nor slower than surface diffusion in Cu. While the total atomic flux in lattice diffusion is much greater than that in grain boundary diffusion or in surface diffusion, so is the larger volume of a void required to cause failure of a solder joint. Therefore, low melting point or fast diffusion is not the key answer. Why electromigration can occur in flip chip solder joints at such low current densities will be explained below; it is due to the low critical product of electromigration of solder alloys [6]. Furthermore, the line-to-bump geometry of a flip chip solder joint leads to a large current crowding at the cathode contact where accelerated electromigration occurs. Currently, there are attempts to use Cu column Table 9.1. Resistance of Al and Cu interconnects and solder bumps

Cross section Resistance Current Current density

Al or Cu interconnects

Solder bumps

0.5 × 0.2 μm2 1–10 Ω 10−3 A 106 A/cm2

100 × 100 μm2 10−3 Ω 1A 103 –104 A/cm2

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bumps to reduce the effect of current crowding; electromigration in Cu column bumps will be covered in Section 9.6.

9.2 Unique Behaviors of Electromigration in Flip Chip Solder Joints 9.2.1 Low Critical Product of Solder Alloys We recall the “critical product” in Eq. (8.21). If we replace Δσ by Y Δε, where Y is Young’s modulus and Δε = 0.2% is the elastic limit, we see that the “critical product” is a function of Young’s modulus, resistivity, and effective charge number of the interconnect material: jΔx =

Y ΔεΩ . Z ∗ eρ

(9.1)

We have used bulk modulus instead of Young’s modulus to explain the back stress generation in Eq. (8.27). Since bulk modulus and Young’s modulus are related, for convenience we use Young’s modulus here. To compare the value of “critical product” among Cu, Al, and eutectic SnPb, we recall that eutectic SnPb has a resistivity that is one order of magnitude larger than those of Al and Cu, see Table 9.1. The Young’s modulus of eutectic SnPb (30 GPa) is a factor of two to four smaller that those of Al (69 GPa) and Cu (110 GPa) [7]. The effective charge number of eutectic SnPb (Z ∗ of lattice diffusion) is about one order of magnitude larger than those of Al (Z ∗ of grain boundary diffusion) and Cu (Z ∗ of surface diffusion). Therefore, in Eq. (9.1), if Δx is kept constant for comparison, the current density needed to cause electromigration damage in eutectic SnPb solder is two orders of magnitude smaller than that needed for Al and Cu interconnects. If Al or Cu interconnect fails in electromigration by a current density of 105 to 106 A/cm2 , solder joint will fail by 103 to 104 A/cm2 . This is the major reason why electromigration in flip chip solder joints can be serious. 9.2.2 Current Crowding in Flip Chip Solder Joints The failure mode in flip chip solder joint by the pancake-type void formation at the cathode contact interface can be explained by current distribution in the unique geometry of a flip chip joint [8–11]. Figure 9.1 is a schematic diagram depicting the geometry of a flip chip solder bump between an interconnect line on the chip side (top) and a conducting trace on the board or module side (bottom). Current crowding occurs at the contact interface between the solder bump and interconnect line (the simulation will be discussed in Section 9.3). The high current density due to current crowding is about one order of magnitude higher than the average current density in the

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eSolder

Al line 2 μm

J = I/A AAl