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

SVNY339-Tu April 6, 2007 10:15 Springer Series in M AT E R I A L S S C I E N C E 92 SVNY339-Tu April 6, 2007 1...

Author: King-Ning Tu

122 downloads 1168 Views 11MB Size Report

This content was uploaded by our users and we assume good faith they have the permission to share this book. If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content from our site. Start by pressing the button below!

Report copyright / DMCA form

DOWNLOAD PDF

SVNY339-Tu

April 6, 2007

10:15

Springer Series in

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

92

SVNY339-Tu

April 6, 2007

10:15

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.

SVNY339-Tu

April 6, 2007

10:15

King-Ning Tu

Solder Joint Technology Materials, Properties, and Reliability

SVNY339-Tu

April 6, 2007

10:15

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

SVNY339-Tu

April 6, 2007

10:15

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

SVNY339-Tu

vi

April 6, 2007

10:15

Contents

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

SVNY339-Tu

April 6, 2007

10:15

Contents

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

SVNY339-Tu

viii

April 6, 2007

10:15

Contents

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 ........................................................................

211 211 214 217 221 222

SVNY339-Tu

April 6, 2007

10:15

Contents

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.................................................................................

ix

8.6

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

SVNY339-Tu

x

April 6, 2007

10:15

Contents

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

SVNY339-Tu

April 6, 2007

10:15

Contents

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

xi

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

SVNY339-Tu

April 6, 2007

10:15

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

SVNY339-Tu

xiv

April 6, 2007

10:15

Preface

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.

SVNY339-Tu

April 6, 2007

10:15

Preface

xv

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

SVNY339-Tu

xvi

April 6, 2007

10:15

Preface

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

SVNY339-Tu

April 5, 2007

17:44

I

Copper–Tin Reactions

SVNY339-Tu

March 2, 2007

22:0

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

SVNY339-Tu

2

March 2, 2007

22:0

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

SVNY339-Tu

March 2, 2007

22:0

Introduction

3

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.

SVNY339-Tu

4

March 2, 2007

22:0

Chapter 1

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.

SVNY339-Tu

March 2, 2007

22:0

Introduction

5

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

SVNY339-Tu

6

March 2, 2007

22:0

Chapter 1

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

SVNY339-Tu

March 2, 2007

22:0

Introduction

7

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

SVNY339-Tu

8

March 2, 2007

22:0

Chapter 1

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.

SVNY339-Tu

March 2, 2007

22:0

Introduction

9

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.

SVNY339-Tu

10

March 2, 2007

22:0

Chapter 1 Sn Whisker Pb-free finish Sn, SnAg, SnCu, and SnPb

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

SVNY339-Tu

March 2, 2007

22:0

Introduction

11

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

SVNY339-Tu

12

March 2, 2007

22:0

Chapter 1

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

SVNY339-Tu

March 2, 2007

22:0

Introduction

13

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,

SVNY339-Tu

14

March 2, 2007

22:0

Chapter 1 C4 solder Joints

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

SVNY339-Tu

March 2, 2007

22:0

Introduction Via

15

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.

SVNY339-Tu

16

March 2, 2007

22:0

Chapter 1

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

SVNY339-Tu

March 2, 2007

22:0

Introduction

17

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

SVNY339-Tu

18

March 2, 2007

22:0

Chapter 1

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.

SVNY339-Tu

March 2, 2007

22:0

Introduction

19

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.

SVNY339-Tu

20

March 2, 2007

22:0

Chapter 1

(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

SVNY339-Tu

March 2, 2007

22:0

Introduction

21

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

SVNY339-Tu

22

March 2, 2007

22:0

Chapter 1

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

SVNY339-Tu

March 2, 2007

22:0

Introduction

23

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.

SVNY339-Tu

24

March 2, 2007

22:0

Chapter 1 Cutting line

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

SVNY339-Tu

March 2, 2007

22:0

Introduction

25

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

SVNY339-Tu

26

March 2, 2007

22:0

Chapter 1

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

SVNY339-Tu

March 2, 2007

22:0

Introduction

27

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.

SVNY339-Tu

28

March 2, 2007

22:0

Chapter 1

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

SVNY339-Tu

March 2, 2007

22:0

Introduction

29

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,

SVNY339-Tu

30

March 2, 2007

22:0

Chapter 1

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,

SVNY339-Tu

March 2, 2007

22:0

Introduction

31

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

SVNY339-Tu

32

March 2, 2007

22:0

Chapter 1

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).

SVNY339-Tu

March 2, 2007

22:0

Introduction

33

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).

SVNY339-Tu

April 5, 2007

17:44

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.

SVNY339-Tu

38

April 5, 2007

17:44

Chapter 2

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.

SVNY339-Tu

April 5, 2007

17:44

Copper–Tin Reactions in Bulk Samples

39

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.

SVNY339-Tu

April 5, 2007

17:44

40 pure Sn/Cu

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.

SVNY339-Tu

April 5, 2007

17:44

Copper–Tin Reactions in Bulk Samples

41

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.

SVNY339-Tu

42

April 5, 2007

17:44

Chapter 2

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

SVNY339-Tu

April 5, 2007

17:44

Copper–Tin Reactions in Bulk Samples

43

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.

SVNY339-Tu

44

April 5, 2007

17:44

Chapter 2

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).

SVNY339-Tu

April 5, 2007

17:44

Copper–Tin Reactions in Bulk Samples

45

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)

SVNY339-Tu

46

April 5, 2007

17:44

Chapter 2

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

SVNY339-Tu

April 5, 2007

17:44

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

48

April 5, 2007

17:44

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)

SVNY339-Tu

400

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

SVNY339-Tu

April 5, 2007

17:44

Copper–Tin Reactions in Bulk Samples

49

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

SVNY339-Tu

April 5, 2007

50

17:44

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.

SVNY339-Tu

April 5, 2007

17:44

Copper–Tin Reactions in Bulk Samples

51

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.

SVNY339-Tu

52

April 5, 2007

17:44

Chapter 2

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.

SVNY339-Tu

April 5, 2007

17:44

Copper–Tin Reactions in Bulk Samples

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

SVNY339-Tu

54

April 5, 2007

17:44

Chapter 2

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.

SVNY339-Tu

April 5, 2007

17:44

Copper–Tin Reactions in Bulk Samples

55

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

SVNY339-Tu

56

April 5, 2007

17:44

Chapter 2

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

SVNY339-Tu

April 5, 2007

17:44

Copper–Tin Reactions in Bulk Samples

57

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

SVNY339-Tu

58

April 5, 2007

17:44

Chapter 2

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,

SVNY339-Tu

April 5, 2007

17:44

Copper–Tin Reactions in Bulk Samples

59

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.

SVNY339-Tu

60

April 5, 2007

17:44

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

SVNY339-Tu

April 5, 2007

17:44

Copper–Tin Reactions in Bulk Samples

61

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

SVNY339-Tu

62

April 5, 2007

17:44

Chapter 2

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

SVNY339-Tu

April 5, 2007

17:44

Copper–Tin Reactions in Bulk Samples (a)

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

SVNY339-Tu

64

April 5, 2007

17:44

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.

SVNY339-Tu

April 5, 2007

17:44

Copper–Tin Reactions in Bulk Samples

65

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

SVNY339-Tu

66

April 5, 2007

17:44

Chapter 2

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,

SVNY339-Tu

April 5, 2007

17:44

Copper–Tin Reactions in Bulk Samples

67

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

SVNY339-Tu

68

April 5, 2007

17:44

Chapter 2

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.

SVNY339-Tu

April 5, 2007

17:44

Copper–Tin Reactions in Bulk Samples

69

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.

SVNY339-Tu

70

April 5, 2007

17:44

Chapter 2

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.

SVNY339-Tu

April 5, 2007

17:44

Copper–Tin Reactions in Bulk Samples

71

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).

SVNY339-Tu

July 12, 2007

15:5

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

SVNY339-Tu

74

July 12, 2007

15:5

Chapter 3

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.

SVNY339-Tu

July 12, 2007

15:5

Copper–Tin Reactions in Thin-Film Samples

75

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

July 12, 2007

15:5

h¢ - Cu Sn 6 5 - Cu3Sn

∋

SVNY339-Tu

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.

SVNY339-Tu

July 12, 2007

15:5

Copper–Tin Reactions in Thin-Film Samples (a)

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

SVNY339-Tu

July 12, 2007

78

15:5

Chapter 3

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

SVNY339-Tu

July 12, 2007

15:5

Copper–Tin Reactions in Thin-Film Samples

79

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

SVNY339-Tu

80

July 12, 2007

15:5

Chapter 3

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 .

SVNY339-Tu

July 12, 2007

15:5

Copper–Tin Reactions in Thin-Film Samples

81

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

SVNY339-Tu

82

July 12, 2007

15:5

Chapter 3 T (°C) 10

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

SVNY339-Tu

July 12, 2007

15:5

Copper–Tin Reactions in Thin-Film Samples 5

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].

SVNY339-Tu

July 12, 2007

84

15:5

Chapter 3

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)

SVNY339-Tu

July 12, 2007

15:5

Copper–Tin Reactions in Thin-Film Samples xbg

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

SVNY339-Tu

86

July 12, 2007

15:5

Chapter 3

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.

SVNY339-Tu

July 12, 2007

15:5

Copper–Tin Reactions in Thin-Film Samples

87

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.

SVNY339-Tu

88

July 12, 2007

15:5

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.

SVNY339-Tu

July 12, 2007

15:5

Copper–Tin Reactions in Thin-Film Samples

89

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.

SVNY339-Tu

90

July 12, 2007

15:5

Chapter 3

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

SVNY339-Tu

July 12, 2007

15:5

Copper–Tin Reactions in Thin-Film Samples

91

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),

SVNY339-Tu

92

July 12, 2007

15:5

Chapter 3

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.

SVNY339-Tu

July 12, 2007

15:5

Copper–Tin Reactions in Thin-Film Samples

93

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

SVNY339-Tu

94

July 12, 2007

15:5

Chapter 3

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

SVNY339-Tu

July 12, 2007

15:5

Copper–Tin Reactions in Thin-Film Samples

95

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

SVNY339-Tu

96

July 12, 2007

15:5

Chapter 3

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.

SVNY339-Tu

July 12, 2007

15:5

Copper–Tin Reactions in Thin-Film Samples

97

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

SVNY339-Tu

98

July 12, 2007

15:5

Chapter 3

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.

SVNY339-Tu

July 12, 2007

15:5

Copper–Tin Reactions in Thin-Film Samples

99

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.)

SVNY339-Tu

100

July 12, 2007

15:5

Chapter 3

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

SVNY339-Tu

July 12, 2007

15:5

Copper–Tin Reactions in Thin-Film Samples

101

(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

SVNY339-Tu

102

July 12, 2007

15:5

Chapter 3

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)

SVNY339-Tu

July 12, 2007

15:5

Copper–Tin Reactions in Thin-Film Samples

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

SVNY339-Tu

104

July 12, 2007

15:5

Chapter 3

(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

SVNY339-Tu

July 12, 2007

15:5

Copper–Tin Reactions in Thin-Film Samples

105

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

SVNY339-Tu

106

July 12, 2007

15:5

Chapter 3

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

SVNY339-Tu

July 12, 2007

15:5

Copper–Tin Reactions in Thin-Film Samples

107

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

SVNY339-Tu

108

July 12, 2007

15:5

Chapter 3

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).

SVNY339-Tu

July 12, 2007

15:5

Copper–Tin Reactions in Thin-Film Samples

109

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).

SVNY339-Tu

March 2, 2007

22:1

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

SVNY339-Tu

112

March 2, 2007

22:1

Chapter 4

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

SVNY339-Tu

March 2, 2007

22:1

Copper–Tin Reactions in Flip Chip Solder Joints

113

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

SVNY339-Tu

114

March 2, 2007

22:1

Chapter 4

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.)

SVNY339-Tu

March 2, 2007

22:1

Copper–Tin Reactions in Flip Chip Solder Joints

115

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

SVNY339-Tu

116

March 2, 2007

22:1

Chapter 4

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

SVNY339-Tu

March 2, 2007

22:1

Copper–Tin Reactions in Flip Chip Solder Joints

117

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

SVNY339-Tu

March 2, 2007

118

22:1

Chapter 4

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.

SVNY339-Tu

March 2, 2007

22:1

Copper–Tin Reactions in Flip Chip Solder Joints

119

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.

SVNY339-Tu

120

March 2, 2007

22:1

Chapter 4

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

SVNY339-Tu

March 2, 2007

22:1

Copper–Tin Reactions in Flip Chip Solder Joints

121

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.

SVNY339-Tu

122

March 2, 2007

22:1

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

Before aging

After one week aging

SVNY339-Tu

March 2, 2007

22:1

Copper–Tin Reactions in Flip Chip Solder Joints

123

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.

SVNY339-Tu

124

March 2, 2007

22:1

Chapter 4

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

SVNY339-Tu

March 2, 2007

22:1

Copper–Tin Reactions in Flip Chip Solder Joints

125

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).

SVNY339-Tu

March 3, 2007

7:44

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

SVNY339-Tu

128

March 3, 2007

7:44

Chapter 5

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

SVNY339-Tu

March 3, 2007

7:44

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

129

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

SVNY339-Tu

130

March 3, 2007

7:44

Chapter 5

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

SVNY339-Tu

March 3, 2007

7:44

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

131

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

SVNY339-Tu

132

March 3, 2007

7:44

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

SVNY339-Tu

March 3, 2007

7:44

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

133

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.

SVNY339-Tu

134

March 3, 2007

7:44

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.

SVNY339-Tu

March 3, 2007

7:44

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

135

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 ,

SVNY339-Tu

March 3, 2007

136

7:44

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.

SVNY339-Tu

March 3, 2007

7:44

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

137

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

SVNY339-Tu

138

March 3, 2007

7:44

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)

SVNY339-Tu

March 3, 2007

7:44

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

139

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
m

1 >= 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)

SVNY339-Tu

140

March 3, 2007

7:44

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

SVNY339-Tu

March 3, 2007

7:44

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

141

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.

SVNY339-Tu

142

March 3, 2007

7:44

Chapter 5

. . . . . . . . . .

ϕ (η )versus h .

Fig. 5.8. Plot of ϕ(η) versus η. k ∼ k ∼ k The parameter b = 9(<η2 >−<η> 2 ) = 0.5535 = <η 3 > . 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

SVNY339-Tu

March 3, 2007

7:44

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

143

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.

SVNY339-Tu

144

March 3, 2007

7:44

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

March 3, 2007

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

SVNY339-Tu 7:44

Kinetic Analysis of Flux-Driven Ripening of Copper–Tin Scallops 145

SVNY339-Tu

March 3, 2007

146

7:44

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

SVNY339-Tu

March 3, 2007

7:44

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

147

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

SVNY339-Tu

148

March 3, 2007

7:44

Chapter 5

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

SVNY339-Tu

March 3, 2007

7:44

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

149

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

SVNY339-Tu

150

March 3, 2007

7:44

Chapter 5

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).

SVNY339-Tu

March 3, 2007

7:44

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

151

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).

SVNY339-Tu

April 5, 2007

17:18

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.

SVNY339-Tu

154

April 5, 2007

17:18

Chapter 6

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.

SVNY339-Tu

April 5, 2007

17:18

Spontaneous Sn Whisker Growth

155

(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

SVNY339-Tu

156

April 5, 2007

17:18

Chapter 6

(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

SVNY339-Tu

April 5, 2007

17:18

Spontaneous Sn Whisker Growth

157

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

SVNY339-Tu

158

April 5, 2007

17:18

Chapter 6

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,

SVNY339-Tu

April 5, 2007

17:18

Spontaneous Sn Whisker Growth

159

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

SVNY339-Tu

160

April 5, 2007

17:18

Chapter 6

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.

SVNY339-Tu

April 5, 2007

17:18

Spontaneous Sn Whisker Growth

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

SVNY339-Tu

April 5, 2007

17:18

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.

SVNY339-Tu

April 5, 2007

17:18

Spontaneous Sn Whisker Growth

163

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

SVNY339-Tu

164

April 5, 2007

17:18

Chapter 6

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

SVNY339-Tu

April 5, 2007

17:18

Spontaneous Sn Whisker Growth

165

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.

SVNY339-Tu

166

April 5, 2007

17:18

Chapter 6 1.5 μm

(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

SVNY339-Tu

April 5, 2007

17:18

Spontaneous Sn Whisker Growth

167

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.

SVNY339-Tu

168

April 5, 2007

17:18

Chapter 6

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.

SVNY339-Tu

April 5, 2007

17:18

Spontaneous Sn Whisker Growth

169

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.

SVNY339-Tu

170

April 5, 2007

17:18

Chapter 6

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

SVNY339-Tu

April 5, 2007

17:18

Spontaneous Sn Whisker Growth

171

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.

SVNY339-Tu

172

April 5, 2007

17:18

Chapter 6

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.

SVNY339-Tu

April 5, 2007

17:18

Spontaneous Sn Whisker Growth

173

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

SVNY339-Tu

174

April 5, 2007

17:18

Chapter 6

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)

SVNY339-Tu

April 5, 2007

17:18

Spontaneous Sn Whisker Growth

175

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

SVNY339-Tu

176

April 5, 2007

17:18

Chapter 6

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.

SVNY339-Tu

April 5, 2007

17:18

Spontaneous Sn Whisker Growth

177

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.)

SVNY339-Tu

178

April 5, 2007

17:18

Chapter 6

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 .

SVNY339-Tu

April 5, 2007

17:18

Spontaneous Sn Whisker Growth

179

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

SVNY339-Tu

180

April 5, 2007

17:18

Chapter 6

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).

SVNY339-Tu

April 5, 2007

17:18

Spontaneous Sn Whisker Growth

181

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).

SVNY339-Tu

April 5, 2007

17:13

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

SVNY339-Tu

184

April 5, 2007

17:13

Chapter 7

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

SVNY339-Tu

April 5, 2007

17:13

Solder Reactions on Ni, Pd, and Au

185

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 (<160◦ C), a metastable phase that has an approximate composition of NiSn3 may form instead of the stable Ni3 Sn4. The NiSn3 grows extremely fast as platelets and can quickly erupt at the surface of solder coatings on nickel, degrading their solderability. Although the exact mechanism of wettability deterioration due to the presence of NiSn3 is unclear, it was proposed that the oxidation of NiSn3 near or at the surface of ﬁnish was most likely the cause. One of the solutions to this NiSn3 oxidation problem would be to decompose it into stable compounds. Recalling the C-4 technology as discussed in Chapter 1, Ni was used on the substrate side, but not on the chip side. This is because of the concern for

SVNY339-Tu

186

April 5, 2007

17:13

Chapter 7

Fig. 7.2. SEM images of the three-dimensional morphology of Ni3 Sn4 formation between eutectic SnPb and Ni at 240◦ C for (a) 1 min, (b) 10 min, and (c) 40 min.

intrinsic stress in Ni thin ﬁlms. To use Ni as UBM on the chip side, one must have a cushion layer below the Ni ﬁlm to absorb the stress. In Sections 3.6 and 3.7, we discussed the thin-ﬁlm Al/Ni(V)/Cu UBM. Otherwise, one must deposit a low-stress Ni. This leads to the discussion of the thick electroless Ni(P) UBM below.

SVNY339-Tu

April 5, 2007

17:13

Fig. 7.3. Rate of consumption of Ni by the wetting reaction in the temperature range from 200 to 240◦ C. After 40 min at 240◦ C, the size (linear dimension) of the Ni3 Sn4 scallops is about 2 μm.

Fig. 7.4. Cross-sectional SEM images of eutectic SnPb on 200 nm Ni/50 nm Ti at 220◦ C for (a) 1 min, (b) 5 min, and (c) 40 min.

SVNY339-Tu

188

April 5, 2007

17:13

Chapter 7

7.2.1 Reaction between Eutectic SnPb and Electroless Ni(P) Electroless Ni(P) contains 15 to 20 at.% P and can be deposited by a maskless plating process on a patterned and zincated Al surface. Its growth is isotropic and has a mushroomlike appearance. The binary phase diagram of Ni-P has a deep eutectic point at 19 at.% P, so it is very easy to form amorphous Ni-P alloys near this composition without rapid quenching. Electroless Ni(P), near the deep eutectic composition, is typically amorphous in the asplated state and has low stress. For UBM applications, it has a thickness more than 10 μm. Figure 7.5(a) shows a schematic diagram of the cross section of a eutectic SnPb solder ball on an electroless Ni(P) UBM. The dielectric which deﬁned the contact opening on the zincated Al surface is SiON. Figure 7.5(b) shows an SEM cross-sectional image of a eutectic SnPb solder ball of 100-μm diameter on an electroless Ni(P) UBM. On the Ni(P), a layer of Ni3 Sn4 is seen. The morphology of the Ni3 Sn4 is faceted, and the grains are either chunky-type or needle-type, unlike round scallops of Cu6 Sn5 . Nevertheless, there are valleys in between the chunky and needle-type grains. Figure 7.5(c) shows an enlarged SEM image of a corner of the Ni(P) UBM. Between the Ni3 Sn4 and electroless Ni(P), there is a layer of Ni3 P compound. Between the electroless Ni(P) and SiON, there is an interfacial layer of Ni3 Sn4 . The Ni3 P has a layer-type morphology. Figure 7.6(a) to (d) show respectively the x-ray mapping of elements of Sn, Ni, Pb, and P across an interfacial region. The distribution of Sn matches that of Ni in the Ni3 Sn4 , and a layer of P corresponds to the Ni3 P layer. During the growth of Ni3 Sn4 , it depletes Ni from the amorphous Ni(P) and enriches the concentration of P toward that of 75Ni25P, which then crystallizes into the Ni3 P compound. This is an enhanced crystallization of the amorphous Ni(P) by the soldering reaction. It is a conservative reaction, in which the Ni3 P consumes nearly all the P in the amorphous Ni(P) and very little P goes into the solder. The formation of a thick Ni3 P layer will lead to brittle fracture since Ni3 P cracks easily. The growth of the Ni3 P is a diﬀusion-controlled growth with an activation energy of 0.33 eV/atom. At the moment it is unclear whether it is the Ni diffusion from the Ni(P)/Ni3 P interface or the P diﬀusion from the Ni3 Sn4 /Ni3 P interface that controls the growth of Ni3 P;. No doubt the valleys or channels in the Ni3 Sn4 enable Ni to dissolve into the molten solder quickly. If P is the dominant diﬀusing species, it implies that Ni3 P would decompose at the Ni3 Sn4 /Ni3 P interface. Then as the Ni diﬀuse into the molten solder, the P will diﬀuse back to the Ni3 P/Ni(P) interface to enrich and crystallize the Ni(P). On the other hand, if Ni is the dominant diﬀusing species, it will depart from the Ni3 P/Ni(P) interface and diﬀuse through the Ni3 P layer to reach the Ni3 Sn4 /Ni3 P interface. However, what is of interest here is that overall it is a low-activation energy process, even with the Ni3 P acting as a diﬀusion barrier! Again, in the wetting reaction, several micrometers of Ni(P) can be consumed in a few minutes at 200 to 240◦ C.

SVNY339-Tu

April 5, 2007

17:13

Solder Reactions on Ni, Pd, and Au

189

Fig. 7.5. Schematic diagram of the cross section of a eutectic SnPb solder ball on an electroless Ni(P) UBM. The dielectric which deﬁned the contact opening on the zincated Al surface is SiON. (b) SEM cross-sectional image of a eutectic SnPb solder ball of 100 μm diameter on an electroless Ni(P) UBM. On the UBM, a layer of Ni3 Sn4 is seen. (c) SEM cross-sectional image of the penetration of Ni3 Sn4 along the interface between SiON and Ni(P).

However, in solid-state aging of eutectic SnPb on electroless Ni(P), the rate of Ni3 Sn4 formation is much slower. Figure 7.7 shows a cross-sectional SEM image of the interface after 500 hr at 150◦ C. The thickness of Ni3 Sn4 is only a few micrometers, and it is unclear whether or not Ni3 P forms at such a low temperature. However, the Ni3 Sn4 now has a layer-type morphology

SVNY339-Tu

April 5, 2007

190

17:13

Chapter 7 P

(b) Ni

(d)

Ni3P Ni3Sn4

Electroless Ni-P

(a)

Electroless Ni-P

Pb

Sn

(c)

Sn-rich solder Pb-rich solder

Ni3Sn4

5 μm

Fig. 7.6. X-ray mapping of elements of Sn (a), Ni (b), Pb (c) and P (d) across an interfacial region. The distribution of Sn matches that of Ni in the Ni3 Sn4 , and a layer of P corresponds to the Ni3 P layer.

rather than the chunky-type or needle-type morphology. By comparing the wetting reaction and solid-state reaction, we again conclude that it is similar to the SnPb/Cu reactions where the wetting reaction is much faster and has a high rate of free energy gain. While the electroless Ni(P) is thick enough that no spalling of IMC takes place, it nevertheless has a weak interface with the dielectric SiON. In Fig. 7.5(c) where the cross section of a solder ball on electroless Ni(P) is shown, the molten solder can penetrate the interface, starting from the triple point where the electroless Ni(P), the SiON, and the molten solder meet together. The penetration forms Ni3 Sn4 compound between the electroless Ni(P) and SiON and it extends all the way to the Al interface. Besides solder, corrosion reagent can also penetrate the interface, so it becomes a reliability issue. The kinetics of penetration is interesting since it involves interfacial diﬀusion and IMC formation. The solution of the penetration has been given as [16] y0 =

12δDi b

1/2

2(bC 0 − C34 ) C34 Dc

1/4 t1/4 ,

(7.1)

SVNY339-Tu

April 5, 2007

17:13

Solder Reactions on Ni, Pd, and Au

191

Fig. 7.7. Cross-sectional SEM image of the interface between eutectic SnPb and electroless Ni(P) after 500 hr at 150◦ C. The rate of Ni3 Sn4 formation is very slow.

where y is the penetration depth, δ is the eﬀective width of the interface, Di is the interfacial diﬀusivity, b(= C34 /Ci ) is the ratio of concentration in the IMC (C34 ) and in the interface (Ci ), C0 is the concentration at the triple point or at the origin of the interface, and Dc is the diﬀusivity in the compound. From the solution, a t1/4 dependence of penetration is found, which is similar to the classic Fisher’s analysis of grain boundary penetration by a diﬀusional process.

7.2.2 Reaction between Eutectic Pb-Free Solders and Electroless Ni(P) The enhanced crystallization of amorphous electroless Ni(P) into Ni3 P and Ni3 Sn4 when it is reﬂowed with eutectic SnPb at 200◦ C is a concern when Pb-free solder is used. Eutectic SnAg solder has a higher concentration of Sn and a higher reﬂow temperature, about 240◦ C, which is very close to the self-crystallization temperature of amorphous Ni(P) of 250◦ C. In a eutectic SnAg solder joint on Ni(P), the interfacial IMC is Ni3 Sn4 . Figure 7.8 shows the interfacial region of a sample after a reﬂow at 250◦ C for

SVNY339-Tu

192

April 5, 2007

17:13

Chapter 7

Fig. 7.8. SEM images of the interfacial region of a sample after a reﬂow at 250◦ C for 1 hr followed by an aging at 215◦ C for 225 hr. A large number of voids can be seen in the Ni3 P layer. Between Ni3 Sn4 and Ni3 P, there exists a layer of NiSnP. (Courtesy of Professor Zhong Chen, Nanyang Technological University, Singapore.)

1 hr followed by an aging at 215◦ C for 225 hr. A large amount of voids can be seen in the Ni3 P layer. Between Ni3 Sn4 and Ni3 P, there exists a layer of NiSnP. Figure 7.9 is a SEM image of the voids in Ni3 P layer when the sample was aged at 190◦ C for 400 hr. Figure 7.10 is a schematic diagram of plausible ﬂuxes of Ni and Sn during the reactions.

Fig. 7.9. SEM image of the voids in Ni3 P layer when the sample was aged at 190◦ C for 400 hr. (Courtesy of Professor Zhong Chen, Nanyang Technological University, Singapore.)

SVNY339-Tu

April 5, 2007

17:13

Solder Reactions on Ni, Pd, and Au

193

Inter-diffusion in Sn-3.5Ag/Ni-P

Fig. 7.10. Schematic diagram of plausible ﬂuxes of Ni and Sn during the reaction between SnAg solder and Ni(P).

For eutectic SnAgCu solder joint on Ni(P), the interfacial IMC is found to be (Cu,Ni)6 Sn5 rather than Ni3 Sn4 . The Ni3 P layer has a well-developed columnar structure. The Sn has penetrated into the Ni3 P layer. Between Ni3 P and (Cu,Ni)6 Sn5 there is a very thin (less than 0.2 μm) dark layer of NiSnP layer, and there are voids in this NiSnP layer. When the sample was aged at 170◦ C for 64 hr, the interfacial structure is similar, but there are more voids in the NiSnP layer, and also more Sn has entered into the Ni3 P layer. The remaining amorphous Ni(P) layer was not crystallized by solid-state aging. 7.2.3 Formation of (Cu, Ni)6 Sn5 versus (Ni, Cu)3 Sn4 Without Cu, the reaction in the binary system of Sn on Ni or in the ternary system of SnPb on Ni leads to the formation of Ni3 Sn4 . With the presence of Cu in the SnAgCu solder, the formation of Ni3 Sn4 is suppressed. Instead, the (Cu, Ni)6 Sn5 forms with some solution of Ni, as reported in the literature. This can be explained by using the thermodynamic–kinetic considerations. Since no Ag was detected in the interfacial IMC layer, it is assumed that Ag was not directly involved in the interfacial reactions. It is found that the amount of Ni in (Cu, Ni)6 Sn5 increased with the number of reﬂows. The maximum solubility of Ni in (Cu, Ni)6 Sn5 in the solder joint, i.e., without the formation of (Ni, Cu)3 Sn4 , has been calculated to be 8 wt% at 260◦ C, which is in good agreement with the experimental ﬁnding. The distribution of Ni within a particle of (Cu, Ni)6 Sn5 is quite uniform. This uniform distribution is expected in a precipitation upon solidiﬁcation, yet it is unexpected in a solid-state

SVNY339-Tu

194

April 5, 2007

17:13

Chapter 7

diﬀusion process, in which Ni atoms diﬀuse from the Ni(V) layer into a particle of Cu6 Sn5 . The ternary phase of (Cu, Ni)6 Sn5 is more stable than (Ni, Cu)3 Sn4 , hence the latter forms by dissolution of Cu into an existing layer Ni3 Sn4 , for example, by interaction across a solder joint as discussed in Section 4.3. 7.2.4 Formation of Kirkendall Voids The formation of Kirkendall voids in the Ni3 P and NiSnP layer, as shown in Fig. 7.9, is a reliability issue since the voids will enhance cracking in a brittle phase. In the reaction, Ni atoms diﬀuse from the Ni(P) layer to the Ni3 Sn4 layer, and in the reverse direction, a ﬂux of Sn diﬀuses to the Ni3 P since Sn has been detected there. A marker motion experiment is needed to determine whether Ni or Sn is the dominant diﬀusing species. Void formation is not a unique phenomenon of the SnAg/Ni(P) reaction. It has also been observed in the eutectic SnPb/Ni(P) as well as SnAgCu/Ni(P) reactions.

7.3 Solder Reactions on Bulk and Thin-Film Pd 7.3.1 Reaction between Eutectic SnPb and Pd Foil The unique property of Pd in soldering reaction is that it is highly resistive to oxidation and very easily wetted by solder to form Pd-Sn IMC [33–41]. Frequently it is used together with Ni to passivate the surface and to enhance wetting of Ni. In the wetting reaction of molten eutectic SnPb on a Pd foil, no stable wetting angle between the solder cap and the Pd was found [34]. This behavior is unlike that on Cu and Ni surfaces, where the wetting angle is stable. The molten solder cap on Pd spreads out unceasingly until all the Sn in the solder cap transforms completely into Pd-Sn compounds. The instability of the wetting tip is due to the extremely fast IMC formation between the molten solder and Pd. The gain in free energy of IMC formation provides the driving force for the tip motion. The IMC formation at the wetting tip does not become a diﬀusion barrier to the wetting reaction; the molten solder tip is able to advance and wet the Pd in front of it unceasingly. Thus, the morphology of the IMC at the wetting tip is of interest; it must have channels to allow the molten solder to pass through. To conﬁrm the ultrafast reaction, strips of pure Pd foil (0.5 mm in thickness and 0.5 cm in width) were rolled into rings 3 mm in diameter, and a eutectic SnPb solder wire was inserted into each of the rings. Then they were immersed in ﬂux at 250◦ C for 1 to 20 min. The ring cross sections were polished, etched, and examined by optical microscopy, SEM, and EDX. Formation of a very thick layer of PdSn3 compound between the Pd and solder was observed [35]. Figure 7.11(a) and (b) show optical microscopic images of a very thick layer of PdSn3 formation, as indicated by the arrow, of 170 and 360 μm in thickness

SVNY339-Tu

April 5, 2007

17:13

Solder Reactions on Ni, Pd, and Au

195

Fig. 7.11. (a,b) Optical microscopic images of a very thick layer of PdSn3 formation (indicated by the arrow) 170 and 360 μm thick after 2 and 5 min of wetting reaction, respectively.

after 2 and 5 min, respectively. The growth rate within this period is linear with time and exceeds 1 μm/sec, which is extraordinarily fast and it may be the fastest IMC growth reported. Figure 7.12(a) and (b) show SEM images of the PdSn3 layer and its interface with Pd, respectively. The layer has a lamellar structure, wherein the bright phase is PdSn3 and the dark areas in between PdSn3 are solder which has been etched away. The lamellar structure is unique in that the molten solder is able to contact the unreacted Pd all the time during the reaction. These molten solder channels serve as fast diﬀusion paths so that a very high rate of reaction can be achieved. The diﬀusivity in the molten solder is about 10−5 cm2 /sec, which is more than enough for the measured linear growth rate. But beyond 5 min, we found that the growth rate slowed down when the thickness was more than 500 μm. This is expected because the growth will eventually become diﬀusion-controlled even if it has a diﬀusivity as high as 10−5 cm2 /sec. The binary phase diagrams of Pd-Sn and Pd-Pb show that Pd forms several compounds with Sn as well as with Pb, such as Pd2 Sn and PdPb2 . Nevertheless, during the wetting reaction at 250◦ C, the only compound formed is PdSn3 . A similar result was obtained at 260◦ C. Among the Pd-Sn

SVNY339-Tu

196

April 5, 2007

17:13

Chapter 7 Fig. 7.12. SEM images of (a) the PdSn3 layer and (b) its interface with Pd. The layer has a lamellar structure, wherein the bright phase is PdSn3 and the dark areas in between PdSn3 are solder which has been etched away.

compounds, PdSn3 has a very low melting point, about 345◦ C, which is much lower than that of Pd2 Sn and Pd3 Sn, which have a melting point around 1300◦ C. If maximum free energy change were the criterion of reaction, those Pd-rich compounds should have formed. Yet, PdSn3 wins the race and becomes the ﬁrst phase of formation because the morphology enables it to have a high rate of growth or a high rate of free energy gain in the reaction. The ﬁrst phase formation has a strong dependence on temperature in the ternary system of SnPbPd. At or above 250◦ C the ﬁrst phase formation in the reaction between eutectic SnPb and Pd is PdSn3 , but at a lower temperature of 220◦ C, PdSn4 forms instead as reported by Ghosh [39–41]. This ﬁnding is in agreement with the ternary phase diagrams of SnPbPd at 250◦ C and 220◦ C, shown in Fig. 7.13(c) and (b), respectively. The phase diagrams are calculated using the set of thermodynamic data optimized by Ghosh [40]. While many compounds exist in these phase diagrams, only one or two of the Sn compounds (PdSn4 and PdSn3 ) have been detected in the wetting reactions, depending on the temperature and time of reaction. Thermodynamic

SVNY339-Tu

April 5, 2007

17:13

Solder Reactions on Ni, Pd, and Au

197

Fig. 7.13. Ternary phase diagrams of SnPbPd at (a) 125◦ C, (b) 220◦ C, (c) 250◦ C, and (d) 303◦ C. (Courtesy of Dr. K. Zeng, TI.)

calculation indicates that below 245◦ C the wetting reaction of eutectic SnPb with Pd produces PdSn4 [see Fig. 7.13(d)], between 245 and 303◦ C PdSn3 forms, but above 303◦ C PdSn2 may form as the ﬁrst reaction product. The solid-state reaction between eutectic SnPb and Pd was found to be much slower. After reaction at 220◦ C for 50 sec, the same sample was aged at 125◦ C for 30 days. In addition to a thicker (130 μm) PdSn4 layer, there were a 50-μm-thick PdSn3 layer and a 40-μm-thick Pb layer. These phase formations are consistent with the calculated phase diagram [Fig. 7.13(a)]. Yet the thickness of the compounds formed in 30 days at 125◦ C is comparable to that formed in a few minutes at 220◦ C. 7.3.2 Reaction between Eutectic SnPb and Pd Thin Film To passivate Ni, the Pd ﬁlm used is typically about 50 to 100 nm thick. When the thin-ﬁlm Pd is in contact with molten solder, it dissolves very

SVNY339-Tu

198

April 5, 2007

17:13

Chapter 7

quickly into the solder and allows the solder/Ni reaction to take place. But a slightly thicker Pd may lead to Pd-Sn compound formation, which could become a diﬀusion barrier in the subsequent reﬂow. The wetting behavior of eutectic SnPb on Pd/Ni plated Cu leadframe has been studied [36–38]. The wetting reaction forms a Pd-Ni-Sn ternary compound and Ni3 Sn4 . The ternary compound grains were broken oﬀ from the interface and scattered into the molten solder. The Ni3 Sn4 , consisting of small scallops, remains as a rather uniform layer on the unreacted Ni.

7.4 Solder Reactions on Bulk and Thin-Film Au Both Au and Pd serve the same purpose for surface passivation and wetting enhancement, yet a major diﬀerence between them is that Au has a very high solubility in molten eutectic SnPb solder, about 7.8 wt% at 220◦ C. When a molten solder joint has dissolved this amount of Au, the precipitation of Au-Sn compound upon solidiﬁcation will form a brittle solder joint, or “cold joint.” On the other hand, a bump of Au may be jointed by a thin layer of solder or Sn. While Au bumps have better dimensional stability or better creep resistance than soft solder bumps, their interfaces are poorer in fracture and fatigue resistance. When the solder layer on the Au bump is thin, it can be transformed completely to Au-Sn IMC during reﬂow. If the IMC is thin and brittle, it will not survive the very large thermal strain we have discussed in direct chip attachment in Chapter 1 [42–53]. Isothermal sections of the SnPbAu ternary phase diagram at varied temperatures are needed for a comparison of wetting reaction and solid-state aging. These diagrams have been calculated on the basis of the optimized binary systems. The ternary phase diagrams of SnPbAu at 160, 200, 225, and 330◦ C are shown in Fig. 7.14(a), (b), (c), and (d), respectively. At 200◦ C, the molten solder will dissolve about 4.5 wt% Au before the formation of AuSn4 . Since AuSn4 is unstable on Au, we expect the other compounds such as AuSn2 and AuSn will form between AuSn4 and Au. 7.4.1 Reaction between Eutectic SnPb and Au Foil Experimentally, in the wetting reaction of a eutectic SnPb solder cap on a Au foil at 200◦ C, the wetting angle is unstable and it decreases with time, but it diﬀers from that on a Pd surface [45, 46]. The cap begins with a wetting angle of 20◦ , decreases to 6◦ in 2 to 3 min, and then stops because all the molten solder in the cap has reacted with Au to form IMC. The surface of the cap becomes very rough and the faceted surface of IMC can be seen. Cross-sectional SEM images of the cap after only 5 and 60 sec at 200◦ C are shown in Fig. 7.15, where the AuSn4 compound has extended all the way to the surface of the cap. The cross-sectional proﬁle of the top surface of the cap

SVNY339-Tu

April 5, 2007

17:13

Solder Reactions on Ni, Pd, and Au

199

Fig. 7.14. Ternary phase diagrams of SnPbAu at (a) 160◦ C, (b) 200◦ C, (c) 225◦ C, and (d) 330◦ C. (Courtesy of Dr. K. Zeng, TI.)

is not smooth and is no longer circular. Also, the bottom surface of the cap has sunken into the Au. A large fraction of the AuSn4 compounds was formed during solidiﬁcation because of the high solubility of Au in the molten solder. With a diﬀusivity of 10−5 cm2 /sec, Au atoms can diﬀuse a distance of 100 μm in 5 sec and reach the top surface of the solder cap, so Au can easily saturate the molten solder during the reﬂow. However, the interesting question here is why the formation of AuSn4 does not become a diﬀusion barrier to stop the interface from sunking into Au. We recall that in the cases of SnPb/Cu and SnPb/Ni, there are no sunken interfaces. We may also ask how the high solubility of Au in molten eutectic SnPb aﬀects IMC formation. According to thermodynamic principles, dissolution of Au into the molten solder must occur ﬁrst when the molten solder is in contact with the Au, and it is assumed that only when the molten solder has reached the solubility limit of Au can the IMC start to form at the interface. However, it is unnecessary for the entire molten solder in the sample to reach

SVNY339-Tu

200

April 5, 2007

17:13

Chapter 7

Fig. 7.15. Cross-sectional SEM images of eutectic SnPb solder cap on Au foil after only 5 sec (a) and 60 sec (b) at 200◦ C. It is seen that the AuSn4 compound has extended all the way to the surface of the cap.

the solubility limit. Rather, it is only necessary to have a boundary layer of molten solder next to the Au become saturated or slightly supersaturated, thereafter the IMC can nucleate heterogeneously and grow. Thus, we may assume that a boundary layer of molten solder next to Au can dissolve Au to supersaturation, the IMC then nucleates and precipitates heterogeneously on the Au surface. The nucleation of IMC may only require a very small supersaturation in the molten solder since the IMC is supercooled at the wetting temperature. When the IMC grows into a continuous layer, it becomes a diﬀusion barrier to the subsequent dissolution. To study such dissolution and reaction issue, a strip of Au foil 0.5 mm thick was rolled into a ring of 0.4-mm diameter and a eutectic SnPb wire was inserted into the ring and immersed in ﬂux for reaction at 200◦ C. Figure 7.16(a) to (c) show the interface after 10, 90, and 210 sec at 200◦ C. To arrest the fast reaction during cooling, the ring sample was quenched in ethanol. The cross section was polished and etched for SEM observation. Both AuSn4 and AuSn2 were found. The latter is a thin continuous layer between the Au and AuSn4 and it has a constant thickness, independent of the annealing time. Because the thickness of the AuSn2 layer is constant, it is believed that it forms during quench, not during the annealing at 200◦ C. The AuSn4 has a chunkytype morphology, has a three-dimensional growth, and becomes longer, wider, and thicker with time. However, there are solder phases or channels in between the chunky grains. The initial growth of AuSn4 is extremely fast, about 1 μm/sec, which is similar to that of PdSn3 . However, unlike PdSn3 which can grow to several hundred micrometers thick, the layer of AuSn4 at the interface

SVNY339-Tu

April 5, 2007

17:13

Solder Reactions on Ni, Pd, and Au

201

Fig. 7.16. Cross-sectional images of a ring of Au foil containing eutectic SnPb after 10 sec (a), 90 sec (b), and 210 sec (c) at 200◦ C.

does not grow very thick. The morphology of AuSn4 is diﬀerent from that of PdSn3 . The AuSn4 tends to disperse all over the solder within the ring and occupied over one quarter of the total volume of the solder. These dispersed AuSn4 crystals come from two processes; one is from the breakage of grains growing from the interface, and the other is from precipitation of the dissolved Au in the molten solder during cooling. Because the AuSn4 contains channels, it is not a diﬀusion barrier and will not prevent the continuous dissolution of Au into the molten solder. The porous morphology of AuSn4 enables it to

SVNY339-Tu

202

April 5, 2007

17:13

Chapter 7

grow fast and at the same time to be accompanied by a fast dissolution of Au into the molten solder. The channels, when they are ﬁlled with molten solder, serve as short-circuit paths for the transport of Au needed to grow the AuSn4 as well as to maintain the dissolution of Au into the pool of molten solder. The dissolution has also been studied by the reaction between Pb-5 wt% Sn on Au at 330◦ C for 10 sec. Figure 7.17(a) and (b) show cross-sectional SEM images of the solder cap and an enlarged image at one end of the cap, respectively. Two striking appearances are to be noted in these ﬁgures. The ﬁrst is a very deep sunken interface, which shows that the molten solder has dissolved about 70 μm of Au in depth. It indicates a dissolution rate of Au of about 7 μm/sec, assuming a linear dissolution rate. This is an extremely fast rate of dissolution. The second is that the solder cap is full of Au2 Pb compound and there is no other IMC at the interface. According to the SnPbAu ternary phase diagram at 330◦ C, shown in Fig. 7.14(d), the molten high-Pb solder can dissolve up to 50 wt% Au and the IMC that forms at 330◦ C is Au2 Pb. On the basis of the phase diagram and the SEM image shown in Fig. 7.17(a), they suggest that in the 10-sec reﬂow, the solder cap has not dissolved all the Au to reach the solubility limit, not even in the boundary layer next to

Fig. 7.17. (a) Cross-sectional SEM image of the solder cap of Pb-5 wt% Sn on Au and (b) an enlarged image at one end of the cap.

SVNY339-Tu

April 5, 2007

17:13

Solder Reactions on Ni, Pd, and Au

203

the Au. Thus, no IMC is formed at the interface. On the other hand, if the sample were annealed more than 10 sec, an interfacial layer of Au2 Pb might have been found. Upon cooling, the dissolved Au comes out in the form of Au2 Pb dispersed all over the solder. What has happened to the 5 wt% Sn in the solder is unclear. According to the liquidus surface projection of the phase diagram, a very small amount of the compound phase AuSn will form after the precipitation of the primary Au2 Pb. Since the sunken interface changes the wetting tip angle, no constant wetting angle exists during the reﬂow. This is another case of a chemical reaction (dissolution) at the wetting interface defeating the Young’s equilibrium condition of the wetting tip. The wetting angle, when the sunken part is included, is not constant but increases with time. Solid-state aging of near-eutectic SnPb on Au has been studied in the temperature range from 80 to 160◦ C. Electro-deposited Au 12 μm thick was patterned into 2-mm-diameter disks and a drop of molten solder of Pb-72 at.% Sn was applied to wet the Au surface with ﬂux in about 1 sec. Solid-state aging was followed after cooling to room temperature. After aging for 7 hr at 160◦ C, a very thin but very Au-rich δ phase was found next to Au and followed by 1.5 μm of AuSn, 10 μm of AuSn2 , and 30 μm of AuSn4 . All three Au-Sn compounds contain a certain amount of Pb. The morphology of AuSn4 is very much like that of PdSn3 shown in Fig. 7.11. The microstructure of AuSn4 was described as having lamellar (columnar) grains with a thickness (diameter) of about 3 μm, lying parallel to the growth direction, with sheets or rods of solder alloy between them along the same direction. The growth of AuSn4 was found to be diﬀusion-controlled with an activation energy of 0.84 eV/atom. No precipitation of Au-Sn and Au-Pb compounds in the remaining solder was reported. According to the phase diagram of SnPbAu at 160◦ C, shown in Fig. 7.14(a), we expect the formation of AuSn4 , AuSn2 , AuSn and perhaps other Au-rich compounds between the solder and the Au. No formation of AuPb compound is expected. The phase formation is in good agreement with the experimental ﬁnding mentioned. Again, the major diﬀerence between the wetting reaction and the solidstate reaction is in the rate of reaction. The wetting reaction at 200◦ C has a rate of IMC formation of about 1 μm/sec, and it takes only a few minutes to form a layer of AuSn4 of 30μm. On the other hand, it takes 7 hr for solid-state reaction at 160◦ C to form the same amount of AuSn4 . Thus, there is a diﬀerence of at least two orders of magnitude in rate between the two reactions. Furthermore, the wetting reaction involves a substantial amount of dissolution of the Au, but not the solid-state reaction. The diﬀerence in rates of IMC formation is not as large as what we have found in the cases of Cu and Ni. We note that this is because the AuSn4 does not form a continuous layer and Au can diﬀuse interstitially in the solid solder lamellae in between the AuSn4 . While the diﬀusivity of Au in molten solder is about 10−5 cm2 /sec, the solid-state diﬀusivity of Au in Pb and Sn at 160◦ C is about 10−7 cm2 /sec, which is quite fast.

SVNY339-Tu

204

April 5, 2007

17:13

Chapter 7

7.4.2 Reaction between Eutectic SnPb and Au Thin Film When the Au ﬁlm is about 100 nm as in the case of a trilayer of Cr/Cu/Au, the molten solder dissolves all the Au very quickly before reacting with the Cu. Tiny Au-Sn particles were segregated out on the surface of Cu6 Sn5 spheroids upon cooling. When the Au is thick and is about 1 μm as in the case of Cu/Ni/Au trilayer used in ball-grid-array (BGA) packaging, the reﬂow at 225◦ C for 10 sec has converted all the Au into a porous layer of AuSn2 and AuSn4 . The grains in this layer then began to separate themselves from the Ni layer and to spall into the molten solder. In the cross-sectional SEM image, a few very large AuSn4 grains can be seen to have dispersed in the solder ball. When Ni(P) is used as UBM in ﬂip chip, a thin coating of Au is deposited on Ni(P) by electroplating. During reﬂow, the Au dissolves into the molten solder and allows the Ni(P) to react with solder. The Au layer is so thin that the overall content of Au in the molten solder bump is below the saturation solubility. The compound AuSn4 will precipitate throughout the bulk of the solder during cooling. However, after a solid-state aging at high temperatures for several hours, some of the AuSn4 crystals that dispersed in the bulk of BGA solder joints before aging have redeposited at the solder/Ni3 Sn4 interface as a continuous layer. The aged joints were found to be signiﬁcantly weaker than those before aging, and they failed by brittle fracture along the interface between the AuSn4 layer and the Ni3 Sn4 layer. To prevent the redeposition problem, one percent of Ni particles was added to the solder so as to keep the dispersion of Au remaining in the bulk of the solder.

References 1. P. W. Dehaven, “The reaction kinetics of liquid 60/40 Sn/Pb solder with copper and nickel: a high temperature X-ray diﬀraction study,” in Proc. Electronic Packaging Materials Science, Materials Research Society, USA, 1984, pp. 123–128. 2. W. G. Bader, “Dissolution of Au, Ag, Pd, Pt, Cu, and Ni in a molten tin-lead solder,” Weld. J. Res. Suppl., 28, 551s–557s (1969). 3. K. N. Tu and R. Rosenberg, “Room temperature interaction in bimetallic thin ﬁlms,” Jpn J. Appl. Phys., Suppl. 2 (Part 1), 633 (1974). 4. C.-Y. Lee and K.-L. Lin, “The interaction kinetics and compound formation between electroless Ni-P and solder,” Thin Solid Films, 249, 201–206 (1994). 5. C.-Y. Lee and K.-L. Lin, “Preparation of solder bumps incorporating electroless nickel-boron deposit and investigation on the interfacial interaction behavior and wetting kinetics,” J. Mater. Sci. Mater. Electron., 8, 377–383 (1997). 6. C.-J. Chen and K.-L. Lin, “The reactions between electroless Ni-Cu-P deposit and 63Sn-37Pb ﬂip chip solder bumps during reﬂow,” J. Electron. Mater. 29, 1007–1014 (2000).

SVNY339-Tu

April 5, 2007

17:13

Solder Reactions on Ni, Pd, and Au

205

7. G. Ghosh, “Thermodynamic modeling of the Ni-Pb-Sn system,” Metall. Mater. Trans. A, 30, 1481–1494 (1999). 8. G. Ghosh, “Kinetics of interfacial reaction between eutectic Sn-Pb solder and Cu/Ni/Pd metallizations,” J. Electron. Mater., 28, 1238–1250, 1999. 9. D. Frear, F. Hosking, and P. Vianco, “Mechanical behavior of solder joint interfacial intermetallics,” in Proc. Materials Developments in Microelectronic Packaging: Performance and Reliability, 19–22 Aug. 1991, Montreal, Canada, ASM International, Materials Park, Ohio, pp. 229–240 (1991). 10. A. C. Harman, “Rapid tin-nickel intermetallic growth: Some eﬀects on solderability,” in Proc. InterNepcon, Brighton, UK, pp. 42–49 (1978). 11. J. Haimovich, “Intermetallic compound growth in tin and tin-lead platings over nickel and its eﬀects on solderability,” Weld. J., 68, 102s–111s (1989). 12. P. J. Kay and C. A. MacKay, “Growth of intermetalic compounds on common basis material coated with tin or tin-lead alloys,” Trans. Inst. Met. Finish., 54, 68–74 (1976). 13. J. W. Jang, P. G. Kim, K. N. Tu, D. R. Frear, and P. Thompson, “Solder reaction-assisted crystallization of electroless Ni-P under bump metallization in low cost ﬂip chip technology,” J. Appl. Phys., 85, 8456–8463 (1999). 14. J. W. Jang, D. R. Frear, T. Y. Lee, and K. N. Tu, “Morphology of interfacial reaction between Pb-free solders and electroless Ni(P) under-bumpmetallization,” J. Appl. Phys., 88, 6359–6363 (2000). 15. P. G. Kim, J. W. Jang, T. Y. Lee, and K. N. Tu, “Interfacial reaction and wetting behavior in eutectic SnPb solder on Ni/Ti thin ﬁlms and Ni foils,” J. Appl. Phys. 86, 6746–6751 (1999). 16. P. G. Kim, J. W. Jang, K. N. Tu, and D. Frear, “Kinetic analysis of interfacial penetration accompanied by intermetallic compound formation,” J. Appl. Phys. 86, 1266–1272 (1999). 17. Y.-D. Jeon, K.-W. Paik, K.-S. Bok, W.-S. Choi, and C.-L. Cho, “Studies on Ni-Sn intermetallic compound and P-rich Ni layer at the electroless nickel UBM–solder interface and their eﬀects on ﬂip chip solder joint reliability,” in Proc. 51st Electronic Components & Technology Conference, May 29-June 31, 2001, Orlando, FL, IEEE, Piscataway, NJ, pp. 1326–1332 (2001). 18. K. C. Hung, Y. C. Chan, C. W. Tang, and H. C. Ong, “Correlation between Ni3 Sn4 intermetallics and Ni3 P due to solder reaction-assisted crystallization of electroless Ni-P metallization in advanced packages,” J. Mater. Res. 15, 2534–2539 (2000). 19. K. C. Hung and Y. C. Chan, “Study of Ni3 P growth due to solder reactionassisted crystallization of electroless Ni-P metallization,” J. Mater. Sci. Lett., 19, 1755–1757 (2000). 20. P. Liu, Z. Xu, and J. K. Shang, “Thermal stability of electroless-Ni/solder interfaces: Part A. Interfacial chemistry and microstructure,” Metall. Mater. A, Trans. 31, 2857–2866 (2000).

SVNY339-Tu

206

April 5, 2007

17:13

Chapter 7

21. K. Zeng, V. Vuorinen, and J. K. Kivilahti, “Intermetallic reactions between lead-free SnAgCu solder and Ni(P)/Au surface ﬁnish on PWBs,” in Proc. 51st Electronic Components & Technology Conference, May 29June 31, 2001, Orlando, FL, IEEE, Piscataway, NJ, pp. 685–690 (2001). 22. 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). 23. 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). 24. K. Y. Lee, M. Li, and K. N. Tu, “Growth and ripening of (Au,Ni)Sn4 phase in Pb-free and Pb containing solder on Ni/Au metallization,” J. Mater. Res., 18, 2562–2570 (2003) 25. M. O. Alam, Y. C. Chan, and K. N. Tu, “Eﬀect of reaction time and Pcontent on mechanical strength of the interfaces formed between eutectic Sn-Ag solder and Au/electroless Ni(P)/Cu bond pad,” J. Appl. Phys., 94, 4108–4115 (2003) 26. M. O. Alam, Y. C. Chan, and K. N. Tu, “Eﬀect of 0.5 wt% Cu addition in the Sn-3.5%Ag solder on the interfacial reaction with Au/Ni metallizaion,” Chem. Mater., 15, 4340–4342 (2003). 27. C. E. Ho, Y. W. Lin, S. C. Yang, C. R. Kao, and D. S. Jiang, “Eﬀect of limited Cu supply on soldering reactions between SnAgCu and Ni,” J. Electron. Mater., 35, 1017–1024 (2006). 28. Y. D. Jeon, S. Nieland, A. Ostmann, H. Reichl, and K. W. Paik, “A study on interfacial reactions between electroless Ni-P under bump metallization and 95.5Sn4Ag 0.5 Cu alloy,” J. Electron. Mater., 32, 548–557 (2006). 29. M. L. Huang, T. Loeher, D. Manessis, L. Boettcher, A. Ostmann, and H. Reichl, “Morphology and growth kinetics of intermetallic compounds in solid-state interfacial reaction of electroless Ni-P with Sn based Pb-free solders,” J. Electron. Mater., 35, 181–188 (2006). 30. K. S. Kim, S. H. Huh, and K. Suganuma, “Eﬀects of intermetallic compounds on properties of SnAgCu Pb-free soldered joints,” J. Alloys Compounds, 352, 226–236 (2006). 31. L. Y. Hsiao, S. T. Kao, and J. G. Duh, “Characterizing metallurgical reaction of Sn3Ag0.5Cu composite solder by mechanical alloying with electroless Ni-P/Cu under bump metallization after various reﬂow cycles,” J. Electron. Mater., 35, 81–88 (2006). 32. C. Lin, J. G. Duh, and B. S. Chiou, “Wettability of electroplated Ni-P in under bump metallization wuth SnAgCu solders,” J. Electron. Mater., 35, 7–14 (2006). 33. K. N. Tu, “Single intermetallic compound formation in Pd-Pb and PdSn thin-ﬁlm couples studied by X-ray diﬀraction”, Mater. Lett., 1, 6–10 (1982).

SVNY339-Tu

April 5, 2007

17:13

Solder Reactions on Ni, Pd, and Au

207

34. Y. Wang, H. K. Kim, H. K. Liou, and K. N. Tu, “Rapid soldering reactions of eutectic SnBi and eutectic SnPb solder on Pd surfaces,” Scr. Metall. Mater., 32, 2087–2092 (1995). 35. 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, 1069–071 (1995). 36. P. G. Kim, K. N. Tu, and D. C. Abbott, “Eﬀect of Pd thickness on soldering reaction between eutectic SnPb and plated Pd/Ni thin ﬁlms on Cu leadframe,” Appl. Phys. Lett., 71, 61–63 (1997). 37. P. G. Kim, K. N. Tu, and D. C. Abbott, “Soldering reaction between eutectic SnPb and plated Pd/Ni thin ﬁlms on Cu leadframe”, Appl. Phys. Lett., 71, 61–63 (1997). 38. P. G. Kim, K. N. Tu, and D. C. Abbott, “Time and temperature dependent wetting behavior of eutectic SnPb on Cu lead-frame plated with Pd/Ni and Au/Pd/Ni thin ﬁlms,” J. Appl. Phys. 84, 770–775 (1998). 39. G. Ghosh, “Diﬀusion and phase transformations during interfacial reaction between lead-tin solders and palladium,” J. Electron. Mater., 27, 1154–1160 (1998). 40. G. Ghosh, “Thermodynamic modeling of the Pd-Pb-Sn system,” Metall. Mater. Trans. A, 30, 5–18 (1999). 41. G. Ghosh, “Interfacial microstructure and the kinetics of interfacial reaction in diﬀusion couples between Sn-Pb solder and Cu/Ni/Pd metallization,” Acta. Mater., 48, 3719–3738 (2000). 42. A. Prince, “The Au-Pb-Sn ternary system,” J. Less-Common Met., 12, 107–116 (1967). 43. G. Humpston and D. S. Evans, “Constitution of Au-AuSn-Pb partial ternary system,” Mater. Sci. Technol., 3, 621–627 (1987). 44. E.-B. Hannech and C. R. Hall, “Diﬀusion controlled reactions in Au/PbSn solder system,” Mater. Sci. Technol., 8, 817–824 (1992). 45. 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). 46. P. G. Kim and K. N. Tu, “Fast dissolution and soldering reactions on Au foils,” Mater. Chem. Phys., 53, 165–171 (1998). 47. Z. Mei, M. Kaufmann, A. Eslambolchi, and P. Johnson, “Brittle interfacial fracture of PBGA packages soldered on electroless nickel/immersion gold,” in Proc. 48th Electronic Components and Technology Conference, 25–28 May 1998, Seattle, WA, IEEE, Piscataway, NJ, pp. 952–961 (1998). 48. Z. Mei, P. Callery, D. Fisher, F. Hua, and J. Glazer, “Interfacial fracture mechanism of BGA packages on electroless Ni/Au,” in Proc. Paciﬁc Rim/ASME International Intersociety Electronic and Photonic Packaging Conf., Advances in Electronic Packaging 1997, ASME, New York, Vol. 2, pp. 1543–1550 (1997). 49. S. C. Hung, P. J. Zheng, S. C. Lee, and J. J. Lee, “The eﬀect of Au plating thickness of BGA substrates on ball shear strength under reliability

SVNY339-Tu

208

50.

51.

52.

53.

April 5, 2007

17:13

Chapter 7

tests,” in Proc. 24th IEEE/CPMT International Electronics Manufacturing Technology Symp., Oct. 18–19, 1999, Austin, TX, IEEE, Piscataway, NJ, pp. 7–15 (1999). C. E. Ho, R. Zheng, G. L. Luo, A. H. Lin, and C. R. Kao, “Formation and resettlement of (Aux Sn1−x )Sn4 in solder joints of ball-grid-array packages with the Au/Ni surface ﬁnish,” J. Electron. Mater., 29, 1175–1181 (2000). A. M. Minor and J. W. Morris, “Growth of a Au-Ni-Sn intermetallic compound on the solder-substrate interface after aging,” Metall. Mater. Trans. A, 31, 798–800 (2000). A. M. Minor and J. W. Morris, “Inhibiting growth of the Au0.5Ni0.5Sn4 intermetallic layer in Pb-Sn solder joints reﬂowed on Au/Ni metallization,” J. Electron. Mater., 29, 1170–1174 (2000). S. Anhock, H. Oppermann, C. Kallmayer, R. Aschenbrenner, L. Thomas, and H. Reichl, “Investigations of Au-Sn alloys on diﬀerent end-metallizations for high temperature applications,” in Proc. 22nd IEEE/CPMT International Symp. Electronics Manuf. Technol., 27–29 April 1998, Berlin, IEEE, pp. 156–165 (1998).

SVNY339-Tu

April 5, 2007

17:25

II

Electromigration and Thermomigration

SVNY339-Tu

April 5, 2007

17:25

8 Fundamentals of Electromigration

8.1 Introduction An ordinary household extension cord conducts electricity without electromigration in the cord because the electric current density in the cord is low, about 102 A/cm2 , and also the ambient temperature is too low for atomic diﬀusion to occur in copper. The free electron model of conductivity of metals assumes that the conduction electrons are free to move in the metal, unconstrained by the perfect lattice of atoms except for scattering interactions due to phonon vibration. The scattering is the cause of electrical resistance and joule heating. When an atom is out of its equilibrium position, for example, a diﬀusing atom at the activated state, it possesses a very large scattering cross section. Nevertheless, when the electric current density is low, the scattering or the momentum exchange between the electrons and the diﬀusing atom does not enhance displacement of the latter and it has no net eﬀect on atomic diﬀusion. However, the scattering by electrons in a high current density, above 104 A/cm2 , enhances atomic displacement in the direction of electron ﬂow. The enhanced atomic displacement and the accumulated eﬀect of mass transport under the inﬂuence of electric ﬁeld (mainly a high-density electric current) are called electromigration. It is worth noting that a household cord is allowed to carry only a very low current density, otherwise joule heating will burn the fuse. Yet, a thinﬁlm interconnect in a Si device can carry a much higher current density, which facilitates electromigration. This is because the Si chip on which interconnects are built is a very good heat conductor, hence the interconnect on Si can carry a very high current density without overheating. On the other hand, in a device having a very dense integration of circuits, the heat management is a serious issue. Typically, a device is cooled by a fan or other means in order to maintain the working temperature around 100◦ C. In very-large-scale integration (VLSI) of circuits on a Si device, assuming an Al or Cu thin-ﬁlm line 0.5 μm wide and 0.2 μm thick carrying a current of 1 mA, for example, the current density will be 106 A/cm2 . Such current density can cause electromigration in the line at the device working temperature of

SVNY339-Tu

212

April 5, 2007

17:25

Chapter 8

Fig. 8.1. (a) SEM image of Al short strips on TiN baseline after electromigration. (b) High-magniﬁcation image of one of the Al strips. (Courtesy of Dr. Alexander Straub, MPI Stuttgart, Germany.)

100◦ C and lead to void formation at the cathode and extrusion at the anode. These defects are the most persistent and most serious reliability failures in thin-ﬁlm integrated circuits. As device miniaturization demands smaller and smaller interconnects, the current density goes up, as does the probability of circuit failure induced by electromigration. This is a subject which has demanded and attracted much attention [1–25]. The phenomenon of electromigration can be observed directly from the response of a set of short Al strips on a baseline of TiN as shown in Fig. 8.1(a). This structure is called the Blech structure for electromigration tests [5, 6]. The Al strips have a line width of 10 μm and thickness of 100 nm. The applied electric current in the TiN baseline took a detour to go along the strips because the latter are paths of low resistance. When the current density and temperature are high enough, atomic transport occurs and void and extrusion formations can be observed directly. Under applied current density of 106 A/cm2 at 225◦ C for 24 hr, depletion at the cathode end and extrusion formation at the anode end of several of the strips can be seen in Fig. 8.1(a). It is worth noting that no electromigration damage can be seen in the shorter strips in the upper right corner. Figure 8.1(b) is a higher-magniﬁcation SEM image of one of the strips. It is important to note that the atomic displacement and mass transport are in the same direction as the electron ﬂow from the lower left corner to the upper right corner. Figure 8.2(a) shows the morphology of a Cu strip in electromigration with a current density of 5 × 105 A/cm2 at 350◦ C for 99 hr [12]. At the cathode end of the strip, a depleted region can be seen, but at the anode end, an extrusion is seen. By conservation of mass, the depletion (void) equals the extrusion in the same strip. The rate of depletion at the cathode can be measured so the drift velocity can be calculated. Figure 8.2(b) is a set of SEM images of the depletion at the cathode of a Cu strip taken at diﬀerent intervals at 400◦ C with a current density of 2.1 × 106 A/cm2 . The drift velocity is about 2 μm/hr.

SVNY339-Tu

April 5, 2007

17:25

Fundamentals of Electromigration

213

(a)

(b)

Fig. 8.2. (a) SEM image of a Cu strip on W baseline after electromigration. (b) SEM images of the depletion at cathode of a Cu strip taken at diﬀerent intervals at 400◦ C with current density of 2.1 × 106 A/cm2 . The drift velocity is about 2 μm/hr.

SVNY339-Tu

214

April 5, 2007

17:25

Chapter 8 (a)

Cu/dielectric cap interface

Current Crowding

(b)

Cu/dielectric cap interface

Current Crowding

Cu/dielectric cap interface

Fig. 8.3. (a) SEM images of void formation at the upper end and lower end (b) of a via in a dual damascene structure of Cu interconnect due to electromigration. (Courtesy of Professor S. G. Mhaisalkar, Nanyang Technological University, Singapore.)

Figure 8.3 shows images of void formation in the upper (a) and lower end (b) of a via at the cathode end in a dual damascene structure of Cu interconnect due to electromigration. Each of them had caused open circuit and was detected by a very large resistance increase. The kinetic process of void formation was the propagation and accumulation of a sequence of small voids on the upper surface of the Cu interconnect. Clearly, electromigration in Cu interconnect is dominated by surface diﬀusion [21–25].

8.2 Electromigration in Metallic Interconnects Electromigration is the result of a combination of thermal and electrical eﬀects on mass transport. If the conducting line is kept at a very low temperature

SVNY339-Tu

April 5, 2007

17:25

Fundamentals of Electromigration

215

Table 8.1. Diﬀusivity of Al, Cu, and SnPb

Cu

Melting point (K)

Temperature ratio 373K/Tm

1356

0.275

Al

933

0.4

Eutectic SnPb

456

0.82

Diﬀusivities at 100◦ C(cm2 /sec)

Diﬀusivities at 350◦ C (cm2 /sec)

Lattice D l = 7 × 10−28 Grain boundary D gb = 3 × 10−15 Surface D s = 10−12 Lattice D l = 1.5 × 10−19 Grain boundary D gb = 6 × 10−11 Lattice D l = 2 × 10−9 to 2 × 10−10

D l = 5 × 10−17 D gb = 1.2 × 10−9 D s = 10−8 D l = 10−11 D gb = 5 × 10−7 Molten state D l > 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

SVNY339-Tu

216

April 5, 2007

17:25

Chapter 8

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

SVNY339-Tu

April 5, 2007

17:25

Fundamentals of Electromigration

217

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)

SVNY339-Tu

218

April 5, 2007

17:25

Chapter 8 (a)

(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 <110> 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.

SVNY339-Tu

April 5, 2007

17:25

Fundamentals of Electromigration

219

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

SVNY339-Tu

220

April 5, 2007

17:25

Chapter 8

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

SVNY339-Tu

April 5, 2007

17:25

Fundamentals of Electromigration

221

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)

SVNY339-Tu

April 5, 2007

222

17:25

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 <110> 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.

SVNY339-Tu

April 5, 2007

17:25

Fundamentals of Electromigration

223

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.

SVNY339-Tu

224

April 5, 2007

17:25

Chapter 8

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

SVNY339-Tu

April 5, 2007

17:25

Fundamentals of Electromigration

225

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

SVNY339-Tu

226

April 5, 2007

17:25

Chapter 8

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.

SVNY339-Tu

April 5, 2007

17:25

Fundamentals of Electromigration

227

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

SVNY339-Tu

228

April 5, 2007

17:25

Chapter 8

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.

SVNY339-Tu

April 5, 2007

17:25

Fundamentals of Electromigration

229

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.

SVNY339-Tu

April 5, 2007

230

17:25

Chapter 8

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,

SVNY339-Tu

April 5, 2007

17:25

Fundamentals of Electromigration

231

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].

SVNY339-Tu

232

April 5, 2007

17:25

Chapter 8

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

SVNY339-Tu

April 5, 2007

17:25

Fundamentals of Electromigration

233

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)

SVNY339-Tu

234

April 5, 2007

17:25

Chapter 8

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.

SVNY339-Tu

April 5, 2007

17:25

Fundamentals of Electromigration

235

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.)

SVNY339-Tu

236

April 5, 2007

17:25

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)

SVNY339-Tu

April 5, 2007

17:25

Fundamentals of Electromigration

237

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 ρc cos2 θ + ρa sin2 θ

cos ϕ =

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

SVNY339-Tu

238

April 5, 2007

17:25

Chapter 8

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.

SVNY339-Tu

April 5, 2007

17:25

Fundamentals of Electromigration

239

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

SVNY339-Tu

240

April 5, 2007

17:25

Chapter 8

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.

SVNY339-Tu

April 5, 2007

17:25

Fundamentals of Electromigration

241

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).

SVNY339-Tu

242

April 5, 2007

17:25

Chapter 8

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).

SVNY339-Tu

April 5, 2007

17:25

Fundamentals of Electromigration

243

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).

SVNY339-Tu

April 5, 2007

17:31

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.

SVNY339-Tu

246

April 5, 2007

17:31

Chapter 9

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

SVNY339-Tu

April 5, 2007

17:31

Electromigration in Flip Chip Solder Joints

247

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

SVNY339-Tu

248

April 5, 2007

17:31

Chapter 9

eSolder

Al line 2 μm

J = I/A AAl<
Fig. 9.1. Schematic diagram depicting the geometry of a ﬂip chip solder bump joining an interconnect line on the chip side (top) and a conducting trace on the board or module side (bottom).

bulk of solder joint. The low threshold of the current density needed to cause electromigration in solder and the high current density induced by current crowding are the key reasons why electromigration in ﬂip chip solder joints can compete with electromigration in Al and Cu interconnects as the major reliability problem in microelectronic devices. Because of the current crowding, the related failure mode of pancake-type void formation in ﬂip chip solder joints is unique (see Section 9.3). 9.2.3 Phase Separation in Eutectic Solder Joints In electromigration, the microstructure change in the bulk of a ﬂip chip solder joint as well as at the cathode and anode interfaces is very diﬀerent from that in Al and Cu interconnects. The reverse ﬂow of Sn at high temperatures or the reverse ﬂow of Pb near room temperature is due to the two-phase eutectic structure of solder alloys. The reverse ﬂow behavior can be explained by assuming a constant volume constraint in segregation in a two-phase structure. Concerning the unique behavior of phase segregation in a two-phase eutectic structure driven by an applied force, a detailed discussion will be given in Sections 9.7 and 12.3. 9.2.4 Narrow Range of Current Density The trend of device miniaturization has reduced the diameter of solder bump below 100 μm, so the average current density in the bump is approaching 104 A/cm2 . While this current density is not high, the joule heating associated with current crowding and pancake-type void formation will cause a large increase in temperature of the solder bump. In a systematic experimental study of melting of certain ﬂip chip eutectic SnPb solder joints, it was found that a threshold current density around 1.6 × 104 A/cm2 exists, above which melting occurs. The melting is time-dependent and partial, meaning it takes time to melt a part of the solder joint. More discussion on time-dependent melting of ﬂip chip solder joint will be given in Section 9.4.7. Since the applied current density in real devices is approaching 1 × 104 A/cm2 and since it is very close to the threshold current density of melting, melting of ﬂip

SVNY339-Tu

April 5, 2007

17:31

Electromigration in Flip Chip Solder Joints

249

chip solder joints has become a new reliability concern because it is timedependent. The reason for melting is unclear. Nevertheless, it is worth mentioning that when the current density in the bump is 1 × 104 A/cm2 , the current density in the interconnect will be about 1 × 106 A/cm2 since the interconnect cross section is two orders of magnitude smaller. Such current density will cause electromigration in the Al interconnect. Hence, from the point of view of reliability, there is a competition between the failure in the solder bump and in the Al interconnect. Especially in the ﬂip chip bump where the electrons ﬂow from the bump to the interconnect, there is an electromigration-induced atomic ﬂux divergence in the Al interconnect, similar to the Al line on a via of W. At the point where current enters the Al interconnect, more Al atoms are driven away due to the very large change in current density. Then the condensation of the reverse ﬂux of vacancies may lead to the formation of a void in the Al above the solder bump. It will increase the resistance and joule heating of the Al. Knowing the upper bound of current density in melting, we may ask what is the lower bound or the threshold current density below which very little electromigration damage occurs in a ﬂip chip solder joint. It is about 1 × 103 A/cm2 . Combining the two bounds, we see that there is only a narrow range of one order of magnitude of diﬀerence in current density, in which electromigration in ﬂip chip solder joints can be studied. The upper bound may depend on the design of UBM and bond pad, and an optimal design may increase the upper bound to 5 × 104 A/cm2 to avoid melting. The lower bound may depend on the composition of the solder, for example, if Pb-free solder is used, it may change to 5 × 103 A/cm2 . Anyway, the range between the two bounds is narrow. 9.2.5 Eﬀect of Under-Bump Metallization on Electromigration Because of the use of under-bump metallization (UBM) to form the solder joint, electromigration has enhanced the dissolution of UBM on the cathode side into solder bump and the transportation of the solute to the anode side, followed by a large amount of intermetallic compound formation near the anode [12–14]. This behavior will be discussed later. The eﬀect of thick Cu UBM will be discussed in Section 9.6.

9.3 Failure Mode of Electromigration in Flip Chip Solder Joints Figure 9.1 depicted the line-to-bump geometry of a ﬂip chip solder joint. Because the cross section of the line on the chip side is at least two orders of magnitude smaller than that of the solder bump, there is a very large current density change at the contact between the bump and the line because the same current is passing between them. Since electric current will take

SVNY339-Tu

250

April 5, 2007

17:31

Chapter 9

the lowest resistance path, electrons will jam at the entrance into the solder bump, resulting in current crowding. There are two signiﬁcant eﬀects due to the current crowding. First, there is an abrupt change in current density in the interconnect, before and beyond the point where current turns into the bump. Second, the current density in the solder bump near the entrance point will be about one order of magnitude higher than the average current density in the middle of the bump. It will be 105 A/cm2 near the entrance when the average current density in the middle of the bump is 104 A/cm2 . Figure 9.2(a) is a two-dimensional simulation of current distribution in a solder joint. Figure 9.2(b) is a display of current density distribution in the joint, where the cross section of the joint is plotted on the x–y plane and

Fig. 9.2. (a) Two-dimensional simulation of current distribution in a solder joint. (b) Current density distribution in the joint, where the cross section of the joint is plotted on the x–y plane and the current density is plotted along the z-axis.

SVNY339-Tu

April 5, 2007

17:31

Electromigration in Flip Chip Solder Joints

251

econtact window e-

e-

Fig. 9.3. SEM images of the damage in a ﬂip chip solder joint caused by electromigration. Electrons of the applied current entered the bump from the upper right corner of the joint. (a) Up to 37 hr at 125◦ C with a current density of 2.25 × 104 A/cm2 , no damage was observed. (b) After 38 hr and (c) after 40 hr, voids are seen at the upper right interface, and the voids have propagated along the interface from right to left. (d) After 43 hr, the joint failed by having a large void across the entire interface.

the current density is plotted along the z-axis. It is the current crowding or the high current density shown at the upper right corner in Fig. 9.2(a) and (b) that leads to electromigration damage in the solder joint, not the average current density in the bulk of the joint. Consequently, electromigration damage in a ﬂip chip solder joint occurs near the cathode contact on the chip side, i.e., the contact between the interconnect and the bump. The damage begins near the entrance point of the electric current. How it propagates across the contact will be explained below. Figure 9.3 displays a set of SEM images of the damage in a ﬂip chip solder joint caused by electromigration. The upper contact of the solder joint to Si consisted of a thin-ﬁlm UBM of Cu/Ni(V)/Al. The total thickness of the thin-ﬁlm UBM is about 1 μm and the thickness of Cu is about 0.4 μm, hence the UBM is not resolved in the SEM image. The applied current of electrons entered the bump from the upper right corner of the joint. Up to 37 hr at 125◦ C with a current density of 2.25 × 104 A/cm2 , no damage was observed as shown in Fig. 9.3(a). Yet, after 38 and 40 hr, voids are seen at the upper right corner of the interface, and the voids have propagated along the interface from

SVNY339-Tu

252

April 5, 2007

17:31

Chapter 9

Fig. 9.4. Corresponding curve of potential change versus time for Fig. 9.3.

right to left, shown in Fig. 9.3(b) and (c), respectively. After 43 hr, the joint failed by having a large pancake-type void across the entire interface, shown in Fig. 9.3(d). The corresponding curve of potential change versus time is shown in Fig. 9.4. The curve shows that the potential change is insensitive to the void formation until the end, where it shows an abrupt jump when the void has propagated across the entire interface. The arrows in Fig. 9.4 indicate the corresponding “time” when the images in Fig. 9.3 were taken. Why the potential change of the solder joint is insensitive to void formation and propagation can be explained by two ﬁndings. The ﬁrst is shown in Fig. 9.5, which depicts the cross section of a solder joint with pancake-type void formation at the upper interface. The formation and propagation of the void displaced the entrance of the current to the front of the void, so there is very little change in resistance of the solder bump by the void formation as long as the current can enter the solder bump. Finally, an abrupt change occurs only when the void has extended across the entire joint or when the contact becomes an open. The second ﬁnding is shown in Table 9.1, which compares the electrical behavior between Al (or Cu) interconnect and solder joint. The resistance of a cubic piece of solder of 100 μm × 100 μm × 100 μm (the size of a solder joint) is about 1 milliohm. The resistivity of Sn and Pb is 11 and 22 μΩ-cm, respectively. The resistance of an Al or Cu line 100 μm long with a cross section of 1μm × 0.2 μm is about 10 ohms. The solder joint is a

SVNY339-Tu

April 5, 2007

17:31

Electromigration in Flip Chip Solder Joints

253

Si e-

e-

e-

Void propagation

Cu

Fig. 9.5. Schematic diagram depicting the cross section of a solder joint with pancaketype void formation and propagation at the upper interface.

low-resistance conductor, but the interconnect is a high-resistance conductor and becomes the source of joule heating. The simple calculation in the above shows that the resistance of the interconnect will be very sensitive to the design of its dimension and to a slight microstructure change and damage. Yet the resistance of the solder bump is not, e.g., not even by the inclusion of a large void within the bulk of the solder bump. Often, the matrix of a solder bump may contain a few very large spherical voids due to residue ﬂux from the solder paste, especially the Pbfree solder paste, yet the voids have little eﬀect on the resistance of the solder bump, except when they move to the contact interface and spread out with the residue. Figure 9.6 is a SEM image of cross section of a daisy chain of ﬂip chip solder joints between a Si chip on the top and a substrate at the bottom. The direction of electron current is indicated by the string of arrows. The cathode contacts on the Si where the electron current enters the solder bump are indicated by small circles. The UBM on the Si chip side was Cu/Ni(V)/Al with 0.8 μm Cu, 0.32 μm Ni(V), and 1 μm Al. The bond pad on the substrate side was Au/Ni(V)/Cu with 0.08 to 0.2 μm Au, 3.8 to 5 μm Ni(V), and 38 μm Cu. The solder bump composition was either eutectic SnPb or 95.5Sn4Ag0.5Cu.

Fig. 9.6. SEM image of cross section of a daisy chain of ﬂip chip solder joints between a Si chip on top and a substrate on the bottom. The arrows indicate the electron ﬂow directions.

SVNY339-Tu

254

April 5, 2007

17:31

Chapter 9

The tests were carried out at 50◦ C ambient with an applied current of 1.7 A for the SnPb solder bumps and 1.8 A for the SnAgCu bumps, and the current density was about 3.5 to 3.7 × 103 A/cm2 [21]. The chip surface temperature was monitored by the temperature coeﬃcient of resistance of 450-ohm serpentine aluminum metal resistors residing on the test chip surface. These resistors were used to determine package thermal resistance characteristics and for in situ monitoring of I 2 R or joule heating. The joule heating was found to increase as electromigration-induced voiding in the bump worsened. The temperature was calculated by adding dT to the ambient temperature of 50◦ C. Tdie = 50 + dT = 50 + RI 2 θja

(9.2)

where θja is deﬁned as the package “junction-to-air” thermal resistance value, which is obtained by measuring dT and by calculating I 2 R. The measured value of θja is about 62 to 72 C/watt. The chip temperature was found to be as high as 175◦ C, indicating an increase of temperature of about 125◦ C due to joule heating. The time for resistance changes of 15% as a function of chip surface temperature was found to have a very sensitive dependence on temperature. Figure 9.7 shows a pancake-type contact void. The failure mode is unique due to the ﬂip chip conﬁguration that void formation occurs only at the cathode contact on the Si chip side, where the electron current enters the solder bump. Hence, void or failure occurs only in one of a pair of bumps, not every bump.

Fig. 9.7. Cross-sectional SEM image of pancake-type void formation. The location of the void formation corresponds to the entrance of electrons into the ﬂip chip bumps.

SVNY339-Tu

April 5, 2007

17:31

Electromigration in Flip Chip Solder Joints

255

9.4 Electromigration in Flip Chip Eutectic Solder Joints Two kinds of solder bumps were tested for comparison of electromigration. Eutectic SnPb and SnAg3.8 Cu0.7 , between electroless Ni UBM on Si and electroplated Cu bond pad on printed circuit board (PCB), were tested at 120◦ C with 1.5 A on a hot plate in atmospheric ambient. The solder bumps were formed by solder paste printing through a stainless mask and reﬂowed twice in a belt furnace with a peak temperature of 240◦ C. The ﬁrst reﬂow was carried out after printing the solder bumps on the chip, and the second reﬂow was carried out to assemble the chip and PCB. After the assembly, the gaps between the chip and the board were ﬁlled with epoxy, i.e., underﬁll. While the IMC on the Ni UBM experienced two reﬂows, the IMC on Cu bond pad has undergone only one reﬂow. To have an in situ observation of electromigration of the solder bump, a pair of solder bumps were cross-sectioned and polished mechanically and chemically before electromigration. The diameter of the contact opening is 100 μm. The average current density through a half contact opening can be calculated to be about 3.8 × 104 A/cm2 when 1.5 A was applied. It was calculated on the basis of half of the SiO2 contact opening, not half of the solder bump diameter. The polishing has left behind embedded SiC and diamond particles on the solder surface. The size of these particles is roughly 1 μm, and they were used as inert diﬀusion markers to calculate the atomic ﬂux driven by electromigration. The marker motion and surface topographic changes due to electromigration were observed with scanning electron microscopy (SEM), energy-dispersive x-ray spectroscopy (EDS), and optical microscopy (OM). In order to perform the observation, electromigration was stopped time to time for observation, i.e., the observation was discontinuous and repeated at various periods. At the end of the test, the samples were cross-sectioned a second time, in a direction perpendicular to the ﬁrst cross section, for SEM observation. Schematic diagrams depicting the ﬁrst and second cross sections are shown in Fig. 9.8 [4, 5].

9.4.1 Electromigration in Eutectic SnPb Flip Chip Solder Joints On the ﬁrst cross-sectioned surface of a eutectic SnPb bump after electromigration of 20 to 40 hr, accumulation of Pb in the anode side and void formation in the cathode side were observed. The ﬂux of atomic motion in the solder bump can be measured with marker motion. In Fig. 9.9(a), the marker positions are shown, and the Pb is the brighter phase in the SEM image. Each marker is either a SiC or a diamond particle. Their displacements are shown in Fig. 9.9(b). Except for marker numbers 1, 10, and 11, all the other markers are similar in magnitude of movement. The average movement, except for

SVNY339-Tu

256

April 5, 2007

17:31

Chapter 9 1st Cross-Section

a)

2nd Cross-Section

b)

Si Ni

Underfill

electron flow FR4

Cu

Fig. 9.8. Schematic diagrams depicting the ﬁrst and second cross sections of ﬂip chip solder joints for observation of electromigration.

Fig. 9.9. (a) Marker positions on the cross-sectional surface. Each marker is either a SiC or a diamond particle. (b) Marker displacements. Except for marker numbers 1, 10, and 11, all the other markers are similar in magnitude of movement. (c) The average movement, except for marker numbers 1, 10, and 11, as a function of time. A linear displacement is seen in the period from 20 to 39.5 hr.

SVNY339-Tu

April 5, 2007

17:31

Electromigration in Flip Chip Solder Joints

257

marker numbers 1, 10, and 11, as a function of time is shown in Fig. 9.9(c). A linear displacement is seen in the period from 20 to 40 hr. In analyzing the atomic ﬂux in the solder joint, electron wind force and the mechanical force were considered to aﬀect the motion of Pb atoms at 120◦ C, Jem = −C

D dσΩ D ∗ +C Z eE, kT dx kT

(9.3)

where Jem is atomic ﬂux in units of atoms/cm2 sec, C the concentration of atoms per unit volume, D/kT the atomic mobility, σ the hydrostatic stress in the metal and dσ/dx the stress gradient along the direction of electron ﬂux, Ω the atomic volume, Z ∗ the eﬀective charge number of electromigration, e the electron charge, E the electric ﬁeld and E = ρj, where ρ is the electrical resistivity and j is the current density. The value of atomic ﬂux of electromigration, Jem , can be estimated by the motion of marker [3,4]: Jem =

u VEM = , ΩAt Ωt

(9.4)

where VEM is the volume of solder moved by electromigration, which was calculated as the marker displacement multiplied by the cross-sectional solder area A · u is the marker displacement, and t is the electromigration time. By ignoring the back stress and by measuring the atomic ﬂux of electromigration, Jem , the product of diﬀusivity and eﬀective charge number, DZ ∗ , can be calculated from the following equation [4, 5]: Jem =

VEM D ≈C· · Z ∗ · e · E. Ω · (A · t) kT

(9.5)

From the calculated values of DZ ∗ , we can estimate Z ∗ by knowing D and assuming no back stress. To examine whether the measured value of DZ ∗ is reasonable or not, we have attempted to unravel Z ∗ from D by using the activation energy of meantime-to-failure (MTTF) of 0.8 eV measured by Brandenburg and Yeh [1] and the prefactor of 0.1 cm2 /sec. The eﬀective charge number is calculated to be about 102 at 120◦ C. If we assume there is joule heating and assume the actual solder temperature to be 140◦ C instead of 120◦ C, the eﬀective charge number would become 34. This value is in better agreement with the eﬀective charge number of pure Pb in Pb, which is about 47, than that of pure Sn in Sn, which is about 17, as discussed in Chapter 8. Figure 9.10 shows the second cross section of the solder bump which has had the ﬁrst cross section. The voids and the indented solder surface at the cathode side and a bulge at the anode side can be seen, indicating that it is not a constant volume transformation. More volume has been transferred from the cathode to the anode. The polished surface, i.e., the free surface,

SVNY339-Tu

258

April 5, 2007

17:31

Chapter 9

(a)

(b) Cu

1st Cross-Section

Underfill

Al

Si

Al

electron flow 2 nd Cross-Section Cross -Section

FR4 Cu

Figure Sample layout (a) Plane view (b) Side view

electron

Ni : 18.4at% Cu : 28.4at% Sn: 50.8 at%

Ni : 15.9at% Cu : 29.6at% Sn:52at%

Ni : 11.8at% Cu : 23.6at% Sn: 46.0at% Pb: 18.6at%

50 μm Cu : 61.8at% Sn: 31.7at% Pb: 5.2

Cu : 42.9at% Sn: 52.3at% Pb: 3.6

Fig. 9.10. The second cross section of the solder bump which has had the ﬁrst cross section. The voids and the indented solder surface can be seen at the cathode side.

enabled the indentation and bulge to take place, and both Pb and Sn were moved to the anode. Without a composition mapping, the relative ﬂuxes of Sn and Pb in the transformation are unclear. The marker motion gives the net ﬂux, so there could be some reverse ﬂux of Sn diﬀusing to the cathode since Pb is the dominant diﬀusing species. Therefore, the calculation of Z ∗ in the above could be inaccurate and it can only serve as an indication of the

SVNY339-Tu

April 5, 2007

17:31

Electromigration in Flip Chip Solder Joints

259

general behavior of electromigration in eutectic SnPb solder joints. We shall address the constant volume process and phase segregation issue in Sections 9.7 and 12.3. In addition, the Ni-Cu-Sn compounds are found in the matrix of the solder bump. The farthest location of this compound from the electroless Ni UBM is about 20 μm, indicating that Cu atoms has diﬀused such a distance to form the ternary compound.

9.4.2 Electromigration in Eutectic SnAgCu Flip Chip Solder Joints Figure 9.11 shows the ﬁrst cross-sectioned surface before and after current stressing at 120◦ C with 1.5 A for 20, 110, and 200 hr of a Pb-free solder bump. The direction of electron ﬂow is from the Ni UBM to Cu bump pad. The voids are formed at the cathode side after 200 hr [see Fig. 9.11(d)]. The void formation is much slower than that in eutectic SnPb solder as discussed in Section 9.4.1. But the IMCs were squeezed out in the anode side as hillocks. In contrast, no compound was pushed out in the eutectic SnPb solder in electromigration. Figure 9.12 shows (a) the marker and (b) marker motion on a crosssectioned surface. The marker motion is much less than that in eutectic SnPb. The markers moved more in the bottom region of solder (marker Nos. 4 and 5), which are close to the squeezed out IMC. However, the markers (Nos. 1 to 3) close to the electroless Ni UBM moved very little. Compared with eutectic SnPb, the marker motion in SnAg3.8 Cu0.7 is much smaller, which indicates that the latter has a slower electromigration than the former.

Fig. 9.11. The ﬁrst crosssectioned surface before (a) and after current stressing at 120◦ C with 1.5 A for (b) 20, (c) 110, and (d) 200 hr of a Pbfree solder bump.

SVNY339-Tu

260

April 5, 2007

17:31

Chapter 9 (a)

Marker

e1 2

4

5

Displacement(μm)

(b)

6

3

20 hr 20+44 hr 200 hr

5 4 3 2 1 0

1

2

3 Marker

4

5

Fig. 9.12. (a) The marker and (b) marker motion on a cross-sectioned surface of the Pb-free solder joint.

The sample was also second cross-sectioned, perpendicular to the ﬁrst cross section. The SEM micrograph is shown in Fig. 9.13; the void formation and dissolution of Ni UBM on the cathode side can be seen. However, the ﬁrst cross-sectioned surface appeared rather ﬂat, and no obvious dimple or bulge. The Ni-Cu-Sn ternary compounds (have a darker image in the micrograph) were found in the matrix of the solder, similar to eutectic SnPb. The compounds grew across the entire cross section of the solder bump during electromigration. The distance of the farthest compound from the electroless Ni UBM is about 90 μm, almost reaching the Cu anode. 9.4.3 Marker Motion Analysis Using Area Array of Nano-indentations An area array of nano-indentation markers can be made on a cross-sectioned solder joint surface using an instrumented system with a Berkovich diamond pyramid tip. Figure 9.14 shows a set of 5 × 6 nano-indentation markers created

SVNY339-Tu

April 5, 2007

17:31

Electromigration in Flip Chip Solder Joints

P :18at% Ni:82at%

P :13at% Ni:85.8at%

261

P :17.3at% Ni:85.8at% Ni:16.43at% Cu:24.8at% Ag : 0.45 Sn : 58.4

Ni:0.47at% Cu:0.42at% Ag : 77.17 Sn : 21.9

Ni:10.95at% Cu:23.8at% Ag : 0.53 Sn : 64.7 Ag3Sn

Ni:12.17at% Cu:28.50at% Ag : 0.34 Sn : 58.99

Ni:6.3at% Cu:28.1at% Ag : 0.99 Sn : 64.6 Ni:1.5at% Cu:38.0at% Ag : 0.22 Sn : 60.3

Fig. 9.13. The second cross section, perpendicular to the ﬁrst cross section of the Pb-free solder joint after electromigration. Void formation and dissolution of Ni UBM on the cathode side can be seen.

on a cross-sectioned eutectic SnPb solder joint before and after electromigration of current stressing of 0.32 A at 125◦ C for 24 and 48 hr. The diameter of the solder joint is about 100 μm. The size of the nano-markers with depth of 1000 nm used in the study was about 5 μm. The electrons entered the sample at the lower left corner and exited at the upper right corner. In Fig. 9.14(b) and (c), hillock formation at the upper right corner can be seen. On the surface, a bulge near the anode and a dimple near the cathode can also be seen. The majority of markers moved down, against atomic mass ﬂow, except a few near the anode side. Figure 9.15 shows an area array of nano-indentation markers created on a cross-sectioned eutectic SnAgCu solder joint before and after electromigration [15]. The electromigration test was performed with an average current density of 1 × 104 A/cm2 at 125◦ C for 15 days. The electrons ﬂowed from the top to the bottom. The size of the solder bump was 300 μm. Upon completion of the test, the specimens were examined by SEM for comparison. The surface

SVNY339-Tu

262

April 5, 2007

17:31

Chapter 9 Pb Mass protrusion and became bigger

e-

e-

e0 hr

e-

Mass depletion

24 hrs

48 hrs

Fig. 9.14. A set of an area array of 5 × 6 nano-indentation markers created on a cross-sectioned eutectic SnPb solder joint before and after electromigration of current stressing of 0.32 A at 125◦ C for 24 and 48 hr. The electron ﬂow entered the sample at the lower left corner and exited at the upper right corner.

topology of eutectic SnAgCu appears to be relatively ﬂat compared to that of eutectic SnPb shown in Fig. 9.14. This is in good agreement with the results shown in Figs. 9.10 and Fig. 9.13. The marker displacements driven by electromigration at diﬀerent locations were determined by measuring the distance from the marker center to the reference line at the anode interface using SEM images. As indicated by the arrows in Fig 9.15, the experimental measurement showed that markers in the top four rows moved upward in the ﬁgure, which was as expected to be against the atomic ﬂux driven by a downward electron ﬂow. However, the markers at the sixth row from the bottom were found to move downward in the ﬁgure. Especially some markers on the sixth row had moved into the anode and disappeared from the SEM image. This indicates that the atomic ﬂux was upward near the anode, which was against the atomic ﬂux of electromigration. For the ﬁfth row, the marker displacements were found to be much smaller than the others. The displacement of markers at diﬀerent rows versus marker locations is plotted in Fig. 9.16. It seems that there exists a “neutral plane” where no net ﬂux moves toward either the cathode or the anode. The location of the neutral plane can be determined by the intersection between the x-axis and displacement curve. As shown in Fig. 9.16, the distance from the neutral plane to the anode interface is 55 μm. A possible mechanism for the reverse marker motion near the anode could be the back stress or Kirkendall shift that induced a reverse ﬂow of Sn from the anode to the cathode. According to the Blech–Herring model of back stress in electromigration, the stress gradient will produce a vacancy concentration gradient, in turn an atomic ﬂux to counteract the electromigration ﬂux. If the stress gradient is large enough, there will be no net electromigration or no electromigration-induced damage of hillock or void formation. This implies that the neutral plane should be at the anode interface. On Kirkendall

SVNY339-Tu

April 5, 2007

17:31

Electromigration in Flip Chip Solder Joints

263

Fig. 9.15. A set of an area array of 5 × 6 nano-indentation markers created on a cross-sectioned eutectic SnAgCu solder joint (a) before and (b) after electromigration of current stressing of 1 × 104 A/cm2 at 125◦ C for 360 hr. The electron ﬂow entered the sample at the top and exited at the bottom.

shift, following Darken’s analysis of marker motion in interdiﬀusion, if lattice planes start to shift from the anode interface, all the markers should move toward the cathode. Hence, to analyze the motion of the sixth row markers, a diﬀerent mechanism is needed and it should take into account the eﬀect of current crowding at the bottom of the joint where the current exited from the solder joint and the fact that the markers were on the surface. The plastic deformation in hillock growth near the anode may play a role too.

9.4.4 Mean-Time-to-Failure of Flip Chip Solder Joints The electronic industry uses the mean-time-to-failure (MTTF) analysis to predict the lifetime of a device. In 1969, Black provided the following equation

SVNY339-Tu

264

April 5, 2007

17:31

Chapter 9

Fig. 9.16. Plot of the displacement of markers at diﬀerent rows after 239 hr versus marker locations. It seems that a “neutral plane” exists.

to analyze failure in Al interconnects caused by electromigration [16]: MTTF = A

1 exp jn

Q kT

.

(9.6)

The derivation of the equation was based on an estimate of the rate of mass transport resulting in the formation of a void across an Al interconnect. The most interesting feature of the equation is the dependence of MTTF on the square power of current density, i.e., n = 2. In the subsequent studies of the MTTF equation, whether the exponent n is 1, 2, or a larger number has been controversial, especially when the eﬀect of joule heating is taken into account. However, assuming that mass ﬂux divergence is required for failure and the nucleation and growth of a void requires vacancy supersaturation, Shatzkes and Lloyd have proposed a model by solving the time-dependence diﬀusion equation and obtained a solution for MTTF in which the square power dependence on current density was also obtained [17]. Nevertheless, whether Black’s equation can be applied to MTTF in ﬂip chip solder joints deserves a careful examination. To determine the activation energy, accelerated tests at high temperatures are performed. Attention must be paid to the temperature range in which lattice diﬀusion might overlap grain boundary diﬀusion and also grain boundary diﬀusion might overlap surface diﬀusion. For eutectic SnPb solder, it is more complicated because of the change of dominant diﬀusion species between Pb and Sn above and below 100◦ C. The formation of a void requires nucleation and growth. In the case of a ﬂip chip solder joint, Fig. 9.5 shows that the bulk part of the time to failure is controlled not by the growth of a void across the contact interface, but by the incubation time of void nucleation. The latter takes about 90% of the time of failure. The propagation of the void across the entire contact takes only about

SVNY339-Tu

April 5, 2007

17:31

Electromigration in Flip Chip Solder Joints

265

Table 9.2. Mean-time-to-failure of eutectic SnPb ﬂip chip solder joints 1.5 A (1.9 × 104 A/cm2 )

100◦ C 125◦ C 140◦ C a

1.8 A (2.25 × 104 A/cm2 )

2.2 A (2.75 × 104 A/cm2 )

Calculated (h)

Measured (h)

Calculated (h)

Measured (h)

Calculated (h)

Measured (h)

··· 108 46

··· 573a 121

380 79.6 34

97 43 32

265 55.5 24

63 3 1

Not failed.

10% of the time. Furthermore, as shown in the earlier sections in this chapter, the eﬀect of current crowding on failure is crucial and cannot be ignored in the analysis of MTTF. Black did point out the importance of current gradient or temperature gradient on interconnect failure, although he did not take them into account in his equation explicitly [16]. On the basis of the unique failure mode of a ﬂip chip solder joint as shown in Figs. 9.3 to 9.7, the major eﬀects of current crowding are to increase greatly the current density at the entrance of the solder joint and also to increase the local temperature due to joule heating. Furthermore, solder joint has IMC formation at both the cathode and the anode interfaces, electromigration aﬀects IMC formation, and in turn IMC formation aﬀects failure time and mode. This was not considered in Black’s original model of MTTF. Therefore, we cannot apply Black’s equation to predict ﬂip chip solder joint lifetime without modiﬁcation. Brandenburg and Yeh used Black’s equation with n = 1.8 and Q = 0.8 eV/atom, without taking into account the eﬀect of current crowding. The equation, with n = 1.8 and Q = 0.8 eV/atom, has been found to have greatly overestimated MTTF of ﬂip chip solder joints at high current densities. Table 9.2 compares the calculated and measured MTTF of eutectic SnPb ﬂip chip solder joints at three current densities and three temperatures. At the low current density of 1.9 × 104 A/cm2 , the measured MTTF is slightly longer than the calculated, but at 2.25 × 104 A/cm2 and 2.75 × 104 A/cm2 , the measured MTTF is much shorter than the calculated. This is also true for the eutectic SnAgCu ﬂip chip solder joints. These ﬁndings show that MTTF of ﬂip chip solder joints is very sensitive to a small increase of current density; the MTTF drops rapidly when the current density is about 3 × 104 A/cm2 . Also, the Pb-free solder has a much longer MTTF than the SnPb solder. For example, at 2.25 × 104 A/cm2 at 125◦ C, the MTTF is 580 hr for the Pb-free versus 43 hr for the SnPb. Black’s equation can be modiﬁed to include the eﬀect of current crowding and joule heating [9]: MTTF = A

1 Q exp , (cj)n k(T + ΔT )

(9.7)

SVNY339-Tu

266

April 5, 2007

17:31

Chapter 9

where c is due to current crowding and has a magnitude of 10 and ΔT is due to joule heating and may be higher than 100◦ C. Both parameters c and ΔT will reduce the MTTF from Black’s equation, i.e., make the solder joint fail much faster. Since ΔT depends strongly on j, the modiﬁed equation is much more sensitive to the change of current density than Black’s equation. We recall that the value of ΔT will depend on the design of ﬂip chip solder joint and interconnect, because of heat generation and heat dissipation. 9.4.5 Comparison between Eutectic SnPb and SnAgCu Flip Chip Solder Joints The marker motion as discussed in Sections 9.4.1 and 9.4.2 shows that electromigration in SnAg3.8 Cu0.7 is much slower than that in eutectic SnPb. In addition, the MTTF of the latter is also shorter than the former. Why is the Pb-free solder better? On the basis of Eq. (9.3), the ﬂux driven by electromigration has the driving force term, Z ∗ eE, and the mobility term, D/kT. In driving force, both Z ∗ and resistivity diﬀer for the two solders, yet the diﬀerence is small. In mobility, the diﬀerence in diﬀusivity can be very large; the diﬀusivity in eutectic SnPb may be one order of magnitude faster than that in eutectic SnAgCu. This is because the melting temperature of SnAg3.8 Cu0.7 (about 220◦ C) is higher than that of eutectic SnPb (183◦ C). Therefore, at the same stressing temperature, the homologous temperature of the Pb-free is lower than that of eutectic SnPb. Also, the smaller grain size and the eutectic lamellar interfaces in the SnPb solder may enhance the diﬀusivity. Thus, electromigration in eutectic SnPb will be faster. Furthermore, in Eq. (9.3), we note the back stress term. The eﬀect of back stress in resisting electromigration in the Pb-free is larger than that in the SnPb. A distinct diﬀerence in electromigration behavior between eutectic SnPb and SnAg3.8 Cu0.7 is the squeezing out of IMC at the anode side of the latter (see Fig. 9.11). It seems that in eutectic SnPb, the compressive stress at the anode can be relaxed by the bulge of the solder surface as shown in Fig. 9.10, indicating that lattice sites can be created easily because of more grain and interface boundaries. But in the SnAg3.8 Cu0.7 , the Sn matrix is mechanically harder and the surface oxide is protective so the cross-sectioned surface remains rather ﬂat as shown in Fig. 9.13. The higher compressive stress or back stress was relaxed by squeezing out the hillocks of IMC. If the Pb-free solder bump is conﬁned by underﬁll which resists surface relief, the buildup of compressive stress at the anode may be even higher. It is worth mentioning that there is a very large reverse ﬂux of Sn in SnPb ﬂip chip solder joints in electromigration at high temperatures, to be discussed in Sections 9.5 and 9.7. The reverse ﬂux is much smaller in the Pb-free solder although the concentration of Sn is higher in the Pb-free, as discussed in Sections 9.4.3 and 9.4.4. The reverse ﬂux has a very serious eﬀect on the stability of thick Cu UBM at the cathode contact, in turn the MTTF of the solder joint, to be discussed in Section 9.5. In thin-ﬁlm Cu UBM, the

SVNY339-Tu

April 5, 2007

17:31

Electromigration in Flip Chip Solder Joints

267

Cu will be consumed during the reﬂow, but in thick Cu UBM, the Cu will also be consumed by solid-state Cu-Sn reaction, which is enhanced by the reverse ﬂux of Sn. The MTTF depends not only on the rate of electromigration, but also on the rate of Cu-Sn reaction in consuming the Cu. 9.4.6 Kinetic Analysis of Pancake-Type Void Growth along the Contact Interface Figure 9.17 is a schematic diagram depicting the growth of a pancake-type void at a contact interface [11]. The bent solid arrow represent current crowding. The vertical solid arrow depict the atomic ﬂux driven by the current crowding from the top of the solder bump to the bottom. Meanwhile, the reverse ﬂux of vacancies moves from the bulk of the solder to the interface indicated by the dotted arrow. If the vacancy ﬂux in the Cu6 Sn5 is ignored, the vacancy ﬂuxes in the solder can be written as v JSn =

bulk DSn ∗ CSn ZSn eρSn j, kT

(9.8)

where D is the diﬀusivity, e is the charge of an electron, ρ is resistivity, and j is current density. Z ∗ is the eﬀective charge number of electromigration. The solder/IMC interface provides the transport path for excess vacancies and enables them to diﬀuse along the interface. The lateral ﬂux along the

Cu6Sn5

Jv

h

J

d

Jint

void

a

d

b' Solder

J*

Sn

Fig. 9.17. In the model, the bent solid arrows represent current crowding. The vertical solid arrows depict the atomic ﬂux driven by the current crowding from the top of the solder bump to the bottom.

SVNY339-Tu

268

April 5, 2007

17:31

Chapter 9

interface due to the divergence of vacancies can be written as v Jint = −Dint

ΔC ΔC ≈ Dint , Δx b

(9.9)

where Dint is the diﬀusivity in the interface, b is the width of current crowding region, and ΔC is the concentration diﬀerence between the concentration in the higher current density and the equilibrium concentration at the tip or growth front of the void. In terms of mass conservation law, we have v v Jint aδ = JSn ab ,

(9.10)

where δ is the eﬀective width of interface and a is a unit length. It is assumed that the initial width of void is d, and Jvoid is the ﬂux of vacancy at the tip of the void. The condition of conservation of ﬂux is applied again v Jint aδ = Jvoid ad.

(9.11)

Substituting Eq. (9.10) into Eq. (9.11), the ﬂux to grow the void can be written as v b Jvoid = (JSn ) . δ

(9.12)

The volume of matter transported by Jvoid along the interface can be given as ΔV = Jvoid AΔtΩ,

(9.13)

where A = aδ, ΔV = adΔl, and Ω is the atomic volume. Inserting Eq. (9.12) into Eq. (9.13), the growth velocity of void becomes v=

Δl v b ) Ω. = (JSn Δt d

(9.14)

If it is assumed that Cvbulk Ω = 1, we obtain v=

ej ∗ b ) . (DSn ρSn ZSn kT d

(9.15)

To verify the mechanism of void propagation, the two key parameters are the width of current crowding region, b , and the width of the void, d. As shown in Fig. 9.17, the Gibbs-Thomas eﬀect may play an important role in

SVNY339-Tu

April 5, 2007

17:31

Electromigration in Flip Chip Solder Joints

269

Current Crowding Region Void

Conducting Line

10-4

Solder Mask

10-1

Solder Bump 102

Fig. 9.18. Two-dimensional simulation of pancake-type void growth.

forming the tip of the void, Cr = C0 exp

2γ Ω r kT

,

(9.16)

where γ is the surface energy per area. By applying the linear approximation, we have the void width as d = 2r =

C0 4γΩ . ΔC kT

(9.17)

Since the model is two-dimensional, the void width is assumed to remain constant. On the other hand, from Eq. (9.9) and (9.10), the width of current crowding is

b =

ΔC kT Dgb δ ∗ ρ C0 ejDSn ZSn Sn

1/2 .

(9.18)

In the two-dimensional simulation shown in Fig. 9.18, the contact window length of eutectic SnAgCu solder joint is taken to be 224 μm and the current crowding region is taken about 15% of the whole length, so the current crowding region, b , is estimated to be about 33.6 μm. From Fig. 9.7 the void width, d, is measured as 2.44 μm. The test temperature is 146◦ C, the electric current density is about 3.67 × 103 A/cm2 , the void length is 33 μm, the duration of void propagation is 6 hr, thus the void growth velocity is about 5 μm/hr. In the other case of eutectic SnPb solder bump stressed at 2.25 × 104 A/cm2 and 125◦ C as discussed in Section 9.4.1, the window length is 140 μm and the

SVNY339-Tu

270

April 5, 2007

17:31

Chapter 9

Table 9.3. Comparison of measured and calculated values of growth rate of pancaketype void in electromigration

b d v

Theory

Experiment

25.49–44.15 μm 0.81–2.42 μm 1.24–6.44 μm/h

37.5 μm 2.44 μm 4.4 μm/h

width of current crowding region is about 9 μm. The voids are formed at 38 hr and failed at 43 hr, therefore, the void growth velocity is about 28 μm/hr. The diﬀusivity is taken to be DSn = 1.3 × 10−10 cm2 /sec for Sn, and the diﬀusivity of the interface is taken to be 4.2 × 10−5 cm2 /sec. The eﬀective ∗ charge is ZSn = 17 for Sn. The resistivity of Sn is ρSn = 13.25 μΩcm. The surface energy γ = 1015 eV/cm2 and Ω is taken as 2.0 × 10−23 cm3 . The eﬀective interfacial width is about 0.5 nm. The only unknown parameter is the ratio of ΔC and C0. In order to obtain reasonable results, we choose the range of ΔC/C0 from 1% to 3%. Using these parameters and experimental conditions, the theoretical values of current crowding length b have been calculated from Eq. (9.18), void width d from Eq. (9.17), and void growth velocity v from Eq. (9.15). The comparison between theoretical values and experimental results are in reasonable agreement as listed in Table 9.3. 9.4.7 Time-Dependent Melting of Flip Chip Solder Joints A rather common cause of failure of ﬂip chip solder joint is melting. For certain eutectic SnPb ﬂip chip solder joints, when the applied current density is above 1.6 × 104 A/cm2 and the test temperature is around 100◦ C, melting occurs. For certain eutectic SnAgCu ﬂip chip solder joints, when the applied current density is above 5 × 104 A/cm2 and the test temperature is around 100◦ C, melting occurs. These current densities have become the upper limit that can be applied to ﬂip chip solder joints. In melting, the temperature should reach the melting point of the solder alloy, for example, 183 or 220◦ C for eutectic SnPb and eutectic SnAgCu, respectively. This indicates that joule heating must have raised the temperature from 100◦ C to the melting point. However, the question is where is the joule heating coming from? Whether it is from the solder bump itself or from the interconnect above the bump is unclear. Melting in principle is a time-independent event. Generally speaking, no superheating is needed in melting, so melting should occur instantaneously when the temperature reaches the melting point as in reﬂow. However, the observed melting of ﬂip chip solder joints induced by electromigration takes time. Typically, under an applied current density, it takes a while, from several hours to a couple of days, for the joule heating to induce melting. In Section 9.3, we reported the use of aluminum resistors to measure the chip temperature and a very large joule heating was found even with an

SVNY339-Tu

April 5, 2007

17:31

Electromigration in Flip Chip Solder Joints

271

applied current density of about 3.5 × 103 A/cm2 . The chip temperature was measured to be as high as 175◦ C, indicating an increase of temperature of about 125◦ C due to joule heating. When a current density of 5 × 104 A/cm2 is applied to a ﬂip chip eutectic SnAgCu solder joint, current crowding will increase it to 5 × 105 A/cm2 . For a ﬂip chip with thin-ﬁlm UBM, the current crowding occurs within the solder bump, thus joule heating in the solder bump is high. In mainframe computers, the Si chips will be cooled in order to maintain a device working temperature of 100◦ C, thus the solder bumps will not melt. However, for most consumer electronic products, there is no cooling or the cooling design is ineﬀective, e.g., by using a fan, so the solder bumps can become very hot and melt. Why joule heating is so large in a ﬂip chip solder bump and why melting takes time require explanation. While the unique current crowding in a ﬂip chip solder bump will cause a large joule heating because of the I 2 R dependence, we must also consider heat dissipation besides heat generation. Since solder alloy itself is a poor electrical conductor, it is also a poor thermal conductor on the basis of the Wiedemann–Franz law [18]. This law states that for a metallic conductor, the ratio of thermal conductivity to electrical conductivity is proportional to temperature. Therefore, it is important to have the joule heating in the solder bump conducted away. Typically, the heat can be conducted away from the bump by the Si chip via the UBM. Heat conduction by Si is important since the on-chip Al or Cu interconnect is the source of joule heating. Hence, the design of the UBM and interconnect is important in heat management. Nevertheless, the design is static and independent of time. On the basis of the design, only when the temperature reaches the melting point of the solder should the bump melt, otherwise it should not. There is no factor of time. However, the melting in ﬂip chip solder joints is a dynamic phenomenon; it is time-dependent [19, 20]. The change of microstructure of the solder joint due to electromigration or thermomigration is a time-dependent event, and it aﬀects the joule heating. When a pancake-type void forms and grows across the cathode contact between the Si chip and the solder bump, there are two signiﬁcant eﬀects that can inﬂuence heat generation and dissipation. First, as the pancake-type void grows, the conducting path of the Al interconnect above the void must increase. This will increase joule heating. When the current density is high, electromigration can induce damage in the Al as discussed in Section 9.2.4. It will cause more joule heating. Second, the void becomes a good heat insulator and prevents the heat from dissipating through the Si chip. Consequently, both joule heating and heat insulation become serious as the void grows, especially when the void grows to eclipse most of the contact opening, which may lead to bump melting. While the Cu trace on the substrate can also conduct heat away from the solder bump, it nevertheless may have produced a temperature gradient in the solder bump and caused thermomigration in the bump. Thermomigration will be covered in Chapter 12.

SVNY339-Tu

272

April 5, 2007

17:31

Chapter 9

9.5 Electromigration in Flip Chip Composite Solder Joints 9.5.1 Thin-Film Cu UBM in Composite Solder Joints In Sections 1.3.3 and 4.2, we discussed the trend of application of ﬂip chip solder joints to low-cost consumer products where polymer substrates are used. Because of the low glass transition temperature of polymer, the solder on the polymer substrate must have a low melting temperature. Therefore, a composite solder joint was developed, which combines the high-melting 97Pb3Sn solder on the chip side and the low-melting eutectic 37Pb63Sn solder on the polymer substrate side. The major advantage of a composite solder joint is that it yields a joint which is compatible with polymer substrates so that direct chip attachment to polymer substrates can be accomplished. However, electromigration is a concern [12, 21]. In Fig. 9.19, a set of cross-sectional SEM images of a pair of composite solder joints with thin-ﬁlm under-bump metallization (UBM) are shown.

Fig. 9.19. Cross-sectional SEM images of a pair of composite solder joints with thinﬁlm UBM subjected to electromigration with a current density of 1.57 × 104 A/cm2 at 150◦ C for (a) 30 min, (b) 1 hr, and (c) 2 hr.

SVNY339-Tu

April 5, 2007

17:31

Electromigration in Flip Chip Solder Joints

273

The composite joint was composed of 97Pb3Sn on the chip side and eutectic 37Pb63Sn on the substrate side. The contact opening on the chip side had a diameter of 90 μm and the bump height was 105 μm. The UBM of trilayer thin ﬁlms on the chip side were Al (∼0.3 μm)/Ni(V) (∼0.3 μm) /Cu (∼0.7 μm). On the substrate side, the bond pad metal layers were Ni (5 μm)/Au (0.05 μm). Electromigration was conducted with a current density of 1.57 × 104 A/cm2 at 150◦ C for 30 min, 1 hr, and 2 hr, and the corresponding cross-sectional SEM images of a pair of joints are shown in Fig. 9.19(a), (b), and (c), respectively. In the pair of joints, electrons came in from the bottom of the right-hand side joint, went up the solder bump, exited the bump at the upper left corner and moved to the left and entered the left-hand side joint from the upper right corner, went down the solder bump, and exited at the bottom. In Fig. 9.19, the darker region in the solder bump is the eutectic phase and the brighter region is the high-Pb phase. The eﬀect of current crowding on phase redistribution is very clear in Fig. 9.19(a) to (c). We recall that Pb is the dominant diﬀusing species in SnPb solder at temperatures around 150◦ C. After 30 min of electromigration at 150◦ C, the eutectic phase in the right-hand side joint has been displaced to the lower right corner, and correspondingly, in the left-hand side bump the eutectic phase displaced to the upper left corner. After 1 hr, the situation was about the same. After 2 hr, as shown in Fig. 9.20 which is a highermagniﬁcation image, a pancake-type void was formed at the cathode contact on the Si side in the left-hand side joint. Interestingly, in Fig. 9.19(c) as well as in Fig. 9.20, the dark eutectic phase has been displaced sidewise to the left with the growth of the pancake-type void. The sidewise displacement of the eutectic phase can be explained by the fact that as the void grows sidewise, the current crowding moves with the tip of the void, electromigration will

Pancake void

Sn-rich

Pb-rich

Fig. 9.20. Higher magniﬁcation of pancake-type void formation in the left-hand side bump in Fig. 9.19(c).

SVNY339-Tu

274

April 5, 2007

17:31

Chapter 9

drive Pb away and back ﬁlled by Sn so the eutectic phase moves with the tip of the void. Consequently, at the end of the pancake-type void growth, the low-meltingpoint eutectic phase is displaced to the upper left corner of the joint. Increased joule heating due to current crowding, longer conducting path in Al interconnect, and improved heat insulation of the void may lead to partial melting of the upper left corner of the solder bump at a low temperature. Indeed, frequently such partial melting in the composite solder joints with thin-ﬁlm UBM has been observed. 9.5.2 Thick Cu UBM in Composite Solder Joints In the composite solder joint to be discussed here, the Cu in the UBM is 5 μm thick. Figure 4.4 showed the cross-sectional SEM images. The UBM on the chip side consisted of TiW(0.2 μm)/Cu (0.4 μm)/electroplated Cu (5 μm), and the bond pad on the substrate side was electroless Ni (5 μm)/Au (0.1 μm). The 97Pb3Sn solder was electroplated onto the sputtered TiW/Cu/electroplated Cu UBM and followed by a reﬂow at 380◦ C. On the polymer substrate, eutectic 37Pb63Sn solder paste was stencil printed on the electroless Ni/Au ﬁnished bonding pads and followed by a reﬂow at 220◦ C. The reﬂowed eutectic solder bumps were ﬂattened by the caking process prior to assembly, discussed in Chapter 4. The thickness of the ﬂattened eutectic solder bump is about 40 μm. To assemble the two solders, a water-soluble ﬂux was coated onto the ﬂattened substrate solder bumps and the reﬂow had a peak temperature of 220◦ C and a dwell time of 90 sec in nitrogen atmosphere. After assembly and cleaning the ﬂux residue, the gap between the chip and the board was ﬁlled with epoxy, i.e. underﬁll. Electromigration was conducted with 0.5 A and the average current density at the 50-μm-diameter contact opening was 2.55 × 104 A/cm2 . Such current density should not cause electromigration damage in the 5-μm-thick Cu. However, the reverse ﬂux of Sn moving from the anode side of eutectic SnPb to the cathode side of high-Pb transforms the Cu into Cu3 Sn, and in turn Cu3 Sn to Cu6 Sn5 . Finally, failure occurs when the Cu is consumed, as shown in Fig. 4.4. Electromigration of the same composite ﬂip chip solder joints at room temperature showed similar failure mode but was found to have a strong dependence on current density [21]. The composite solder joints did not fail after 1 month stressed at 4.07 × 104 A/cm2 , but failed after 10 hr stressed at 4.58 × 104 A/cm2 . At just a slightly higher current stressing of 5.00 × 104 A/cm2 , they failed after only 0.6 hr by the melting of the composite solder bumps. Due to the growth of Cu6 Sn5 at the cathode side, the Cu UBM was quickly consumed and was followed by void formation at the contact area. The void reduced the contact area and displaced the electrical path, aﬀecting the current crowding and joule heating inside the solder bump.

SVNY339-Tu

April 5, 2007

17:31

Electromigration in Flip Chip Solder Joints

275

It is known that at room temperature, Sn is the dominant diﬀusing species in eutectic SnPb solder, and Sn has been found to move to the anode in electromigration. Without Sn moving to the cathode, the Cu3 Sn at the cathode contact should be stable and the device should not fail easily. The samples tested at room temperature failed only in tests at very high current density, which tends to suggest that it was due to joule heating and the temperature in the solder joint was actually above 100◦ C so that Sn moves to the cathodes.

9.6 Eﬀect of Thickness of Cu UBM on Current Crowding and Failure Mode If Cu is part of the UBM, the thickness of the Cu can aﬀect current crowding greatly. For a thick Cu UBM of 5 μm in the composite solder joint, as discussed in Section 9.5, the highest current density due to current crowding will occur within the Cu. More importantly, the thick Cu will enable a redistribution of current laterally in the entire Cu UBM, so the current density in the solder bump will be much closer to the average value, i.e., only a slight current crowding occurs in the solder near the Cu/solder interface. By using threedimensional simulations, the eﬀect of current redistribution in the thick Cu and the solder can be made clear. In the following, we shall consider four cases of diﬀerent Cu thickness; from 0.4 μm, 5 μm, 10 μm, and to 50 μm for comparison. The last case is a Cu column bump. In the ﬁrst case of thin Cu, for example, the Cu in the thin-ﬁlm UBM of Al/Ni(V)/Cu is about 0.4 μm, the current crowding will occur in the solder and will aﬀect strongly electromigration of the solder. In the thin UBM, all of the 0.4 μm Cu was consumed to form IMC. Since the resistivities of the IMC and Ni(V) are high, very little electric current will be conducted by them, so very little current will be redistributed to the periphery of UBM which is the IMC under the dielectric. Typically, electromigration induces void formation and propagation along the contact interface. Importantly, the void has extended to the entire periphery of the contact, as shown in Fig. 9.7. We note that how the void can extend itself to the low current density region in the periphery of the contact under the dielectric is an interesting question. Also, the nucleation site of the void is unclear; whether it is at the highest current density region in the current crowding or in the periphery region of low current density is unknown. In the second case of a thick Cu UBM of 5 μm, most current crowding occurs within the Cu. While part of the current crowding has extended into the solder but the degree of crowding in the solder is small, the current density in most of the solder joint is quite uniform and close to the calculated average value of current density in the bulk of the solder. Besides, the thick Cu in the periphery region will not be consumed completely by solder reaction during reﬂow, so the remaining Cu UBM will conduct electric current and thus a

SVNY339-Tu

276

April 5, 2007

17:31

Chapter 9

fraction of the current will be redistributed around the periphery of the contact. The void formation in this case, as shown in the composite solder joint in Fig. 4.4, is located in the entrance of the current to the bump and the void will grow bigger with time, but it does not extend to the edge of the periphery. This mode of failure indicates the important role of conduction by the thick Cu UBM. Nevertheless, with time, the interaction between electromigration and chemical reaction will convert Cu into Cu3 Sn and Cu6 Sn5 , and then the resistance of the contact will increase quickly and lead to failure. In the third case of a thick Cu UBM of 10 μm on eutectic SnPb solder bump, current crowding occurs completely within the Cu; there is no current crowding in the solder, not even in the region near the Cu/solder interface. The failure is more gradual than the case of 5-μm-thick Cu. First, electromigration dissolves the Cu into the solder and reduces the thickness of the Cu. When the Cu thickness is reduced to 5 μm, the failure mode repeats itself as discussed in the above. Figure 9.21 is a set of cross-sectional SEM images of the sequence of failure of the 10 μm Cu UBM. The applied current was 0.6 A and the average current density at the 50-μm-diameter contact opening was 3.0 × 104 A/cm2 . Figure 9.21(a) to (d) are SEM images of the cross-sectioned ﬂip chip solder joints after current stressing for 50, 75, 100, and 120 hr, respectively. Electrons entered from the upper left-hand side, went down the bumps, and exited to the lower right-hand side of solder joints as indicated by the white arrow. After 50 hr of current stressing, as shown in Fig. 9.21(a), the size of Cu6 Sn5 IMC increased at the whole interface under Cu UBM and the layer-type dissolution of Cu UBM was observed. After 75 hr as shown in Fig. 9.21(b), the continuous and uniform decrease of Cu UBM thickness at the whole interface of Cu UBM/solder increase was clearly observable. After 100 hr as shown in Fig. 9.21(c), accompanying the consumption of Cu UBM many large Cu6 Sn5 IMCs started to form at the left-hand side corner of the contact window. After 120 hr as shown in Fig. 9.21(d), there is no more Cu or Cu6 Sn5 at the left-hand side corner. The ﬁnal failure was the consumption of almost all Cu UBM at the cathode interface. The failure sequence of Fig. 9.21(c) to (d) is similar to the 5-μm-thick Cu UBM as shown in Fig. 4.4. In the fourth case of a Cu column bump of 50 μm or more in height and in diameter, the bulk part of the solder bump is replaced by the Cu bump, so the remaining solder is about 20 μm thick. There is no current crowding at all in the solder part of the joint.

9.6.1 Cu Column Bumps Figure 9.22 shows SEM images of the cross-sectioned ﬂip chip joints of Cu column bumps with eutectic SnPb solder bumps after current stressing for

SVNY339-Tu

April 5, 2007

17:31

Electromigration in Flip Chip Solder Joints

277

Fig. 9.21. SEM images of cross-sectioned ﬂip chip eutectic SnPb solder joints having 10-μm-thick Cu UBM after current stressing for (a) 50 hr, (b) 75 hr, (c) 100 hr, and (d) 120 hr.

SVNY339-Tu

278

April 5, 2007

17:31

Chapter 9 (a) e-

50 μm (b) e-

50 μm (c) e-

50 μm Fig. 9.22. SEM images of the cross-sectioned ﬂip chip joints of Cu column bumps with eutectic SnPb solder bumps after current stressing for 1 month at 100◦ C with current density of (a) 3.4 × 103 , (b) 4.7 × 103 , and (c) 1 × 104 A/cm2 .

1 month at 100◦ C with current densities of (a) 3.4 × 103 , (b) 4.7 × 103 , and (c) 1 × 104 A/cm2 [22]. The arrows labeled e− indicate the direction of electron ﬂow. The ﬂip chip joints did not fail after 1 month of current stressing at these three current densities. In a simulation of current distribution in a joint at the initial state of applied current density of 1 × 104 A/cm2 , current crowding

SVNY339-Tu

April 5, 2007

17:31

Electromigration in Flip Chip Solder Joints

279

occurs in the upper left corner of Cu column bump and has spread about 5 μm wide and 10 μm deep into the Cu column; the current distribution in the solder region was uniform. The eﬀect of current density on the rate of IMC formation is clearly seen in Fig. 9.22(a) to (c). What is surprising to ﬁnd in these ﬁgures is the absence of polarity eﬀect of electromigration; the amount of IMC formation at the Cu/solder interface is almost the same in the pairs of joints, shown in Fig. 9.22(a) to (c). Electrons went from Cu to IMC in the left-hand side one but went from IMC to Cu in the right-hand side one, yet the amount of Cu3 Sn and Cu6 Sn5 formed is almost the same [see Fig. 9.22(c)]. The thick Cu-Sn IMCs were made up of two diﬀerent kinds of IMCs. EDX identiﬁed the thin dark layer near the Cu as Cu3 Sn and the thick white layer near the solder as Cu6 Sn5 . After 1 month with a current density of 1 × 104 A/cm2 at 100◦ C, the Cu3 Sn grew much thicker and its thickness became comparable to that of Cu6 Sn5 as shown in Fig. 9.22(c). In addition, an important ﬁnding here is that a large number of voids appeared in the Cu3 Sn layer, with the majority of them being closer to the Cu3 Sn/Cu interface. The thickness of Cu3 Sn and the number of voids increased signiﬁcantly with the increase of current density. In the present system of a limited amount of Sn combined with an inﬁnite amount of Cu, Cu3 Sn grew thicker at the expense of Cu6 Sn5 and is accompanied by an extensive formation of Kirkendall voids, as shown in Fig. 9.22(c). These voids will fail the joint mechanically. When one molecule of Cu6 Sn5 is concerted into two Cu3 Sn, it releases three Sn atoms which will attract nine Cu atoms to form Cu3 Sn. The vacancies that are needed for the Cu diﬀusion may condense to form voids. Therefore, in the combination of a very thick Cu column bump and a relatively thin solder bump, the Cu6 Sn5 transforms to the Cu3 Sn and the latter can grow very thick, so the vacancy ﬂux that opposes the Cu ﬂux will form Kirkendall voids. The eﬀect of these Kirkendall voids on electrical and thermal conductivity of Cu3 Sn, in turn the eﬀect on joule heating and heat dissipation of the solder joint is, of great concern. It might aﬀect the temperature gradient in the solder joint too. Above 100◦ C, it is known that electromigration in a SnPb solder joint will drive Pb to the anode, so Sn is pushed back to the cathode. This will enhance the IMC formation at the Cu interface in the left-hand side one, but not the right-hand side one. Why a similar amount of IMC forms at the Cu interface in the right-hand side joint requires an answer; a plausible one is thermomigration, which will be discussed in Chapter 12. Thermomigration drives Pb to the cold side and Sn to the hot side. A temperature diﬀerence of only 2◦ C across a solder joint 20 μm thick produces a temperature gradient of 1000◦ C/cm, which is suﬃcient for thermomigration. Thus, electromigration accompanied by thermomigration and the formation of Kirkendall voids could replace current crowding as a serious reliability issue regarding use of Cu column bumps.

SVNY339-Tu

280

April 5, 2007

17:31

Chapter 9

9.6.2 The Design of a Near-Ideal Flip Chip Solder Joint Assuming that we must use solder in chip joint, how can we design a ﬂip chip joint that will have the best resistance to electromigration and other reliability concerns? To improve reliability against electromigration, we must reduce current crowding. This can be achieved by improving the design of the ﬂip chip conﬁguration and materials. Since the basic principle in current distribution is that electric current will take the least resistive path, there are options in the design of a ﬂip chip to reduce current crowding. Using ﬁnite element analysis, current distribution in a ﬂip chip solder joint can be studied as a function of geometry and resistance of all the conducting elements associated with a solder joint, including the Al or Cu interconnect, the UBM, and the solder bump itself. The factors that aﬀect current distribution the most have been found to be the thickness and resistance of under-bump metallization. The factor that aﬀects joule heating the most is the Al or Cu interconnect over the solder bump. The advantage of Cu column bump on current distribution was presented in the last section. However, the Cu column bump has caused the growth of thick Cu3 Sn accompanied by Kirkendall void formation. We need to prevent the growth of Cu3 Sn. This can be achieved by using high-Pb solder with a limited amount of Sn. Thus, the combination of Cu column and high-Pb solder is attractive. Among all solder joints, the high-Pb or C-4 solder joint has the best electromigration resistance. Although the high-Pb forms Cu3 Sn at the Cu/solder interface, Cu3 Sn will not grow or transform if there is no Sn in the solder and thus no Kirkendall void formation. If the thickness of the high-Pb in the joint is about 10 μm, it is about the critical length below which electromigration can be balanced by back stress and no electromigration damage will occur. Hence, if we design a ﬂip chip joint, consisting of Cu column/Cu3 Sn/highPb/Cu3 Sn/Cu trace and if the thickness of the middle layer of high-Pb, which we note is almost pure Pb after its Sn content has been consumed by the Cu3 Sn formation, is below the critical length of electromigration, it is most likely the best solder joint from the point of view of resisting electromigration. In addition, while the high-Pb may climb up the side wall of the Cu column, the reﬂow reaction to form the Cu3 Sn causes no harm or there is no Kirkendall void formation. The challenge is that ceramic substrate must be used since the high-Pb has a high reﬂow temperature. Because of the high melting point of high-Pb solder, we cannot use it on polymer-based substrates; we need to use a composite solder, consisting of a high-Pb solder on the Cu column side and a eutectic SnPb (or eutectic Pbfree) on the polymer substrate side. But as we have shown in Section 9.5, electromigration will drive the Sn from the eutectic solder to the cathode and convert the Cu3 Sn to Cu6 Sn5 , and eventually failure will occur even for a 10-μm-thick Cu UBM. Nevertheless, for a Cu column the time needed to consume all the Cu may be too long to be of concern or not all the Cu can be consumed. Instead, the problem of the column/composite will be the growth

SVNY339-Tu

April 5, 2007

17:31

Electromigration in Flip Chip Solder Joints

281

of Cu3 Sn and Kirkendall void formation, especially on the side wall of the Cu column. Hence, we must prevent the reverse ﬂux of Sn in the composite solder joint or we need to prevent the transformation of Cu6 Sn5 to Cu3 Sn. This can be accomplished by using a diﬀusion barrier between the high-Pb and the eutectic solder. The diﬀusion barrier can be a layer of Cu or Ni or a bilayer of Cu/Ni 5 to 10 μm thick and it can be electroplated on the high-Pb solder. In using a bilayer of Cu/Ni, the Cu will be on the high-Pb side and the Ni on the eutectic side. Both the high-Pb solder and eutectic Pb-free solder react with Cu or Ni, so there is no problem in joining them to the diﬀusion barrier. To prevent the transformation of Cu6 Sn5 to Cu3 Sn, it is known that (Cu, Ni)6 Sn5 is stable and by adding Ni to Cu6 Sn5 has prevented or slowed down much of the growth of Cu3 Sn. In the design, we can make the thickness of both the high-Pb and the eutectic solder below their critical length of electromigration. However, there is a problem with the thin layer of eutectic Pb-free solder because it will react with Cu and the reaction can transform the entire Pb-free eutectic solder into Cu-Sn IMC. While electromigration will be slower in IMC, the mechanical properties of an IMC joint should be studied. The advantage of Ni or Ni(P) is that the rate of IMC formation is much slower than Cu. Concerning the side wall, even if the eutectic solder climbs up and forms a coating on the high-Pb side wall, there will be no mixing during aging in the solid state since the current density in the side wall is low. Finally, we can slow down atomic diﬀusivity in the solder bump by alloying, so the Pb-free solder may have an electromigration resistance as good as the high-Pb solder.

9.7 Electromigration-Induced Phase Separation in Eutectic Two-Phase Solder Alloy Below eutectic temperature, the microstructure of a eutectic alloy consists of two primary phases according to its eutectic phase diagram. Typically, the two phases form a lamellar microstructure. They are in equilibrium with each other, hence there is no chemical potential diﬀerence between them, and it is possible to induce redistribution of the two phases without counteraction. For example, there is no well-deﬁned lamellar thickness of each phase in the lamellar microstructure except the principle of reduction of the total area of lamellar interfaces. Therefore, it is possible to have a near-complete phase separation into two parts, one of each of the two primary phases, under an external driving force. Indeed, this has been shown to occur in electromigration in eutectic SnPb solder joints at 150◦ C by Brandenburg and Yeh [1]. Figure 4.6(a) and (b) show SEM images of a eutectic SnPb solder joint before and after electromigration. A near-complete phase separation is seen after electromigration. Also, in electromigration in composite solder joint as discussed in Section 9.5, electromigration has induced the redistribution or

SVNY339-Tu

282

April 5, 2007

17:31

Chapter 9

segregation of Sn and Pb to the cathode and the anode, respectively. The kinetic analysis of phase segregation in a eutectic two-phase mixture driven by electromigration will be presented in this section. In a eutectic two-phase mixture, the change of concentration under a constant temperature does not mean any change of chemical potential since the two phases are coexisting with each other in equilibrium. When there is segregation in the mixture, it means a change of volume fraction of the two phases, in other words, it leads to a gradient of volume fraction, but not a gradient of chemical potential, so we do not have ﬂux governed by Fick’s ﬁrst law. Gradient of volume fraction is not a driving force for atomic diﬀusion, therefore a redistribution of volume fraction is not counteracted by a chemical force as in uphill diﬀusion. Thus, the segregation in eutectic two-phase mixtures can be enormous. What is also unique is that due to the lack of counteracting force, the segregation is not smoothed by diﬀusional process. In the diﬀusion equation, the time rate change of concentration, dC/dt, equals the second derivative of concentration by space coordinate, d2 C/dx2 , times diﬀusivity. Thus, the second derivative tends to smoothen concentration with time. Without it, because we do not have Fick’s ﬁrst law to describe the ﬂux, the tendency for a stochastic process occurs. We shall show in the following that this occurs in electromigration of the eutectic mixture. We will not ﬁnd a smooth change of concentration, but rather will ﬁnd random states or random phase distribution in the two-phase structure. In Section 9.5, we discussed that upon electromigration in a composite solder joint, while the Pb is being driven to the anode, the Sn diﬀuses reversely to the cathode. It is this back-diﬀusion of Sn that leads to failure at the cathode. Since we should also expect Sn atoms to be driven by electromigration from the cathode to the anode, the back-diﬀusion is puzzling. Below, we shall analyze the kinetics of ﬂux migration in a two-phase structure assuming the constraint of constant volume. The constraint leads to the back-diﬀusion. In the two-phase structure of a eutectic system, the alloy composition is not restricted at the eutectic point. Rather it can be a two-phase mixture below the eutectic temperature having any composition between the two primary phases. The main assumptions are the following. (1) Conservation of volume and shape of samples (equalizing of volume ﬂuxes) at under-critical regimes, meaning no void or hillock formation. There are two ways of equalizing volume ﬂuxes, either by back stress or by Kirkendall lattice shift. (2) The ﬂuxes do not contain concentration gradient terms as in Fick’s ﬁrst law. Instead, a ﬂux in terms of drift velocity, which is a product of mobility and driving force, is used. Stability issues for the concentration proﬁles will be analyzed, and it will be shown that the concentration proﬁle in eutectic structures under electromigration should demonstrate the stochastic tendency. Consider a two-phase mixture of almost pure components; therefore, hereafter the indices 1 and 2 correspond to phases as well as to species. Since we shall limit ourselves within the “under-critical” regime, where the shape of the sample remains unchanged, we have the constraint of constant

SVNY339-Tu

April 5, 2007

17:31

Electromigration in Flip Chip Solder Joints

283

volume in every part of the sample. This means that in the laboratory reference frame the sum of volume ﬂuxes of two species should be zero everywhere: Ω1 J1 + Ω2 J2 = 0,

(9.19)

where J1 , J2 are ﬂuxes of atoms per unit area, and Ω1 , Ω2 are atomic volumes. For convenience, we introduce p1 , p2 , the local volume fractions of phases: Ω i n i = Ωi

ΔVi /Ωi ΔVi = = pi , ΔV ΔV p1 + p2 = 1,

(9.20)

where ni is the number of atoms of either species 1 or 2 per unit volume. In the coarsened space scale, the unit volume ΔV includes at least a few grains. The electromigration ﬂuxes of each component are determined by standard expressions: n1 D1 n 1 D1 Z1 eE = Ω1 Z1 eρj, kT kT n2 D2 n 2 D2 Z2 eE = Ω2 Z2 eρj. = Ω2 kT kT

Ω1 J1EM = Ω1 Ω2 J2EM

(9.21)

Once more, the constraint of constant volume in Eq. (9.19) means that these ﬂuxes should contain additional terms for a convective ﬂow. To satisfy the constraint of constant volume in Eq. (9.19), we assume that there are two alternative ways: back stress and lattice shift, or maybe a combination of these two ways.

9.7.1 Electromigration-Induced Back Stress in Two-Phase Structure We apply the back-stress story in electromigration in Al interconnects to electromigration in a mixture of two coexisting phases. Accumulation of atoms at the anode and of vacancies at the cathode leads to a stress gradient, changing the ﬂuxes, so that the total change of ﬂux volume becomes zero. Namely,

Ω1 J1 =

p1 D1 kT

p2 D2 Ω2 J2 = kT

Z1 eE + Ω1

∂σ ∂x

∂σ Z2 eE + Ω2 ∂x

,

(9.22) .

SVNY339-Tu

284

April 5, 2007

17:31

Chapter 9

Substituting Eq. (9.22) into the constraint of Eq. (9.19), we obtain an expression for arising stress gradient: ∂σ p1 D1 Z1 + p2 D2 Z2 = −eE . ∂x p1 D1 Ω1 + p2 D2 Ω2

(9.23)

Due to this back-stress inﬂuence, the larger ﬂux becomes smaller, and the smaller ﬂux reverses its sign, so that now they compensate each other. Substituting Eq. (9.23) into Eqs. (9.22), we obtain Ω1 J1 =

p1 p2 D1 D2 eE Ω 1 Ω2 · kT p1 D1 Ω1 + p2 D2 Ω2

Z1 Z2 − Ω1 Ω2

= −Ω2 J2

(9.24)

We note that the above derivation is independent of the ﬁnite length of the sample. On the other hand, for a given length, Δx, of the sample, we obtain the critical stress in Eq. (9.23) where there is no electromigration-induced damage since the two opposing ﬂuxes are equal to each other. Below or above the critical stress, the ﬂuxes become unequal and reverse themselves. We can also interpret the above equation by stating that at a given current density, there exists a critical length at which the two ﬂuxes are equal and opposite to each other. Then for lengths longer or shorter than the critical length, the ﬂuxes become unequal and change direction. We note that when the two ﬂuxes are equal and opposite, there is always electromigration, but no electromigrationinduced damage until complete phase separation occurs. Equation (9.24) demonstrates the electromigration-driven segregation under back stress. It is seen that in the case of equalizing ﬂuxes by back stress, the rate of segregation is determined by the slow species: if, say, diﬀusivity of species 2 is much less than that of species 1, and if the fraction p1 is not too small, we have D1 D2 D2 D1 D2 = ≈ . p1 D1 Ω1 + p2 D2 Ω2 p1 D1 Ω1 + 0 p1 Ω1 Moreover, the sign of segregation is determined not by the diﬀerence of diﬀuZ2 1 sivities, but instead by the diﬀerence of ratios of ( Z Ω1 − Ω2 ). For example, the depletion of Pb at the cathode and corresponding enrichment by Sn at the cathode does not necessarily mean that Pb is a faster diﬀusant than Sn. It ZSn Pb means ( Z ΩPb > ΩSn ). The redistribution of volume fractions is determined by the continuity equation, ∂p1 ∂(Ω1 J1 ) ∂n1 = Ω1 =− , ∂t ∂t ∂x

SVNY339-Tu

April 5, 2007

17:31

Electromigration in Flip Chip Solder Joints

285

so that ∂p1 eE =− Ω 1 Ω2 ∂t kT

Z1 Z2 − Ω1 Ω2

D1 D2 ∂ · p1 (1 − p1 ) . ∂x p1 D1 Ω1 + (1 − p1 )D2 Ω2 (9.25)

We shall discuss the stochastic behavior of Eq. (9.25) and the experimentally observed random states later. 9.7.2 Electromigration-Induced Kirkendall Shift in Two-Phase Structure In the alternative case, there is no back stress at all, meaning all possible stresses are immediately relaxed by lattice shift. In a usual polycrystalline body with large grains, it is described by dislocation climb and corresponding construction of extra planes in the region of atom accumulation, and deconstruction of extra planes in the region of vacancy accumulation. Vacancy is at equilibrium everywhere. Yet, in a eutectic two-phase mixture, the picture may not be so simple because of growth and shrinkage of grains of the two phases. We assume that by some mechanism the Kirkendall lattice shift with a velocity U is guaranteed, and it equalizes ﬂuxes without any back stress. Then, in the laboratory reference frame: p1 D1 Z1 eE + p1 U, kT p2 D2 Ω2 J2 = Z2 eE + p2 U. kT Ω1 J1 =

(9.26)

Substituting Eqs. (9.26) into the constraint of Eq. (9.19), we obtain the velocity of Kirkendall shift, U =−

eE (p1 D1 Z1 + p2 D2 Z2 ) . kT

Substituting the last equation into the constraint of Eq. (9.26), we obtain the ﬁnal equations for ﬂuxes of both species in the laboratory reference frame: Ω1 J1 =

eE (Z1 D1 − Z2 D2 ) p1 p2 = −Ω2 J2 . kT

As we can see in this case, the rate of segregation will be determined mainly by the fast species and the sign of segregation is now determined by the diﬀusivity in (Z1 D1 − Z2 D2 ) since the diﬀerence between the eﬀective charge numbers is

SVNY339-Tu

286

April 5, 2007

17:31

Chapter 9

not large. ∂p1 eE ∂ =− [(Z1 D1 − Z2 D2 ) p1 (1 − p1 )] . ∂t kT ∂x

(9.27)

The implicit assumption in Kirkendall lattice shift is that vacancies are in equilibrium everywhere in the diﬀusion zone, so there will be no void formation at the cathode and no hillock formation at the anode. The above equations should provide a correct description of electromigration in solder prior to void formation. A comparison between the model of back stress and Kirkendall shift is made here. Experimentally when we perform electromigration in V-groove samples of eutectic SnPb solder at temperatures above 100◦ C, Pb is driven predominantly to the anode, but near room temperature Sn is driven predominantly to the anode. At temperatures above 100◦ C, solder has a very high homologous temperature, therefore thermal activated process will relax stress fast enough that back stress will not build up. Kirkendall shift model applies. The selection will be controlled by (Z1 D1 − Z2 D2 ) and Pb has the faster diﬀusivity and moves to the anode. However, at a very high current density and after a long duration of electromigration, a lump of solder forms at the anode and back stress exists. At room temperature, while diﬀusion in solder is still quite fast, it is likely that both Kirkendall shift and back stress operate together and Sn is being pushed to the anode. 9.7.3 Stochastic Tendency in Electromigration in Two-Phase Structure In the above two cases, back stress and Kirkendall shift, the equation for redistribution of volume fractions is of the type ∂p1 ∂ =− [V (p1 )p1 (1 − p1 )] , ∂t ∂x

(9.28)

but with diﬀerent explicit expressions for the kinetic coeﬃcient V (which has the units of velocity). It is a ﬁrst-order nonlinear equation, which is very diﬀerent from Fick’s second law or from Fick’s second law with a drift term. The main eﬀect is that it does not contain the second space derivatives, which tend to smooth any local ﬂuctuation of the composition proﬁle by diﬀusion. If V is a constant, Eq. (9.25) is reduced to the well-known Burger’s equation with zero viscosity term, having peculiarities of solutions like shocks. This means that even a smooth waviness of composition proﬁle should evolve into sharp breaks in the concentration proﬁle. Since noble and near-noble metals, such as Cu and Ni, are used as UBM and bond pads in ﬂip chip solder joints, their dissolution into the solder and the formation of IMC are known to be enhanced by electromigration. More

SVNY339-Tu

April 5, 2007

17:31

Electromigration in Flip Chip Solder Joints

287

importantly, the IMC of Cu6 Sn5 and Sn form a eutectic two-phase mixture. Therefore, electromigration can induce the segregation of a large amount of the IMC in Sn or in Pb-free solder. Figure 1.16 showed the growth of randomly distributed Cu6 Sn5 in ﬂip chip solder joint in electromigration. Electromigration has enhanced the dissolution of Cu from the thick Cu UBM into the solder to form a large amount of IMC.

References 1. S. Brandenburg and S. Yeh, Proceedings of Surface Mount International Conference and Exhibition, SMI98, San Jose, CA, Aug. 1998, p. 337– 344. 2. C. Y. Liu, C. Chen, 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). 3. C. Y. Liu, C. Chen, and K. N. Tu, “Electromigraiton of thin strips of SnPb solder as a function of composition,” J. Appl. Phys., 88, 5703–5709 (2000). 4. 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). 5. T. Y. Lee, K. N. Tu, and D. R. Frear, “Electromigration of eutectic SnPb and SnAgCu ﬂip chip solder bumps and under-bump-metallization,” J. Appl. Phys., 90, 4502–4508 (2001). 6. K. N. Tu, “Recent advances on electromigration in very-large-scaleintegration of interconnects,” J. Appl. Phys., 94, 5451–5473 (2003). 7. W. D. Callister, Jr., “Materials Science and Engineering: An Introduction,” 5th ed., Wiley, New York (2000). Chapter 6 (Table 6.1) and Appendix B (Table B.2) 8. E. C.C. Yeh, W.J. Choi, K.N. Tu, P. Elenius, and H. Balkan, “Currentcrowding-induced electromigration failure in ﬂip chip solder joints,” Appl. Phys. Lett., 80, 580–582 (2002). 9. W. J. Choi, E. C. C. Yeh, and K. N. Tu, “Mean-time-to-failure study of ﬂip chip solder joints on Cu/Ni(V)/Al thin ﬁlm under-bump metallization,” J. Appl. Phys., 94, 5665–5671 (2003). 10. H. Gan, W. J. Choi, G. Xu, and K. N. Tu, “Electromigration in ﬂip chip solder joints and solder lines,” JOM, 6, 34–37 (2002). 11. L. Zhang, S. Ou, J. Huang, K. N. Tu, S. Gee, and L. Nguyen, “Eﬀect of current crowding on void propagation at the interface between intermetallic compound and solder in ﬂip chip solder joints, “ Appl. Phys. Lett., 88, 012106 (2006). 12. 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).

SVNY339-Tu

288

April 5, 2007

17:31

Chapter 9

13. 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). 14. 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). (Dissolution of thick Cu UBM) 15. L. Xu, J. Pang, and K. N. Tu, Appl. Phys. Lett., to be published. 16. J. R. Black, Proc. IEEE, 57, 1587 (1969). 17. M. Shatzkes and J. R. Lloyd, J. Appl. Phys., 59, 3890 (1986). 18. N. F. Mott and H. Jones, “The Theory of the Properties of Metals and Alloys,” Dover, New York, p. 242 (1958). (Wiedemann-Franz law) 19. A. T. Huang, Ph.D. dissertation, UCLA (2006). 20. F. Y. Ouyang, Personal communication. 21. J. W. Nah, J. O. Suh, and K. N. Tu, “Eﬀect of current crowding and joule heating on electromigration induced failure in ﬂip chip composite solder joints tested at room temperature,” J. Appl. Phys., 98, 013715 (2005). 22. J. W. Nah, J. O. Suh, K. N. Tu, S. W. Yoon, V. S. Rao, K. Vaidyanathan, and F. Hua, “Electromigration in ﬂip chip solder joints having a thick Cu column bump and a shallow solder interconnect,” J. Appl. Phys., 100, 123513 (2006).

SVNY339-Tu

April 5, 2007

17:34

10 Polarity Eﬀect of Electromigration on Solder Reactions

10.1 Introduction In ﬂip chip solder joints, electromigration-induced failure is dominated by current crowding at the cathode area of contact. The high current density in the current crowding region enhances the dissolution of UBM at the cathode and transforms Cu to Cu3 Sn and to Cu6 Sn5 and ﬁnally leads to void formation and failure; the interaction between electrical force and chemical force is a key factor in the failure. To understand the interaction and to avoid the complication due to current crowding, straight V-groove samples having Cu wires as electrodes were introduced. The V-groove samples have the following advantages. First, their cross section is of similar dimension as that of a ﬂip chip solder joint, so they can carry the working current density. Second, they are highly reproducible. Third, the eﬀect of electromigration-induced mass transport or damage can be observed directly, without cross-sectioning as in ﬂip chip samples. Fourth and perhaps most important, there is no current crowding and the interaction between electrical and chemical forces can thus be studied under a uniform current distribution. The polarity eﬀect of electromigration on chemical reactions at the cathode and the anode can be analyzed [1] as well as the eﬀect of electromigration on phase separation in the two-phase eutectic structure.

10.2 Preparation of V-Groove Samples V-grooves were etched on (001) silicon wafers along {110} directions by using lithographic technique and anisotropic etching process. The width of the V-grooves can be 100 μm and the length can be 1 cm. Then a thin Si dioxide of 100 nm was grown by wet oxidation at 1000◦ C, and was followed by a trilayer of Ti/Cu/Au thin-ﬁlm deposition of thickness 50 nm, 1 μm, and 50 nm, respectively. The silicon wafer was diced into rectangular pieces about 0.25 cm wide and 1 cm long; each contained a V-groove in the middle. Two

SVNY339-Tu

290

April 5, 2007

17:34

Chapter 10

Si V-groove Si (001) (a)

Cu wire

Cu wire

<110>

(b)

Si Wafer

Cu wire

Solder line 100 μm

(c)

Solder SiO2 (0.1 μm)

69.4 μm 69.4 ∝m

Cr or Ti (0.05 μm) m) Cu (1Cuμ(1 ∝ Au (0.05 μm) Fig. 10.1. (a) V-groove sample with two Cu wires before joining. (b) Top view, and (c) cross-sectional view of a V-groove sample.

Cu wires were placed at the ends of a V-groove, and the assembly was kept in resin mild active (RMA) ﬂux and placed on a hot plate at 230◦ C and a solder bead was placed on the V-groove. The bead melted and ran into the V-groove and joined the Cu wires, which will serve as electrodes. After the sample was removed from the hot plate, a V-shaped solder line approximately 200 to 800 μm long, 100 μm wide, and around 69 μm deep was obtained. Figure 10.1(a) illustrates a V-groove sample with two Cu wires as electrodes, and Fig. 10.1(b) and (c) depict the top view and the cross-sectional view of a V-groove sample. The length of the solder line can be controlled by the

SVNY339-Tu

April 5, 2007

17:34

Polarity Eﬀect of Electromigration on Solder Reactions

291

Solder V-groove sample after reflow (a)

Si wafer Cu

Solder line

Cu

Polished sample ready for EM test (b)

Si wafer Cu

e-

Cu

Solder line

Cu

Cu

(c) IMC Cu

Cu

Solder

e-

Cathode

e-

Anode

Fig. 10.2. SEM images of sample (a) before and (b) after polishing for current stressing. (c) Interfacial intermetallic compounds (IMC) can be seen to form at Cu/solder interfaces.

spacing between the two Cu electrodes or by using several solder beads of known diameter as spacers between the Cu wires before reﬂow. To make the solder line the only conductive path between the two Cu electrodes, the surface of the soldered V-groove sample was polished until the metal ﬁlms on the silicon (001) ﬂat surface disappeared. Figure 10.2(a) and (b) show SEM images of sample before and after polishing for current stressing. Interfacial intermetallic compounds (IMC) can be seen to form at Cu/solder interfaces in Fig. 10.2(c) [1–4]. 10.2.1 Electromigration of Eutectic SnPb as a Function of Temperature Electromigration in the eutectic SnPb alloy depends on temperature. At 150◦ C, electromigration of eutectic SnPb V-groove samples was stressed at

SVNY339-Tu

292

April 5, 2007

17:34

Chapter 10

Fig. 10.3. (a) Electromigration of eutectic SnPb at 150◦ C and 2.8 × 104 A/cm2 . The growth of a lump at the anode and void at the cathode can be seen. (b) The void becomes very clear after polishing away a top layer of the sample. (c) Electromigration of eutectic SnPb at room temperature stressed at current density of 5.7 × 104 A/cm2 for 12 days. SEM image of the growth of hillock at the anode and void at the cathode is shown.

2.8 × 104 A/cm2 for 8 days, and led to the growth of a hillock at the anode and a void at the cathode, as shown in Fig. 10.3(a). The void becomes very clear after polishing away a top layer of the sample, as shown in Fig. 10.3(b). To analyze compositional change induced by electromigration along the solder line, a series of EDX spots along the line was measured on the surface. A very large compositional redistribution or phase segregation was observed (see Fig. 10. 4). Electromigration has led to the accumulation of Pb at the anode. At room temperature, the V-groove solder lines of eutectic SnPb were stressed at a current density of 5.7 × 104 A/cm2 for 12 days. Figure 10.3(c) is a SEM image of the growth of hillock at the anode and void at the cathode. Composition analysis by EDX has shown that the amount of Sn at the anode side is consistently higher than that at the cathode side and the increase

SVNY339-Tu

April 5, 2007

17:34

Polarity Eﬀect of Electromigration on Solder Reactions

293

Fig. 10.4. Electromigration of eutectic SnPb at 150◦ C and 2.8 × 104 A/cm2 has led to the accumulation of Pb, instead of Sn, at the anode. A very large compositional redistribution or phase segregation was observed.

of Sn has occurred along the entire length of the solder line. The average Sn concentration on the surface appears higher than that in the bulk of the solder line. The accumulation of Sn at the anode reveals that at room temperature Sn rather than Pb is the dominant diﬀusing species along the direction of electron ﬂow. The temperature dependence is in agreement with the ﬁndings using tracer diﬀusion of radioactive Sn and Pb in eutectic SnPb alloy. Above 100◦ C, Pb diﬀuses faster than Sn, but Sn diﬀuses faster than Pb near room temperature [3]. While Pb and Sn have been observed to be the dominant diﬀusing species in the eutectic SnPb solder driven by electromigration at 150◦ C and room temperature, respectively, it is unknown which one will diﬀuse faster at 100◦ C, the device working temperature. Using V-groove samples of eutectic SnPb, it was found that Pb accumulated at the anode, so Pb is the dominant diﬀusing species at 100◦ C. Thus, we can perform accelerated tests for eutectic SnPb solder above 100◦ C since the dominant diﬀusing species is the same [5].

10.3 Polarity Eﬀect on IMC Growth at the Anode Solder V-groove samples with a width of 100 μm and a cross section of 3.5 × 10−5 cm2 were used to investigate the polarity eﬀect of electromigration on IMC formation. The two Cu wires at the two ends of the V-groove serve as electrodes. The lead-free solder of SnAg3.8Cu0.7 (in wt%) was reﬂowed into the V-groove between the two Cu wires with ﬂux. The reﬂow temperature is 260◦ C and duration is 1 min. While interfacial IMCs form at the two Cu/solder interfaces during reﬂow, we shall focus on the growth of these interfacial IMCs under the inﬂuence of electric current density. The V-groove samples were placed in a furnace with temperature settings of 120, 150, and 180◦ C, and stressed with current density in the range of 103 to104 A/cm2 . The sample was polished slightly after a given time of stressing in order to observe and identify the change of IMC by SEM and EDX. The thickness of IMC is determined by dividing the area of IMC by the length

SVNY339-Tu

294

April 5, 2007

17:34

Chapter 10

of interface. The measurements of area and length are obtained from digital SEM pictures and imaging processing software. The area is measured in the number of pixels in the IMC image, and the thickness and length are also in units of pixels and then converted to micrometers. A standard having a length of 30 μm as a reference was used to calibrate measured data. 10.3.1 IMC Growth without Electric Current (see Section 2.8) As shown in Chapter 2 and Fig. 10.2(c), Cu6 Sn5 scallops formed after reﬂow, but they grew into layer-type on aging. A very thin layer of Cu3 Sn may also form between the Cu6 Sn5 scallops and Cu electrode at the initial stage, yet it is too thin to be recognized in the SEM image. Planar Cu6 Sn5 along with Cu3 Sn kept growing during solid-state annealing at 180◦ C. After 120 hr, the thickness of Cu3 Sn layer is about half that of Cu6 Sn5 . At the Cu3 Sn/Cu interface, Kirkendall voids (the dark dots) formed. 10.3.2 Growth of IMC at Anode and Cathode with Electric Current Figure 10.5 shows the thickness change of IMC in four pairs of SEM images at both the anode and the cathode, after current stressing with current density of 3.2 × 104 A/cm2 at 180◦ C for 0, 10, 21, and 87 hr. For easy comparison, the SEM images of the anode and the cathode were placed side by side, the anode at the left and the cathode at the right, using arrows beside the SEM images to indicate the thickness of the IMC. The major diﬀerence between the anode and the cathode is the polarity eﬀect or the direction of electron ﬂow which is away from the cathode but toward the anode, as indicated in Fig. 10.5. The long arrows outside the images indicate the direction of electron ﬂow. The same kind of IMC of Cu3 Sn and Cu6 Sn5 formed at the anode and the cathode with or without application of electric current. As can be seen in Fig. 10.5(a) and (b), the same scallop-type Cu6 Sn5 compounds formed at solder/Cu interfaces in the initial stage, but they transformed into layer-type after current stressing of 10 hr, as shown in Fig. 10.5(c) and (d). At the anode, as shown in the left column in Fig.10.5, both Cu3 Sn and Cu6 Sn5 layers kept growing with current stressing time and the total thickness approached 10 μm after 87 hr, comparable to that of thermal aging for 200 hr at the same temperature without applying current. The Cu3 Sn phase between the Cu6 Sn5 and Cu had darker color and became apparent in the SEM image in Fig. 10.5(g). The total IMC at the anode was always much thicker than that at the cathode, as indicated by the short arrows beside the images. Compared to the case of thermal aging without current, there were fewer Kirkendall voids formed at the Cu3 Sn/Cu interface at the anode. At the cathode, it is hard to tell directly how the thickness of IMC changes from SEM images in the right column in Fig.10.5. The IMC grew much slower

SVNY339-Tu

April 5, 2007

17:34

Polarity Eﬀect of Electromigration on Solder Reactions

295

Fig. 10.5. Thickness change of IMC at the anode and cathode, after current stressing with current density of 3.2 × 104 A/cm2 at 180◦ C for 0, 10, 21, and 87 hr.

than that at the anode. Voids started appearing in the solder part just in front of the solder/IMC cathode interface after 21 hr and grew bigger after 87 hr, marked by arrows in Fig. 10.5(f) and (h). After the development of big voids, IMC seems thicker in Fig. 10.5(h) due to the transformation of Cu6 Sn5 into Cu3 Sn (darker phase). Void formation brings complexity into the analysis of change of IMC thickness at the cathode.

10.3.3 IMC Thickness Change with Current Density and Temperature The thickness changes of IMC at 180, 150, and 120◦ C, with diﬀerent current densities, were measured and are shown in Fig. 10.6(a), (b), and (c),

SVNY339-Tu

April 5, 2007

296

Chapter 10

(a)

4

(b)

2

Anode(4x10 A/cm ) 4 2 Cathode(4x10A/cm ) 4 2 Anode(3x10 A/cm ) 4 2 Cathode(3x10 A/cm ) 4 2 Anode(2x10 A/cm ) 4 2 Cathode(2x10 A/cm ) 3 2 Anode(4x10 A/cm ) 3 Cathode(4x10 A/cm2) Without Current Linear Fit

250

200

Anode(4x104A/cm2) 4 2 Cathode(4x10 A/cm ) Anode(3x104A/cm2) 4 Cathode(3x10 A/cm2) Anode(2x104A/cm2) Cathode(2x104A/cm2) Anode(4x103A/cm2) Cathode(4x103A/cm2) Without Current Linear Fit

60

(Δ X)2 (μm2)

300

(Δ X)2 (μ m2)

17:34

50 40

150

30

100

20

50

10

0

0 0

10

20

30

40

50

60

70

80

0

90

10

20

30

40

50

60

70

80

90

100

Time (hour)

Time (hour)

(c) Anode(4x104A/cm2) Cathode(4x104A/cm2) Anode(3x104A/cm2) Cathode(3x104A/cm2) Anode(2x104A/cm2) Cathode(2x104A/cm2) Without current Linear Fit

(Δ X)2 (μ m2)

22 20 18 16 14 12 10 8 6 4 2 0

25

50

75

100

125

150

Time (hour)

Fig. 10.6. Measured thickness changes of IMC at (a) 180◦ C, (b) 150◦ C, and (c) 120◦ C, with diﬀerent current densities.

respectively. The measured thickness is the total thickness of Cu6 Sn5 and Cu3 Sn. The ﬁgures contain the thickness data for both the anode and the cathode for current stressing with current densities of 4 × 103 , 2 × 104 , 3 × 104 , and 4 × 104 A/cm2 . The square of thickness (Δx)2 of IMC is plotted as a function of time, and the data for the no-current case is included as reference. The solid symbols designate the data of the anode side, while the hollow symbols of the same shapes represent the corresponding data of the cathode side. The solid star is for the no-current case, or the case of thermal aging. There are several common phenomena for IMC growth for all three test temperatures, as shown in Fig. 10.6. First, the growth of IMC at the anode has a parabolic dependence on time since the square of thickness (Δx)2 of IMC increases linearly with time. Second, the thickness data of the anode are above the no-current curve, while those of the cathode fall below it. Therefore, IMC grows faster at the anode and slower at the cathode, compared with the

SVNY339-Tu

April 5, 2007

17:34

Polarity Eﬀect of Electromigration on Solder Reactions

297

no-current case. In other words, electric current enhances the growth of IMC at the anode and retards it at the cathode due to the polarity eﬀect. Third, IMC grows much faster with higher current density at the anode than in the nocurrent case. The enhancement of growth at the anode increases with current density. After the same stressing time, the sample with the largest current density (4 x 104 A/cm2 ) has the thickest IMC at the anode, and the one with the lowest current density (4 x 103 A/cm2 ) has the thinnest, just slightly larger than the no-current case. Finally, the thickness of IMC at the cathode does not change as much, remaining around the initial thickness (around 2.5 μm) or below. We shall discuss this behavior under dynamic equilibrium in a later section. The situation at the cathode side also becomes more complicated due to void formation in long time stressing. The growth of IMC at the anode was studied at various temperatures when current density was held constant at 4 × 104 , 3 × 104 , 2 × 104 , and 0.4 × 104 A/cm2 [4]. The growth at 180◦ C is above that of 150◦ C, while the growth at 120◦ C is always the lowest, indicating that IMC grows faster at higher temperature. The activation energy of the growth of total IMC is 1.03 eV, obtained from the slope of ln(D) versus 1/kT . This is close to the reported value of 0.94 eV [6]. 10.3.4 Comparison among Electrodes of Cu, Ni, and Pd in V-Groove Samples In Chapter 7, interfacial reaction between solder and Cu was shown to be faster than that between solder and Ni. However, the reaction between solder and Pd is the fastest among the three. When electromigration in V-groove samples is conducted using Cu, Ni, or Pd electrodes, it is expected that the chemical force will dominant over the electrical force in the case of Pd electrodes, if the applied current density is not too high. On the other hand, the electrical force may dominant over the chemical force in the case of Ni electrodes. Indeed, the IMC growth at the cathode and at the anode of Pd are fast and parabolic, and they are much less aﬀected by electromigration. In the case of Ni, a linear growth was observed at the anode, indicating the dominant eﬀect of electromigration.

10.4 Polarity Eﬀect on IMC Growth at the Cathode The polarity eﬀect slows down IMC growth at the cathode. The electric current may enhance the diﬀusion of Cu in IMC since Cu is the dominant diﬀusing species in IMC growth. The Cu diﬀusion is in the same direction as the electron current, and therefore may enhance the growth of Cu3 Sn and Cu6 Sn5 . However, the electric current may also enhance the dissolution of Cu6 Sn5 into the solder. To monitor the dissolution of the IMC at the cathode side, the samples was aged at 150◦ C for 200 hr to form a thick layer of Cu6 Sn5 before

SVNY339-Tu

298

April 5, 2007

17:34

Chapter 10 Previous: Reflow+EM Cu6Sn5

Cu Cathode

Cu6Sn5

Cu

Sn3.8Ag0.7Cu

e-

Anode

Present: Reflow+Aging+EM Cu6Sn5 Cu3Sn

Cu3Sn Cu6Sn5

Cu Reaction

Cathode

Sn3.8Ag0.7Cu

Cu

Dissolution

e-

Anode

Fig. 10.7. Schematic diagram of a V-groove sample before and after solid-state aging for the purpose of monitoring the dissolution of IMC at the cathode side.

current stressing. This is shown in the schematic diagram of Fig. 10.7. In aging, a thin layer of Cu3 Sn compound is also formed between Cu and Cu6 Sn5 . Since the change of Cu3 Sn layer after electromigration was not as obvious as the Cu6 Sn5 layer, especially at low current density, we shall focus only on the change of Cu6 Sn5 layer for a simple analysis. At 150◦ C, current densities of 2 × 104 , 1 × 104 , and 5 × 103 A/cm2 were applied to the aged V-groove sample to study the eﬀect of current density on the dissolution rate of Cu6 Sn5 compound. All the V-groove samples have the same solder length of 550 μm. As shown in Fig. 10.8 by the triangular symbols, at the current density of 2 × 104 A/cm2 , the thick layer of Cu6 Sn5 compound becomes very thin in 10 hr. This rapid dissolution corrupts the cathode side and voids start to form. When the current density was lowered to 1 × 104 A/cm2 , a uniform dissolution of Cu6 Sn5 compound at the cathode was observed. After 158 hr of electromigration at this current density, a layer of Cu6 Sn5 compound of about 1 μm can still exist at the cathode. No void formation has been found at this stage. Further reducing the current density to 5 × 103 A/cm2 , the dissolution behavior of the IMC became diﬀerent from that under the higher current densities; there was a fast dissolution of Cu6 Sn5 in the ﬁrst 50 hr, but after that, in some places it started to grow. This growth of the IMC was more localized and much slower than the dissolution of the IMC. Due to this localized growth, somehow, the thickness of the IMC stabilized at the cathode after 240 hr of electromigration. Figure 10.8 is a plot of the thickness change of the Cu6 Sn5 as a function of time at diﬀerent current densities.

SVNY339-Tu

April 5, 2007

17:34

Polarity Eﬀect of Electromigration on Solder Reactions

299

5

4

ΔX μm) Δ (μ

3

2

5×103 A/cm2 1×104 A/cm2 2×104 A/cm2

1

0

0

50

100

150 200 Time (hour)

250

300

Fig. 10.8. Plot of thickness of the anode of aged V-groove samples stressed at current density of 2 × 104 A/cm2 versus time. The thick layer of Cu6 Sn5 compound becomes very thin in 10 hr. This rapid dissolution corrupts the cathode side. Voids started to form in some locations. When the current density was lowered to 1 × 104 A/cm2 , a uniform dissolution of Cu6 Sn5 compound at the cathode was observed. After 158 hr of electromigration at this current density, a layer of Cu6 Sn5 compound of about 1μm can still be seen clearly at the cathode. Further reducing the current density to 5 × 103 A/cm2 , there was a fast dissolution of Cu6 Sn5 in the ﬁrst 50 hr, but after that, in some places where the IMC layer was very thin as identiﬁed by the arrow, it started to grow.

10.4.1 Dynamic Equilibrium The most interesting curve in Fig. 10.8 occurs for the current density of 5 × 103 A/cm2 , using the square symbols. After 85 hr of electromigration, a steady state of the IMC thickness is observed. As we have discussed, there are two driving forces contributing to the change of thickness of the IMC; they are the chemical force and the electrical force. The ﬂux equation for the mass transportation can be given as D ∂μ D ∗ J = Jchem + Jem = C (10.1) Z ejρ, − +C kT ∂x kT where C is concentration, D is diﬀusivity, kT has the usual meaning, ∂μ/∂x is chemical potential gradient, Z ∗ is eﬀective charge number, e is electron charge, ρ is resistivity, and j is current density. At the cathode side, the chemical force grows the IMC, whereas,the electrical force dissolves the IMC. These two forces compete during the entire electromigration process. The solid-state aging study has illustrated that the

SVNY339-Tu

300

April 5, 2007

17:34

Chapter 10

layer-type IMC growth driven by chemical potential gradient force alone is diﬀusion-controlled. The growth rate satisﬁes dx/dt ∝ A/x. This means that when a layer thickness approaches zero (x → 0), the growth velocity dx/dt goes to inﬁnity. Thus, the layer cannot disappear in the diﬀusion-controlled mode. In other words, the chemical potential gradient becomes inﬁnite as x → 0. When the electrical force is weak, the chemical force may exceed the electrical force, and the growth of IMC can occur at the cathode side. The growth of IMC was observed at the cathode when the current density was only 4 × 103 A/cm2 . When the electrical force is comparable to the chemical force, a plateau in the IMC thickness curve is found, which indicates a dynamic equilibrium between growth and dissolution. We deﬁne this state as a dynamic equilibrium state between chemical and electrical forces [7]. Why is dynamic equilibrium intersting? First, a critical product can be obtained from this equilibrium, similar to that in the electromigration study in Al short strips, where a static equilibrium can be achieved between the electrical force and back stress. We have the net J = 0 in Eq. (10.1), so Δμ ∗ = ZCu ejρCu6 Sn5 . 6 Sn5 Δx

(10.2)

By rearranging the equation, we obtain a critical product as (jΔx)critical =

Δμ . ∗ ZCu eρCu6 Sn5 6 Sn5

(10.3)

Knowing the critical product, we can calculate at a given current density the thickness of IMC that can reach a dynamic equilibrium. As long as the IMC thickness is equal to or larger than the critical thickness at the given current density, there is no void formation at the cathode. Experimentally, the thickness of the IMC at the equilibrium has been found to be about 2.9 μm at 5 × 103 A/cm2 . Next, the dissolution rate of the Cu electrode can be obtained, from which the lifetime of a Cu UBM of a given thickness can be calculated. At dynamic equilibrium, the thickness of the IMC will not change with time, and the moving velocities of the Cu/IMC interface and the IMC/Sn interface are equal to each other. The moving velocity is related to the ﬂux by the equation J = Cv, and based on the experimental data, the measured dissolution rate of Cu with current density 5 × 103 A/cm2 at 150◦ C is about 0.076 μm/hr. In the last two sections, we discussed the polarity eﬀect of electromigration on IMC formation at the cathode and the anode. What is the eﬀect of electromigration on the bulk of the solder in between the two electrodes? We recall from Section 9.7 that the eutectic two-phase microstructure in the bulk of the eutectic solder becomes intrinsically unstable driven by electromigration.

SVNY339-Tu

April 5, 2007

17:34

Polarity Eﬀect of Electromigration on Solder Reactions

301

10.5 Eﬀect of Electromigration on the Competing Growth of IMC Greer and his co-worker published a paper recently about the eﬀect of electromigration on the competing growth between two IMCs [8]. It is similar to the competing growth between two-layered IMCs presented in Section 3.2.4. However, in electromigration, the interaction across a solder joint between the IMC at the cathode and the IMC at the anode should be considered. As shown in Sections 10.3 and 10.4, the formation of IMC at the anode is accelerated and that at the cathode is retarded, due to the interaction. The interaction occurs because in conducting electromigration in a solder joint, there must be a cathode and an anode. The solid-state diﬀusion of Cu and Ni in the solder

(a)

(b)

Scan line

(c)

Fig. 10.9. (a) SEM image of a V-groove joint of 10-μm-thick eutectic SnAgCu solder between two Cu electrodes. (b) The sample was current stressed with a current density of 2 × 104 A/cm2 at 150◦ C for 144 hr. SEM image shows a trilayer of IMC formation between the two Cu electrodes as in Cu/Cu3 Sn/Cu6 Sn5 /Cu3 Sn/Cu. (c) The composition proﬁle shows that the Cu3 Sn at the cathode side grows faster than the Cu3 Sn at the anode side. (Courtesy of Minyu Yan, UCLA).

SVNY339-Tu

302

April 5, 2007

17:34

Chapter 10

is extremely fast, and generally speaking, electromigration in solder occurs at a high homologous temperature. To address the eﬀect of electromigration on competing growth of IMC accompanied by the interaction, the dissolution of IMC into the solder at the cathode side cannot be ignored and the precipitation of IMC at the anode side must be considered. Even if an inﬁnite sink of solder is used as the anode, while there is no precipitation, the dissolution will be inﬁnite too. However, owing to the trend of miniaturization, the size of solder joint will approach 10 μm in diameter or in thickness, and the entire joint can become IMC. Therefore, we may have a joint consisting of a trilayer of IMC between two Cu electrodes as in Cu/Cu3 Sn/Cu6 Sn5 /Cu3 Sn/Cu. Such structure has been formed in a V-groove sample as shown in Fig. 10.9. A 10-μmthick eutectic SnAgCu solder was joined between two Cu wires in a V-groove and followed by electromigration with a current density of 2 × 104 A/cm2 at 150◦ C for 144 hr. Interfacial reaction between the solder and the two Cu electrodes has transformed the entire solder into a trilayer of IMC. The SEM images before and after reaction are shown respectively in Fig. 10.9(a) and (b), and composition proﬁle after the reaction measured by electron probe is shown in Fig. 10.9(c). The white line in Fig. 10.9(b) indicates the composition scanned by electron probe. Using such kinds of samples, it is possible to investigate the eﬀect of electromigration on the competing growth among the trilayer of IMC. The preliminary result shows that the Cu3 Sn at the cathode side grows faster than the Cu3 Sn at the anode side as shown in Fig. 10.9(c).

References 1. 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). 2. Q. T. Huynh, C. Y. Liu, C. Chen, and K. N. Tu, “Electromigration in eutectic PbSn solder lines,” J. Appl. Phys., 89, 4332–4335 (2001). 3. H. Gan, W. J. Choi, G. Xu, and K. N. Tu, “Electromigration in ﬂip chip solder joints and solder lines,” JOM, 6, 34–37 (2002). 4. 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). 5. R. Aquawal, S. Ou, and K. N. Tu, “Electromigration and critical product in eutectic SnPb solder lines at 100◦ C,” J. Appl. Phys., 100, 024909 (2006). 6. 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

SVNY339-Tu

April 5, 2007

17:34

Polarity Eﬀect of Electromigration on Solder Reactions

303

solders (SnAg, SnAgCu, and SnCu) on Cu,” J. Mater. Res., 17, 291–301 (2002). 7. S. Ou, Ph.D. dissertation, UCLA, (2004). 8. H. T. Orchard and A. L. Greer, “Electromigration eﬀects on compound growth at interfaces,” Appl. Phys. Lett., 86, 231906 (2005).

SVNY339-Tu

March 23, 2007

16:20

11 Ductile–to-Brittle Transition of Solder Joints Aﬀected by Copper–Tin Reaction and Electromigration

11.1 Introduction Concerning the mechanical properties of solder joints, there are two unique characteristics worth mentioning again and again. The ﬁrst is that solder alloys have a very high homologous temperature at the device working temperature or at room temperature. Take the melting point of eutectic SnAgCu at 217◦ C as an example. Room temperature is 0.6 of the melting point on the absolute temperature scale. Therefore, thermally activated atomic process must be taken into account when the mechanical properties of a solder joint are considered, especially at a slow strain rate. The second is that a solder joint has two interfaces. Its mechanical properties can be very diﬀerent from those of a dog-bone-type bulk sample of solder without interfaces. Its mechanical failure tends to occur near the interfaces because the interfaces can become more and more brittle with time due to IMC formation and vacancy accumulation from Cu-Sn reaction as well as from electromigration. At a high strain rate impact, a brittle fracture occurs at the interface. In this chapter, the eﬀect of Cu-Sn reaction and electromigration on mechanical properties of ﬂip chip solder joints will be emphasized. We recall that chemical reaction can aﬀect stress generation and stress relaxation in spontaneous Sn whisker growth as discussed in Chapter 6. Also, electromigration can induce back stress and the back stress can inﬂuence electromigration as discussed in Chapter 9. These are internal stresses. Here, we discuss the effect of Cu-Sn reaction and electromigration on mechanical properties of solder joints when an external force is applied to the joint, especially the force of impact in dropping by free fall. For portable and hand-held devices, the most frequent failure is caused by an accidental drop to the ground. Mechanical properties of solder alloys have been covered in many books. What is covered in this chapter is the eﬀect of Cu-Sn reaction and electromigration on the mechanical properties of a ﬂip chip solder joint, emphasizing

SVNY339-Tu

306

March 23, 2007

16:20

Chapter 11

especially the interfaces of the solder joint. Due to interfacial reaction and polarity eﬀect of electromigration on the interfaces, a ductile solder joint can become a brittle solder joint. The ductile-to-brittle transition is very sensitive to a high-speed shear stress applied to the joint by an impact. Because solder alloys are ductile by nature, it is of interest to understand how electromigration and Cu-Sn reaction can aﬀect the mechanical properties of a solder joint interface and change its ductile nature. We shall examine the mechanisms in the next section. Owing to the polarity eﬀect of electromigration, vacancies will accumulate to form voids at the cathode interface of the joint. Besides electromigration, the ductile-to-brittle transition in solder joints can also be caused by aging because there will be much more intermetallic compound (IMC) formation at the joint interfaces due to Cu-Sn reaction, especially when Kirkendall voids accompany IMC formation. When a brittle interface encounters a high-speed impact in dropping, fracture failure occurs easily. Actually, impact stress is catching up with thermal stress to become another important issue from the point of view of mechanical reliability of devices because more and more portable consumer electronic products are expected to fail by dropping.

11.2 Tensile Test Aﬀected by Electromigration To examine the eﬀect of electromigration on mechanical properties of solder joints, samples having the conﬁguration of Cu (wire)–solder ball (Sn95.5 Ag3.8Cu0.7)–Cu (wire) were designed and prepared, as shown in Fig.11.1. Si V-groove

Cu

300 μm

Si (001)

Cu SiO 2 Si

<110>

270 m

Cu wire with polymer coating

300 m

Solder ball: 95.5Sn-4Ag-0.5Cu

Fig. 11.1. A Cu(wire)–solder ball(Sn95.5Ag3.8Cu0.7)–Cu(wire) sample was prepared by etching a V-groove on a silicon chip with a width of 300 μm, and then two Cu wires as electrodes and two identical solder balls 300 μm in diameter were aligned in the V-groove.

SVNY339-Tu

March 23, 2007

16:20

Ductile–to-Brittle Transition of Solder Joints Fig. 11.2. (a) Optical micrograph of the sample. (b) Crosssectional image after polishing.

b

~440 μm

a

307

300 μm

Cross-section

First, a V-groove on a silicon chip with a width of 300 μm was etched. After the etching, the Si was oxidized to form an oxide layer on the wall of the V-groove without depositing the trilayer of metal ﬁlms as discussed in Chapter 10; molten solder will therefore not wet the oxidized V-groove. Next, two Cu wires 300 μm in diameter with polymer coating were placed in the V-groove, and two identical solder balls 300 μm in diameter were aligned in between the Cu wires in the V-groove. Then the assembly was heated to 250◦ C for a few minutes, the solder balls melted, and joined to the two Cu electrodes by interfacial IMC formation. The polymer coating on the Cu wire will limit the molten solder to wet only the cross-sectional surface of the wires. After cooling, the one-dimensional wire sample was removed from the V-groove by ultrasonic vibration. Figure 11.2(a) is an optical micrograph of the sample, and Fig. 11.2 (b) is its longitudinal cross-section image after polishing [1]. The advantage of such one-dimensional samples is that tensile stress can be applied to study solder joints. Furthermore, using the Cu wires as electrodes, electric current and tensile stress can be applied serially or simultaneously. Unlike dog-bone-type bulk test samples, these samples have two interfaces with IMC formation, which makes them closer to real solder joints in a device. The one-dimensional Cu–solder–Cu samples were divided into two groups. The ﬁrst group was subjected to the tensile test without applying current. The strain rate was 10−2 /sec. The second group was subjected to electromigration before the tensile test. The current density was 1.68 × 103 and 5.03 × 103 A/cm2 at 145◦ C for 24 and 48 hr. Then the tensile test was performed with a strain rate of 10−2 /sec. Figure 11.3(a) and (b) show stress–strain curves of the tensile test. Figure 11.3(a) demonstrates the current density eﬀect of electromigration on tensile strength. The top curve is a pure tensile test. The middle curve is after electromigration with 1.68 × 103 A/cm2 at 145◦ C for 48 hr. The bottom curve

SVNY339-Tu

March 23, 2007

308

16:20

Chapter 11 50

No electromigration

Stress MPa

(a) 40

48hours, 145°C,

30

1.68×103 A/cm2

20

48hours, 145°C

10

5×103 A/cm2

0 0.0

0.1

0.2

0.3

0.4

0.5

Strain

Stress MPa

50

(b)

No electromigration

40

24 hours, 145°C, 30

5×103 A/cm2

20

48hours, 145°C 10

5×103 A/cm2 0 0.0

0.1

0.2

0.3

0.4

0.5

Strain

Fig. 11.3. Stress–strain curves before and after electromigration. (a) The upper curve is pure tensile test. The middle curve is after electromigration with 1.68 × 103 A/cm2 at 145◦ C for 48 hr. The lower curve is after electromigration with 5.03 × 103 A/cm2 at 145◦ C for 48 hr. (b) The upper curve is the tensile test result without current stressing, and the middle and lower curves are samples stressed with 5 × 103 A/cm2 at 145◦ C for 24 and 48 hr, respectively.

is after electromigration with 5.03 × 103 A/cm2 at 145◦ C for 48 hr. It illustrates the change of tensile strength with electromigration. In Fig. 11.3(b), the top curve is the tensile test result without current stressing, and the middle and bottom curves are samples stressed by 5 × 103 A/cm2 at 145◦ C for 24 and 48 hr, respectively. A longer time or a higher current density of electromigration will cause more vacancies to move from the anode to the cathode, thus weakening the interfacial mechanical strength of the cathode by vacancy condensation. To analyze whether the weaker cathode interface is the reason for decreasing tensile strength due to electromigration, fracture images were taken after tensile test with and without electromigration, as shown in Fig. 11.4. Without current stressing, the sample was broken in the bulk of the solder because the Pb-free solder is much softer than the copper wire, as shown in Fig. 11.4(a). After 96 hr of electromigration at 145◦ C, the sample was broken near the interface of the cathode even though there was some plastic deformation observed in the solder joint, as shown in Fig. 11.4 (b). After current stressing for 144 hr with the same current density, the sample was broken abruptly at the interface of the cathode side while the bulk of the solder joint

SVNY339-Tu

March 23, 2007

16:20

Ductile–to-Brittle Transition of Solder Joints

(a)

No electromigration

(b)

(c)

e-

e-

96 hours electromigration 5×103 A/cm2, 145°C

309

144 hours electromigration 5×103 A/cm2, 145°C

Fig. 11.4. Fracture images taken after tensile test with and without electromigration. (a) Without electromigration. (b, c) After electromigration for 96 and 144 hr, respectively.

maintained the original shape, which indicates a brittle fracture, as shown in Fig. 11.4(c).

11.3 Shear Test Aﬀected by Electromigration To examine the eﬀect of electromigration on shear behavior of solder joints, Fig. 11.5 is an optical image of a ﬂip chip bonded to an organic board. The large white arrow indicates the shear force which pushes the chip and produces shear to the solder joints between the chip and the board. In the ﬂip chip No underfil l Shear direction

Fig. 11.5. Optical image of a ﬂip chip sample in shear test. In the ﬂip chip sample, a daisy chain of composite solder balls formed between the silicon chip and organic board.

B

+

A

-

SVNY339-Tu

310

a

March 23, 2007

16:20

Chapter 11

B

A

b

c

A

B

d

Fig. 11.6. SEM fracture images of the second group of sample with electromigration. (a) Chip side; (c) substrate side. (b, d) Magniﬁed pictures of two pairs of powered solder joints showing alternate fracture in (a) and (c), respectively.

sample, a daisy chain of composite solder joints formed between the silicon chip and organic board. The composite consists of a high-Pb solder on the chip side and eutectic SnPb solder on the substrate side. In shear tests, the ﬂip chip samples were divided into two groups. The ﬁrst group was sheared without electromigration. The strain rate was 0.2 μm/sec. The second group underwent electromigration with 2.55 × 104 A/cm2 at 155◦ C for 10 hr before they were sheared with the same strain rate [2]. Figure 11.6 shows top views of SEM fracture images of the second group of sample. Figure 11.6(a) is from the chip side and Fig. 11.6(c) is from the substrate side. The letters A and B in these two ﬁgures indicate two pairs of solder joints in the powered daisy chain. Figure 11.6(b) and (d) are magniﬁed images of these two pairs, respectively. They fractured alternately. On the other hand, the rest of the unpowered joints shown in Figure 11.7(a) and (c) fractured at the high-Pb side. Figure 11.7 shows side views of SEM fracture images of the second group which was sheared after electromigration. Figure 11.7(a) is the chip side image and (c) is the substrate side image. Figure 11.7(b) and (d) are the magniﬁed images of (a) and (c), respectively.

SVNY339-Tu

March 23, 2007

16:20

Ductile–to-Brittle Transition of Solder Joints

311

Fig. 11.7. SEM fracture images of the side view of second group of samples which were sheared after electromigration. (a) Chip side image; (c) substrate side image. (b, d) Magniﬁed pictures of (a) and (c), respectively. The arrow shows the electron ﬂow direction, and it alternates downward and upward in the daisy chain of solder joints.

The arrow shows the electron ﬂow direction, and it alternates downward and upward in the daisy chain of solder joints. To explain the fracture mode, we recall that a composite solder joint has the high-Pb region and the eutectic SnPb region. It was found that without electromigration, solder joints fail in the high-Pb region because Pb is softer than eutectic SnPb. However, after electromigrtion, the fracture always occurs at the cathode interfaces in the daisy chain, regardless of whether the cathode was the high-Pb region or the eutectic SnPb region. The phenomenon of alternately failure in a daisy chain in shear test, as shown in Figs. 11.6 and 11.7, shows that electromigration weakens the cathodes by void formation at the cathode interfaces, which is similar to the results of tensile tests.

11.4 Impact Test 11.4.1 Charpy Test Wireless, hand-held, and movable consumer electronic products are ubiquitous. A frequent cause of failure of these devices is an accidental drop to the

SVNY339-Tu

312

March 23, 2007

16:20

Chapter 11

ground. The impact tends to cause interfacial fracture of those wire-bonds or solder joints between a Si chip and its packaging module, and especially those ball-grid-array (BGA) solder joints without underﬁll. While the molding compound on wire-bonding and the epoxy underﬁll in ﬂip chip solder joints are eﬀective in preventing physical separation of the chip from its module on impact, an interfacial crack induced by the impact is enough to cause an electrical open failure. Hence, the reliability of solder joints concerning the combined eﬀect of electromigration-induced damage at the cathode interface and impact-induced high-speed shear stress in dropping cannot be ignored. The drop-induced fracture of BGA solder joints is of major concern. This is because BGA solder balls are much heavier than ﬂip chip solder balls. Without the protection of underﬁll, they have a much higher probability of interfacial fracture failure on dropping when a torque is involved. At present, the microelectronics industry has the JEDEC speciﬁcations on a free fall drop test, in which a board about 13 cm by 8 cm having an array of 3 × 5 chip-size packaging substrates on the board is dropped with a drop table. The board is attached to the drop table with four corners of the board ﬁxed on standoﬀs, so the board can have ﬂexional vibration. In the drop test, the board is positioned horizontally. The impact of the free fall drop will cause bending and vibration of the board, which will induce fracture at the solder joint interfaces with the substrate. However, the size of the test board is too big to be meaningful for hand-held devices, especially the eﬀect of impact on small packaging boards. No standard drop machine and speciﬁcations are available to test small packaging samples, e.g., a chip-size packaging in which a piece of 1 cm2 ﬂip chip is packaged on a board of similar dimensions. Further discussion of the drop test will be given in Section 11.5. Next we discuss the classic Charpy impact test. The classic Charpy impact test is a standard test for fracture toughness of bulk samples of steel, and the typical test sample is a rectangular bar of size about 1 cm × 1 cm × 5 cm. The test measures the impact toughness of the sample by measuring the potential energy loss of a pendulum before and after fracturing the sample. The pendulum of the machine hits the backside of the sample which has a notch on the front side. Impact toughness is measured by the energy spent to create the two fracture surfaces in the test sample. In most body-centered-cubic metals, including steels, a ductile-to-brittle transition temperature (DBTT) exists. The metal is ductile above DBTT, yet it becomes brittle below DBTT. The “Titanic” ship may have sunk in cold water after hitting an iceberg which caused brittle fracture in its hull. The Charpy impact test was invented to characterize the DBTT in a metal, so that the lower limit of its application temperature which should be above DBTT is known [3]. The energy spent during the impact is measured by the gravitational potential energy change of the pendulum before and after the impact. The potential energy change is measured from the diﬀerence between the initial pendulum height, h1 , and the maximum height achieved during the followthrough, h2 , or the diﬀerence in height before and after the impact, as shown

SVNY339-Tu

March 23, 2007

16:20

Ductile–to-Brittle Transition of Solder Joints

313

Fig. 11.8. Schematic diagram of geometry of Charpy impact test. The heights and angles of the hammer before and after impact are shown.

in Fig. 11.8. PE = mgh1 − mgh2 = mgΔh,

(11.1)

where m is the mass of the pendulum (in grams), g is gravity constant or acceleration of gravity (980 cm/sec2 ), Δh = h1 − h2 = L (cos θ1 − cos θ2 ), where L is the length of the swing pendulum in centimeters, and θ1 and θ2 are the angles of the pendulum before and after impact, respectively. The potential energy has units of Newton-cm. In the Charpy test, the heights or angles are measured from a readable angle-indicator (a needle) on a scale before and after the impact. The accuracy of the reading of angles is about 0.5 to 1 degree. For large bulk samples and very tough materials such as steel bars, the reading from the scale is good enough. What we have learned from the Charpy test is that there are three key factors which contribute to a brittle fracture: (1) low temperature, (2) highspeed shear, and (3) a geometrical notch. When a structure of ductile material has all three factors, it tends to show a brittle behavior. If these factors do not exist, it remains ductile, except materials which are brittle by nature such as glasses. Most materials become brittle at low temperatures, including pure Sn which is known to have a sluggish phase change from beta-Sn (metallic, with a body-centered tetragonal lattice) to alpha-Sn (semiconducting, with a diamond lattice) at 13◦ C. Due to an extremely large molar volume change, the phase change in pure Sn, known as tin pest, has caused structural fracture. Nevertheless, for most applications of eutectic solder joints

SVNY339-Tu

314

March 23, 2007

16:20

Chapter 11

near room temperature, owing to the intrinsic nature of high homologous temperature of these alloys, the ﬁrst factor of low temperature is not a concern. But when the application takes place in very cold weather, it will be a concern. On the second factor of high-speed shear, this is serious because the failure due to dropping involves a high-speed shear. Therefore, a standard shear test by push which is a low-speed shear will not be able to characterize the brittle behavior of a solder joint in dropping. To do so, an impact shear which is as fast as that in a drop is required. The third factor of a geometrical notch suggests that in a solder joint, if a sharp geometrical corner exists between the solder bump and its substrate, it serves as a notch and may contribute to the ductile-to-brittle transition. However, for solder joints, we must add the fourth factor of IMC and Kirkendall void formation at the joint interfaces. Void formation can be caused by interdiﬀusion and electromigration. 11.4.2 Mini Charpy Machine to Test Solder Joints To apply the Charpy impact test to small samples, e.g., a single BGA or a single ﬂip chip solder ball joint in electronic packaging, where the diameter of a solder ball is from about 760 μm to 100 μm, a mini impact testing machine, as shown in Fig. 11.9, was built in order to test the bonding nature of one of these solder balls to their substrate [4–7]. Basically it is a portable mini Charpy testing machine. An electromagnet was used to release the hammer having an arm of 1 foot. The hammer velocity released from the height of 1 foot is about 2.44 m/sec at the lowest position. The velocity is about three orders of magnitude faster than the shear speed in a typical push test which is about 1 mm/sec. The solder ball sample is placed on an XYZ positioning stage at the lowest position. The initial position of the hammer and its ﬁnal position after impact are recorded by a needle pointer in an angle recorder on a hemispherical dial as shown in the upper left corner in Fig. 11.9. On the dial surface, the angle can be read to an accuracy of 0.5 degree. Since the measured angle diﬀerence in a typical impact test is about 10 degrees, the resolution is about 10 to 5% of the measured energy change. The mini Charpy impact test machine has been used to study the impact toughness of solder balls bonded to BGA substrates. The arrangement of solder balls on the BGA substrate is such that there is only one bump in the path of swing of the hammer. Figure 11.10 shows SEM images of the fractured surface of the solder joints. Figure 11.10(a) shows a fracture within the bulk of the solder bump. The fractured surface has the marking of ductile deformation by shear. Figure 11.10(b) shows a brittle fracture along the interface between the solder bump and the IMC phase. The fractured surface appears rather smooth. A change from ductile fracture to brittle fracture in a solder joint as shown in Fig. 11.10 is undesirable. Qualitatively, the cause of the

SVNY339-Tu

March 23, 2007

16:20

Ductile–to-Brittle Transition of Solder Joints

315

Electromagnet

Sample Hammer Angle Recorder

XYZ - positioning Stage inch 1 1inch

Fig. 11.9. Photograph of a micro-impact testing machine which was constructed on the principle of Charpy test to test the bonding of solder balls to their substrate.

ductile-to-brittle transition is due to heat treatment of the solder joint, in turn the formation of a large amount of IMC as well as voids at the interface between the solder and the metallization on the BGA board. Quantitatively, to characterize the transition, we need to use the mini Charpy machine to perform a systematic study of a large number of solder joints as a function of temperature, time, solder composition, under-bump metallization, and location of the bump on the BGA substrate. We note that the ductile-to-brittle transition in solder joints is not due to temperature change as in body-centered cubic metals, rather it is due to interfacial IMC formation in aging or interfacial void formation in electromigration. When a thick IMC formation is accompanied by a large number of Kirkendall void formation, a brittle behavior is expected. When electromigration has led to the accumulation of a large number of vacancies at the

SVNY339-Tu

316

March 23, 2007

16:20

Chapter 11 (a)

(b)

Fig. 11.10. SEM images of the fractured surface of the solder joints. (a) A fracture within the solder ball. The fractured surface has the marking of ductile deformation by shear. (b) A fracture along the interface between the solder ball and the IMC phase. The fractured surface appears rather smooth.

cathode interface of a joint, it has produced a brittle interface at the cathode too. During the high-speed shear in the impact test, the impact energy should have been distributed between the formation of the two fracture surfaces and the deformation of the bulk of the solder ball. The softer the solder ball is, the larger the deformation. The more brittle the joint interface is, the smaller the deformation. The deformed balls can be collected after they were knocked oﬀ the substrate and examined by SEM for the amount of plastic deformation in them. For comparison, the energy needed to obtain the same amount of plastic deformation in a set of free solder balls can be measured in an Instron machine, and it was found that the average deformation energy is about 10% the total impact energy measured from the mini Charpy machine. Thus, most of the impact energy is spent to create the fracture surfaces.

11.5 Drop Test 11.5.1 JEDEC-JESD22-B111 Standard of Drop Test We review brieﬂy here the speciﬁcation of a widely adopted industry standard of drop test of JEDEC (Joint Electronic Device Engineering Council) standard JESD22-B111 (board level drop test method of components for hand-held electronic products), issued in July 2003. A schematic diagram of the test machine and test sample is shown in Fig. 11.11. The test sample is a printed circuit (PC) board measuring about 13 cm × 8 cm, which are placed upside down on four standoﬀs on a drop table, as depicted in Fig. 11.11. On the board, there are typically 5 × 3 arrays of 15 components or packaging modules. The four corners of the board are ﬁxed tightly on the standoﬀs by screws. The free fall of the drop table is guided by two guiding rods from a height of 0.82 m to

SVNY339-Tu

March 23, 2007

16:20

Ductile–to-Brittle Transition of Solder Joints

317

Guide Rods

PCB Assembly

Stand offs

Accelerometer

Base Plate

Drop Table

Fig. 11.11. Schematic diagram of a drop test arrangement.

hit a shock pad, which is typically a stone or a cement block but its surface can be modiﬁed for shock absorption. When the table hits the shock pad, the PC board will bend and vibrate. An accelerometer is attached to the table and another one to the board to record the “input acceleration” and “output acceleration,” respectively, during the impact when the drop table hits the shock pad. A typical dumping curve of output acceleration is shown in Fig. 11.12. It shows the drop has reached an acceleration of 1500g upon hitting the pad, in a period of half of the half-sine pulse of 0.5 ms when the ﬁrst dumping of deceleration has occurred. This is the key speciﬁcation in the drop test—it must achieve an acceleration of 1500g in a period of half of the half sine pulse of 0.5 ms. Since force is measured by the change of momentum in a very short time, 0.5 ms is the period when the momentum change occurs in the impact, so it is the key parameter in a drop test and is used to deﬁne the force acting on the solder joints [8–10]. In a free fall from a height of h, if we assume the velocity upon reaching the ground or the shock pad is v, we have from the conservation of energy that mgh =

1 2 mv , 2 1

(11.2)

v = (2gh) /2 , 2

where the gravity factor g = 9.8 m/sec . In a free fall, the velocity v is independent of mass. The velocity will be 4 m/sec when the free fall height is 0.816 m.

SVNY339-Tu

318

March 23, 2007

16:20

Chapter 11

Fig. 11.12. Dumping of acceleration in dropping test.

Upon hitting the ground, the velocity of the drop table as well as the PC board will change from v to zero. Assuming the impact is elastic, especially the impact of the board, it will have a reverse change of velocity from zero to −v. Let Δt be the transition time of the change of velocity from v to −v, and −a is deceleration in the event of impact. If we assume that Δt is 0.5 ms as shown in Fig. 11.11, then we have −a =

Δv 8 m/ sec = = 16, 000 m/ sec2 ∼ = 1600g, Δt 0.5 × 10−3 sec

(11.3)

where g = 9.8 m/sec2 . Thus, we note that −a is unrelated to the gravity acceleration but is related to the rate of change of velocity in the impact, and it can reach a value of 1600g in the drop test if we take into account the reverse velocity in the change. Experimentally, ΔV can be measured from the area under the ﬁrst peak shown in Fig. 11.12, provided that there is no interference from higher order harmonic vibrations. Where is the 0.5 ms coming from? It is from the frequency of vibration of the board attached to the drop table [11–13] The momentum change in impact will be Δ(mv), where m is the mass of the table. Because of the coupling between the table and the board, the momentum change will induce a vibration or bending of the board that carries the packages. Assuming the fundamental mode of vibration of the rectangular board has a frequency of f = 1 kHz or 1000 sec−1 , the period of one cycle is 1 ms and a half-sine pulse will be 0.5 ms. This is what is shown in Fig. 11.12. As we have mentioned, force

SVNY339-Tu

March 23, 2007

16:20

Ductile–to-Brittle Transition of Solder Joints

319

is measured by the change of momentum in a very short time, so the time or the frequency of vibration is the key parameter in a drop test of solder joints. A low-frequency test, for example, a four-point bending applied mechanically to a board, will not produce the force encountered in a drop. We can calculate the frequency by dividing the acoustic velocity in the board by the length of the board, using Eq. (11.4). The acoustic velocity in the board is proportional to (Y /ρ)1/2 where Y and ρ are Young’s modulus and density of the board, respectively, and l is the length. 1 f= 2l

Y . ρ

(11.4)

For example, if we take the Young’s modulus and density of polyethylene 2 to be 0.011 × 1011 dyn/cm and 1 g/cm3 , respectively, and take the length of a beam to be 0.41 m, we ﬁnd that the frequency is about 1 kHz [14]. For a quick estimate, we know that the velocity of sound in air is 5 × 104 cm/sec. The time for sound to travel a distance of 0.5 m in air is 1 × 10−3 sec, so the frequency, which is the inverse of time, is 1 kHz. Since sound travels faster in solids than in air, the estimate shows that the discussion and calculation in the above are correct. Besides the vibration frequency, the amplitude of the vibration or bending of the board is crucial in deforming the solder joints. The amplitude is determined by the mechanical coupling between the drop table and the board. Assuming a beam model or a plate model, the bending can be simulated [9, 10]. In the drop test, the shock pad is typically a 100-kg stone and its surface can be modiﬁed by covering with cloth to absorb the impact as a soft ground. The oscillation of the board upon impact is measured by an accelerometer of model No. 8704B5000, Kistler. If an acceleration sensor is placed on the drop table, the input acceleration can be measured. This input acceleration has a strong dependence on the hardness of the surface of the shock pad. If we place a cloth over it, the input acceleration will be greatly reduced. The output acceleration, measured on the board, can reach 2000g when the drop height is 1.3 m (about 4 ft), which is the height of the pocket on a shirt, and the velocity upon hitting the ground will be about 5 m/sec. The output acceleration reduces to 1500g when the drop height is 0.82 m (close to 3 ft) which is the height of a table. The vibration-induced failure of the solder joint can be measured by a speciﬁc resistance change of the solder joint interconnection beyond a minimum resistance value, for example, beyond 1000 ohms. The PC board used in the standard drop test is much larger than most modules or substrates used in hand-held-size electron devices, yet the large board is needed for vibration. While the horizontal arrangement of the test board enables us to measure the eﬀect of vibration induced by impact, it does not measure the eﬀect of torque on solder joints when the board hits

SVNY339-Tu

320

March 23, 2007

16:20

Chapter 11 Fig. 11.13. Schematic diagram of free fall of a solder ball and its substrate board. The board falls vertically so that its edge hits the ground.

the pad vertically. We need to build a new drop test machine to do so, yet the new machine must have the same characteristics of the standard drop test discussed above, such as 0.5 ms and 1500g. Also, we should be able to measure the torque on BGA solder joints by the drop test. 11.5.2 Dropping of a Packaging Board Vertically and the Torque on Solder Balls Figure 11.13 depicts the vertical free fall of a solder ball joined to a substrate board. We assume the board falls vertically so that its edge will hit the ground with a velocity of v. Upon hitting the ground, the velocity will change from v to zero and to −v for both the board and the solder ball. The momentum change of the solder ball will be Δ(mv), where m is the mass of the solder ball. The change will induce a shear force F and a torque Q acting on the ball and they tend to fracture the interface between the ball and the board. The force can be calculated from the following relation, F Δt = Δ(mv), F = −m Δv Δt = −ma,

(11.5)

where Δt is the transition time of the change of velocity from v to 0 and to −v or the time of change of momentum. A short time will produce a large force and a large torque. Since we can calculate (or measure) the free fall velocity v and also know the mass m, the challenge in the vertical drop test is how to measure the transition time Δt or the deceleration −a accurately because it aﬀects directly the magnitude of the force and the torque. Thus, in designing a drop test, the interpretation of Δt is the most critical task.

SVNY339-Tu

March 23, 2007

16:20

Ductile–to-Brittle Transition of Solder Joints Fig. 11.14. In the vertical drop test, the torque will cause a stress distribution at the interface between the solder ball and the bond pad. A schematic diagram of the stress distribution is depicted, with tensile stress at the top and compressive stress at the bottom.

321

Substrate

σmax

Solder Bump r F

Knowing the force, we obtain the torque Q = F × r, where r is the shortest distance between the gravity center of the solder ball and the interface. The force F tends to shear the interface between the ball and the board, and the torque Q will exert a normal force on the interface. But the distribution of the normal force due to the torque is such that it is tension at the upper end but compression at the bottom end of the interface, as depicted in Fig. 11.14. To analyze the stress distribution, we consider in Fig. 11.14 a schematic diagram of the cross section of a solder ball attached to a vertical board. We assume that the contact area between the solder ball and the substrate is rectangular with a width of w and length of 2R. A linear variation of stress distribution from tension in the upper half to compression in the lower half of the contact is assumed. If the maximum stress at the two ends is taken to be ±σmax , the following relationship is obtained from geometrical proportion. σ=

z σmax , R

(11.6)

where σ is the normal stress at a distance z from the middle origin where the normal stress is zero. The total moment produced by the stress distribution should equal the torque. A very simple analysis gives the moment as w

R

−R

zσdz = w

R

−R

z

z σmax σmax dz = w R R

R

−R

z 2 dz =

2 wσmax R2 . 3

(11.7)

In the last equation, σ(wdz ) is the force acting on a thin strip of (wdz) at a

SVNY339-Tu

322

March 23, 2007

16:20

Chapter 11

distance of z from the origin, so zσ(wdz) is the moment. The total moment should equal the torque, F × r, so we obtain σmax =

3 Fr . 2 wR2

(11.8)

The last equation enables us to calculate the σmax when the torque from the impact has been measured. As discussed above, the σmax depends on the torque, the torque depends on the force, and the force depends on the Δt. From the magnitude of σmax , we may be able to determine whether the drop will lead to crack formation at the interface or not. Besides the normal force due to the torque, the interface also experiences a shear force. Therefore, at the upper corner and lower corner of the joint, the normal and shear forces must be combined together when considering crack initiation and propagation.

11.6 Converting a Mini Charpy Impact Machine to Perform Drop Test We shall use the mini Charpy impact machine to conduct the drop test and measure the Δt for both horizontal and vertical drops. To do so, the major change is to transfer the ﬂexional vibration (frequency and amplitude) of the large printed circuit board in the standard drop test to the ﬂexional vibration of a beam or the arm of the Charpy impact machine. The vibration of a hinged beam will produce the acceleration required in both horizontal and vertical drops. Therefore, the arm shall be made by using a material similar to the polymer-based printed circuit board so that the Young’s modulus and density are kept nearly the same, in turn the fundamental vibration mode is similar to that in the standard test. A single ﬂip chip and its packaging module can be attached to the hammer at the end of the swing arm. One end of the arm is hinged and the other end with the hammer and sample is free to swing. When the hammer hits a ﬁxed wall at the lowest position and the arm vibrates, it produces the same eﬀect on the attached sample as in the standard test. To diﬀerentiate the horizontal drop and the vertical drop in order to measure the torque, the chip-size package will be attached to the hammer in such a manner that its surface is parallel to the swing direction of the hammer (see Section 11.6.2). To achieve the free fall from a height of 0.82 m (close to 3 ft, which is the typical height of a household table), we can build a table-top machine with an arm of 0.41 m and swing the arm from a vertical position of 0.82 m height as depicted in Fig. 11.15. At the end of the arm, we can add a hammer and an acceleration sensor. A rigid wall is built at the lowest position. When the hammer hits the wall, the arm vibrates. Also, we can design the mass of the hammer to change the amplitude of the vibration of the arm. An alternative way to conduct the test is to replace the rigid wall by another arm that has an identical arrangement, i.e., the arm with a hammer

SVNY339-Tu

March 23, 2007

16:20

Ductile–to-Brittle Transition of Solder Joints Fig. 11.15. A table-top drop machine with an arm of 0.41 m. The arm swings from a vertical position of 0.82 m height. In the test, the test samples are attached to the arm. At the end of the arm, there is a hammer to hit the ﬁxed wall to induce the vibration.

323

Start position

h = 2L

Rotation center

wall

L M, hammer

and an acceleration sensor. In other words, there are two arms in the test; one is the swing arm and the other is free hanging, and both of them are hinged. We let the former hit the latter so that the momentum change is conserved in the impact event. This is depicted in Fig. 11.16. Furthermore, the free hanging arm can be hinged as the swing arm, but it can also be ﬁxed at the upper end. The advantage of the arm with one end ﬁxed is that we can build a detective circuit in the sample for in situ measurement of the failure induced by the impact. Thus, the impact test is the reverse process of a free fall drop. In the swing arm, the velocity of the substrate and ball changes from v to 0, and in the free hanging arm after the impact, the velocity of its substrate and balls changes from 0 to v. While the velocity change is in the vertical direction in the free fall, it becomes horizontal in the impact test. The conservation of momentum ensures that the velocity change, Δv, is the same as in the free fall. To measure the Δt, we can place acceleration sensors on the swing harmmer and the free hanging harmmer. 11.6.1 Dropping of a Chip Size Package Horizontally in Mini Charpy Machine Figures 11.15 and 11.16 depict the arrangement of a ﬂip chip and its substrate glued near the end of an arm. The normal of the chip surface and its substrate are parallel to the swing direction of the arm. At the end of the arm, there is a weight or hammer. When the arm and the weight swing down

SVNY339-Tu

324

March 23, 2007

16:20

Chapter 11

Free hang Swing arm

Test sample

Hammer Fig. 11.16. To replace the ﬁxed wall, the schematic diagram here depicts two arms in the test; one is the swing arm and the other is free hanging, and both arms have the hinged end. We let the former hit the latter so that the momentum change is conserved in the impact event. In the test, the test samples are attached to the arms in symmetrical positions.

together and hit the ﬁxed wall, the arm bends and vibrates. No doubt the weight will modify the frequency and amplitude of vibration of the arm. The vibration will exert both normal and shear forces to the solder joints. This sample arrangement is similar to the JESD22-B111 standard of drop test of a horizontal board discussed in Section 11.5.1, because the direction of impact is parallel to the normal of the chip and the substrate. Here we can test a smaller sample with BGA solder joints on a chip-size packaging and also can test ﬂip chip solder joints between a single Si chip and its module. If we can join the chip to the arm directly using solder bumps, the test will be more effective. Also, we can place the chip in the middle of the arm instead of near the end of the arm. The amplitude of vibration in the middle of the arm is quite large too. Alternatively, we can remove the rigid wall and have two arms; one will swing and the other one will be free hanging. Both of them will carry the same load; a sample, a hammer, and an acceleration sensor. The swing arm will hit the free hanging one. We can obtain cyclic impact with them. Actually, we can study failure in the two samples on the two arms in the impact. The simple tests described above will enable us to analyze the materials behavior of solder joints in dropping and to correlate the behavior to processing conditions. The eﬀect of Cu-Sn reaction and the polarity eﬀect of

SVNY339-Tu

March 23, 2007

16:20

Ductile–to-Brittle Transition of Solder Joints

325

electromigration on the fracture behavior of solder joints in dropping can be studied quantitatively and systematically. On the other hand, in electronic consumer products, the packaging design, structure, and materials, e.g., systems-in-packaging, may also aﬀect its impact behavior in dropping. 11.6.2 Dropping of a Chip Size Package Vertically in Mini Charpy Machine If we rotate the ﬂip chip by 90◦ from the arrangement shown in Fig. 11.16, and glue it to the beam so that the surface of the chip is parallel to the swing direction of the hammer, we can study the eﬀect of torque on the solder ball when the hammer hits a rigid wall. For this purpose, we can also attach the sample to the side surface or bottom surface of the hammer. Similar to the discussion presented in the last section, we can remove the rigid wall and employ a pair of the same arms and let them hit each other. Again, the free hanging arm can have a hinged or ﬁxed end. The weight of the hammers can be changed to adjust the momentum change in the impact. To test an advanced packaging in which a stack of chips are wire-bonded to a substrate and buried within molding compound, and the substrate is joined by an array of ball-grid-array of solder balls to a packaging board, the mass of the chips, the wires, the substrate, and the molding compound will add to the force and/or torque on the interfaces between the solder balls and the packaging board in a vertical and/or horizontal drop test of the packaging. It is a much more complicated engineering problem. But the principle and measurement methods presented above can be used to analyze the impact of the drop step by step.

11.7 Creep and Electromigration Creep is a long time event of deformation or a time-dependent deformation. The basic process is atomic diﬀusion driven by a stress gradient. An example of creep is the sagging of lead (Pb) pipes by their own weight on the wall of some very old houses in Europe. Room temperature is at 0.5 of the homologous temperature for Pb, which melts at 327◦ C, and atomic diﬀusion is thus suﬃciently fast for creep to occur, even though the stress gradient due to gravity force is quite low. Since eutectic SnPb or eutectic Pb-free solder melts at a much lower temperature than Pb, creep is expected to occur at room temperature or the device working temperature of 100◦ C. Electromigration is also a long time event of diﬀusion driven by electron wind force. We expect these two long time events to interact with each other. No doubt, the basic interaction between electrical force and mechanical force on atomic diﬀusion is similar to what we have discussed in Section 8.5 between electromigration and back stress. Here the stress is external. Since a solder joint has two interfaces, the polarity eﬀect of electromigration on creep will

SVNY339-Tu

326

March 23, 2007

16:20

Chapter 11

be diﬀerent between the cathode and the anode interfaces. When electromigration drives vacancies to the cathode interface, the creep rate there will be enhanced. On the other hand, because vacancies will be driven away from the anode, the creep will be reduced there. In other words, the back stress induced by electromigration will add tensile stress to enhance the creep at the cathode side, but it will add compressive stress to reduce the creep at the anode side.

References 1. F. Ren, J. W. Nah, K. N. Tu, B. S. Xiong, L. H. Xu, and J. Pang, “Electromigration induced ductile-to-brittle transition in Pb-free solder joints,” Appl. Phys. Lett., 89 141914 (2006). 2. J.-W. Nah, F. Ren, K.-W. Paik, and K. N. Tu, “Eﬀect of electromigration on mechanical shear behavior of ﬂip chip solder joints,” J. Mater. Res., 21, 698–702 (2006). 3. J. M. Holt (Ed.), “Charpy Impact Test: Factors and Variables,” ASTM STP 1072, Philadelphia, PA (1990). 4. T. Shoji, K. Yamamoto, R. Kajiwara, T. Morita, K. Sato, and M. Date, Proceedings of the 16th JIEP Annual Meeting, 2002, p. 97. 5. 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(2004). 6. M. Date, T. Shoji, M. Fujiyoshi, K. Sato, and K. N. Tu, “Impact reliability of solder joints,” Proceedings of the 54th ECTC, Las Vegas, NV, June 2004, pp. 668–674. 7. S. Ou, Y. Xu, K. N. Tu, M. O. Alam, and Y. C. Chan, “A study of impact reliability of lead-free BGA balls on Au/electrolytic Ni/Cu bond pad,” MRS 2005 Spring Meeting Proceedings, Symposium B, 10.5. 8. M. Alajok, L. Nguyen, and J. Kivilakti, “Drop test reliability of wafer level chip scale packages,” IEEE 2005, Electronic Components and Technology Conference, pp. 637–643. 9. E. H. Wong, Y.-W. Mai, and S. K. W. Seah, “Board level drop impact— fundamental and parametric analysis,” Trans. ASME, 127, 496–502 (2005). 10. E. H. Wong and Y.-W. Mai, “New insight into board level drop impact,” Microelectron. Reliab., 46, 930–938 (2006). 11. M. Roseau, “Vibrations in Mechanical System,” pp. 111–136, SpringerVerlag, Berlin 1987. 12. L. Meirovitch, “Fundamentals of Vibrations,” pp. 14–39, McGraw–Hill Higher Education, New York (2001). 13. W. Goldsmith, “Impact: The Theory and Physical Behavior of Colliding Solids,” Edward Arnold Publishers, London (1960). 14. J. J. Tuma, “Handbook of Physical Calculations,” 2nd Enlarged & Revised Ed., pp. 311–312, McGraw–Hill, New York (1983).

SVNY339-Tu

April 5, 2007

17:37

12 Thermomigration

12.1 Introduction When an inhomogeneous binary solid solution or alloy is annealed at constant temperature and constant pressure, it will become homogeneous. On the contrary, when a homogeneous binary alloy is annealed at atmospheric pressure but under a temperature gradient, i.e., one end of it is hotter than the other end, the opposite will happen and the alloy will become inhomogeneous. This de-alloying phenomenon is called the Soret eﬀect [1, 2]. It is due to thermomigration or mass migration driven by a temperature gradient. Since the inhomogeneous alloy has higher free energy than the homogeneous alloy, thermomigration is an energetic process which transforms a phase from a low-energy state to a high-energy state. It is unlike a conventional phase transformation which occurs by lowering Gibbs free energy. In thermodynamics, under homogeneous external conditions deﬁned by a constant temperature and constant pressure (for example, if T is ﬁxed at 100◦ C and p is ﬁxed at atmospheric pressure), a thermodynamic system will minimize its Gibbs free energy, and it will move toward the equilibrium condition at the given T and p. Both enthalpy and entropy are state functions, so the equilibrium state is deﬁned when T and p are given. On the other hand, if the external conditions are inhomogeneous, for example, different temperatures at the two ends of a sample in thermomigration, the equilibrium state of minimum Gibbs free energy is unattainable. Instead, if the deviation from homogeneity is small, the minimum entropy production should be reached, and the system will move toward a steady state, instead of equilibrium. This is the Prigogine principle of irreversible thermodynamics. It means that the entropy production inside the inhomogeneous system is caused by the ﬂux of heat due to the external inhomogeneity. Consider two chambers 1 and 2, at diﬀerent temperatures (T1 > T2 ) connected by a conductive partition. If a quantity of heat δQ ﬂows from 1 to 2, the net change in

SVNY339-Tu

328

April 5, 2007

17:37

Chapter 12

entropy is T1 − T2 1 1 = δQ . dSnet = dS1 + dS2 = δQ − + T1 T2 T1 T2

(12.1)

This is the entropy generated by the process of heat ﬂow. In thermomigration, a steady state of a linear concentration gradient is obtained by the Soret eﬀect in Fe-C system, to be discussed in Section 12.2.3. Besides inhomogeneous temperature, we can also have inhomogeneous pressure as in creep. Creep occurs under a stress gradient, hence it is an irreversible process too. Thermomigration should occur in a pure metal, as in electromigration in Al. One would expect that an Al kitchen utensil, such as a cooking pot, should expand in size after years of use. This is because if the outside of the pot is hotter than the inside in cooking, Al atoms would have diﬀused from the outside to the inside and the latter should have expanded. Yet, this does not seem to happen. One reason is that the lattice diﬀusion in Al occurs by vacancy mechanism. The outside of the pot which is hotter will have a higher concentration of vacancies than the inside. The vacancy concentration gradient induces a counter atomic ﬂux which might have compensated nearly all of the ﬂux of Al atoms driven by the temperature gradient. The net change may be too small to be noticed. Another reason is due to back stress. The temperature inside the pod is 100◦ C, which is too low for creep to take place. As thermomigration drives more and more Al atoms into the cold side and builds up a high compressive stress there, the stress gradient will produce an atomic ﬂux of Al against the thermomigration. The equilibrium vacancy concentration is aﬀected by the stress. Solder is typically a binary system, so the Soret eﬀect can be found. Actually, the Soret eﬀect has been reported to occur in PbIn alloy which forms a solid solution over a wide range of concentration [3, 4]. On the other hand, eutectic solder has a two-phase microstructure, and the eﬀect of thermomigration in a eutectic two-phase structure is diﬀerent from that in a solid solution, to be discussed in later sections. Thermomigration in solder joints has been a harder subject to study than electromigration for two reasons. First, it is diﬃcult to apply a temperature gradient across a small ﬂip chip solder joint. For a solder joint 100 μm in diameter, if we can apply a temperature diﬀerence of 10◦ C across it, we have a temperature gradient of 1000◦ C/cm, which is suﬃcient to induce thermomigration in the solder, to be discussed in Section 12.3 [5–7]. Therefore, a temperature diﬀerence of 10◦ C or even a few degrees centigrade in a solder joint is of our concern. Second, the heat dissipation is hard to control because of the two interfaces in a joint. Therefore, it is diﬃcult to simulate temperature distribution or temperature gradient in a solder joint because of the complicated boundary conditions of UBM and bond-pad structure. We have to simplify the test structure of thermomigration. On the other hand, solder

SVNY339-Tu

April 5, 2007

17:37

Thermomigration

329

has a low melting point, so we can use the melting of the solder as an internal calibration. The condition of heat generation and dissipation in the melting experiment can be used to check the simulation. Due to joule heating, electromigration may have caused a nonuniform temperature distribution in a ﬂip chip solder joint, and thus there may be a component of thermomigration in any electromigration experiment. In other words, electromigration in a ﬂip chip solder joint is accompanied by thermomigration when a large current density is applied and when the current distribution is nonuniform due to current crowding. This is an advantage that one can combine electromigration and thermomigration in a study. Nevertheless, one has to design experiments in order to study thermomigration with and without electromigration. In Section 12.2, we shall discuss the design of a test structure of ﬂip chip solder joints which will enable us to conduct thermomigration with and without electromigration. It will be shown that if a composite solder joint of high Pb and eutectic SnPb is used, the redistribution of Sn and Pb in thermomigration can be recognized easily by optical microscopy, even though the original compositional distribution is not homogeneous in the composite sample. Observation of thermomigration in eutectic SnPb ﬂip chip solder joints will also be covered. In Section 12.3, the fundamentals of thermomigration will be presented and the driving force of thermomigration and heat of transport will be discussed. In Sections 12.4 and 12.5, thermomigration under DC and AC electromigration will be covered. In Section 12.6, we will discuss the use of V-groove solder line samples for studying thermomigration and its interaction with interfacial chemical reactions. In Section 12.7, the interaction between thermomigration and stress migration will be discussed.

12.2 Thermomigration in Flip Chip Solder Joints of SnPb 12.2.1 Thermomigration in Unpowered Composite Solder Joints Figure 12.1 shows (a) the schematic diagram of a ﬂip chip on a substrate, (b) the cross section of a composite ﬂip chip solder joint, and (c) SEM image. In Fig. 12.1(a), the small squares on the substrate are the electrical contact pads. The composite joint was composed of 97Pb3Sn on the chip side and eutectic 37Pb63Sn on the substrate side. It had a contact opening diameter of 90 μm on the chip side and a bump height of 105 μm. The trilayer thin ﬁlms of under-bump metallization (UBM) on the chip side were Al (∼0.3 μm)/Ni(V) (∼0.3 μm) /Cu (∼0.7 μm). On the substrate side, the bond-pad metal layers were Ni (5 μm)/Au (0.05 μm). As a control experiment, uniform heating on ﬂip chip samples was performed in an oven at a constant temperature of 150◦ C and atmospheric

SVNY339-Tu

330

April 5, 2007

17:37

Chapter 12 Fig. 12.1. Schematic diagram of a ﬂip chip on a substrate. The small squares on the substrate are the electrical contact pads. (b) Cross section of a composite ﬂip chip solder joint. (c) SEM image of the cross section. The darker image at the bottom is the eutectic phase. The brighter image is the high-Pb phase.

pressure for a period of 1 month. For cross-sectional examination, the sample was polished with SiC paper, then with Al2 O3 powder to the center of the solder joints. The microstructures of the cross section were examined by optical microscope (OM) and scanning electron microscope (SEM). Composition was analyzed using energy-dispersive x-ray analysis (EDX) and electron probe microanalysis (EPMA). No mixing between the high-Pb and eutectic solders was observed and the image was the same as that shown in Fig. 12.1(c). To conduct thermomigration by using the temperature gradient induced from joule heating, two sets of ﬂip chip samples were prepared. In the ﬁrst set, as depicted in Fig. 12.1(a), the sample as received was used. There were 24 bumps on the periphery of the Si chip, and Fig. 12.2(a) depicts a total of 24 solder bumps from right to left at the periphery of a chip and each bump has the original microstructure shown in Fig. 12.1(c) before electromigration stressing. We recall that the darker region in the bottom area of each bump is the eutectic SnPb and the brighter region in the top part is 97Pb3Sn. Electromigration was conducted through only four pairs of bumps on the periphery of the chip. They were the pairs of 6/7, 10/11, 14/15, and 18/19 as numbered in Fig. 12.2(b). The arrows indicate the electron path. The electron current went from one of the contact pads to the bottom of one of the bumps, up the bump to the Al thin-ﬁlm interconnect on the Si strip, then to the top of the next bump, down the bump, and to the other contact pad on the substrate. It is worth noting that one can pass current through just a pair of bumps or several pairs in the row to conduct electromigration. The joule heating from

SVNY339-Tu

April 5, 2007

17:37

Thermomigration (a)

331

Silicon chip side

24 23 22 21 20 19 18 17 16 15 14 13 12 11 10

9

8

7

6

5

4

3

2 1

FR4 substrate side (b)

Fig. 12.2. (a) Schematic diagram depicting 24 bumps on the periphery of the Si chip. Each bump has the original microstructure shown in Fig. 12.1(c) before electromigration stressing. Electromigration was conducted through only four pairs of bumps on the periphery of the chip. They are the pairs of 6/7, 10/11, 14/15, and 18/19 as numbered. (b) The eﬀect of thermomigration is clearly visible across the entire row of the unpowered solder joints—the darker eutectic phase has moved to the Si side, the hot end.

the Al thin-ﬁlm line on the strip is the heat source. Due to the excellent thermal conduction of Si, the neighboring unpowered solder joints would have experienced a thermal gradient similar to the pairs under DC or AC current. Since both DC and AC were used, the arrows indicate both directions. Cross sectioning was performed after the bump pair 10 and 11 failed after 5 hr of current stressing at 1.6 × 104 A/cm2 at 150◦ C. For studying thermomigration, the unpowered neighboring bumps were examined. The eﬀect of thermomigration is clearly visible across the entire row of the unpowered solder joints, as shown in Fig. 12.2(b), because in all of them Sn has migrated to the Si side, the hot end, and Pb has migrated to the substrate side, the cold end. The redistribution of Sn and Pb was caused by a temperature gradient across the solder joints since no current was applied to them. For the unpowered bumps which were the nearest neighbors of the powered bumps, the Sn redistribution is also tilted toward the powered bumps. For example, the powered bump 10 is to the left of the unpowered bump 9, the Sn-rich region in bump 9 is tilted to the left, and a void is observed. Then the powered bump 15 is to the right of the unpowered bump 16, and the Sn-rich region in bump 16 is tilted to the right. In those bumps farther away from the powered bumps, for example, from bump 1 to bump 4 and bump 21 to 23, Sn accumulated rather uniformly on the Si side.

SVNY339-Tu

332

April 5, 2007

17:37

Chapter 12 (a)

e(b)

20μm

Fig. 12.3. (a) Schematic diagram of the Si strip and a row of four of the crosssectioned bumps. The chip was cut and only a thin strip of Si was kept. The strip has one row of solder bumps connecting it to the substrate. The bumps were cut to the middle so that the cross section of the bump was exposed for in situ observation during electromigration. (b) The pair of joints on the left was powered at 2 × 104 A/cm2 for 20 hr at 150◦ C. The pair of joints on the right had no electric current at all. Yet all of them showed composition redistribution and damage.

In powering the four pairs of bumps in the ﬁrst set of samples, part of the circuit consists of the thick Cu traces in the substrate, there will be joule heating too. Nevertheless, the Al lines on the Si were the dominant heaters. 12.2.2 InSitu Observation of Thermomigration In the second set, as depicted in Fig. 12.3(a), the chip was cut and only a thin strip of Si was kept. The strip has one row of solder bumps connecting it to the substrate. The bumps were cut and polished to the middle so that the cross section of the bump was exposed for in situ observation during electromigration. Figure 12.3(a) is a schematic diagram of the Si strip and a row of four of the cross-sectioned bumps. Due to the excellent thermal conduction of Si and the small strip used, when one pair of the bumps is under DC or AC current, the other pair of solder joints would experience almost the same thermal gradient as the powered pair. This set of samples can be used to conduct in situ experiments by observing changes on the cross-sectioned surface directly during electromigration. The major diﬀerence between the ﬁrst set and this set of samples is that the latter has a free surface during the test. Thus, surface bulging can occur if a large amount of materials is driven to the cold end by thermomigration, and the bulge can be observed easily. The pair of joints on the left shown in Fig. 12.3(a) was powered at 2 × 104 A/cm2 for 20 hr at 150◦ C. The pair of joints on the right had no electric

SVNY339-Tu

April 5, 2007

17:37

Thermomigration

333

current at all. Yet all of them showed composition redistribution and damage. The pair on the right (unpowered) showed a uniform void formation at the interface on the top side, i.e., the Si side which is also the hot side. In the bulk of the joint, some phase redistribution can be recognized. The redistribution of elements of Sn, Pb, and Cu can be measured by electron microprobe from the cross sections of this unpowered pair on the right. The Sn has migrated to the hot end and there is more Cu in the hot end too and Pb has moved to the cold end. If we assume there were no temperature gradient in the pair of bumps on the right in Fig. 12.3, in other words, the temperatures were uniform in these bumps, then its thermal history is similar to isothermal annealing, no phase redistribution or void formation should be found since isothermal annealing has no eﬀect on phase mixing or unmixing, as shown in Fig. 12.1(c). However, we may ask if there are other kinds of driving force that can lead to phase change as observed. Besides electrical and thermal force, we could have mechanical force. Yet, the mechanical force should have been present in the isothermal annealing. The annealing does cause interfacial chemical reactions between solder and UBM on the chip side and between solder and bond-pad metal on the substrate side. The growth of intermetallic compound may generate stress owing to molar volume change. However, this eﬀect should have occurred in the sample which was isothermally annealed at 150◦ C for 4 weeks, yet no noticeable change was detected. Furthermore, solder has a very high homologous temperature at 150◦ C, so it is unlikely that stress would not be relaxed in 4 weeks. Thus, we conclude that the composition redistribution and the damage (void formation) in the unpowered bumps are due to thermomigration. Then, which is the dominant diﬀusing species in thermomigration or which species diﬀuses with the temperature gradient is of interest. During electromigration at 150◦ C, Pb has been found to be the dominant diﬀusing species. In thermomigration of the composite solder joint, the temperature gradient drives Pb from the hot side to the cold side and Sn atoms from the cold side to the hot side. The void found on the hot side indicates that Pb is the dominant diﬀusing species and the ﬂux of Pb is greater than the ﬂux of Sn. The high-Pb forms Cu3 Sn after reﬂow, but the Cu3 Sn will transform to Cu6 Sn5 after the diﬀusion of Sn to the hot side. The formation of void and Cu6 Sn5 is rather uniform across the entire contact area to the Si side. Why Sn diﬀuses against a temperature gradient is an interesting question. To answer it, we shall discuss the driving force and the ﬂux motion in a two-phase microstructure under the constraint of constant volume. 12.2.3 Random States of Phase Separation in Eutectic Two-Phase Structures Figure 12.4 shows a set of cross-sectional images of unpowered composite solder joints after thermomigration of (a) 30 min, (b) 2 hr, and (c) 12 hr.

SVNY339-Tu

334

April 5, 2007

17:37

Chapter 12

Fig. 12.4. Set of cross-sectional images of unpowered solder joints after thermomigration of (a) 30 min, (b) 2 hr, and (c) 12 hr. Before thermomigration, the image is similar to that shown in Fig. 12.1(a). A random state of phase separation is observed in (a), the eutectic is segregated toward the hot end in (b), and a near-complete phase separation is achieved in (c).

Before thermomigration, the image is similar to that shown in Fig. 12.1(a). In Fig. 12.4(a) a random state of phase separation is observed. In Fig. 12.4(b) the eutectic is segregated toward the hot end. In Fig. 12.4(c) a near-complete phase separation is achieved. Many images similar to Fig. 12.4(a) in both DC and AC stressing were obtained, and four of them are shown in Fig. 12.5 to illustrate the random state of phase separation in the microstructure before achieving complete phase separation. It appears that a ﬂuidlike motion occurs in the solid-state phase separation. When an electron microprobe was used to measure composition distribution across a polished cross section of the ﬂip chip sample after thermomigration, a highly irregular or stochastic composition distribution was observed as shown in Fig. 12.6; no smooth concentration proﬁle was observed. If the

Fig. 12.5. Four images of random states of phase separation. The two-phase microstructure in both DC and AC stressing are shown.

SVNY339-Tu

April 5, 2007

17:37

Thermomigration

335

Sn %mass concentration

Mass% Concentration of Sn in Flip Chip Solder Joint 90 80 70 60 50 40 30 20 10 0

left line center line right line Before thermomigration

0

10

20

30

40

50

60

70

80

90 100 110 120

Distance from the Copper line on Chip Side (μm)

Fig. 12.6. Electron microprobe measurement of composition redistribution across a polished cross section of the ﬂip chip sample after thermomigration. A highly irregular or stochastic composition distribution was found; no smooth concentration proﬁle was observed.

electromigration experiment was extended to several days, a clear and nearly complete phase separation of Sn and Pb in the unpowered joints was found. 12.2.4 Thermomigration in Unpowered Eutectic SnPb Solder Joints The eutectic 37Pb63Sn ﬂip chip solder joints used for the thermomigration test were arranged similarly to that shown in Fig. 12.2(a) with 11 bumps. The UBM thin ﬁlms on the chip side were Al (∼0.3 μm)/Ni(V) (∼0.3 μm) /Cu (∼0.7 μm) deposited by sputtering. The bond-pad metal layers on the substrate side were Ni (5 μm)/Au (0.05 μm) prepared by electroplating. The bump height between the UBM and the bond pad is 90 μm. The contact opening on the chip side has a diameter of 90 μm. Only one pair of bumps was current stressed with DC current of 0.95 A at 100◦ C for 27 hr. The average current density at the contact opening was 1.5 × 104 A/cm2 . The unpowered bumps neighboring the powered pair were used to study thermomigration. Figure 12.7 displays SEM images of the cross section of four of the unpowered bumps after the electromigration test. The lighter color in the images is the Pb-rich phase and the darker color is the Sn-rich phase. Compared to the as-received sample, the results show that the Pb–rich phase has moved to the substrate side (the cold side) in the unpowered neighboring bumps of the powered bumps. Also, one of the unpowered neighboring bumps, shown in Fig, 12.7(c), has some dendritic structure of crystallization of a liquid phase, indicating that it was partially melted in the test. It is worth noting that crystallization of a molten eutectic phase should show a eutectic

SVNY339-Tu

336

April 5, 2007

17:37

Chapter 12

Fig. 12.7. SEM images of cross section of 4 of the unpowered bumps. The lighter color in the images is the Pb-rich phase and the darker color is the Sn-rich phase. In (c), some dendritic structures of crystalization of a liquid phase are shown.

microstructure. The dendritic structure indicates that phase separation has occurred before melting. Figure 12.8(a) shows an enlarged SEM image of an unpowered bump. The redistribution of Sn and Pb is shown by the accumulation of a large amount of Pb to the substrate side (the cold side), yet there is no accumulation of Sn to the chip side (the hot side). A very surprising ﬁnding is not only that the microstructure in the bulk of the bump is quite uniform (except the accumulated Pb-rich phase), but also the lamellar structure is much ﬁner, indicating the existence of many more interfaces in the microstructure after the phase separation, in turn a higher energy state. We recall that when a eutectic twophase microstructure is annealed at constant temperature, grain growth and coarsening, instead of reﬁnement, of the two-phase lamellar microstructure should occur to reduce the surface energy, as shown in Fig. 2.23. Since the interface is disordered, the formation of a ﬁner lamellar structure creates a more disordered state or more entropy production. However, the diﬀusion along the interfaces is faster than the lattice, so kinetically the rate of entropy production is faster with a ﬁner lamellar structure. The concentration proﬁles across the bump by EPMA are shown in Fig. 12.8(b) and (c). Three proﬁle lines across the bumps were scanned and

SVNY339-Tu

April 5, 2007

17:37

Thermomigration

337

Fig. 12.8. (a) Enlarged SEM image of bump No. 11. The redistribution of Sn and Pb can be seen. It shows the migration of a large amount of Pb to the substrate side (the cold side), yet there is no accumulation of Sn to the chip side (the hot side). (b, c) Concentration proﬁles across the bump by EPMA of Pb and Sn, respectively. Three proﬁle lines across the bumps were scanned and every line is the average of three sets of data points. Each point was taken at each 5-μm step from the chip side to the substrate side.

every line is the average of three sets of data points. Each point was taken at every 5-μm step from the chip side to the substrate side. The results shows that the concentration of Pb on the substrate side is about 73% and that of Sn on the chip side is around from 70% to 80%. However, the concentration distribution reveals that there is no linear concentration gradient. Near the cold end, the accumulation of Pb and depletion of Sn occurred. However, away from the cold end, the average distribution of Pb and Sn in the rest of the sample is quite uniform, except for some minor local ﬂuctuations due to the two-phase microstructure. Clearly, Pb moves with the temperature gradient and is the dominant diﬀusing species in the thermomigration because it accumulates at the cold end, but there is no concentration gradient of Pb for the diﬀusion, unlike precipitation. If Sn were the dominant diﬀusing species, the concentration proﬁle of Pb would have increased uniformly in the bulk of the sample, but not a pile-up at the cold side. The higher concentration of Sn at the end of the substrate side is due to the formation of Cu6 Sn5 IMC.

SVNY339-Tu

338

April 5, 2007

17:37

Chapter 12

12.3 Fundamentals of Thermomigration 12.3.1 Driving Force of Thermomigration Similar to the thermoelectric eﬀect whereby a temperature gradient can drive electrons to move, it can also drive atoms. In essence, the electrons in the high-temperature region have higher energy in scattering or interaction with diﬀusing atoms, hence atoms move down the temperature gradient. On the driving force of atomic diﬀusion, we recall that the atomic ﬂux driven by chemical potential can be given as (see Appendix A) J = Cv = CMF = C

D kT

−

∂μ ∂x

,

(12.2)

where v is drift velocity, M = D/kT is mobility, and μ is chemical potential energy. Considering temperature gradient as the driving force, we have D Q∗ J =C kT T

∂T − ∂x

,

(12.3)

where Q∗ is deﬁned as heat of transport. Comparing the last two equations, we see that Q∗ has the same dimension as μ, so it is the heat energy per atom. In other words, if we take entropy S = Q/T , we have SdT which is thermal energy. The deﬁnition of Q∗ is the diﬀerence between the heat carried by the moving atom and the heat of the atom at the initial state (the hot end or the cold end) [see Eq. (12.1)]. For the element which moves from the hot end to the cold end, Q∗ is negative since it loses heat. For an element moving from cold to hot, its Q∗ is positive. The driving force of thermomigration is given as F =−

Q∗ T

∂T ∂x

.

(12.4)

To make a simple estimation, we take ΔT /Δx = 1000 K/cm, and consider the temperature diﬀerence across an atomic jump and take the jump distance to be a = 3 × 10−8 cm. We have a temperature change of 3 × 10−5 K across an atomic spacing. Thus, the thermal energy change will be 3kΔT = 3 × 1.38 × 10−23 (joule/K) × 3 × 10−5 K ≈ 1.3 × 10−27 joule. As a comparison, we shall consider the driving force, F , of electromigration at a current density of 1 × 104 A/cm2 or 1 × 108 A/m2 which we know has

SVNY339-Tu

April 5, 2007

17:37

Thermomigration

339

induced electromigration in solder alloys: F = Z ∗ eE = Z ∗ eρj. We shall take ρ = 10 × 10−8 Ω-m, Z ∗ of the order of 10, and e = 1.602 × 10−19 coulomb, and we have F = 10 × 1.6 × 10−19 (coulomb) × 10 × 10−8 (ohm-meter) × 108 amp/meter2 = 1.6 × 10−17 coulomb-volt/meter = 1.6 × 10−17 newton. The work done by the force in a distance of atomic jump of 3 × 10−10 m will be Δw = 4.8 × 10−27 newton-meter = 4.8 × 10−27 joule. This value is close to the thermal energy change we have calculated for thermomigration. Thus, if a current density of 104 A/cm2 can induce electromigration in a solder joint, a temperature gradient of 1000◦ C/cm will induce thermomigration in a solder joint. On heat of transport, we note that Q∗ can be positive or negative. In the Fe-C system, carbon was found to move to the hot end interstitially with a positive heat of transport. In alloys of SnPb, when thermomigration drives Pb to move from the hot zone to the cold zone, it moves down the temperature gradient. But the thermomigration drives Sn to move in the opposite direction, against the temperature gradient. The Q∗ for Pb is negative or the heat decreases, but for Sn, it seems that the Q∗ is positive since it moves to the hot end and gains heat. This is because we have one temperature gradient in thermomigration for both species, unlike interdiﬀusion in a diﬀusion couple, in which the concentration gradient of the two interdiﬀusing species is in the opposite direction, so the chemical potential change can be positive for both species. To measure Q∗ , if we know the atomic ﬂux, we can use the ﬂux equation, i.e., Eq. (12.3), to determine Q∗ when diﬀusivity, the average temperature, and temperature gradient are known. The heat of transport of Pb in thermomigration discussed in Section 12.2.4 is estimated below by using the ﬂux equation, Eq. (12.3). By measuring the accumulation width of Pb (12.5 μm) on the substrate side from Fig. 12.8(a), the total volume of atomic transportation can be obtained from the product of the width and the cross section of the solder joint. Taking the density of 27Sn73Pb as 10.25g/cm3 and the molecular weight of 27Sn73Pb as 183.3 g/mole, the ﬂux of JTM = 4.26 × 1014 atoms/cm2 sec is obtained. Assuming a temperature gradient of 1000 K/cm, a temperature of 180◦ C, which is very close to the melting temperature of eutectic SnPb, and a diﬀusivity of DPb = 4.41 × 10−13 cm2 /sec, the molar heat of transport Q∗Pb is estimated to be −25 kJ/mole. The accuracy of determination of Q∗ may be aﬀected by the measurement of ﬂux in Eq. (12.3) since the concentration distribution is non-uniform. The assumed temperature gradient may be incorrect. However, more serious is the basic assumption in the analysis that both Pb and Sn move with the temperature gradient. Actually if Pb is the dominant diﬀusing species and

SVNY339-Tu

340

April 5, 2007

17:37

Chapter 12

moves from the hot side to the cold side, the Sn will be pushed back in the opposite direction if a constant volume process is assumed. The eﬀect of reverse ﬂux of Sn on the calculation of heat of transport in a two-phase microstructure should be studied. 12.3.2 Entropy Production Onsager deﬁned the conjugated ﬂux and force in irreversible processes so that their product is equal to the product of temperature and entropy production per unit volume. In thermomigration, the major entropy production is due to heat propagation under a temperature gradient, so T dS = V dt

−κ

dT dx

−

1 dT T dx

,

(12.5)

where V is volume and S is entropy. If we take heat conductivity in solder as κ∼ = 50 joule/m-sec-K, dT /dx = 1000 K/cm, and T = 400 K, we obtain [8] T dS joule = 1.2 × 109 3 . V dt m sec Other source of entropy production during thermomigration will be much smaller. The entropy production by atomic migration, the cross-eﬀect, can be estimated as T dS = V dt

C

D F kT

F =C

D kT

3k

dT dx

2 ,

(12.6)

where we have assumed the driving force F = 3k(dT /dx) where k is Boltzmann’s constant, and by taking dT /dx = 1000 K/cm, we obtain T dS joule = 3 × 102 3 , V dt m sec which is much smaller than that due to heat propagation. For comparison, in electromigration, the major entropy production is due to joule heating: T dS dϕ 2 , = jem − = ρjem V dt dx

(12.7)

where jem is electric current density and ϕ is electric potential or voltage. If we take jem = 104 A/cm2 and ρ = 10−5 Ω-cm (for solder), we obtain T dS joule = 109 3 , V dt m sec

SVNY339-Tu

April 5, 2007

17:37

Thermomigration

341

which is of the same order of magnitude of entropy production in thermomigration in a temperature gradient of 1000 K/cm near the temperature of 400 K. Similarly, all other sources of entropy production in electromigration are much weaker. The entropy production by atomic migration (electromigration) under electron wind force is T dS = V dt

C

D F kT

F =C

D 2 (Z ∗ eρj) . kT

(12.8)

If we take C = 1029 /m3 , T = 400 K, D = 10−12 m2 /sec, Z ∗ e = 10−18 coulomb, ρ = 10−7 Ω-m, and j = 108 A/m2 , we obtain T dS joule = 10 3 . V dt m sec The value is much smaller than that from joule heating. Since entropy production by joule heating or heat propagation is many orders of magnitude larger than that by atomic migration, it is conceivable that entropy production in electromigration or thermomigration can aﬀect microstructure greatly. 12.3.3 Eﬀect of Concentration Gradient on Thermomigration Thermomigration can cause a uniform single phase solid solution to become nonuniform. From the point of view of kinetics, the change from a uniform to a nonuniform solid solution requires uphill diﬀusion of the components against their composition gradient, so thermomigration is opposed by the concentration gradient. It is worth noting that in thermomigration, the diﬀusion of the element to the hot end is against both the temperature gradient and the concentration gradient. Thus, in the ﬂux equation of thermomigration we need to add the opposing ﬂux as J = −C

D Q∗ ∂T ∂C +D . kT T ∂x ∂x

(12.9)

The sign of the last term is positive because it is uphill diﬀusion. Accordingly, when the concentration gradient in uphill diﬀusion is large enough, there can be no net eﬀect of thermomigration, i.e., J = 0. Thus, a steady state is reached, in which a constant concentration gradient will be maintained. In the steady state, 1 ΔC d(ln C) 1 = = C Δx dx kT

Q∗ ΔT T Δx

(12.10)

SVNY339-Tu

342

April 5, 2007

17:37

Chapter 12

This was achieved in a thermomigration experiment in the Fe-C system by Shewmon, and carbon was found to diﬀuse to the hot end. The concentration of C in Fe reached a constant linear gradient [1]. The concentration gradient that has balanced the thermomigration can be measured, and the Q∗ can be calculated by knowing the temperature gradient and temperature. While there is an uncertainty in choosing the temperature, the uncertainty is negligible because ΔT /T is typically small. However, if we examine Eq. (12.10), it is unclear if the equation can be satisﬁed arbitrarily. If we keep C, T , and Q∗ as constants, there are variables of ΔC, Δx, and ΔT . Among the three variables, we have to ﬁx two of them in order to solve the third one. For example, if the length and the temperature diﬀerence between the two ends of the sample are given, the variable ΔC is ﬁxed by Eq. (12.6). But it is unclear if it can be satisﬁed arbitrarily, since the initial homogeneous concentration is given, so the maximum ΔC is limited by (2C − 0). The steady-state concentration gradient depends on the length of the sample, Δx, as well as the initial homogeneous concentration in the sample. When the length is short, we can have a larger concentration gradient, yet there may be a back stress in the cold end and we need to assume equilibrium vacancy distribution in order to remove the back stress. Also, a larger temperature gradient exists in a shorter sample if the same temperature diﬀerence is maintained. When the length is long, the concentration gradient may not be large enough to balance thermomigration since the gradient depends on the original concentration of the homogeneous solid solution. Yet, the temperature gradient will be lower too if the same temperature diﬀerence is maintained in a longer sample. 12.3.4 The Critical Length below Which No Thermomigration Occurs in a Pure Metal In electromigration in a pure Al strip, there exists a critical length of sample below which there will be no net eﬀect of electromigration due to back stress. The back stress induced a reverse ﬂux to balance the ﬂux of electromigration. In thermomigration of pure Al or Sn, this should also happen when back stress occurs. And we have Q∗ ∂T ΔσΩ = T ∂x Δx or Δx

∂T ∂x

=

ΔσΩ T. Q∗

(12.11)

In the above equation, Δx(dT /dx) can be taken to be a critical product of the sample below which there will be no net eﬀect of thermomigration. Or

SVNY339-Tu

April 5, 2007

17:37

Thermomigration

343

for a given temperature gradient, below a critical length, Δx, there will be no net eﬀect of thermomigration. However, this case is more complicated than that in electromigration because of temperature gradient. Equilibrium vacancy concentration is a function of temperature.

12.3.5 Thermomigration in a Eutectic Two-Phase Alloy Thermomigration in a eutectic alloy is diﬀerent from that in a solid solution. A eutectic alloy below the eutectic temperature is a two-phase alloy. In a two-phase mixture the change of composition does not mean any change of chemical potential, instead it means just the change of local volume fractions of the two phases. Composition of each primary phase is determined by thermodynamic equilibrium between them and is known from the equilibrium phase diagram. Thus, if some segregation in a eutectic solder is induced by thermomigration, it means a change of gradient of volume fractions, not gradient of chemical potentials. Thus, the segregation can be enormous due to the lack of a counteracting force. Strictly speaking, the equilibrium phase diagram is obtained under the assumption of constant temperature and constant pressure. Thus, the concept of constant chemical potential between the two eutectic phases cannot be applied to thermomigration as discussed in the last paragraph because the temperature is not constant. It is an approximation. At the end of thermomigration in a eutectic two-phase structure, no steady state of a linear concentration gradient is achieved, instead a near-complete segregation of the two eutectic phases occurs. Furthermore, since a gradient of volume fractions is not a driving force, the lack of counteracting force in the form of ΔC/Δx will not produce a smooth segregation. Thus, a tendency of stochastic behavior occurs in thermomigration of the eutectic mixture, as shown experimentally in Fig. 12.5, Section 12.2.3. No smooth concentration gradient exists as in the Soret eﬀect of a solid solution. A description of thermomigration in a eutectic structure can be given, which is similar to the presentation in Section 9.7 for electromigration in a two-phase structure. The ﬂuxes generated by the temperature gradient are given as

Ω1 J1TM Ω2 J2TM

n 1 D1 ∂ ln T ∂ ln T ∂(1/kT ) p1 D1 = Ω1 · −Q1 =− · Q1 = p1 D1 Q1 , kT ∂x kT ∂x ∂x n 2 D2 ∂ ln T ∂ ln T ∂(1/kT ) p2 D2 = Ω2 · −Q2 =− · Q2 = p2 D2 Q2 . kT ∂x kT ∂x ∂x (12.12)

If they have the same direction (if Qi have the same sign), they will not satisfy the constraint of constant volume as given in Eqs. (9.19) and (9.20).

SVNY339-Tu

344

April 5, 2007

17:37

Chapter 12

12.4 Thermomigration and DC Electromigration in Flip Chip Solder Joints In DC electromigration, there is a polarity eﬀect. When a daisy chain of bumps is tested by DC electromigration, the void formation at the cathode contact to the Si occurs on every alternative bump. Therefore, it is very easy to recognize DC electromigration. However, we have to consider the contribution of thermomigration to DC electromigration. Thermomigration may accompany electromigration when the joule heating of the latter has induced a temperature gradient of the magnitude of 1000◦ C/cm across the solder joint. If we assume the temperature is hotter on the Si chip side, i.e., the top side in Fig. 12.3, thermomigration will drive the dominant diﬀusing species down, and it is in the same direction as electromigration in the downward ﬂow electrons, so the eﬀects of thermomigration and electromigration are combined. If we consider DC electromigration in the pair of bumps on the left in Fig. 12.3(a), we assume electrons ﬂow down on the left-side bump. Both thermomigration and electromigration will drive vacancies to go to the Si contact and void formation will occur near the contact. However, in the right-side bump of the pair, electromigration will drive atoms in the opposite direction and counteract thermomigration, i.e., the two eﬀects tend to cancel each other. Since we can obtain diﬀerent experimental results in a pair of bumps, we should be able to decouple the contribution of thermomigration and electromigration. If we use pure Sn ﬂip chip samples, we have a simple case of diﬀusion of one element and we can use marker to determine the net eﬀect of ﬂuxes. With two elements in eutectic SnPb bumps or in solid solution PbIn bumps, the problem is more complicated. In these cases, besides marker motion, the concentration change of the ﬂux of Sn and Pb (or Pb and In) should be determined. Due to stochastic behavior, the analysis of eutectic SnPb is even more complicated than that of PbIn.

12.5 Thermomigration and AC Electromigration in Flip Chip Solder Joints There is no diﬀerence in joule heating whether we apply AC or DC to stress a pair of ﬂip chip solder bumps. This is because the current distribution in the pair of powered bumps as shown in Fig. 12.3 is independent of the current direction or polarity, therefore joule heating is the same whether we apply AC or DC in electromigration, except there may be a diﬀerence at a very high frequency AC. However, unlike DC, it is generally assumed that AC does not induce mass ﬂow. If the assumption is correct that there is no electromigration-induced mass migration in a pair of bumps stressed by AC, we should expect only thermomigration in the pair of bumps powered by AC, if AC has generated a temperature gradient in the pair of bumps. This is the

SVNY339-Tu

April 5, 2007

17:37

Thermomigration

345

advantage of using AC to study thermomigration in a ﬂip chip solder joint; AC serves just as a heating source to generate a temperature gradient across the solder bump and makes no contribution to electromigration. We should be able to verify the assumption that AC does not induce mass migration by examining very carefully a pair of bumps that have been stressed by AC together with a neighboring bump that was unpowered. That arrangement was depicted in Fig. 12.3, in which the bump pair on the lefthand side can be stressed by AC, but the neighboring pair on the right-hand side are dummies and will carry no current. The joule heating generated by the left pair stressed by AC will cause the same thermomigration in both pairs. Marker displacement experiments should be conducted in both pairs to determine whether the mass migration is the same or not. Direct comparison should be made to DC experiments too.

12.6 Thermomigration and Chemical Reaction in Solder Joints When Sn is driven to the hot end in a ﬂip chip solder joint by thermomigration, more Cu-Sn intermetallic compound will form at the hot end. Solder line in V-grooves on (001) Si wafer can be used to study the interaction between thermomigration and chemical reaction. For thermomigration, we can keep one end of the Cu wire at 100◦ C (boiling water) and the other end at 180◦ C (heating source); there is thus a very large temperature gradient between the two ends of the solder line, if the length of the wire is short. For thermomigration in solder alloys, the temperature at the hot end will be limited by the melting of the solder. Also, it is not good to cool the cold end to a very low temperature which will limit atomic diﬀusion. Compared to ﬂip chip samples, the advantages of V-groove samples are that the temperature gradient can be measured more easily and in situ observation of damage development in the sample during thermomigration can be performed.

12.7 Thermomigration and Creep in Solder Joints The sample of Cu-wire/solder-ball/Cu-wire as discussed in section 11.2 can be used to study the interaction between thermomigration and mechanical stress in solder joints, same as the study of the interaction between electromigration and mechanical stress. The diameter of the Cu wire can be varied from 1000 μm (1 mm) to 300 μm, and the size of the solder bead should be similar to the diameter of the Cu wire. The larger diameter samples will be better for sample preparation and measurement in thermomigration. After thermomigration, tensile test of the sample can be conducted and compared to a sample without thermomigration. If vacancies move to the hot

SVNY339-Tu

346

April 5, 2007

17:37

Chapter 12

end in thermomigration, the interface at the hot end will become weaker. For shear test, a solder joint between two parallel Cu plates can be prepared, instead of Cu wires. We note that a solder joint between two parallel Cu plates has been used widely to study shear properties of solder alloy at constant temperature. Here the two plates should be kept at diﬀerent temperatures during shear. Back stress is expected in thermomigration in solder joints, especially at the cold end. The interaction between back stress and applied stress is of interest. More interestingly, a weight can be attached to the cold end for the study of thermomigration and creep together. The sample will experience both a gradient of temperature and a gradient of stress at the same time, but the gradients are along diﬀerent directions. To analyze the combined eﬀect, the eﬀect of creep alone on phase change in a solid solution and in a eutectic two-phase structure should be studied ﬁrst.

References 1. P. Shewmon, “Diﬀusion in Solids,” 2nd ed., Chapter 7 “Thermo- and electro-transport in solids,” TMS, Warrendale, PA (1989). 2. D. V. Ragone, “Thermodynamics of Materials,” Volume II, Chapter 8 “Nonequilibrium thermodynamics,” Wiley, New York (1995). 3. W. Roush and J. Jaspal, “Thermomigration in Pb-In solder,” IEEE Proc., CH1781, pp. 342–345 (1982). 4. D. R. Campbell, K. N. Tu and R. E. Robinson, “Interdiﬀusion in a bulk couple of Pb-PbIn alloy,” Acta Metall., 24, 609 (1976). 5. H. Ye, C. Basaran, and D. C. Hopkins, “Thermomigration in Pb-Sn solder joints under joule heating during electric current stressing,” Appl. Phys. Lett., 82, 1045–1047 (2003). 6. A. T. Huang, A. M. Gusak, and K. N. Tu, “Thermomigration in SnPb composite ﬂip chip solder joints,” Appl. Phys. Lett., 88, 141911 (2006). 7. Y. C. Chuang and C. Y. Liu, “Thermomigration in eutectic SnPb alloy,” Appl. Phys. Lett., 88, 174105 (2006). 8. Fan-yi Ouyang, K. N. Tu, Yi-Shao Lai, and Andriy M. Gusak, “Eﬀect of entropy production on microstructure change in eutectic SnPb ﬂip chip solder joints by thermomigration,” Appl. Phys. Lett., 89, 221906 (2006).

SVNY339-Tu

March 2, 2007

22:4

Appendix A: Diﬀusivity of Vacancy Mechanism of Diﬀusion in Solids

To analyze atomic diﬀusivity, we shall consider the vacancy mechanism of diﬀusion in a face-centered-cubic metal. We make the following assumptions in order to develop the analytical model. 1. It is a thermally activated unimolecular process. Unimolecular process means that we consider a single atom in the diﬀusion process and it is a near-equilibrium process. This is unlike chemical reactions that are bimolecular processes, such as rock salt formation, in which the collision of two atoms of Na and Cl is involved and the process is far from equilibrium. 2. It is a defect-mediated process. Here the defect is a vacancy. 3. The activated state obeys a Boltzmann’s equilibrium distribution from transition state theory. Hence, the Boltzmann distribution function is used. 4. It is assumed that the probability of reverse jumps is large due to small driving force, so we have to consider reverse processes. In other words, the process is not far from equilibrium. 5. Statistically, atomic diﬀusion obeys the principle of random walk. 6. A long-range diﬀusion requires a driving force.

v ΔGm

B

A

x

λ Distance

At equilibrium, in a one-dimensional conﬁguration, atoms are attempting to jump over the potential energy barrier with the attempt frequency, ν0 , to exchange position with a neighboring vacancy, as depicted in Fig. A.1.

SVNY339-Tu

348

March 2, 2007

22:4

Appendix A

The successful or exchange jump frequency is given below on the basis of Boltzmann’s distribution: ν = ν0 exp

−ΔGm kT

,

where ν0 = attempt frequency, ν = exchange frequency, ΔGm = saddle point energy (activation energy of motion). We note that there is a reverse jump at the same attempt frequency.

v+

v–

ΔGm λ

Now consider a driving force F (which equals the slope of the base line in Fig. A.2). The meaning of F will be discussed later. The forward jump is increased by

λF v = v exp + 2kT

+

,

where λ is the jump distance. The reverse jump is decreased by λF v − = v exp − . 2kT And the net frequency is −

vn = v − v = 2v sinh +

Now, we take the “condition of linearization,” λF 1. kT

λF 2kT

.

SVNY339-Tu

March 2, 2007

22:4

Appendix A

349

Then the net frequency jump vn is “linearly” proportional to the driving force F: vn = v

λF . kT

We can deﬁne a drift velocity v = λvn =

vλ2 F. kT

Then, the atomic ﬂux J, which has units of number of atoms per unit area per unit time, is J = Cv =

Cvλ2 F, kT

where M = vλ2 /kT is deﬁned as the atomic mobility. The atomic ﬂux J is “linearly” proportional to the driving force F. The driving force is generally deﬁned as a potential gradient, F =−

∂μ . ∂x

In atomic diﬀusion, here μ is the chemical potential of an atom and is deﬁned at constant temperature and pressure to be ∂G μ= , ∂C T,p where G is Gibbs free energy and C is concentration. For an ideal dilute solid solution, μ = kT ln C, ∂μ ∂C kT ∂C F =− =− , ∂C ∂x C ∂x Cvλ2 ∂C Cvλ2 kT ∂C ∂C J= F = − = −vλ2 = −D . kT kT C ∂x ∂x ∂x Hence, we have obtained Fick’s ﬁrst law of diﬀusion: −

J ∂C = D = vλ2 , ∂x

where D is the diﬀusion coeﬃcient (or diﬀusivity) in units of cm2 /sec. Then, M = D/kT . In the above derivation, as depicted in Fig. A.1, we have assumed

SVNY339-Tu

350

March 2, 2007

22:4

Appendix A

that the diﬀusing atom has a neighboring vacancy. For the majority of atoms in the lattice, this is not true, and we must deﬁne the probability of an atom having a neighboring vacancy in the solid as nv ΔGf = exp − . n kT nv is the total number of vacancies in the solid, n is the total number of lattice sites in the solid, and ΔGf is the Gibbs free energy of formation of a vacancy. Since in a face-centered-cubic metal, a lattice atom has 12 nearest neighbors, the probability of a particular atom having a vacancy as a neighbor is nv ΔGf nc = nc exp − n kT

nc = 12.

Next, we have to consider the correlation factor in the face-centered-cubic lattice. The physical meaning of the factor is the probability of reverse jump; after the atom has exchanged position with a vacancy, it has a high probability of returning to its original position before the activated conﬁguration is relaxed. The factor has a range between zero and unity. When f = 0, it means the probability of reverse jump is 100%, so the atom and the vacancy are exchanging position back and forth, which will not lead to any random walk but instead a correlated walk. When f = 1, it means that after the jump, the atom will not return to its original position, and it is a random walk because the next jump will depend on the random probability of a vacancy coming to the neighborhood of this atom. In fcc metals, f = 0.78, so about 80% of jumps are random walk, and about 20% are correlated walk. Finally, we have the diﬀusivity as ΔGm + ΔGf D = f nc a2 ν0 exp − , kT ΔSm + ΔSf ΔH ΔHm + ΔHf D = f nc λ2 ν0 exp exp − = D0 exp − . k kT kT

SVNY339-Tu

March 3, 2007

7:35

Appendix B: Growth and Ripening Equations of Precipitates

The distribution function of a set of precipitates is obtained by solving the continuity equation in size space: ∂f ∂f =v , ∂t ∂x where f is the size distribution function of the precipitates and v is the growth/dissolution velocity of the precipitates. To solve the continuity equation, the ﬁrst step is to ﬁnd the growth/dissolution velocity. In this appendix we shall derive the velocity of a spherical precipitate. When the diameter of the precipitates is in nanoscale, it is important to take into account the Gibbs–Thomson potential of curvature as in the LSW theory of ripening. In other words, the equilibrium concentration at the precipitate/matrix interface is a function of radius. When the precipitate diameter is large, we can assume the equilibrium concentration to be constant, independent of the radius.

B.1 Kinetics of Precipitation We consider the growth or dissolution of a spherical particle or precipitate. Letting R be the variable, the diﬀusion equation in spherical coordination, assuming a steady state, is ∂2C 2 ∂C = 0. + ∂R2 R ∂R The solution is C=

b + d. R

(B.1)

SVNY339-Tu

352

March 3, 2007

7:35

Appendix B

The boundary conditions are At R = r0 , C = C0 , At R = r, C = Cr ,

we have we have

b + d. r0 b Cr = + d. r C0 =

(B.2) (B.3)

Now, if we take the diﬀerence between the last two equations, we have 1 r0 − r ∼ b 1 Cr − C0 = b − where r0 r. =b (B.4) = r r0 rr0 r This is an important assumption. It means that precipitates are far apart. Note that if we take the volume fraction, f , the ratio of volume of the precipitate particles to the volume of the diﬀusion ﬁeld, or the total volume of the precipitated phase to the total volume of the matrix, is 4π 3 r r3 f= 3 = 3 → 0. 4π 3 r0 r 3 0 It is a very small value: f → 0. (This is a very important assumption in the LSW theory of ripening to be discussed later.) We have b = r(Cr − C0 ). Substituting b into Eq. (B.3), we have Cr =

r(Cr − C0 ) + d. r

(B.5)

We have d = C0 , and Eq. (B.1) becomes (Cr − C0 )r + C0 . R dC (Cr − C0 )r . =− dR R2 C(R) =

Therefore,

(B.6)

At the particle/matrix interface for a particle of radius r, or R = r, we have dC Cr − C0 =− . dR r

(B.7)

Then the ﬂux of atoms arriving at the interface is J = +D

∂C D(C0 − Cr ) = ∂R r

at R = r.

(B.8)

Note that when Cr > C0 , J < 0, the net ﬂux is toward the particle, and thus

SVNY339-Tu

March 3, 2007

7:35

Appendix B

353

it grows. When Cr < C0 , J > 0, the ﬂux leaves the particle so the particle dissolves.

B.2 Growth Rate of a Spherical Particle Assuming Cr Is Constant If Ω is atomic volume, in time dt, a volume is added to the spherical particle, ΩJAdt = ΩJ4πr2 dt = 4πr2 dr, where the last term is the increment of a spherical shell due to the growth. Hence, dr ΩD(C0 − Cr ) = ΩJ = . dt r

(B.9)

B.2.1 Case 1: The Growth of a Precipitate By integration and assuming when t = 0, r = 0, r2 = 2ΩD(C0 − Cr )t.

(B.10)

Note here that if we follow Ham’s approach and take Cr as a constant, it is not a function of r as given by the Gibbs–Thomson equation. From the above 1 equation, we see that r ∼ = t /2 and r3 ∼ = t3/2 . Or we have r3 = [2ΩD(C0 − Cr )t]3/2 .

(B.11)

B.2.2 Case 2: The Depletion of Concentration in the Matrix (Mean-Field Consideration) On the other hand, we consider the loss of average concentration in the matrix, ΔC = C0 − C, due to the formation of the precipitate, where the average concentration in the matrix is C, which can be regarded as the “mean-ﬁeld” concentration (the conception of mean-ﬁeld theory). In the beginning, the average concentration is C0 , and it changes to Cwhen the precipitate grows. Let 1/Ω = Cp be the concentration in the solid precipitate. We have simply by mass balance, 4π 3 4π 3 1 4π r0 (C0 − C) = r = [2ΩD(C0 − Cr )t]3/2 , 3 3 Ω 3Ω 3/2 3/2 2D(C0 − Cr )Ω1/3 2Bt C = C0 − t = C − , 0 r02 3

(B.12) (B.13)

SVNY339-Tu

354

March 3, 2007

7:35

Appendix B

where B≡

3D(C0 − Cr ) 1/3

Cp r02

.

We note that the above equation is the same as Eq. (1–36) in Chapter 1 in Shewmon. B.2.3 Case 3: Consider Growth of Precipitate and Depletion of the Matrix Together We can derive the last equation in a slightly diﬀerent way. The growth of the precipitate reduces the concentration in the matrix. The amount of solute atoms diﬀusing to the precipitate in time Δt is J(r)4πr2 Δt = number of atoms. It should be equal to the reduction of the average concentration in the volume of the sphere of diﬀusion of r0 . Hence, if take the average concentration in the matrix to be C, 4πr03 ΔC = J(r)4πr2 Δt. 3 Or, we have ΔC 3D 3 4πr2 J(r) = − 3 (C0 − Cr )r. = Δt 4πr03 r0

(B.14)

The conservation of mass requires that 4π 3 4π 3 r (C0 − C) = r Cp , 3 0 3

(B.15)

where Cp is the concentration of solute in the solid precipitate and Cp = 1/Ω. Hence, r = r0

C0 − C Cp

1/3 .

(B.16)

By substituting r into the rate equation above, we have ΔC 1 3D = − 2 (C0 − Cr ) 1/3 (C0 − C)1/3 . Δt r0 Cp

(B.17)

SVNY339-Tu

March 3, 2007

7:35

Appendix B

355

Let B≡

3D(C0 − Cr ) 1/3

Cp r02

.

We have dC = −B(C0 − C)1/3 . dt By integration we obtain 3 − (C0 − C)2/3 = −Bt + β. 2 At t = 0, C0 = C, so β = 0. Thus, we have the solution, C = C0 −

2Bt 3

3/2 ,

(B.18)

which is the same as what we have obtained. Hence, we have C0 − C ∼ = t3/2 for 3-dimensional growth. ⎡

Let C = C0 ⎣1 −

2Bt

3/2 ⎤

⎦ = C0

2/3

3C0

3/2 3/2 t t 1− = C0 exp − τ τ (B.19)

if we assume t τ, 1/3

where

2/3

Cp r02 C0 r2 ∼ τ= = 0 2D(C0 − Cr ) 2D

Cp C0

1/3 .

(B.20)

Usually D, Cp , C0 are known, and we can design the experiment to control the growth of the precipitate.

B.3 Gibbs–Thomson Potential: Eﬀect of Surface Curvature Consider a sphere with radius r and surface energy per unit area γ. The surface energy exerts a compressive pressure on the sphere because it tends

SVNY339-Tu

356

March 3, 2007

7:35

Appendix B

to shrink to reduce the surface energy. The pressure is dE d4πr2 γ − − F 8πrγ 2γ dr p= =− =− . = dr = 2 2 A A 4πr 4πr r

(B.21)

If we multiply p by the atomic volume Ω, we have the chemical potential μr = −

2γΩ . r

(B.22)

This is called the Gibbs–Thomson potential due to the curvature of surface. We note that it is not just the potential of the surface atoms of the precipitate, it is the potential energy of all the atoms in the precipitate. We see that for a ﬂat surface r = ∞, μ∞ = 0 so we have ur − μ∞ =

2γΩ . r

(B.23)

In the following, we shall apply this potential to determine the eﬀect of curvature on solubility. We consider an alloy of α = A(B), where B is solute in solvent A. At temperature T, B will precipitate out. We consider two precipitates of B, one larger than the other. The solubility of B surrounding the large one is less than that surrounding the smaller one. If we take X to be the solubility, we have X∞ < Xlarge < Xsmall . To relate the solubility to Gibbs–Thomson potential, we have the chemical potential of B as a function of its radius as μB,r − μB,∞ =

2γΩ , r

(B.24)

where γ is the interfacial energy between the precipitate and the matrix. If we deﬁne the standard state of B as pure B with r = ∞, we have μB,r = μB,∞ + RT ln aB ,

(B.25)

where aB is the activity. According to Henry’s law, aB = kXB , r, where XB,r is the solubility of B surrounding a precipitate of radius r. At r = ∞, μB,∞ = μB,∞ + RT ln aB .

SVNY339-Tu

March 3, 2007

7:35

Appendix B

357

This implies that RT ln aB = 0, or aB = 1. So k = 1/XB,∞ . Therefore, μB,r = μB,∞ + RT ln

XB,r . XB,∞

(B.26)

Hence, ln

XB,r μB,r − μB,∞ 2γΩ = = . XB,∞ RT rRT

Or if we consider kT instead of RT, we have XB,r = XB,∞ exp

2γΩ rkT

.

(B.27)

B.4 Eﬀect of Curvature on Solubility (Ripening) The solubility of B around a spherical particle of B of radius r is given by XB,r = XB,∞ exp

2γΩ rkT

,

where r = ∞, the exponential equals unity. Thus, XB,r goes up when r goes down. Now we replace XB,r by Cr and XB,∞ by C∞ , which is the equilibrium concentration on a ﬂat surface. We have Cr = C∞ exp

2γΩ rkT

.

(B.28)

If 2γΩ rkT , we have 2γΩ Cr = C∞ 1 + , rkT Cr − C∞ = where α =

α 2γΩC∞ = , rkT r

(B.29)

α . r

(B.30)

2γΩ kT C∞ ,

Cr = C∞ +

SVNY339-Tu

March 3, 2007

358

7:35

Appendix B

Thus, Cr is not a constant, but a function of r. Now we substitute Cr into the growth equation of dr ΩD(C0 − Cr ) = ΩJ = . dt r We have dr ΩD α = C0 − C∞ − . dt r r

(B.31)

Note that C0 − C∞ > 0 always. We can deﬁne a critical radius r∗ such that C0 − C∞ =

α . r∗

Then we have dr αΩD = dt r

1 1 − r∗ r

.

(B.32)

The parameter r∗ is deﬁned such that r > r∗ , dr dt > 0 r<

r∗ , dr dt

<0

r = r∗ , dr dt = 0

The particle is growing. The particle is dissolving. The particle is in a state of metastable equilibrium. It has a concentration C at the interface, or Cr∗ = C.

In ripening, the larger particles grow at the expense of the smaller ones. It will approach a dynamic equilibrium distribution of size of the particles. The distribution function can be obtained by solving the continuity equation in size space. Knowing dr/dt, it is the beginning of the LSW theory of ripening.

SVNY339-Tu

March 3, 2007

7:40

Appendix C: Derivation of Huntington’s Electron Wind Force

In the following we present the assumptions and step-by-step derivation of Huntington’s model of electron wind force. (1) Considerations are hemiclassical. Each electron is treated as a group of waves or Bloch waves with an average wave vector k and group velocity of V = h¯1 ∂E(k) , where the function E(k)should be found from the electron ∂k 2 2

¯ k band theory (dispersion law). For free electrons, E(k) = h2m ∗ , and for elec2 2 trons at the bottom of the conduction band, E(k) = Emin + h¯2mk0 , where 2

m∗ = h ¯ 2 ( ∂∂kE2 )−1 is the eﬀective electron mass. We note that ∂E means ∂k ∂E ∂E ∂E gradient in k-space, e.g., a vector with components of ∂kx , ∂ky , ∂kz . For Bloch waves, according to the Bloch theorem, we recall that each quantum state of independent electron in the periodic potential U (r + R) = U (r) and R = n1 a1 + n2 a2 + n3 a3 can be described by the product of a planar wave and periodic function Ψh¯ k (r) = eikr Wh¯ k (r), where Wh¯ k (r + R) = Wh¯ k (r) and n is the band index. (2) h¯1 ( ∂E − ∂E ) = V − V is the change of electron’s group velocity as a ∂k ∂k result of scattering. ∂E ∂E (3) − mh¯ 0 ( ∂k − ∂kx ) = −(px − px ) is momentum along the x-axis, transfer x to defect during mentioned individual scattering. (4) f (k) is the probability that the quantum state k is occupied by some electron. The quantum cell in k-space with a “k-volume” is given by Ω = 2μ 2μ 2μ 8π 3 Lx · Ly · Lz = V , where V is the real total volume. At equilibrium, we have 1 f0 = E−μ (Fermi–Dirac distribution). e

kT

+1

(5) 1 − f (k ) is a probability that the quantum state k was free or unoccupied before scattering, so that the Pauli exclusion principle does not forbid the k → k transition. (6) Wd (k → k ) is a probability of this transition per unit time. It means that the product Wd dt is a probability of transition during dt, if dt τd .

SVNY339-Tu

360

March 3, 2007

7:40

Appendix C

(7) According to the Pauli principle, each quantum cell in k-space (with 3 Ω = 8π V ) may contain up to two electrons with opposite spins, so the k-volume 3 per electron is Ω2 = 4π V . (8) Now we consider unit volume V = 1 m3 . (9) The number of possible electron states in the “elementary” k3 3 volume d3k = dkx dky dkz is dΩk = d4πk3 . The elementary k-volume is physically 2 small. (10) The momentum, Mx along the x-axis, transferring from electrons to the defects in the unit volume V = 1 m3 per unit time is given as −

d3 k d3 k (p − px )f (k)(1 − f (k ))Wd (k, k ). 4π 3 4π 3 x

Or dMx =− dt

1 4π 3

2

m0 h ¯

∂E ∂E ))W (k, k d3 k d3 k. − )f (k)(1 − f (k d ∂kx ∂kx

(11) We shall represent the last equation by two integrals. dMx = I1 + I2 , dt where I1 = − I2 = −

1 4π 3 1 4π 3

2 2

m0 ∂E f (k)(1 − f (k ))Wd (k, k )d3 k d3 k, ¯h ∂kx m0 ∂E f (k)(1 − f (k ))Wd (k, k )d3 k d3 k. ¯h ∂kx

Since the integration is being made over all k and all k , we can interchange the variables in the ﬁrst integral as I1 = −

1 4π 3

2

m0 ∂E f (k )(1 − f (k))Wd (k , k)d3 k d3 k. ¯h ∂kx

Then in I1 and I2 , we have the same dMx = (−I2 ) − (−I1 ) dt

=

1 4π 3

2

∂E ∂kx ,

and thus we have (C.1)

m0 ∂E f (k )(1 − f (k))Wd (k, k) −f (k )(1 −f (k))Wd (k , k) d3 k d3 k. ¯h ∂kx

SVNY339-Tu

March 3, 2007

7:40

Appendix C

361

(12) Huntington showed that to simplify the expression of the last equation, he used the concept of relaxation time τd . This notion was ﬁrst introduced for the analysis of the kinetic Boltzmann equation for gases. With certain approximation, the rate of change of the distribution function can be represented as ∂f (t, k) 1 = ∂t 4π 3

f (k)(1 − f (k ))Wd (k, k )

f (t, k) − f (k) −f (k )(1 − f (k))Wd (k , k) d3 k − τd for the equilibrium distribution. For the stationary case, 1 4π 3 =

∂f ∂t

= 0, so that

f (k)(1 − f (k ))Wd (k, k ) − f (k )(1 − f (k))Wd (k , k) d3 k

f (t, k) − f (k) . τd

(C.2)

In the above equation, f (k)(1 − f (k ))Wd (k, k ) is the probability per unit time of k → k transition, provided that the state k before transition was ﬁlled and the state k was empty. The function f (k )(1 − f (k))Wd (k , k) is the probability per unit time of the inverse transition. (13) By substituting Eq. (C.2) into Eq. (C.1), we have

dMx 1 = dt 4π 3

d3 k

m0 ∂E(k) f (k) − f0 (k) . ¯h ∂kx τd

(14) Let the relaxation time be independent of k and τd = constant. Then dMx m0 1 = dt ¯ τd 4π 3 h

d3 k

∂E(k) m0 1 f (k) − ∂kx ¯hτd 4π 3

d3 k

∂E(k) f0 (k). ∂kx

(15) Evidently, the average vector velocity of electrons in equilibrium is zero: Vx =

1 ∂E 1 ∂E 1 ∂E |eq = |eq = |eq = 0. ¯ ∂kx h ¯ ∂ky h ¯ ∂kz h

Therefore,

∂E f0 (k)d3 k = 0. ∂kx

SVNY339-Tu

362

March 3, 2007

7:40

Appendix C

Thus, dMx m0 1 = dt ¯ τd 4π 3 h

∂E f (k)d3 k. ∂kx

(C.3)

(16) To relate the momentum change to force, we have the current density given as jx = (−e)nVx = (−e)

d3 k 1 ∂E(k) f (k) · , 4π 3 ¯h ∂kx

(C.4)

3

where n = d4πk3 f (k) is the number of electrons per unit volume with k belonging 3 to d3 k. Indeed, d4πk3 is the number of “single electron cells” in the “volume” of d3 k of k-space, and f (k) is the “inhabitance” of cell. (17) Combining Eqs. (C.3) and (C.4), we obtain dMx jx m0 . =− dt eτd

(C.5)

This is a momentum change along the x-direction, transferred to defects (the diﬀusing atoms) per unit time per unit volume. (18) Let Nd be the density of defects (number of defects per unit volume). Then, according to Newton’s second law, the force at one defect, caused by electron wind, is Fx =

1 dMx jx m0 . =− Nd dt eτd Nd

(C.6)

This force has a clear physical meaning assuming the condition that during atomic jump the defect feels much more than one collision. Characteristic time of one successful jump is of the order of Debye time, τDebye ∼ 10−13 sec. So for Eq. (C.6) to be reasonable, it is necessary that the product of scattering frequency, υscatter , and Debye time be much less than unity: νscatter ≈

kT VF εp l

where l is the mean free path length of electron around defect, VF /l is the frequency of “possible” collisions, and kT/εp is the fraction of electrons which are able to be scattered according to the Pauli principle. 1 l ≈ nσ , where σ is the cross section and is about 10−19 m2 (according to Huntington’s estimate). n ∼ 1029 m−3 (nex ≈

kT kT ¯hkF n ≈ 1027 m−3 ), ≈ 10−2 , VF = ≈ 106 m/ sec . εp εp m0

SVNY339-Tu

March 3, 2007

7:40

Appendix C

363

Thus, νscatter ≈ 10−1 106 nσ ≈ 10−2 106 1029 10−19 ≈ 1014 sec−1 . So νscatter τDebye ≈ 10 1. (19) Let us now transform Eq. (C.6) in terms of electric ﬁeld: jx = ερx , where ρ is an average resistance of metal. According to the Drude–Lorentz– Sommerfeld model, the resistance ρ of a metal can be written as ρ= where m∗ =

h ¯2

∂2 E ∂k2

|m∗ | , ne2 τ

is the eﬀective electron mass.

Huntington used the same expression for the resistance of defects, ρd =

|m∗ | |m∗ | , so that we have τ = . d ne2 τd ne2 ρd

Thus, from Eq. (C.6), we obtain εx m0 ne2 ρd Fx = − =− ρ eNd |m∗ |

m0 ZN ρd |m| Nd ρ

eεx ,

(C.7)

where N is the density of ions and Z is the valence number; n = ZN . Thus, we have the eﬀective charge m0 ZN ρd m0 =Z ∗ |m∗ | Nd ρ |m |

Q∗ = −Z ∗ e, where Z ∗ =

ρd Nd ρ N

.

(20) Now, let us take into account the fact that τd , ρd , and Fx change from position to position. Obviously, they shall reach a maximum at the saddle point of diﬀusion. Assume that F (y) = Fm sin2 ( πy d ), where y is not the y-axis. Rather it is a coordinate along the jumping path, which usually does not coincide with the x-axis. Work or change of potential barrier is Uj =

aj /2

0

a/2

sin2

F (y)dy = Fm cos θj 0

πy aj Fm dy = cos θj . a 4

After averaging in all possible jump directions, we have Jx = C

D 1 Fm . kT 2

SVNY339-Tu

364

March 3, 2007

7:40

Appendix C

The factor of 1/2 is due to the integral of

a/2

sin2 0

1a πy dy = . a 22

(21) Thus, we have ﬁnally the eﬀective charge number: ∗ Zeﬀ

1 ∗ = Zmax −Z =Z 2

1 m0 2 |m∗ |

ρmax d Nd ρ N

−1 .

SVNY339-Tu

March 2, 2007

20:27

Subject Index

A accelerated test of Sn whisker growth, 175 accelerometer, 319 Al electromigration, 212, 215, 216, 222, 224, 225, 226, 229, 230 anisotropic conductor, 235, 238 anisotropic conducting polymer tapes, 31 Au/Cu/Cr under-bump metallization, 15, 73, 94 Au/Cu/Cu-Cr, 97, 100 Au Sn4 , 183, 198 AuSnPb ternary phase diagram, 199 B back stress, 222, 225 back stress build-up, 228 back stress measurement, 229 back stress of electromigration, 222, 226 ball-grid array (BGA) solder balls, 16 ball-limiting metallization (BLM), 15 Burger’s equation, 286 beta-Sn (β-Sn), 153, 235 ball-grid array (BGA) board, 315 Blech structure, 212, 228, 231 bond pad, 9, 23, 24 bronze, 1 bulk diﬀusion couple of SnPb, 123 C C-4 ﬂip chip technology, 12 Coble creep model, 160

cakine, 115 Charpy impact test, 311, 314 channel between scallops, 128, 150 chemical potential, 90, 170, 224 chip-packaging interaction, 30, 124 chip-size packaging, 29 cold joint, 7, 183, 198 composite solder joint, 20, 113, 272, 310, 329 compressive stress gradient, 16, 153, 160, 163 constant volume constraint, 283, 343 consumption rate of Cu, 48, 69 continuity equation, 173 controlled-collapse-chip-connection (C-4) solder joint, 14, 97 Coﬃn-Manson mode of low cycle fatigue, 22 copper-tin binary system, 1 copper-tin reaction, 3, 37, 73, 111, 127, 154 creep, 16, 74, 154, 325, 345 critical length of electromigration, 223, 225 critical product of electromigration, 224, 247 (Cu, Ni)6 Sn5, 102, 104, 193 Cu/Ni(V)/Al under-bump metallization, 73, 100, 251, 273, 275, 329, 335 Cu/Sn room temperature reaction, 74 Cu-solder-Cu samples for tensile test, 306

SVNY339-Tu

366

March 2, 2007

20:27

Subject Index

Cu column bump, 276 CuSnPb ternary phase diagram, 56 Cu3 Sn, crystal structure, 45, 75, 78 Cu6 Sn5 , crystal structure, 44, 75 Cu6 Sn5 , crystallographic orientation, 43, 45 Cu6 Sn5 , growth kinetics, 75, 80 Cu6 Sn5 , sequential formation, 81 current crowding, 230, 247, 250 current density gradient force, 230 D daisy chain of ﬂip chip solder joint, 253 Darken’s analysis of interdiﬀusion, 157, 227 deformation potential, 225 deviatoric strain, 166 dewetting, 96 diﬀusion barrier, 178, 280 diﬀusion controlled reaction (or growth), 63, 84 dilatation strain, 166 direct chip attachment, 17 direct force of electromigration, 218 drift velocity, 212, 220 drop test, 316 dual damascene structure, 214 ductile-to-brittle transition in solder joint, 25, 306 ductile-to-brittle transition temperature (DBTT), 312 dynamic equilibrium, 299 E eﬀective charge number of electromigration, 220, 257, 364 electroless Ni(P) UBM, 19, 188 electromigration, 25, 119, 176, 212, 245 electromigration in eutectic solder joint, 249, 255 electron wind force of electromigration, 217 eutectic eﬀect of phase separation, 119 eutectic SnAgCu, 6, 67 eutectic SnAg, 6, 67 eutectic SnCu, 6, 67

eutectic two-phase structure, 119, 281 F facetted scallop, 53, 143, 15 ﬂexional vibration, 322 ﬂux divergence, 216 ﬂip chip solder joint, 111, 245 ﬂip chip technology, 12 focused ion beam thinning, 172 free energy of formation of vacancy, 89, 350 free energy of motion of vacancy, 89, 348 frequency of vibration, 319 G glancing incidence x-ray diﬀraction, 74 gradient of chemical potential, 112, 119 gradient of current density, 234 gradient of volume fraction, 112, 119, 282 grain boundary precipitation, 156, 158, 179 H halo formation, 42 high speed shear, 314, 316 hillock, 155, 292 homogenization, 120, 327 homologous temperature, 215, 228, 305 I intermetallic compound (IMC), 17, 38, 60, 62, 69, 73, 128, 131, 158, 183, 194, 198, 293, 296, 298, 301 immersion Sn, 11 impact fracture, 25, 316 input/output (I/O) pads, 12 interconnect, 214 interdiﬀusion coeﬃcient, 62, 87 interfacial reaction coeﬃcient, 89 interfacial reaction-controlled reaction, 62, 87, 89 interfacial tension of SnPb alloy, 51 interstitial diﬀusion, 74, 117

SVNY339-Tu

March 2, 2007

20:27

Subject Index J JEDEC-JESP22-B111 standard of drop test, 316 JEDEC speciﬁcation of drop test, 312, 316 joule heating, 26, 211, 254, 270 K Kirkendall eﬀect of interdiﬀusion, 159 Kirkendall shift, 159, 285 Kirkendall void, 59, 101, 192, 279, 295 L lamellar microstructure, 112, 119, 281 Laue pattern, 164 layer-type (layered) morphology, 61, 84, 88, 131, 133 leadframe, 9, 16, 153 line-to-bump geometry, 26, 246, 249 low cycle fatigue, 1, 22 LSW theory of conservative ripening, 137, 148 M marker displacement, 80, 262, 263 matte Sn, 17, 153 mean-time-to-failure (MTTF), 245, 264 mini Charpy machine, 314 miniaturization, 28 Moire interferometry, 124 mono-size distribution, 135, 137 monochromator, 167 morphological stability of scallops, 128 multi-chip module, 14 multi-level metal-ceramic module, 14 N Nabarro-Herring creep model, 160 near-ideal ﬂip-chip solder joint, 280 NEMI (National Electronics Manufacturing Initiative), 178 NiSnPb ternary phase diagram, 185 Ni3 P, 188, 192 Ni3 Sn4 , 184, 188

367

(Ni, Cu)3 Sn4 , 193 non-conservative ripening, 128, 139 O Onsager’s reciprocity relations, 170, 225 over-hang, 232 P pancake-type void, 245, 253, 254, 267 Pb-free solder, 4, 38, 68 PdSnPb ternary phase diagram, 197 phased-in Cu-Cr UBM, 14, 97 phase separation, 121, 248, 281, 333 pin-through-hole technology, 10, 12 polarity eﬀect, 289 polarity eﬀect on IMC growth, 293, 297, 301 R random phase distribution, 282, 286, 334 random state, 282, 334 reﬂow, 2, 15 reliability of solder joint technology, 16 ripening, 41, 64, 139 RMA (mildly activated rosin ﬂux), 38 Rutherford backscattering spectrum (RBS), 77, 83 S scallop, 40, 41, 43, 53, 64, 68, 93, 127, 131, 1 scallop-type morphology, 131 Seeman-Bohlin x-ray diﬀractometer, 74, 92 silicide, 82, 129 single-phase growth, 82, 129 SIP (system-in-packaging), 29 size distribution function, 141, 148 Sn whisker, 16, 153 SOP (system-on-packaging), 29 SOC (system-on-chip), 29 solder ﬁnish, 153 solder-less joint, 31 solder bumping, 114 solder cap, 39

SVNY339-Tu

368

March 2, 2007

20:27

Subject Index

solder fountain, 10 Soret eﬀect, 119, 327, 343 spalling, 17, 93, 100, 101, 104, 117 spontaneous Sn whisker growth, 153 surface mount technology, 12, 153 stochastic behavior, 343 stochastic tendency, 286 synchrotron radiation, x-ray micro-diﬀraction, 43, 163

U ultra-low k materials, 30 under-bump metallization (UBM), 14, 60, 7 underﬁll, 1, 23, 30

T temperature gradient, 327 theory of non-conservative ripening, 139 thermal mechanical stress, 22, 30, 124 thermal mismatch, 2 thermomigration, 25, 327 thermomigration in eutectic two-phase alloy, 329, 343 thermomigration in SnPb solder, 335 thermomigration, fundamentals, 338 thin-ﬁlm under-bump-metalligation, 111 time-dependent melting, 270 torque, 237, 320 two level packaging, 14

W wear-out failure of electromigration, 232 wetting angle, 38, 40, 49, 50 wetting reaction, 2, 3, 38 wetting reaction as a function of SnPb composition, 48 wetting tip, 43, 105 Wiedemann-Franz law, 271 wire bonding, 9, 12

V v-groove, 105, 289, 306 very-large-scale-integration (VLSI), 12, 211

X x-ray micro-diﬀraction, 229 Y Young’s equation, 49 Z zincated Al surface, 188

SVNY339-Tu

March 3, 2007

8:18

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 30 Process Technology for Semiconductor Lasers Crystal Growth and Microprocesses By K. Iga and S. Kinoshita 31 Nanostructures and Quantum Effects By H. Sakaki and H. Noge 32 Nitride Semiconductors and Devices By H. Morkoc¸ 33 Supercarbon Synthesis, Properties and Applications Editors: S. Yoshimura and R. P. H. Chang 34 Computational Materials Design Editor: T. Saito 35 Macromolecular Science and Engineering New Aspects Editor: Y. Tanabe 36 Ceramics Mechanical Properties, Failure Behaviour, Materials Selection By D. Munz and T. Fett 37 Technology and Applications of Amorphous Silicon Editor: R. A. Street 38 Fullerene Polymers and Fullerene Polymer Composites Editors: P. C. Eklund and A. M. Rao 39 Semiconducting Silicides Editor: V. E. Borisenko 40 Reference Materials in Analytical Chemistry A Guide for Selection and Use Editor: A. Zschunke 41 Organic Electronic Materials Conjugated Polymers and Low Molecular Weight Organic Solids Editors: R. Farchioni and G. Grosso 42 Raman Scattering in Materials Science Editors: W. H. Weber and R. Merlin

43 The Atomistic Nature of Crystal Growth By B. Mutaftschiev 44 Thermodynamic Basis of Crystal Growth P–T–X Phase Equilibrium and Non-Stoichiometry By J. Greenberg 45 Thermoelectrics Basic Principles and New Materials Developments By G. S. Nolas, J. Sharp, and H. J. Goldsmid 46 Fundamental Aspects of Silicon Oxidation Editor: Y. J. Chabal 47 Disorder and Order in Strongly Nonstoichiometric Compounds Transition Metal Carbides, Nitrides and Oxides By A. I. Gusev, A. A. Rempel, and A. J. Magerl 48 The Glass Transition Relaxation Dynamics in Liquids and Disordered Materials By E. Donth 49 Alkali Halides A Handbook of Physical Properties By D. B. Sirdeshmukh, L. Sirdeshmukh, and K. G. Subhadra 50 High-Resolution Imaging and Spectrometry of Materials Editors: F. Ernst and M. R¨uhle 51 Point Defects in Semiconductors and Insulators Determination of Atomic and Electronic Structure from Paramagnetic Hyperfine Interactions By J.-M. Spaeth and H. Overhof 52 Polymer Films with Embedded Metal Nanoparticles By A. Heilmann

SVNY339-Tu

March 3, 2007

8:18

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 53 Nanocrystalline Ceramics Synthesis and Structure By M. Winterer

65 Transport Processes in Ion-Irradiated Polymers By D. Fink

54 Electronic Structure and Magnetism of Complex Materials Editors: D.J. Singh and D. A. Papaconstantopoulos

66 Multiphased Ceramic Materials Processing and Potential Editors: W.-H. Tuan and J.-K. Guo

55 Quasicrystals An Introduction to Structure, Physical Properties and Applications Editors: J.-B. Suck, M. Schreiber, and P.H¨aussler 56 SiO2 in Si Microdevices By M. Itsumi 57 Radiation Effects in Advanced Semiconductor Materials and Devices By C. Claeys and E. Simoen 58 Functional Thin Films and Functional Materials New Concepts and Technologies Editor: D. Shi 59 Dielectric Properties of Porous Media By S.O. Gladkov 60 Organic Photovoltaics Concepts and Realization Editors: C. Brabec, V. Dyakonov, J. Parisi and N. Sariciftci 61 Fatigue in Ferroelectric Ceramics and Related Issues By D.C. Lupascu 62 Epitaxy Physical Principles and Technical Implementation By M.A. Herman, W. Richter, and H. Sitter 63 Fundamentals of Ion-Irradiated Polymers By D. Fink 64 Morphology Control of Materials and Nanoparticles Advanced Materials Processing and Characterization Editors: Y. Waseda and A. Muramatsu

67 Nondestructive Materials Characterization With Applications to Aerospace Materials Editors: N.G.H. Meyendorf, P.B. Nagy, and S.I. Rokhlin 68 Diffraction Analysis of the Microstructure of Materials Editors: E.J. Mittemeijer and P. Scardi 69 Chemical–Mechanical Planarization of Semiconductor Materials Editor: M.R. Oliver 70 Applications of the Isotopic Effect in Solids By V.G. Plekhanov 71 Dissipative Phenomena in Condensed Matter Some Applications By S. Dattagupta and S. Puri 72 Predictive Simulation of Semiconductor Processing Status and Challenges Editors: J. Dabrowski and E.R. Weber 73 SiC Power Materials Devices and Applications Editor: Z.C. Feng 74 Plastic Deformation in Nanocrystalline Materials By M.Yu. Gutkin and I.A. Ovid'ko 75 Wafer Bonding Applications and Technology Editors: M. Alexe and U. G¨osele 76 Spirally Anisotropic Composites By G.E. Freger, V.N. Kestelman, and D.G. Freger 77 Impurities Confined in Quantum Structures By P.O. Holtz and Q.X. Zhao

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

Photonic Crystal Fibers: Properties and Applications (Springer Series in Materials Science) (Springer Series in Materials Science)

Photonic Crystal Fibers: Properties and Applications (Springer Series in Materials Science) (Springer Series in Materials Science)

Photonic Crystal Fibers: Properties and Applications (Springer Series in Materials Science) (Springer Series in Materials Science)

Photonic Crystal Fibers: Properties and Applications (Springer Series in Materials Science) (Springer Series in Materials Science)

Photonic Crystal Fibers: Properties and Applications (Springer Series in Materials Science) (Springer Series in Materials Science)

Solder joint reliability

Atomistic Properties of Solids (Springer Series in Materials Science)

Polarons in Advanced Materials (Springer Series in Materials Science)

Polarons in Advanced Materials (Springer Series in Materials Science)

Atomistic Properties of Solids (Springer Series in Materials Science)

Spectroscopic Properties of Rare Earths in Optical Materials (Springer Series in Materials Science, Volume 83)

Spectroscopic Properties of Rare Earths in Optical Materials (Springer Series in Materials Science, Volume 83)

Solder Joint Reliability Prediction for Multiple Environments

Micro- and Macro-Properties of Solids: Thermal, Mechanical and Dielectric Properties (Springer Series in Materials Science)

Micro- and Macro-Properties of Solids: Thermal, Mechanical and Dielectric Properties (Springer Series in Materials Science)

Computational Materials Science: The Simulation of Materials Microstructures and Properties

Aerospace Materials (Graduate Student Series in Materials Science and Engineering)

Magnetism and Structure in Functional Materials (Springer Series in Materials Science)

Radiation Effects in Advanced Semiconductor Materials and Devices (Springer Series in Materials Science)

Crystal Growth Technology (Springer Series in Materials Processing)

Magnetism and Structure in Functional Materials (Springer Series in Materials Science)

Materials Science and Technology, vol. 10 - Nuclear Materials

Photovoltaic Materials (Series on Properties of Semiconductor Materials Vol 1)

Gallium Nitride Electronics (Springer Series in Materials Science)

Microstructuring of Glasses (Springer Series in Materials Science)

Laser Precision Microfabrication (Springer Series in Materials Science)

Electronic Properties of Engineering Materials (Mit Series in Materials Science and Engineering)

Electroceramics: Materials, Properties, Applications

Electronic properties of materials

Laser-Surface Interactions for New Materials Production: Tailoring Structure and Properties (Springer Series in Materials Science, 130)

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

Photonic Crystal Fibers: Properties and Applications (Springer Series in Materials Science) (Springer Series in Materials Science)

Photonic Crystal Fibers: Properties and Applications (Springer Series in Materials Science) (Springer Series in Materials Science)

Photonic Crystal Fibers: Properties and Applications (Springer Series in Materials Science) (Springer Series in Materials Science)

Photonic Crystal Fibers: Properties and Applications (Springer Series in Materials Science) (Springer Series in Materials Science)

Photonic Crystal Fibers: Properties and Applications (Springer Series in Materials Science) (Springer Series in Materials Science)

Solder joint reliability

Atomistic Properties of Solids (Springer Series in Materials Science)

Polarons in Advanced Materials (Springer Series in Materials Science)

Polarons in Advanced Materials (Springer Series in Materials Science)

Atomistic Properties of Solids (Springer Series in Materials Science)

Spectroscopic Properties of Rare Earths in Optical Materials (Springer Series in Materials Science, Volume 83)

Spectroscopic Properties of Rare Earths in Optical Materials (Springer Series in Materials Science, Volume 83)

Solder Joint Reliability Prediction for Multiple Environments

Micro- and Macro-Properties of Solids: Thermal, Mechanical and Dielectric Properties (Springer Series in Materials Science)

Micro- and Macro-Properties of Solids: Thermal, Mechanical and Dielectric Properties (Springer Series in Materials Science)

Computational Materials Science: The Simulation of Materials Microstructures and Properties

Aerospace Materials (Graduate Student Series in Materials Science and Engineering)

Magnetism and Structure in Functional Materials (Springer Series in Materials Science)

Radiation Effects in Advanced Semiconductor Materials and Devices (Springer Series in Materials Science)

Crystal Growth Technology (Springer Series in Materials Processing)

Magnetism and Structure in Functional Materials (Springer Series in Materials Science)

Materials Science and Technology, vol. 10 - Nuclear Materials

Photovoltaic Materials (Series on Properties of Semiconductor Materials Vol 1)

Gallium Nitride Electronics (Springer Series in Materials Science)

Microstructuring of Glasses (Springer Series in Materials Science)

Laser Precision Microfabrication (Springer Series in Materials Science)

Electronic Properties of Engineering Materials (Mit Series in Materials Science and Engineering)

Electroceramics: Materials, Properties, Applications

Electronic properties of materials

Laser-Surface Interactions for New Materials Production: Tailoring Structure and Properties (Springer Series in Materials Science, 130)

Recommend Documents