UCLA-Materials Science Electronic Thin Film Lab at UCLA



King-Ning Tu and Andriy M. Gusak, "Kinetics in Nanoscale Materials," 296 pages, Wiley, New York, 2014. ISBN: 978-0-470-88140-8.

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King-Ning Tu,"Electronic Thin-Film Reliability", 396 pages, published by Cambridge University Press in 2010, ISBN 978-0-521-51613-6.

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Thin films are widely used in the electronic device industry. As the trend for miniaturization of electronic devices moves into the nanoscale domain, the reliability of thin films becomes an increasing concern. Building on the author¡¯s previous book, ¡°Electronic Thin Film Science¡± by Tu, Mayer, and Feldman, and based on a graduate course at UCLA given by the author, this new book focuses on reliability science and the processing of thin films. Early chapters address fundamental topics in thin-film processes and reliability, including deposition, surface energy, and atomic diffusion, before moving on to explain irreversible processes in interconnect and packaging technologies systematically (Chapter 10). Describing electromigration, thermomigration, and stress-migration, with a closing chapter dedicated to failure analysis, linking statistical and physical examinations (Chapter 15), the reader will come away with a complete theoretical and practical understanding of electronic thin-film reliability. Kept mathematically simple, with real-world examples, this book is ideal for graduate students, researchers, and practitioners.

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Table of Contents:.

Electronic Thin Film Reliability

K. N. Tu

Dept. of Materials Science and Engineering University of California at Los Angeles Los Angeles, CA 90095-1595

Chapter 1 Thin Film Applications to Microelectronic Technology

    1.1 Introduction

    1.2 Metal-oxide-semiconductor field-effect-transistor (MOSFET) devices

      1.2.1 Self-aligned silicide contact and gate

    1.3 Thin film under-bump-metallization in flip chip technology

    1.4 Why do we seldom encounter reliability failure in our computers?

    1.5 Trend and transition from micro to nano electronic technology

    1.6 Impact of the end of Moore¡¯s law on microelectronics

Chapter 2 Thin Film Deposition

    2.1 Introduction

    2.1 Introduction

    2.2 Flux equation in thin film deposition

    2.3 Thin film deposition rate

    2.4 Ideal gas law

    2.5 Kinetic energy of gas molecules

    2.6 Equilibrium flux on a free surface

    2.7 Effect of ultra-high-vacuum on purity of the deposited film

    2.8 Frequency of collision of gas molecules

    2.9 Boltzmann¡¯s velocity distribution function and ideal gas law

    2.10 Maxwell¡¯s velocity distribution function and kinetic energy of gas molecules

    2.11 Parameters of deposition that affect nucleation and growth of thin films

Chapter 3 Surface Energy in Thin Films

    3.1 Introduction

    3.2 Definition of surface energy, binding energy, and bonding energy

    3.3 Interatomic potential energy ¨C Lennard-Jones pair potential

    3.4 Short range interaction and quasi-chemical assumption

    3.5 Relationship between binding energy and latent heat

    3.6 Surface energy and surface tension

    3.7 Liquid surface energy measured by capillary effect

    3.8 Solid surface energy measured by zero creep

    3.9 Surface energy systematic

    3.10 Magnitude of surface energies

      3.10.1 Thermodynamic approach

      3.10.2 Mechanical approach

      3.10.3 Atomic approach

    3.11 Surface crystallography

      3.11.1 Atoms on a Surface

      3.11.2 Crystallographic notation

      3.11.3 Crystal directions and planes

Chapter 4 Atomic Diffusion in Crystalline Solids

    4.1 Introduction

    4.2 Jump frequency and diffusional flux

    4.3 Fick¡¯s first law (Flux equation)

    4.4 Diffusivity

    4.5 Fick¡¯s second law (Continuity equation)

      4.5.1 Derivation of continuity equation

    4.6 A solutions of the diffusion equation in tracer diffusion

    4.7 Diffusion coefficient

    4.8 Calculation of diffusion coefficient

    4.9 Parameters in diffusion coefficient

      4.9.1 Atomic vibration frequency

      4.9.2 Activation enthalpy

      4.9.3 Pre-exponential factor

Chapter 5 Applications of Diffusion Equation

    5.1 Introduction

    5.2 Applications of Fick¡¯s first law (flux equation)

      5.2.1 Zener¡¯s growth model of a planar precipitate

      5.2.2 Kidson¡¯s analysis of planar growth in layered thin films

    5.3 Applications of Fick¡¯s second law (diffusion equation)

      5.3.1 Effect of diffusion on composition homogenization Homogenization in a periodic structure

      5.3.2 Interdiffusion in a bulk diffusion couple Darken¡¯s analysis of Kirkendall shift and marker motion Boltzmann and Matano¡¯s analysis of interdiffusion Kirkendall (Frenkel) void formation without lattice shift Interdiffusion coefficient

    5.4 Analysis of growth of a solid precipitate

      5.4.1 Ham¡¯s model of growth of a large spherical precipitate

      5.4.2 Mean field consideration

      5.4.3 Growth of a spherical nanoparticle by ripening

Chapter 6 Elastic Stress and Strain in Thin Films

    6.1 Introduction

    6.2 Elastic stress-strain relationship

    6.3 Strain energy

    6.4 Biaxial stress in thin films

    6.5 Stoney¡¯s equation of biaxial stress in thin films

    6.6 Measurement of thermal stress in Al thin films

    6.7 Application of Stoney¡¯s equation to thermal expansion measurement

    6.8 Anharmonicity and thermal expansion

    6.9 The origin of intrinsic stress in thin films

    6.10 Elastic energy of a misfit dislocation

Chapter 7 Surface Kinetic Processes on Thin Films

    7.1 Introduction

    7.2 Adatoms on a surface

    7.3 Equilibrium vapor pressure above a flat surface

    7.4 Surface diffusion

    7.5 Step mediated growth in homoepitaxy

    7.6 Deposition and growth of an amorphous thin film

    7.7 Growth modes of homoepitaxy

    7.8 Homogeneous nucleation of a surface disc

    7.9 Mass transport on patterned surfaces

      7.9.1 Early stage of diffusion on a patterned surface

      7.9.2 Later stage of diffusion on a patterned surface

    7.10 Ripening of a hemispherical particle on a surface

Chapter 8 Interdiffusion and Reaction in Thin Films

    8.1 Introduction

    8.2 Silicide formation

      8.2.1 Sequential Ni silicide formation

      8.2.2 First phase in silicide formation

    8.3 Kinetics of interfacial-reaction-controlled growth in thin film reactions

    8.4 Kinetics of competitive growth of two layered phases

    8.5 Marker analysis in intermetallic compound formation

    8.6 Reaction of mono-layer of metal on Si

Chapter 9 Grain Boundary Diffusion

    9.1 Introduction

    9.2 Comparison between grain boundary diffusion and lattice diffusion

    9.3 Fisher¡¯s analysis of grain boundary diffusion

    9.4 Whipple¡¯s analysis of grain boundary diffusion

    9.5 Diffusion in small angle grain boundaries

    9.6 Diffusion induced grain boundary migration

Chapter 10 Irreversible Processes in Interconnect and Packaging Technology

    10.1 Introduction

    10.2 Flux equations

    10.3 Entropy production

      10.3.1 Heat conduction

      10.3.2 Atomic diffusion

      10.3.3 Electrical conduction

    10.4 Conjugate forces when temperature is a variable

      10.4.1 Atomic diffusion

      10.4.2 Electrical conduction

    10.5 Joule heating

    10.6 Electromigration, thermomigration, and stress-migration

    10.7 Irreversible processes in electromigration

      10.7.1 Electromigration and creep in Al strips

    10.8 Irreversible processes in thermomigration

      10.8.1 Thermomigration in unpowered flip chip solder joints

    10.9 Irreversible processes in thermo-electric effects

      10.9.1 Thomson effect and Seebeck effect

      10.9.2 Peltier effect

Chapter 11 Electromigration in Metals

    11.1 Introduction

    11.2 Ohm¡¯s law

    11.3 Electromigration in metallic interconnects

    11.4 Electron wind force of electromgiration

    11.5 Calculation of the effective charge number

    11.6 Effect of back stress and measurement of critical length, critical product, and effective charge number

    11.7 Why is there a back stress in electromigration?

    11.8 Measurement of the back stress induced by electromigration

    11.9 Current crowding

    11.10 Current density gradient force of electromigration

    11.11 Electromigration in anisotropic conductor

    11.12 Electromigration of a grain boundary in anisotropic conductor

    11.13 AC electromigration

Chapter 12 Electromigration induced failure in Al and Cu Interconnects

    12.1 Introduction

    12.2 Electromigration induced failure due to atomic flux divergence

    12.3 Electromigration induced failure due to electric current crowding

    12.3.1 Void formation in the low current density region

    12.4 Electromigration induced failure in Al interconnects

      12.4.1 Effect of microstructure in Al on Electromigration

      12.4.2 Wear-out failure mode in multi-layered Al lines and W vias

      12.4.3 Solute effect of Cu on electromigration in Al

      12.4.4 Mean-time-to-failure in Al interconnects

    12.5 Electromigration induced failure in Cu interconnects

      12.5.1 Effect of microstructure on electromigration

      12.5.2 Effect of solute on electromigration

      12.5.3 Effect of stress on electromigration

      12.5.4 Effect of nano-twins on electromigration

Chapter 13 Thermomigration

    13.1 Introduction

    13.2 Thermomigration in flip chip solder joints of SnPb

      13.2.1 Thermomigration in un-powered composite SnPb solder joints

      13.2.2 In-situ observation of thermomigration

      13.2.3 Random states of phase separation in eutectic two-phase structures

      13.2.4 Thermomigration in un-powered eutectic SnPb solder joints

    13.3 Analysis of thermomigration

      13.3.1 Driving force of thermomigration

      13.3.2 Thermomigration in eutectic two-phase microstructures

    13.4 Thermomigration under DC or AC stressing in flip chip solder joints

    13.5 Thermomigration in Pb-free flip chip solder joints

    13.6 Thermomigration and creep in Pb-free flip chip solder joints

Chapter 14 Stress Migration in Thin Films

    14.1 Introduction

    14.2 Chemical potential in a stressed solid

    14.3 Diffusion creep (Nabarro-Herring equation)

    14.4 Void growth in Al interconnects driven by tensile stress

    14.5 Whisker growth in Sn/Cu thin films driven by compressive stress

      14.5.1 Morphology of spontaneous Sn whisker growth

      14.5.2 Stress generation (Driving force) in Sn whisker growth

      14.5.3 Effect of surface Sn oxide on stress gradient generation

      14.5.4 Measurement of stress distribution by synchrotron radiation micro-diffraction

      14.5.5 Stress relaxation by creep: Broken oxide model in Sn whisker growth

Chapter 15 Reliability Science and Analysis

    15.1 Introduction

    15.2 Constant volume and non-constant volume processes

    15.3 Effect of lattice shift on divergence of mass flux in irreversible processes

      15.3.1 Initial distribution of current density, temperature, and chemical potential in a device structure before operation

      15.3.2 Change of the distributions during device operation

      15.3.3 Effect of lattice shift on divergence of mass flux

    15.4 Physical analysis of electromigration failure in flip chip solder joints

      15.4.1 Distribution of current density in a pair of joints

      15.4.2 Distribution of temperature in a pair of joints

      15.4.3 Effect of current crowding on pancake-type void growth

    15.5 Statistical analysis of electromigration failure in flip chip solder joints

      15.5.1 Time to failure and Weibull distribution

      15.5.2 To calculate the parameters in Black¡¯s equation of MTTF

      15.5.3 Modification of Black¡¯s equation for flip chip solder joints

      15.5.4 Weibull distribution function and JMA equation of phase transformations

      15.5.5 Physical analysis of statistical distribution of failure

    15.6 Simulation

Appendix A: A brief review of thermodynamic Functions
Appendix B: Defect concentration in solids
Appendix C: Step-by-step derivation of Huntington¡¯s electron wind force
Appendix D: Elastic constants tables and conversions
Appendix E: Terrace size distribution in Si MBE
Appendix F: Interdiffusion coefficient

King-Ning Tu, "Solder Joint Technology: Materials, properties, and reliability", 368 pages, Springer, 2007. ISBN - 13: 978-0-387-38890-8.

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The trend in consumer electronic products will be more and more wireless, portable, and handheld. To manufacture these multi-functional products, high-density circuit interconnections between a Si chip and its substrate are needed. The demand of flip chip solder joint technology is growing rapidly, in which an area array of solder bumps is used to join a chip to its substrate. 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 concern of toxicity of Pb-based solders, European Union Parliament has a directive to ban the use of Pb-based solders in consumer products on July 1st, 2006. The application of Pb-free solder joints to a wide range of devices is urgent, so the R&D of Pb-free solders for electronic manufacturing is very active at the moment. While solder joint technology is mature, Pb-free solder technology is not, hence their reliability has to be assured. 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 a joint 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 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.

The contents of the book are divided into two parts. Part I, from Chapter 2 to 7, covers copper-tin reactions, and Part II, from Chapter 8 to 12, covers electromigration and thermomigration of solder joints.

Chapter 1 is an overview of flip chip technology. Why it is important and what are the known reliability problems are explained. The future trend in electronic packaging technology and its effect on solder joint technology is given. Chapter 2 is about 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 is about Cu-Sn 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 is on 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 is about 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 what is different 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 is about 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 given. Chapter 10 is about 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 is about 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 addressed

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 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, Chih Chen, Cheng-Yi Liu, Woo-Jin Choi, Hua Gan, Albert T. Wu, Emily Shengquan Ou, Minyu Yan, Fei Ren, Jong-ook Suh, Annie Huang, and Tiffany Fanyi Ouyang are acknowledged. Also included are the work of several post-docs (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 would like to acknowledge the generous support and to thank these students and post-docs. 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 stepping stone 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 Appendix, 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. I would like to acknowledge that the last 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 on the kinetic analyses presented in this book, for example, irreversible processes. Also I am grateful to Dr. Yuhuan Xu at UCLA and Prof. Yiping Wu at Huazhong University of Science and Technology, China, for helpful comments on drop test in Chapter 11. I would like to thank Prof. Chih Chen, National Chiao Tung University, Hsinchu, Taiwan, ROC and Prof. Cheng-Yi Liu, National Central University, Chungli, Taiwan, ROC, for a critical review of the book, and to Mr. Jong-ook Suh at UCLA for preparation of all the figures and Miss Fanyi Ouyang for revision corrections. Finally, I would like to thank Prof. Y. C. Chan of the Department of Electrical Engineering, City University of Hong Kong, and Prof. 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.

King-Ning Tu, June 2006

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Table of Contents:.

Solder Joint Technology: Materials, Properties, and Reliability

K. N. Tu

Dept. of Materials Science and Engineering University of California at Los Angeles Los Angeles, CA 90095-1595

Chapter 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 whisker

      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 non-equilibrium thermodynamics

    1.5 Future trends in electronic packaging technology

      1.5.1 The trend of miniaturization

      1.5.2 The trend of packaging integration evolution ¡V SIP, SOP, and SOC

      1.5.3 Chip-packaging interaction

      1.5.4 Solder-less joints

Part I Copper-tin Reactions

Chapter 2 Copper-tin reaction in bulk samples

    2.1 Introduction

    2.2 Wetting reaction of eutectic SnPb on Cu foils

      2.2.1 Crystallographic relationship between Cu6Sn5 scallop and Cu

      2.2.2 Rate of consumption of Cu in wetting 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 Sn-Pb-Cu phase diagram at various temperatures

      2.5.2 5Sn95Pb/Cu reaction at 350 ¢XC

    2.6 Solid state reaction of eutectic SnPb on Cu foils

      2.6.1 Formation of Cu3Sn and Kirkendall voids

    2.7 Comparison between wetting reactions and solid state reactions

      2.7.1 Morphology of wetting reaction and solid state reactions

      2.7.2 Kinetics of wetting reaction and solid state reaction

      2.7.3 Reaction controlled by rate of Gibbs free energy change

    2.8 Wetting reaction of Pb-free eutectic solders on thick Cu UBM

Chapter 3 Copper-tin reaction 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 Cu6Sn5 and Cu3Sn

      3.2.3 Copper is the dominant diffusing species

      3.2.4 Kinetic analysis of sequential formation of Cu6Sn5 and Cu3Sn

      3.2.5 Atomistic model of interfacial-reaction-limited 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 film

    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

    3.7 Spalling in eutectic SnAgCu solder on Cu/Ni(V)/Al thin film

    3.8 Enhanced spalling due to interaction across a solder joint

    3.9 Wetting tip reaction on thin film coated V-grooves

Chapter 4 Copper-tin reaction in flip chip solder joints

    4.1 Introduction

    4.2 Processing a flip chip 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 alloy

    4.7 Thermal stress due to chip-to-packaging interaction

    4.8 Design and materials selection of a flip chip solder joint

Chapter 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 of growth of mono-size hemispheres

    5.4 Theory of non-conservative ripening with a constant surface area

    5.5 Size distribution of scallops

      5.5.1 Dependence of Cu6Sn5 morphology on solder composition

      5.5.2 Size distribution and average radius of scallops

    5.6 Nano channels between scallops

Chapter 6 Spontaneous tin whisker growth: Mechanism and prevention

    6.1 Introduction

    6.2 Morphology of spontaneous Sn whisker growth

    6.3 Stress generation (driving force) in Sn whisker growth by Cu-Sn reaction

    6.4 Effect of surface Sn oxide on stress generation and whisker growth

    6.5 Measurement of stress 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

Chapter 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)6Sn5 vs. (Ni, Cu)3Sn4

      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

Part II Electromigration and Thermomigration

Chapter 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

    8.6 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

    8.11 Electromigration of a grain boundary in anisotropic conductor

    8.12 AC electromigration

Chapter 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-indentions

      9.4.4 Mean-time-to-failure of eutectic flip chip solder joints

      9.4.5 Kinetic analysis of pancake-type void growth along the contact interface

      9.4.6 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

    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 a two-phase structure

Chapter 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 (Section 2.8)

      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

    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

Chapter 11 Ductile¡Vto-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 To convert a mini Charpy machine to perform drop test

      11.6.1 Dropping of a chip size package horizontally in mini Charpy machine

      11.6.2 Dropping of a chip size package vertically in mini Charpy machine

    11.7 Creep and electromigration

Chapter 12 Thermomigration

    12.1 Introduction

    12.2 Thermomigration in flip chip solder joints

      12.2.1 Thermomigration on un-powered solder joints

      12.2.2 In-situ observation of thermomigration

      12.2.3 Random states of phase separation in eutectic two-phase structures

    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 Thermomigration in eutectic two-phase mixture

    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

Appendix A: Diffusivity of vacancy mechanism of diffusion in solids
Appendix B: Growth and ripening equations of precipitates
Appendix C: Derivation of Huntington¡¦s electron wind force

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