Gupta D. (Ed.). Diffusion Processes in Advanced Technological Materials
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5.3.2 Interdiffusion Between Two or More
Materials in Contact ....................................................... 246
5.3.3 Role of Material Properties ............................................ 248
5.4 Diffusion Barrier Materials ..................................................... 260
5.4.1 Metal Nitrides, Carbides, and Borides as APDB
Used with Al .................................................................. 260
5.4.2 Barriers Between the ILD and Cu ................................. 262
5.5 New Concepts in Affecting APDB Behavior at
the Interfaces ............................................................................ 269
5.5.1 Alloying of Cu to Form an APDB at
Interfaces/Surfaces ......................................................... 269
5.5.2 Self-Assembled Molecular Monolayers ........................ 270
5.5.3 Zero-Flux Diffusion Zones (Multicomponent
Diffusion Effects) ........................................................... 272
5.6 Brief Discussion of an APDB for Low-k ILD Materials ........ 275
5.7 Summary .................................................................................. 277
References ....................................................................................... 278
6 Reactive Phase Formation: Some Theory
and Applications ........................................................................... 283
6.1 Introduction .............................................................................. 283
6.2 Theoretical Considerations ....................................................... 284
6.2.1 One Phase Growing, Diffusion Controlled .................... 284
6.2.2 Two Phases Growing Simultaneously,
Diffusion Controlled ...................................................... 287
6.2.3 Linear Parabolic Kinetics, One-Phase Growth,
Oxides, Equilibrium, Plotting of Data ........................... 290
6.2.4 Linear-Parabolic Kinetics: Sequential Phase
Growth, Grain Boundary Versus Lattice Diffusion ...... 292
6.2.5 First Phase Formed ........................................................ 294
6.2.6 Nucleation of the First or Second Phases ...................... 294
6.2.7 Nucleation-Controlled Reactions and Consequences:
Sequence of Phase Formation, Bulk Samples, Stresses .... 301
6.2.8 Amorphous and Other Metastable Phases,
Quasicrystals, Ternary Systems ..................................... 304
6.2.9 Other Effects: Grain Boundaries and Impurities,
Diffusion Coefficients Varying with Composition ........ 307
6.3 Practical Problems in Electronic Technology .......................... 309
6.3.1 Titanium Disilicide, Activation Energy for the
Motion of the Interface Between the C49 and
C54 Phases, Nucleation of the C49 Structure ............... 310
6.3.2 Cobalt Disilicide, Entropy of Mixing, (Possible) Enthalpy
and Density-of-State Effects in Ternary Reactions .......... 317
6.3.3 Nickel Monosilicide ....................................................... 323
xCONTENTS
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CONTENTS xi
6.4 Conclusions .............................................................................. 324
Acknowledgments .......................................................................... 326
References ....................................................................................... 327
7 Metal Diffusion in Polymers and on Polymer Surfaces ............ 333
7.1 Introduction .............................................................................. 333
7.2 Diffusion During Nucleation and Growth of
Metal Films on Polymers ......................................................... 336
7.3 Metal-Polymer Interaction ....................................................... 341
7.4 Diffusion in the Polymer Bulk ................................................ 342
7.5 Summary and Conclusions ...................................................... 358
Acknowledgments .......................................................................... 359
References ....................................................................................... 359
8 Measurement of Stresses in Thin Films and
Their Relaxation ........................................................................... 365
8.1 Introduction .............................................................................. 365
8.2 Measurement Techniques ........................................................ 368
8.2.1 Substrate Curvature ........................................................ 370
8.2.2 X-Ray Diffraction .......................................................... 373
8.3 Stress Relaxation ..................................................................... 378
8.3.1 Experimental Observations ............................................ 378
8.3.2 Dislocation Plasticity ..................................................... 381
8.3.3 Diffusional Creep ........................................................... 393
8.4 Conclusion ............................................................................... 398
References ....................................................................................... 400
9 Electromigration in Cu Thin Films ............................................ 405
9.1 Introduction .............................................................................. 405
9.2 Cu Interconnection Integration ................................................ 407
9.3 Test Structure and Experiment ................................................ 409
9.4 Microstructure .......................................................................... 411
9.5 Theory ...................................................................................... 414
9.5.1 Drift Velocity ................................................................. 414
9.5.2 Diffusivity ...................................................................... 415
9.5.3 Effective Diffusivity and Microstructure ....................... 416
9.5.4 Electromigration-Induced Backflow .............................. 418
9.5.5 Partial Blocking Boundary ............................................ 419
9.6 Resistance and Void Growth .................................................... 419
9.7 Fast Diffusion Paths ................................................................. 422
9.7.1 Free Surface and Grain Boundary Diffusion ................. 422
9.7.2 Ambient Effect ............................................................... 427
9.7.3 Alloying Effect .............................................................. 428
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9.8 Lifetime Distribution ........................................................... 433
9.8.1 Single-Damascene Line on W Via ............................. 433
9.8.2 Dual-Damascene Line on W Line .............................. 435
9.9 Current Density Dependence ............................................... 453
9.10 Lifetime vs. Linewidth ........................................................ 458
9.11 Lifetime Scaling Rule .......................................................... 461
9.11.1 Single-Damascene Line ............................................ 461
9.11.2 Dual-Damascene Line .............................................. 462
9.12 Short-Length Effect ............................................................. 468
9.13 Reduced Cu Interface Diffusion .......................................... 474
9.14 Conclusion ........................................................................... 480
References ..................................................................................... 482
10 Diffusion in Some Perovskites: HTSC Cuprates and
a Piezoelectric Ceramic .............................................................. 489
10.1 Introduction .......................................................................... 489
10.2 Cation Diffusion .................................................................. 491
10.2.1 Characteristics of YBCO Bulk and
Thin-Film Specimens .............................................. 491
10.2.2 Diffusion and Interactions Between YBCO Thin
Films and Substrates ................................................ 493
10.2.3 Self-Diffusion of the Constituent Cations
(Y, Ba, and Cu) of YBCO ....................................... 498
10.2.4 Diffusion of Cation Impurities in YBCO ................ 503
10.3 Anion Diffusion in Several HTSC Cuprates ....................... 509
10.3.1 Oxygen Diffusion Data in HTSC Cuprates ............. 510
10.3.2 Comparison Between Cation and Anion Diffusion 513
10.4 Grain Boundary Diffusion and Solute Segregation
Effects in Perovskites .......................................................... 514
10.4.1 Grain Boundary Self-Diffusion of Nonsegregating
Cations in the YBa
2
Cu
3
O
7x
Superconductor .......... 515
10.4.2 Grain Boundary Diffusion of a Segregating Cation
in the YBa
2
Cu
3
O
7x
Superconductor and a
Piezoelectric Ceramic .............................................. 520
10.4.3 Grain Boundary Diffusion of Oxygen in the
YBa
2
Cu
3
O
7x
Superconductor ................................. 522
10.5 Summary .............................................................................. 524
Acknowledgments ........................................................................ 524
References ..................................................................................... 525
Index.................................................................................................... 529
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Contributors
Sergiy Divinski, professor at the Institut für Materialphysik, Universität
Münster, received his Ph.D. from the Institute for Physics of Metals, Kiev,
Ukraine in 1990. He received an Alexander-von-Humboldt Fellowship in
1998 and the Werner-Köster Award in 2002. His research interests are
bulk and grain boundary diffusion in intermatallic compounds, metals and
nanocrystalline materials. He has authored/co-authored numerous journal
publications.
François M. d’Heurle, an emeritus research staff member at the IBM
Thomas J. Watson Research Center in Yorktown Heights, New York,
received his Ph.D. from the Illinois Institute of Technology, Chicago, in
1958. His research interests are thin film electromigration, solid-state
reactions, and silicide formation. He has received awards from IEEE,
AVS, AIP, TMS, and IBM, and Doctor honoris causa from the Royal
Institute of Technology, Sweden.
Franz Faupel, Professor of Multicomponent Materials at the University
of Kiel, Germany, received his Ph.D. from the University of Göttingen
in 1985. His research interests include diffusion and reactions in metal-
polymer interfaces, organic thin films, and crystalline solids and amor-
phous metallic alloys. He is Chairman of the Metal Physics Division of
the German Physical Society and Associate Editor of the Journal of
Materials Research. He has published more than 140 research papers.
Huajian Gao, a director at the Max Planck Institute for Metals Research
in Stuttgart, Germany, received his Ph.D. from Harvard University in
1988. He is a member of the scientific advisory board of the Institutes for
Mechanics and Metals Research of the Chinese Academy of Sciences. His
research interests include the mechanics of thin films and of biological
and bio-inspired materials. He has received ASME and Guggenheim fel-
lowships and awards from the National Science Foundation, IBM, and
ALCOA. He has published more than 100 papers.
Patrick Gas, Vice Director of the Provence Laboratory for Materials and
Microelectronics, Marseille, received his Ph.D. in materials science and
his Doctorat ès Sciences from the University of Aix-Marseille in 1975 and
1982, respectively. His research interests are the thermodynamic and
kinetic aspects of solid-state reactions and diffusion in microelectronic
materials. He has authored or co-authored more than 100 publications.
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Lynne M. Gignac, a senior engineer at the IBM Watson Research Center,
obtained her Ph.D. in materials science and engineering from the
University of Arizona in 1988. Her research interests include analytical
and microstructural characterization of microelectronic materials via elec-
tron and focused ion beam microscopy and general reliability of Si to sub-
strate interconnections.
Devendra Gupta, an emeritus research staff member at the IBM Watson
Research Center, received his Ph.D. from the University of Illinois,
Urbana-Champaign, in 1961, under Prof. D. Lazarus. His research inter-
ests include diffusion, mass transport, and defects in solids and thin films
for microelectronic applications. A fellow of the American Physical
Society, he has written more than 100 articles and edited six books in the
field of diffusion.
Christian Herzig, an emeritus professor at the Institut für
Materialphysik, Universität Münster, received his Ph.D. from the
University of Münster in 1968. His research interests include diffusion,
lattice dynamics, and defects in intermetallic compounds and interfaces.
He received the Gustav Tammann Memorial Award in 1982 and the
Werner-Köster Award in 2002.
Chao-Kun Hu, a research staff member in the Materials and Reliability
Sciences Department at the IBM Watson Research Center, received his
Ph.D. in physics from Brandeis University in 1979. He has written several
book chapters and more than 130 papers.
Yoshiaki Iijima, a professor at Tohoku University, Japan, received his
Doctor of Engineering degree from Tohoku University in 1983. His
research interests are hydrogen diffusion and storage in materials.
Michael Kiene, an engineer at Advanced Micro Devices in Austin, Texas,
and Dresden, Germany, received his Ph.D. in 1997 under Prof. Franz
Faupel at the University of Kiel. His research interests are the microstruc-
ture and chemistry of metal-polyimide interfaces.
Oliver Kraft, a director at the Institute for Materials Research at the
Forschungszentrum Karlsruhe, Germany, and Professor of Reliability in
Mechanical Engineering at the University of Karlsruhe, received his
Ph.D. from the University of Stuttgart in 1995. His research interests
range from advanced structural materials to thin film systems related to
the reliability of microelectronic and MEMS devices.
xiv CONTRIBUTORS
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xv CONTRIBUTORS
Christian Lavoie, a research staff member at the IBM Watson Research
Center, received his Ph.D. from the University of British Columbia in
1995. He has written or co-authored more than 90 scientific publications
and holds 20 patents.
Radhey S. Mehrotra, Head of the Fast Reactor Fuels Section at the
Bhabha Atomic Research Center, Trombay-Mumbai, India, received his
Ph.D. from the Indian Institute of Technology, Mumbai, in 1990. His
research and development activities are in the area of ceramic-based
nuclear fuel systems.
Yuri Mishin, Professor of Materials Science at George Mason University,
Fairfax, Virginia, received his Ph.D. from the Moscow Institute of Steel
and Alloys in 1985. His research interests are atomistic modeling and
computer simulation of diffusion processes and interfaces.
Shyam P. Murarka, an emeritus professor at Rensselaer Polytechnic
Institute, received his Ph.D. in chemistry from Agra University, India, and
his Ph.D. in metallurgy and materials science from the University of
Minnesota in 1970. His research interests are diffusion and defects in met-
als, oxides/insulators, and semiconductors, and thin film metallization.
Jean Philibert, an emeritus professor at the Université de Paris-Sud,
Orsay, received his Docteur ès Sciences from the University of Paris in
1955. His research interests are structural transformations, electron probe
microanalysis, diffusion, and plasticity. He has edited or written seven
books and 190 publications. He has received the Grande Médalle Henry
Le Chatelier (Société Francaise de Métallurgie), Presidential Award of the
Microbeam Analysis Society, and Gold Medal from Acta Metallurgica; he
is a member of the Academa Europea.
Robert Rosenberg, Manager of the Materials and Reliability Sciences
Department at the IBM Watson Research Center, received his Ph.D. from
New York University in 1962. He is a charter member of the IBM
Academy of Technology. His research interests are degradation mecha-
nisms, reliability of metallic conductor films, and metal-dielectric inte-
gration issues. He has published more than 70 papers and edited seven
treatises in related fields.
Thomas Strunskus, a member of the research group of Prof. C. Wöll at
Ruhr-University, Bochum, received his Ph.D. in physical chemistry from
the University of Heidelberg in 1988, working with Prof. M. Grunzein.
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His research interests are the vapor deposition of polyimide and formation
of metal/polymer interfaces.
Axel Thran, a staff scientist at Philips Research in Hamburg, Germany,
received his Ph.D. from the University of Göttingen. He has conducted
research on diffusion of metals and gases in polymers, working in the
group of Dr. Franz Faupel at the University of Kiel.
Gyanendra P. Tiwari, a senior scientist in the Department of Atomic
Energy, Board of Research in Nuclear Sciences at the Bhabha Atomic
Research Center, Trombay-Mumbai, received his Ph.D. from Banaras
Hindu University, Varanasi, India, in 1971. His research interests include
diffusion in solids, inert gas behavior in solids, hydrogen embrittlement of
steels, and characterization of powders.
Vladimir Zaporojtchenko, currently working in the group of Prof. Franz
Faupel at the University of Kiel, received his Ph.D. in physics under Prof.
V.L. Ginzburg at the Academy of Science of the USSR in 1975. His
research interests include growth of thin metal films on polymer, metal-
polymer interfaces, and novel metal-polymer nanocomposites. He has
published more than 100 research papers.
xvi CONTRIBUTORS
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Preface
My 12-year-old granddaughter Nina Alesi once asked me, “Grandpa,
you are a scientist at IBM, so what do you do?”
I tried to reply, “Oh, I watch atoms move…”
But before I could finish this sentence, my 7-year-old grandson
Vinnie interjected, “Grandpa, do atoms play soccer?”
This book is about the games atoms play in diffusion and various
other properties of materials. While diffusion has been studied for more
than 100 years in solids, its importance, excitement, and intellectual chal-
lenges remain undiminished with time. It is central to understanding the
relationship between the structure and properties of naturally occurring
and synthetic materials, which is at the root of current technological
development and innovations. The diversity of material has led to spec-
tacular progress in functional inorganics, polymers, granular materials,
photonics, complex oxides, metallic glasses, quasi-crystals, and strongly
correlated electronic materials. The integrity of complex materials pack-
ages is determined by diffusion, a highly interactive and synergic phe-
nomenon that interrelates to the microstructure, the microchemistry, and
the superimposed physical fields. While the various physico-chemical
properties of the materials are affected by diffusion, they determine diffu-
sion itself.
This book, which is intended to document the diffusive processes
operative in advanced technological materials, has been written by pio-
neers in industry and academia. Because the field is vast, it has only been
possible to address some critical materials where systematic investiga-
tions have been conducted and reasonable understanding of the under-
lying processes has been reached. The book may be considered a sequel
to Diffusion Phenomena in Thin Films and Microelectronic Materials,
edited by Devendra Gupta and P. S. Ho, published in 1988 by Noyes
Publications.
Chapter 1 provides phenomenological examples of diffusion in bulk
solids and thin films that have a variety of atomic arrangements, such as
single crystals, poly-crystals, quasi-crystals, and noncrystalline amor-
phous solids. This is followed by discussions of relationships of solid-
state diffusion with other bulk physical properties in Chapter 2. Chapter 3
discusses atomic computer simulations of diffusion processes in elemen-
tal solids, nonstoichiometric compounds, and grain boundaries. Chapter 4
discusses bulk and grain boundary diffusion in intermetallic compounds,
which are important to super alloys for high-temperature applications.
Principles of diffusion barriers used in semiconductor devices and circuits
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xviii PREFACE
are elucidated in Chapter 5, with numerous examples. Chapter 6 is con-
cerned with the theory and applications of reactive phase formation, with
emphasis on silicides and oxide, which are so vital to the microelectron-
ics industry. In Chapter 7, metal diffusion in polymers and on polymer
surfaces is discussed, as polymers are also assuming importance in micro-
electronics applications. Chapter 8 covers the measurement of stresses in
thin films and their relaxation behavior, since the latter is also a diffusive
process. Chapter 9 delves into electromigration in Cu thin films. Copper
is currently a metallization of choice on Si chips in high-end computers.
Finally, Chapter 10 discusses diffusion of perovskites, which consist of
the newly discovered high-temperature superconducting cuprates and
some piezoelectric ceramics, used as actuators and sensors.
The contributors and I hope that this book will be useful to people in
both industry and universities who are interested in applications of diverse
materials in various combinations.
I edited and prepared the manuscripts electronically, possessing only
rudimentary knowledge of word processors. Credit for the successful
completion of the book goes to my family as a whole: my daughter Chitra
and her husband Vincent Alesi, my older son Sudhir Gupta, and my
younger son Devratna Gupta, who taught and helped me with various
computer-related skills.
It is a pleasure to thank Karen Ailor of Eugene, Oregon, a freelance
writer and editor, for reading all the manuscripts carefully and bringing
them into conformance with standard English. I am also grateful to James
Leonard of the Strategic Knowledge Group at the IBM Thomas J. Watson
Research Center in Yorktown, New York, for cheerfully providing the
needed library support.
Devendra Gupta
Yorktown Heights, NY
December 1, 2004
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1 Diffusion in Bulk Solids and Thin
Films: Some Phenomenological
Examples
Devendra Gupta
IBM T. J. Watson Research Center
Yorktown Heights, New York
1.1 Introduction
The science of diffusion had its beginnings in the early nineteenth
century, although the metal artisans of antiquity used the phenomenon to
make such objects as the Damascus swords by the cementation process
and gilded bronze and copper wares from gold amalgam. Mercury in the
amalgam was later oxidized, leaving behind a gold gilding film. John Dalton
in 1808 is usually credited as the earliest person to describe diffusion.
[1]
Thomas Graham studied the diffusion phenomenon in the 1828 to 1833
period with simple, elegant, and definitive experiments.
[2]
His major
observations were that diffusion, or spontaneous intermixing of two gases
in contact or separated by porous membranes, is effected by an inter-
change in position of indefinitely minute volumes. The mixing rate
depends on the concentration difference and is inversely proportional to
the square root of the density of the gas. Furthermore, he established that
“diffusion followed a diminishing progression – at longer intervals of time
the mixing process decreased,” and that the diffusion rates in liquids are
much slower than in gases. These concepts later became the bases for
mathematical treatment of the diffusion process.
The next major landmark in the theory of diffusion came from Adolf
Fick, a young pathologist at the University of Zürich. He was interested in
movement of water confined by membranes, a basic process of organic life
as we know it. His work titled “Über Diffusion” was published in the pres-
tigious Poggerdorf’s Annalen der Physik.
[3]
Fick’s original formulation is
still considered a basis for later modifications, notably by Albert Einstein,
[4]
on Brownian motion in liquids. Recognition of diffusion in solids had to
wait until 1896, when W. C. Roberts-Austen reported the first measurement
of Au in Pb metal.
[5]
Diffusion is now considered ubiquitous in all three
states of matter. In materials of technological interest, diffusion has assumed
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