Table Of ContentH A N D B O OK OF CRYSTAL GROWTH
Volume 1: FUNDAMENTALS
A: T h e r m o d y n a m i cs a nd Kinetics
B: Transport a nd Stability
Volume 2: BULK CRYSTAL GROWTH
A: Basic Techniques
B: Growth M e c h a n i s ms a nd D3niamics
Volume 3: THIN FILMS A ND EPITAXY
A: Basic Techniques
B: Growth Mechanisms a nd D5niamics
NORTH-HOLLAND
Amsterdam - London - New York - Tokyo
HANDBOOK OF CRYSTAL GROWTH 1
FUNDAMENTALS
Part A: Thermodynamics and Kinetics
Edited by
D.T.J. Hurle
H.H. Wills Physics Laboratory
University ofBnstol
Bristol, UKBSSm
i
1993
NORTH-HOLLAND
Amsterdam - London - New York - Tokyo
ELSEVIER SCIENCE PUBUSHERS
Sara Burgerhartstraat 25
P.O. Box 211,1000 AE Amsterdam, The Netherlands
Library of Congress Cataloging-in-Publication Data
Handbook of crystal growth / edited by D.T.J. Hurle,
cm.
Includes bibliographical references and index.
ISBN 0-444-88908-6
1. Crystals-<;rowth. L Hurle, D.T.J.
(ÍD921.H32 1993
548' .5-dc20 93-7317
CIP
The beautiful natural snowflake on the front cover was photographed by Yoshinori Furukawa on
Mt. Asahidake in Japan. The adjacant vertical strip is from a transmission electron micrograph
taken by Tony Cullis of an In-implanted Si layer exhibiting cellular microsegregation produced by
pulsed laser reciystallisation from the melt. The two images were chosen to reflect the natural and
man-made aspects of crystal growth respectively.
ISBN: 0 444 88908 6 (Part A and B)
0 444 89933 2 (Series)
© 1993 Elsevier Science Publishers B.V. All rights reserved.
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PREFACE
The study of crystals and their growth has a long history, which Hans Scheel charts in
his introductory chapter to this volume. The growth of single crystals for commercial
application is more recent, of course, with the work of Verneuil at the turn of the
century representing a milestone. But the major importance which the field enjoys
today owes most to the development of solid state electronics in the post-war period.
This growing importance has been recorded through the ICCG conferences or
ganised by the International Organisation for Crystal Growth formed at the time of
the first ICCG in 1966. Professor Sunagawa has recently stated: "Before the organisa
tion of ICCG, crystal growth was regarded as a minor or subsidiary field, which was
allowed to live at the mercy of other fields of science." During the ensuing quarter of
a century, much has changed; crystal growth has developed from a largely academic
subject to one of the key disciplines in materials science. It is now represented
worldwide by no less than fourteen national associations affiliated to lOCG. The
ability to produce high-quality single crystals and epitaxial layers is, and is likely to
remain, the key to progress in electronics. The control of yield and crystal form
underpins many industrial crystallisation processes. The growth of protein single
crystals for X-ray structure determination poses new challenges. In short, the areas in
which the control of crystal growth is paramount are expanding steadily.
Indeed, the subdiscipline of crystal growth has truly come of age. But whilst
numerous reviews of the state of the art-in particular, on growth technologies and on
the growth of particular materials - appear regularly in the hterature, the field has,
hitherto, lacked a comprehensive and definitive work of reference on its underlying
science. This Handbook seeks to fill that gap.
The field of crystal growth can be classified by technique or by material; both are
equally valid. Crystal growth is both a commercial technology and art and a science.
But the state of that technology and art moves rapidly and needs to be reviewed
regularly, material by material; such reviews are periodically to be found in the
proceedings of specialist international conferences. The science, on the other hand,
develops more slowly and, unlike the technology, is not frequently supplanted by the
new. I hope that the reader will, therefore, understand the reasons for structuring the
Handbook in the way that it has been done, devoting this, the first, volume to the
fundamentals of the subject of potential relevance to the development and utilisation
of ah techniques and ah materials. The subsequent two volumes are classified by
techniques and cover bulk crystal growth, and thin films and epitaxy, respectively.
Specific materials are not considered as such, with the exception of protein crystals in
Volume II and diamond films in Volume III.
The objective has been to expose the underlying scientific basis of the subject in
a most authoritative way possible, by soliciting contributed chapters from recognised
international authorities on their subjects. By focusing on the underlying principles, it
is hoped that this Handbook will help to keep theory and practice in touch with each
χ Preface
Other. Each chapter stands alone, but the chapters are ordered to provide a progres
sion through the principal topics.
I am profoundly honoured to have had the opportunity to edit this work and owe
a considerable debt of gratitude to ah the authors. Pressures at work and diminished
job security have become more evident throughout the world in recent years, thus
increasing the difficulty and the commitment required to undertake a major addi
tional task such as that involved in writing a chapter for this Handbook. Almost ah of
the authors I approached agreed to contribute, making the Handbook, I believe,
an outstandingly authoritative work. In commissioning the work, I sought authors on
the basis of their knowledge of and expertise in their particular fields and on their
abihty to contribute within the imposed timeframe, but not on their nationahty,
seniority or other considerations.
No handbook can be exhaustive. Inevitably, the selection reflects the editor's
background to some degree and I can only apologise for the omission of topics which
readers would have wished to have been included.
I am particularly grateful to Sir Charles Frank, who celebrated his eightieth
birthday last year, for agreeing to contribute a foreword to this Handbook. His
reminiscences bring alive our heritage in this field, to which he himself has contributed
so much. He urges us not to neglect to read those pioneering works written, as he
puts it, "when the facts were sparser and treated as all the more precious". It is to be
hoped that this Handbook wih also prove to be a valuable guide to the earlier
literature.
This first volume, after a historical introduction, starts with the thermodynamic
aspects of phase equilibria, point defects and nucleation. This is followed by kinetic
and crystallographic aspects, including computer simulation by molecular dynamics
and Monte Carlo methods.
The remainder of the volume is devoted to bulk transport effects and the influence
of transport-limited growth on the stability of both isolated growth forms (such as the
dendrite) and arrays and on the co-operative effects involved in determining the
configurations of such dissipative structures.
I have been pleased to note that there is, between most of the chapters, that very
small degree of overlap which is vital to enable the reader to put each topic in the
context of the overall field. This, I believe, makes the value of the volume more than
the sum of its parts, superbly authoritative as they are.
Don Hurle
May 1992
FOREWORD
Merely to scan the chapter headings of this handbook is enough to show how much
work has been required to fulfil the growth potential its subject already had when
I was first brought into it about 46 years ago. I had joined Neville Mott's solid state
physics group at Bristol at the end of 1946, anxious to return to basic science after six
years of application of my science to mihtary matters. It was much the same case with
ah of us. Speciahties of Mott's group were crystal point defects and crystal dis
locations. I knew something of the former from before the war, and I began to learn
something about the dislocations from my colleagues. I think I had not considered
crystal growth before, but two of my desk-neighbours in Mott's group were Nicolas
Cabrera, working with Mott on the theory of surface oxidation of metals, a kind of
crystal growth, and Keith Burton, seconded by his employer, ICI, explicitly to work
with Mott on the theory of crystal growth. My pre-war German friend Karl Wirtz had
sent me, as a post-war present, Volmer's Kinetik der Phasenbildung, published during
the war. Mott said to me, "You have that Volmer book, and can read German: how
about giving us three or four seminars about it?" I did that, presenting as faithfuhy as
I could the gospel according to Volmer. For the crystal growth problem. Burton was
able to put numerical estimates into Volmer's algebraic expressions, and did so after
one of my seminars, enabling us to say that 10^^^^ was the largest factor of discrep
ancy between theory and experiment which had ever been called agreement. That
made me realize that we had to take seriously what I had previously said almost as
a joke, that the presence of dislocations in crystals could overthrow the basis of the
theory of crystal growth, layer by layer, as it existed until then. The concept and
interpretation of growth spirals on crystal surfaces, and Burton and Cabrera's recog
nition of a surface roughening temperature, below which these features should play an
essential role, followed quickly after that. Stranski, still considered one of the leaders
in crystal growth theory and experiment at that time, took a httle while to be
persuaded. But it was his former colleague Kaischew who later on produced what is
still the best quantitative verification of the theory (and also of Zeldovitch's surface
nucleation theory), from studies of electrolytic deposition of silver. We Bristolians
were particularly pleased to present sceptical metahurgists with visual evidence of the
reahty of dislocations.
During the next decade or two, it would be generahy accepted that dislocations are
present in almost all crystals, and play an essential role in their growth. I would have
said that, and I would have been wrong. The most numerous crystals produced
annually on Earth are surely snow crystals, and they are mostly dislocation-free. For
the most important industrial production of single crystals, the great demand was for
a dislocation-free product. Either Bruce Chalmers or I would explain why a lower
dislocation content could be obtained by slower growth. Then somebody producing
single crystal silicon for the electronics industry (Bhl Dash) ignored all that and
said "Pull hke hell", obtained a very different condition at the growth surface, and
produced virtuahy dislocation-free crystals. Both these examples must involve growth
xii Foreword
by surface nucleation (the first, certainly, and I fancy the second also), the theory of
which still deserves some further development.
This last remark carries the implication that while the student of the subject should
acquaint himself with the current state-of-the-art knowledge about it, and it is the
endeavour of this book to enable him to do that, he should not lose sight of the fact
that last words are yet to come: he stih has the prospects of adding to the sum of
human wisdom about it. And in seeking last words, he can be advised to pay some
attention to first words, to mix in with his reading of up-to-the-minute knowledge, as
in this book, some occasional reading of much earlier work. Those who first entered
the field saw facts of observation, or points of theory, which they found difficult to
understand: difficulties which may have been glossed over, or circumvented, in later
work, but which remain real nevertheless. There are passages in Willard Gibbs' great
paper on heterogeneous equilibria where he seems to be making unnecessary difficul
ties for himself, over points which later writers were able to omit. Until one tackles for
oneself problems which are related but sufficiently different not to be solved by slavish
copying of the textbook, one does not appreciate Gibbs' perception of where particu
lar care is needed.
When starting the study of crystal growth, I acquired phenomenological knowl
edge, among other sources, from Robert Mehl's English translation (1925) of Gustav
Tamman's States of Aggregation. I was wrong not to go back to Tamman's earlier
book Kristallisieren und Schmelzen (1903). I wrongly assumed that the sequel would
incorporate everything of importance in the earlier work. I have only very recently
learnt from Professor Keller that unusual pressure-temperature phase diagrams can
occur for crystallizing polymers and their melts (polymers can have several different
mutually frustrating kinds of disorder because of the complexity of their molecular
structure), which were discussed as thermodynamic possibilities in Tamman's earlier
book but are omitted from later literature because no examples were known.
Make sure that this compendium of present knowledge is in your departmental
library, but do not allow pioneering earlier works, written when the facts were sparser
and treated as all the more precious, to be transferred to some inaccessible store, or,
worse still, disposed of, just because they are fifty or more years old.
Sir Charles Frank
CONTENTS OF V O L U ME 1
Preface
Foreword
Sir Charles Frank
Part A. Thermodynamics and Kinetics
1. Historical introduction 1
HJ. Scheel
2. Phase equihbria 43
R.F. Brebrick
3. Defect thermodynamics and phase diagrams in compound crystal
growth processes 103
H. Wenzl W.A. Oates and K. Mika
4. Nucleation theory 187
B. Mutaftschiev
5. The structure of supersaturated solutions 249
.4.5. Myerson and A.F. Izmailov
6. Crystal growth mechanisms 307
J.P. van der Eerden
1. Growth and morphology of crystals: Integration of theories of
roughening and Hartman-Perdok theory 477
P. Bennema
8. Atomic-scale models of crystal growth 583
G.H. Gilmer
9. Low-energy ion/surface interactions during crystal growth from the
vapor phase: Effects on nucleation and growth, defect creation and
annihilation, microstructure evolution and synthesis of
metastable phases 639
J.E. Greene
Part B. Transport and Stability
10. Description of transport processes 683
A.A. Wheeler
11. Bulk models of solidification 741
H.E. Huppert
12. Morphological stability 785
S.R. Coriell and G.B. McFadden
13. Effects of flow on morphological stability 859
S.H. Davis
xiv Contents of Volume 1
14. Pattern formation in crystal growth 899
B. Billia and R. Trevedi
15. The dendrite 1075
M.E. Glicksman and S.P. Marsh
16. Kinetics of electrocrystalhsation 1123
P. Ramasamy
Subject Index 1207
CHAPTER 1
Historical Introduction
Hans J. SCHEEL
Crystal Growth Group, Institute of Micro- and Optoelectronics, Swiss Federal Institute of Technology,
CH-1007 Lausanne, Switzerland
Contents
Introduction 3
1. Crystallization phenomena in ancient technologies 3
2. Empirical experiences with crystallization phenomena in the Middle Ages 6
3. Presentiments about crystals and their formation from the age of enlightenment
to the 19th century 9
4. Development of crystal growth science and technology in the 20th century 18
4.1. The role of the crystal structure 19
4.2. Progress in understanding crystal growth phenomena 22
4.3. Development of techniques for growth of crystals and layers 26
5. Outlook 37
References 39
HANDBOOK OF CRYSTAL GROWTH, VOL. 1
edited by D.T.J. Hurle
© 1993 Elsevier Science Publishers B.V. All rights reserved
