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Klaus-Werner Benz and Wolfgang Neumann Introduction to Crystal Growth and Characterization Related Titles Herlach, D. M., Matson, D. M. (eds.) Capper, P., Rudolph, P. (eds.) Solidification of Containerless Crystal Growth Technology Undercooled Melts Semiconductors and Dielectrics 2012 2010 Print ISBN: 978-3-527-33122-2, Print ISBN: 978-3-527-32593-1, also available in digital formats also available in digital formats Nikrityuk, P.A. Zolotoyabko, E. Computational Thermo-Fluid Basic Concepts of Dynamics Crystallography In Materials Science and Engineering 2011 2011 Print ISBN: 978-3-527-33009-6 Print ISBN: 978-3-527-33101-7, also available in digital formats Duffar, T. (ed.) Crystal Growth Processes Based on Capillarity Czochralski, Floating Zone, Shaping and Crucible Techniques 2010 Print ISBN: 978-0-470-71244-3, also available in digital formats Klaus-Werner Benz and Wolfgang Neumann Introduction to Crystal Growth and Characterization With a contribution by Anna Mogilatenko The Authors All books published by Wiley-VCH are carefully produced. Nevertheless, authors, Prof. Dr. Klaus-Werner Benz editors, and publisher do not warrant the Freiburger Materialforschungszentrum information contained in these books, (FMF), Albert-Ludwigs-Universität including this book, to be free of errors. Freiburg Readers are advised to keep in mind that Stefan-Meier-Str. 21 statements, data, illustrations, procedural 79104 Freiburg details or other items may inadvertently Germany be inaccurate. Prof. Dr. Wolfgang Neumann Library of Congress Card No.: applied for Humboldt-UniversitätzuBerlin Institut fürPhysik British Library Cataloguing-in-Publication Newtonstr. 15 Data 12489 Berlin A catalogue record for this book is avail- Germany able from the British Library. Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed biblio- graphic data are available on the Internet at <http://dnb.d-nb.de>. © 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Boschstr. 12, 69469 Weinheim, Germany All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language with- out written permission from the publish- ers. Registered names, trademarks, etc. used in this book, even when not specif- ically marked as such, are not to be con- sidered unprotected by law. Print ISBN: 978-3-527-31840-7 ePDF ISBN: 978-3-527-68436-6 ePub ISBN: 978-3-527-68434-2 Mobi ISBN: 978-3-527-68435-9 oBook ISBN: P-010-18947-1 Cover-Design Adam-Design, Weinheim, Germany Typesetting Laserwords Private Limited, Chennai, India Printing and Binding Markono Print Media Pte Ltd., Singapore Printed on acid-free paper V Contents Preface IX Acknowledgments XIII 1 Fundamentals of Crystalline Materials 1 1.1 Crystalline State 1 1.2 Fundamentals of Geometrical Crystallography 12 1.2.1 Crystal Lattices 12 1.2.2 Crystal Axes Systems, Crystal Systems, and Crystal Families 14 1.2.3 Crystal Faces and Zones 15 1.2.4 Indexing in the Hexagonal Crystal Family 24 1.3 Morphological Symmetry of Crystals 25 1.3.1 Crystallographic Point Groups 40 1.3.2 Some Basic Facts of Group Theory 52 1.4 Structural Symmetry 60 1.4.1 Crystal Lattices, Motifs, and Crystal Structures 60 1.4.1.1 Bravais Lattices 61 1.4.1.2 The Reciprocal Lattice 62 1.4.1.3 Lattice Transformations 68 1.4.2 Crystallographic Space Groups 71 1.4.2.1 General Remarks 72 1.4.2.2 The International Tables for Crystallography – The Reference Book for the Representation of Space Group Symmetries 76 1.4.2.3 Mathematical Description of the Space Group Symmetry 93 1.4.3 Generalized Crystallographic Symmetry 101 1.5 Crystal Structures 104 1.5.1 Sphere Packings 108 1.5.2 Selected Examples of Inorganic Structure Types 112 1.5.2.1 Polymorphism and Polytypism 124 1.5.3 Selected Examples of Molecular Crystals 126 1.5.4 Symmetry Relations between Crystal Structures 145 VI Contents 1.6 Crystallographic Databases and Crystallographic Computer Programs 152 Appendix: Supplementary Material S1 Special Crystal Forms of Cubic Crystal Classes 159 References 164 2 Basics of Growth Mechanism and Solidification 171 2.1 Nucleation Processes 171 2.1.1 Homogeneous Nucleation 175 2.1.2 Heterogeneous Nucleation 177 2.1.3 Metastable Zone Regime 179 2.1.4 Equilibrium Shape of Crystals 180 2.2 Kinetic Processes and Growth Mechanism 182 2.2.1 Molecular Kinetic Theory of Crystal Growth 183 2.2.2 Interfaces and Roughening of Surfaces 185 2.2.3 Vapor–Liquid–Solid (VLS) Mechanism 189 2.2.4 Crystal Growth from Ambient Phases on Rough Surfaces: Vapor Phase, Solution, and Melt Media 190 2.2.5 Crystal Growth on Flat Surfaces 193 2.3 Phase Diagrams and Principles of Segregation 195 2.3.1 Phase Diagrams with a Continuous Miscibility in the Solid and Liquid Phases 196 2.3.2 Segregation and Segregation Coefficients 201 2.3.3 Constitutional Supercooling and Morphological Stability 212 2.4 Principles of Flow Regimes in Growth Melts 214 2.4.1 Buoyancy Convection 215 2.4.2 Marangoni Convection 216 References 218 3 Growth Techniques in Correlation with Related Growth Mechanism 221 3.1 Overview on Main Growth Techniques 221 3.2 Principles of Melt Growth Techniques 224 3.2.1 The Czochralski Crystal Growth Process 224 3.2.2 Growth Method after Bridgman 234 3.2.3 The Float Zone Crystal Growth Process 244 3.2.4 Bulk Crystal Growth from Metallic Solutions 253 3.2.4.1 Traveling Solvent Method (TSM) 253 3.2.4.2 Traveling Heater Method (THM) 255 3.2.4.3 The Solute, Synthesis, Diffusion Method (SSD) 259 3.3 Bulk Crystal Growth of II–VI Compounds from the Vapor 260 3.3.1 Crystal Growth of CdTe by a Sublimation Traveling Heater Method, STHM, in Closed Ampoules 262 3.3.2 Crystal Growth of CdTe by the Markov Method in Semiclosed Ampoules 264 Contents VII 3.4 Epitaxial Growth Techniques 267 3.4.1 Liquid Phase Epitaxy (LPE) 270 3.4.2 Vapor Phase Epitaxy (VPE) 279 3.5 Supplementary Material: Principles of Verneuil Technique, Growth from High and Low Temperature, Nonmetallic Solutions 295 3.5.1 Verneuil Technique 295 3.5.2 Growth from High Temperature Solutions (Flux Growth) 295 3.5.3 Growth from Low Temperature Solutions (Aqueous Solutions) 296 References 298 4 Characterization of Crystals 301 4.1 Crystal Defects 302 4.1.1 Zero-Dimensional Defects 303 4.1.2 One-Dimensional Defects 314 4.1.3 Two-Dimensional Defects (Planar Defects) 326 4.1.3.1 Grain Boundaries 328 4.1.3.2 Stacking Faults 336 4.1.3.3 Antiphase Boundaries 340 4.1.3.4 Twins 342 4.1.3.5 Domain Boundaries 355 4.1.3.6 Crystal Surfaces 363 4.1.4 Three-Dimensional defects 368 4.1.4.1 Inclusions 369 4.1.4.2 Precipitates 370 4.1.4.3 Voids 374 4.2 Crystal Quality 375 4.2.1 Criteria of Crystal Quality 376 4.2.2 Crystal Quality and Application 378 4.3 Selected Methods of Crystal Characterization 382 4.3.1 Etching of Crystals 382 4.3.2 X-Ray Topography 383 4.3.3 Electron Microscopy 385 4.3.3.1 Scanning Electron Microscopy 387 4.3.3.2 Transmission Electron Microscopy 388 4.4 Materials Engineering by Correlation of Crystal Growth and Characterization 392 Anna Mogilatenko 4.4.1 Epitaxial Growth of GaN on LiAlO2 Substrates 393 References 408 Index 415 IX Preface Crystalline materials play an important role both in science and industry in the development of modern materials such as semiconductors for electronic devices, solar cells, and lasers. New fields of application require a consequent improvement of crystal quality, which is covered with a thorough understanding of the basics of crystal growth and characterization. The main aim of this book, therefore, is to provide an introduction to Crys- tal Growth where the fundamentals of both the crystallization processes and the various growth procedures of technical importance will be treated in detail. Fur- thermore, selected methods for the characterization of the grown crystals as well as their properties will be discussed. The actual question may arise: Is it really necessary to have a new book on crystal growth when numerous books already exist in the market describing the basics and thermodynamics of crystal growth and the growth technologies? Our longstanding experience as academic teachers in the fields of crystallog- raphy and crystal growth has shown us that the majority of students whom we have taught in more than two decades had sufficient knowledge either in crystal- lography or in crystal growth technology. For the students and their subsequent activities in materials science, it would be much more advantageous and effective to have knowledge in both fields of study. With this textbook, our idea is to provide a compendium where the basics of crystallography as well as crystal growth will be outlined in a unified manner. We have carefully chosen the content of this textbook in such a way that students of natural sciences, materials science, and technology should all be equally inter- ested in this subject. The state-of-the-art content should also be useful for crystal growers, material science researchers and engineers, solid state physicists, and crystallographers. This book will give a description about the fundamentals on an actual basis of crystals, their growth and production technologies. The crystal properties strongly depend on their real structure. Therefore, the characterization of the grown crystals by various methods will be outlined. Furthermore, the different steps from growth to characterization and description of material properties will be discussed on selected examples.