Herlach, D. M., Matson, D. M. (eds.)

Solidification of Containerless Undercooled Melts

2012

Print ISBN: 978-3-527-33122-2, also available in digital formats

Nikrityuk, P. A.

Computational Thermo-Fluid Dynamics

In Materials Science and Engineering

2011

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

Capper, P., Rudolph, P. (eds.)

Crystal Growth Technology

Semiconductors and Dielectrics

2010

Print ISBN: 978-3-527-32593-1, also available in digital formats

Zolotoyabko, E.

Basic Concepts of Crystallography

2011

Print ISBN: 978-3-527-33009-6

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 Crystal Growth where the fundamentals of both the crystallization processes and the various growth procedures of technical importance will be treated in detail. Furthermore, 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 crystallography 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 crystallography 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 interested 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.

The content of the book is divided into the following four chapters:

• Fundamentals of crystalline materials
• Basics of growth mechanisms and solidification
• Growth techniques in correlation with related growth mechanisms
• Characterization of crystals.

The chapter “Fundamentals of crystalline materials” begins with the definition of the crystalline state where the various stages of order from the ideal periodic arrangement to the topological disorder are described in detail. Thus, the different types of periodic as well as aperiodic crystals are considered. In addition, the possible transitional stages between crystals and liquids are briefly mentioned. In order to get a thorough understanding of the morphological symmetry of crystals, the fundamentals of symmetry operations necessary for the treatment of the polyhedral shape are described. Within this framework, terms such as crystal coordinate systems, crystal faces, and zones are defined. In order to represent the three-dimensional crystal in the two-dimensional space the commonly used crystal projection, the stereographic projection will be illustrated. To show the correspondence between the morphological and structural symmetry, the lattice concept in crystal space and Fourier-space is explained.

After a phenomenological treatment of symmetry, the fundamentals of group theory for the description of point groups and space groups are comprehensively discussed. The reader will be familiarized with the application of crystallographic point and space groups for the explanation of morphology and structure of periodic crystals, respectively. The extension of the symmetry concept (crystallography in higher dimensions, black-white symmetry) will be considered briefly. Furthermore, the usage of the “International Tables for Crystallography” as the important among reference books in the various branches of crystallography will also be demonstrated particularly for the description of crystal structures.

The various possibilities for the classification of structures (structure types according to the Strukturbericht designation, Pearson symbol, geometric and analytical descriptors) will be introduced. Selected examples of inorganic and organic crystal structures will be described in detail.

Chapter 2 “Basics of growth mechanism and solidification” describes the fundamentals of nucleation processes, the kinetics, and main growth mechanisms. The basic equations for homogeneous and heterogeneous nucleation are derived. Furthermore, the importance of the Oswald-Miers-Regime as a function of supersaturation with respect to the equilibrium shape of crystals is represented. The kinetic processes of crystal growth from vapor phase, solution, and melt media are illustrated. A special point of interest is the role of interfaces for the morphology of surfaces formed. In order to get a thorough understanding of the growth mechanism phase, diagrams with continuous miscibility in the solid and liquid phases are treated in detail. The various aspects of segregation of dopants and residual impurities on a macro- and microscale for the growth process and growth mechanism are discussed. The influence of the different types of convection regimes in the nutrients on growth and segregation numerically given by specific dimensionless numbers is outlined. The methods that are mainly applied for growing crystals are comprehensively treated in Chapter 3 “Growth techniques in correlation with related growth mechanism.” Numerous modern materials are grown from melt and metallic solutions. The Czochralski and the Bridgman methods, as the most versatile melt growth techniques for semiconducting materials, are described in detail. Specific crystals may be grown only by means of the containerless Float Zone Technique. The role of external fields (magnetic fields, microgravity) as an additional tool to improve the crystal quality via flow control within the melt is described for different semiconductor materials. Possibilities and limitations for the methods of bulk crystal growth from metallic solutions are described for a selection of III–V and II–VI semiconductors. Crystal growth experiments using the Traveling Heater Method (THM) under earth and microgravity conditions are compared. The specific mechanisms of THM are outlined and illustrated by concrete examples for the growth of InP and GaSb. The advantages of bulk crystal growth methods from the vapor phase for high quality crystals are explained in detail for CdTe and related II–VI compounds. Nowadays, growth processes of epitaxial films are of great importance for innovative industrial applications such as LEDs and detectors. Therefore, an elaboration of terms and concepts of Liquid Phase Epitaxy (LPE), Vapor Phase Epitaxy (VPE), and Molecular Beam Epitaxy (MBE) is given. Fundamental chemical reactions and growth processes are discussed and illustrated for the III–V semiconductors InP an GaSb.

Chapter 4 “Crystal characterization” outlines under which criteria the grown crystals have to be evaluated. The defect analysis is an essential part of the evaluation of crystals. The main characteristics of following structural defects classified according to their dimensionality are described in detail:

• Zero-dimensional defects
  1. – point defects
• One-dimensional defects
  1. – dislocations
• Two-dimensional defects
  1. – grain boundaries, stacking faults, antiphase boundaries, twins, domain boundaries, crystal surfaces
• Three-dimensional defects
  1. – inclusions, precipitates, voids.

The essential crystal features that mainly determine the quality of a crystal are outlined. The correlation between crystal quality and field of application is discussed for diamond and protein crystals.

Among the numerous characterization techniques of crystals, the methods of selective etching, X-ray topography, and electron microscopy play a specific role, particularly for defect analysis. The fundamentals of those methods are briefly discussed. The possibilities and limitations for the defect analysis are illustrated by selected examples. Finally, the correlation between crystal growth, characterization, and the feedback to the growth process for improving the crystal quality (defect engineering) is illustrated for the case study of epitaxial growth of GaN on LiAlO₂ substrates.

We are grateful to many friends, colleagues, our former PhD students, post-docs, and co-workers who contributed with their research to the growth and characterization of crystal, which are discussed in this book.

In particular, we are very thankful to Dr. I. Häusler and F. Krahl for their tremendous support with preparing the drawings and figures. We gratefully acknowledge the revision of the language of selected parts of this book by Prof. P. Moeck, a German-British applied crystallographer.

KWB is thankful to former colleagues of the Semiconductor Crystal Growth Laboratory (4. Physical Institute, University of Stuttgart) for an excellent cooperation in the time period 1974–1986: in particular, Prof. M. Pilkuhn as head of the institute; Profs G. Baumann and F. Scholz; and Drs H. Eisele, H. Haspeklo, W. Jakowetz, W. Koerber, R. Linnebach, G. Nagel, N. Stath, and Th. Voigt. Several common publications have been an important guide to this book. Thanks also to Prof. J. Weidlein and Drs G. Laube and H. Renz of the Anorganic Institute, University of Stuttgart, for their interdisciplinary cooperation (MOVPE with metal organic adducts).

The cooperation and helpful discussions with active and former members of the Crystallographic Institute and the Freiburg Materials Research Center, FMF, of the Albert-Ludwigs-Universität, Freiburg, is gratefully acknowledged. Special thanks to Profs A. Croell, M. Fiederle, and P. Dold, as well as to Drs V. Babentsov, A. Danilewsky, A. Fauler, Th. Kaiser, M. Laasch, N. Salk, and P. Sickinger for supplying scientific results and figures.

Some of the TEM experiments and results discussed in this book were carried out in the Institute of Solid State Physics and Electron Microscopy of the Academy of Sciences in Halle (Saale) and since 1992 in the newly founded Max Planck Institute of Microstructure Physics (at the same place). For the excellent working conditions in these institutes, WN would like to thank the late Prof. H. Bethge, Prof. V. Schmidt, Prof. J. Heydenreich, his PhD supervisor at Halle, and the late Prof. U. Gösele. WN is indebted to his former colleagues Drs H.-Chr. Gerstengarbe, H. Hofmeister, and K. Scheerschmidt for collaborative results, which will be discussed to some extent in this book.

For valuable discussions and contributions of joint research carried out at the Humboldt University in Berlin, WN is grateful to Drs I. Häusler, I. Hähnert, A. Mogilatenko, Th. Höche, H. Kirmse, the late U. Richter, Private Docent R. Schneider, and Ch. Zheng.

WN appreciates very much the opportunity of having worked together with his colleague and friend Prof. R. Köhler at the Humboldt University, Berlin. RK and WN taught together courses on “Real Structure of Solids” and “Methods of Materials Characterization” over more than a decade. WN wants to thank RK for his permission to reproduce some figures of his part of the joint lecture manuscripts in this book.

We are grateful to the following colleagues for granting permission to reproduce figures from their work or to use their computer programs for generating figures:

1. Prof. W. Kaminsky (Figures 1.98, 1.99, S1.1–S1.10 program: WinXMorph),
2. Dr. R. Scholz (Figure 4.24), Prof. N.D. Browning (Figure 4.27), Prof. D. Hesse (Figure 4.32),
3. Prof. K. Hermann (Figures 4.52, 4.53, program: Surface explorer), Dr. K.W. Keller (Figure 4.54), Dr. M. Schmidbauer (Figure 4.59).

K.W. Benz

W. Neumann