Thierry Duffar (Hrsg.)

Crystal Growth Processes Based on Capillarity

Czochralski, Floating Zone, Shaping and Crucible Techniques
Herausgeber: Duffar, Thierry

• Gebundenes Buch

Produktbeschreibung

The demand for large, high-quality single crystals has increased rapidly as a result of the growing semiconductor and optics industry, where perfect single crystals are used as substrates or components for devices. Crystal Growth Processes Based on Capillarity covers all crystal growth techniques and explains why and how they are dependent on liquid surface phenomena, or capillarity. Each chapter addresses fundamental capillary effects, detailed experimental developments, technically important processes, and associated software. The book includes: * Basic principles of capillarity, wetting and growth angle data and detailed mathematical treatments * Shape stability in capillary crystal growth, including Verneuil and Czochralski techniques * Czochralski process dynamics and control * Floating Zone crystal growth * Shaped crystal growth of silicon and sapphire, micro-pulling down techniques * Vertical Bridgman and dewetting processes * Marangoni convection in crystal growth With over 25 years experience, Duffar brings together a good balance of theory and experimental techniques, making this a resource for all crystal growers in both research and in industry.

Produktdetails

• Verlag: John Wiley & Sons / Wiley
• 1. Auflage
• Seitenzahl: 566
• Erscheinungstermin: 21. Juni 2010
• Englisch
• Abmessung: 249mm x 173mm x 36mm
• Gewicht: 1057g
• ISBN-13: 9780470712443
• ISBN-10: 0470712449
• Artikelnr.: 27832247

Autorenporträt

Thierry Duffar is professor at Grenoble Polytechnic Institute (France) where he received his PhD in chemical engineering. Professor Duffar is a member of various scientific committees including the International Organization of Crystal Growth and the International Union of Crystallography and he was chair of the organizing committee for 14th International Conference on Crystal Growth in Grenoble in 2004. Professor Duffar is the (co)author of more than 100 publications in refereed scientific journals. His current research interests include the electromagnetic processing of materials, the effect of electromagnetic and gravity fields on crystal growth processes, studies on structural defect generation in materials and the means to control them and the elaboration of photovoltaic silicon.

Inhaltsangabe

Preface. Introduction. Acknowledgements. Nomenclature. Contributors. 1.
Basic Principles of Capillarity in Relation to Crystal Growth (Nicolas
Eustathopoulos, Béatrice Drevet, Simon Brandon and Alexander Virozub). 1.1
Definitions. 1.1.1 Characteristic Energies of Surfaces and Interfaces.
1.1.2 Capillary Pressure. 1.1.3 Surface Energy versus Surface Tension. 1.2
Contact Angles. 1.2.1 Thermodynamics. 1.2.2 Dynamics of Wetting. 1.2.3
Measurements of Contact Angle and Surface Tension by the Sessile Drop
Technique. 1.2.4 Selected Data for the Contact Angle for Systems of
Interest for Crystal Growth. 1.3 Growth Angles. 1.3.1 Theory. 1.3.2
Measurements of Growth Angles: Methods and Values. 1.3.3 Application of the
Growth Angle Condition in Simulations of Crystal Growth. 1.3.4 Summary.
Acknowledgements. References. 2. The Possibility of Shape Stability in
Capillary Crystal Growth and Practical Realization of Shaped Crystals
(Vitali A. Tatartchenko). 2.1 Crucible-Free Crystal Growth - Capillary
Shaping Techniques. 2.2 Dynamic Stability of Crystallization - the Basis of
Shaped Crystal Growth by CST. 2.2.1 Lyapunov Equations. 2.2.2 Capillary
Problem - Common Approach. 2.2.3 Equation of Crystal Dimension Change Rate.
2.2.4 Equation of Crystallization Front Displacement Rate. 2.2.5 Stability
Analysis in a System with Two Degrees of Freedom. 2.3 Stability Analysis
and Growth of Shaped Crystals by the Cz Technique. 2.3.1 Capillary Problem.
2.3.2 Temperature Distribution in the Crystal-Melt System. 2.3.3 Stability
Analysis and Shaped Crystal Growth. 2.3.4 Dynamic Stability Problem for the
Kyropoulos Technique. 2.4 Stability Analysis and Growth of Shaped Crystals
by the Verneuil Technique. 2.4.1 Principal Schemes of Growth. 2.4.2
Theoretical Investigation. 2.4.3 Practical Results of the Theoretical
Analysis. 2.4.4 Stability Analysis-Based Automation. 2.5 Stability Analysis
and Growth of Shaped Crystals by the FZ Technique. 2.6 TPS Techniques:
Capillary Shaping and Impurity Distribution. 2.6.1 Capillary Boundary
Problem for TPS. 2.6.2 Stability Analysis. 2.6.3 Experimental Tests of the
Capillary Shaping Theory Statements. 2.6.4 Impurity Distribution. 2.6.5
Definition of TPS. 2.6.6 Brief History of TPS. 2.7 Shaped Growth of Ge,
Sapphire, Si, and Metals: a Brief Presentation. 2.7.1 Ge. 2.7.2 Sapphire.
2.7.3 Si. 2.7.4 Metals and Alloys. 2.8 TPS Peculiarities. References. 3
Czochralski Process Dynamics and Control Design (Jan Winkler, Michael
Neubert, Joachim Rudolph, Ning Duanmu and Michael Gevelber). 3.1
Introduction and Motivation. 3.1.1 Overview of Cz Control Issues. 3.1.2
Diameter Control. 3.1.3 Growth Rate Control. 3.1.4 Reconstruction of
Quantities not Directly Measured. 3.1.5 Specifi c Problems for Control in
Cz Crystal Growth. 3.1.6 PID Control vs. Model-Based Control. 3.1.7
Components of a Control System. 3.1.8 Modelling in Crystal Growth Analysis
and Control. 3.2 Cz Control Approaches. 3.2.1 Proper Choice of Manipulated
Variables. 3.2.2 Feedforward Control. 3.2.3 Model-Based Analysis of the
Process. 3.2.4 Stability. 3.2.5 Model-Based Control. 3.2.6 Identification.
3.2.7 Measurement Issues and State Estimation. 3.3 Mathematical Model.
3.3.1 Hydromechanical-Geometrical Model. 3.3.2 Model of Thermal Behaviour.
3.3.3 Linear System Model Analysis. 3.4 Process Dynamics Analysis for
Control. 3.4.1 Operating Regime and Batch Implications. 3.4.2 Actuator
Performance Analysis. 3.4.3 Curved Interface. 3.4.4 Nonlinear Dynamics. 3.5
Conventional Control Design. 3.5.1 Control Based on Optical Diameter
Estimation. 3.5.2 Weight-Based Control. 3.6 Geometry-Based Nonlinear
Control Design. 3.6.1 Basic Idea. 3.6.2 Parametrization of the
Hydromechanical-Geometrical Model in Crystal Length. 3.6.3 Flatness and
Model-Based Feedback Control of the Length-Parametrized Model. 3.6.4
Control of Radius and Growth Rate. 3.7 Advanced Techniques. 3.7.1 Linear
Observer Design. 3.7.2 Nonlinear Observer Design. 3.7.3 Control Structure
Design for Batch Disturbance Rejection. References. 4 Floating Zone Crystal
Growth (Anke Lüdge, Helge Riemann, Michael Wünscher, Günter Behr, Wolfgang
Löser, Andris Muiznieks and Arne Cröll). 4.1 FZ Processes with RF Heating.
4.1.1 FZ Method for Si by RF Heating. 4.1.2 FZ Growth for Metallic Melts.
4.2 FZ Growth with Optical Heating. 4.2.1 Introduction. 4.2.2 Image
Furnaces. 4.2.3 Laser Heating. 4.2.4 FZ Growth for Oxide Melts. 4.3
Numerical Analysis of the Needle-Eye FZ Process. 4.3.1 Literature Overview.
4.3.2 Quasi-Stationary Axisymmetric Mathematical Model of the Shape of the
Molten Zone. 4.3.3 Numerical Investigation of the Influence of Growth
Parameters on the Shape of the Molten Zone. 4.3.4 Nonstationary
Axisymmetric Mathematical Model for Transient Crystal Growth Processes.
Appendix: Code for Calculating the Free Surface During a FZ Process in
Python. References. 5 Shaped Crystal Growth (Vladimir N. Kurlov, Sergei N.
Rossolenko, Nikolai V. Abrosimov and Kheirreddine Lebbou). 5.1
Introduction. 5.2 Shaped Si. 5.2.1 EFG Method. 5.2.2 Dendritic Web Growth.
5.2.3 String Ribbon. 5.2.4 Ribbon Growth on Substrate (RGS). 5.3 Sapphire
Shaped Crystal Growth. 5.3.1 EFG. 5.3.2 Variable Shaping Technique (VST).
5.3.3 Noncapillary Shaping (NCS). 5.3.4 Growth from an Element of Shape
(GES). 5.3.5 Modulation-Doped Shaped Crystal Growth Techniques. 5.3.6
Automated Control of Shaped Crystal Growth. 5.4 Shaped Crystals Grown by
the Micro-Pulling Down Technique (1/4-PD). 5.4.1 Crucible-Melt Relation
During Crystal Growth by the 1/4-PD Technique. 5.4.2 Examples of Crystals
Grown by the 1/4-PD Technique. 5.5 Conclusions. References. 6 Vertical
Bridgman Technique and Dewetting (Thierry Duffar and Lamine Sylla). 6.1
Peculiarities and Drawbacks of the Bridgman Processes. 6.1.1 Thermal
Interface Curvature. 6.1.2 Melt-Crystal-Crucible Contact Angle. 6.1.3
Crystal-Crucible Adhesion and Thermomechanical Detachment. 6.1.4 Spurious
Nucleation on Crucible Walls. 6.2 Full Encapsulation. 6.2.1 Introduction.
6.2.2 LiCl-KCl Encapsulant for Antimonides. 6.2.3 B2O3 Encapsulant. 6.2.4
Conclusion. 6.3 The Dewetting Process: a Modified VB Technique. 6.3.1
Introduction. 6.3.2 Dewetting in Microgravity. 6.3.3 Dewetting in Normal
Gravity. 6.3.4 Theoretical Models of Dewetting. 6.3.5 Stability Analysis.
6.4 Conclusion and Outlook. References. 7 Marangoni Convection in Crystal
Growth (Arne Cröll, Taketoshi Hibiya, Suguru Shiratori, Koichi Kakimoto and
Lijun Liu). 7.1 Thermocapillary Convection in Float Zones. 7.1.1 Model
Materials. 7.1.2 Semiconductors and Metals. 7.1.3 Effect of Oxygen Partial
Pressure on Thermocapillary Flow in Si. 7.1.4 Fluid Dynamics of
Thermocapillary Flow in Half-Zones. 7.1.5 Full Float Zones. 7.1.6 The
Critical Marangoni Number Mac2. 7.1.7 Controlling Thermocapillary
Convection in Float Zones. 7.2 Thermocapillary Convection in Cz Crystal
Growth of Si. 7.2.1 Introduction. 7.2.2 Surface Tension-Driven Flow in Cz
Growth. 7.2.3 Numerical Model. 7.2.4 Calculation Results. 7.2.5 Summary of
Cz Results. 7.3 Thermocapillary Convection in EFG Set-Ups. 7.4
Thermocapillary Convection in Bridgman and Related Set-Ups. 7.5
Solutocapillary Convection. References. 8 Mathematical and Numerical
Analysis of Capillarity Problems and Processes (Liliana Braescu, Simona
Epure and Thierry Duffar). 8.1 Mathematical Formulation of the Capillary
Problem. 8.1.1 Boundary Value Problems for the Young-Laplace Equation.
8.1.2 Initial and Boundary Conditions of the Meniscus Problem. 8.1.3
Approximate Solutions of the Axisymmetric Meniscus Problem. 8.2 Analytical
and Numerical Solutions for the Meniscus Equation in the Cz Method. 8.3
Analytical and Numerical Solutions for the Meniscus Equation in the EFG
Method. 8.3.1 Sheets. 8.3.2 Cylindrical Crystals. 8.4 Analytical and
Numerical Solutions for the Meniscus Equation in the Dewetted Bridgman
Method. 8.4.1 Zero Gravity. 8.4.2 Normal Gravity. 8.5 Conclusions.
Appendix: Runge-Kutta Methods. A.1 Fourth-Order Runge-Kutta Method (RK4).
A.2 Rkfixed and Rkadapt Routines for Solving IVP. References. Index.