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.

Preface
Acknowledgements

Nomenclature

List of Contributors

1. Basic Principles of Capillarity in Relation with Crystal Growth

N. Eustathopoulos and B. Drevet


1.1 Introduction

1.2 Definitions

1.3 Contact Angles

1.4 Growth angles

Acknowledgments

References


2. Shape Stability in Capillary Crystal Growth as Possibility and Practical Realization of Shaped Crystals

V. A. Tatartchenko


2.1 Introduction

2.2 Crucible-less Crystal Growth – Capillary Shaping Techniques (CST)

2.3 Dynamic Stability of Crystallization- the Basis of Shaped Crystal Growth by CST

2.4 Stability Analysis and Growth of Shaped Crystals by the Cz Technique

2.5 Stability Analysis and Growth of Shaped Crystals by the Verneuil technique

2.5. Stability Analysis and Growth of Shaped Crystals by the FZ Technique

2.6. TPS-Capillary Shaping

2.7 Brief presentation of shaped Ge, sapphire, Si, and Metal growth

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

3.2 Czochralski control approaches

3.3 Mathematical model

3.4 Process Dynamics Analysis for Control

3.5 Conventional control design

3.6 Geometry based nonlinear control design

3.7 Advanced Techniques

References


4 Floating Zone Crystal Growth

Anke Lüdge, Helge Riemann, Michael Wünscher, Günter Behr, Wolfgang Löser, Andris Muiznieks and Arne Cröll


4.1 Introduction

4.2 FZ Processes with RF Heating

4.3 Floating Zone Growth with Optical Heating

4.4 Numerical Analysis of the Needle-eye Floating Zone Process

References


5 Shaped Crystal Growth

V. N. Kurlov, S. N. Rossolenko, N. V. Abrosimov and K. Lebbou

5.1 Introduction

5.2 Shaped Silicon

5.3 Sapphire Shaped Crystal Growth

5.4. Shaped crystals grown by micro-pulling down technique (µ-PD)

5.5 Conclusions

References


6 Vertical Bridgman and Dewetting

Thierry Duffar and Lamine Sylla


6.1 Introduction

6.2 Peculiarities and Drawbacks of the Bridgman Processes

6.3 Full Encapsulation

6.4 The Dewetting Process: a Modified Vertical Bridgman Technique

6.5 Conclusion and Outlook

References


7 Marangoni Convection in Crystal Growth

Arne Cröll, Taketoshi Hibiya, Suguru Shiratori, Koichi Kakimoto and Lijun Liu


7.1 Introduction

7.2 Thermocapillary Convection in Float Zones

7.3 Thermocapillary Convection in Czochralski Crystal Growth of Silicon

7.4 Thermocapillary Convection in EFG Setups

7.5 Thermocapillary Convection in Bridgman and Related setups

7.6 Solutocapillary Convection

References


8 Mathematical and Numerical Analysis of Capillarity Problems and Processes

Liliana Braescu, Simona Epure, Thierry Duffar


8.1 Introduction

8.2 Mathematical formulation of the capillary problem

8.3 Analytical and numerical solutions for the meniscus equation in the case of Cz method

8.4 Analytical and numerical solutions for the meniscus equation in the case of the EFG method

8.5 Analytical and numerical solutions for the meniscus equation in the case of Dewetted Bridgman method

8.6 Conclusions

Appendix

References

Index