Crystal Pulling from the Melt

1 Introduction and Historical Perspective.- 2 Elements of the Process.- 2.1 Introduction.- 2.2 Heat Balance and Growth Rate.- 2.3 The Meniscus.- 2.4 Crystal Rotation.- 3 Techniques and Technology.- 3.1 Introduction.- 3.2 Silicon.- 3.3 Gallium Arsenide.- 3.4 Oxides.- 4 Convection and Flow in the Melt.- 4.1 Melt Convection.- 4.1.1 Introduction.- 4.1.2 The Navier-Stokes Equation.- 4.2 Flow Due to a Rotating Disc.- 4.3 Natural Convective Flow.- 4.3.1 Buoyancy-Driven Flow.- 4.3.2 Marangoni Flow.- 4.3.3 Convective Turbulence.- 5 Heat Transport.- 5.1 Introduction.- 5.2 Heat Loss from the Cooling Crystal.- 5.3 The Thermal-Capillary Model.- 5.4 Heat Transfer in the Encapsulant.- 5.5 Global Heat Transport.- 5.6 Optically Semi-Transparent Crystals.- 6 Mass Transport and Solute Segregation.- 6.1 Introduction.- 6.2 The Burton, Prim and Slichter Analysis.- 6.3 Macrosegregation.- 6.4 Microsegregation.- 7 The Use of a Magnetic Field.- 7.1 Motivation.- 7.2 Interaction of a Magnetic Field with Melt Flow.- 7.3 Generation of the Magnetic Field.- 7.4 Magnetic Field Configurations.- 7.5 Flow and Segregation in a Magnetic Field.- 7.5.1 Flow and Temperature Fields.- 7.5.2 Segregation.- 7.6 Applications.- 7.6.1 Silicon.- 7.6.2 Gallium Arsenide.- 7.6.3 Indium Phosphide.- 7.7 Concluding Remarks.- 8 System Dynamics and Automatic Diameter Control.- 8.1 Introduction.- 8.2 Dynamic Stability.- 8.3 Meniscus Dynamics.- 8.4 Linear Stability Analysis.- 8.5 Automatic Diameter Control.- 8.5.1 Introduction.- 8.5.2 Reflection from the Meniscus.- 8.5.3 Crystal Imaging.- 8.5.4 Crystal and Crucible Weighing.- 8.5.5 The Use of Dies.- 8.6 Dynamics of Control by the Weighing Technique.- 9 Morphological Stability of a Planar Rotating Interface.- 9.1 Introduction.- 9.2 Constitutional Supercooling.- 9.3 Cellular Structures.- 9.4 Linear Stability Theory.- 10 The Cooling Crystal.- 10.1 Introduction.- 10.2 Stress Distribution and Dislocation Generation in Gallium Arsenide and Indium Phosphide.- 10.3 Point Defect Equilibria in the Cooling Crystal.- 11 Future Developments.- 12 References.