Crystal Growth - From Fundamentals to Technology

Preface

Acknowledgements

Chapter 1: Fundamentals

Thermodynamics of Modern Epitaxial Growth Processes (G.B. Stringfellow)
1. Introduction
2. Thermodynamic driving force for epitaxy
3. Binary phase diagrams
4. Surface phase diagrams
5. Solution thermodynamics
5.1. Surface thermodynamics
5.2. Effect of surface on growth processes
6. Effects of surfactants
7. Antimony

Actual Concepts of Interface Kinetics (K.A. Jackson)
1. General considerations
1.1. Atoms at an interface
1.2. General equation for the growth rate of crystals
1.3. Entropy change on crystallization
1.4. Early models for melt growth
1.5. Growth rate from the melt
1.6. Nucleation of layers
1.7. Growth on screw dislocations
2. Molecular dynamics simulations of crystal growth
2.1. Crystallization from the melt
3. The Kossel-Stranksi model
3.1. Bonding at an interface
3.2. Surface roughness
3.3. Monte Carlo simulations of crystallization
3.4. Equilibrium surface structure
3.5. Monte Carlo computer simulation results
3.6. Simulations of silicon growth
3.7. Kinetic roughening
4. The fluctuation dissipation theorem
4.1. Interface fluctuations
4.2. Determination of the kinetic coefficient from fluctuations
5. Non-equilibrium segregation in binary systems
5.1. Experimental observations
5.2. Monte Carlo computer modeling
5.3. Analytical model
5.4. Comparison with experiment

Theory of Crystal Growth Morphology (R.F. Sekerka)
1. Introduction
2. Equilibrium and kinetic Wulff shapes
2.1. Equilibrium shape
2.2. Kinetic Wulff shape
3. Long-range transport
3.1. Morphological stability
4. Phase field model
4.1. Basis of the model
5. Discussion and conclusions

Crystallization Physics in Biomacromolecular Solutions (A.A. Chernov)
1. Biomacromolecule – structure and function
2. The techniques
3. Nucleation
3.1. Making solution supersaturated
3.2. Nucleation rate
3.3. Time lag
3.4. Processes in the cluster-solution mixture
4. Crystal growth
4.1. Crystal growth kinetics
4.2. Facetting
5. Biocrystal perfection
5.1. Types of defects
5.2. Trapping of impurities
6. Conclusion

Dentritic Crystal Growth in Microgravity (M.E. Glicksman)
1. History and background
1.1. Approach
1.2. Steady-states of characteristics of dendrites
1.3. Time-dependent aspects of dendrites
1.4. Physico-chemical basis for dendritic growth
1.5. Thermodynamics and kinetics of dendritic crystal growth
1.6. Anisotropy
2. Steady-state dendritic growth
2.1. Transport theory
2.2. Ivantsov´s transport solution
2.3. Interfacial physics
3. Experimental verification
3.1. Model test systems
3.2. Microgravity experiments
3.3. IDGE
3.4. Verification of transport theory
3.5. Verification of interfacial physics
3.6. Scaling constants for dendritic growth
4. Applications of microgravity data
5. Summary and conclusions

Chapter 2: Modeling

Modeling of Crystal Growth Processes (J.J. Derby)
1. Introduction
2. Historical overview
3. Modeling approaches
3.1. Governing equations for continuum transport
3.2. Boundary conditions
3.3. Interface growth
3.4. Radiation heat transfer
3.5. Magnetic fields
3.6. Turbulence
4. Numerical methods
4.1. Discretization of field equations
4.2. Numerical interface representation
4.3. Deforming grids and ALE methods
4.4. Quasi-steady-state models
5. Sample modeling result
5.1. Axisymmetric analysis: Effects of ACRT
6. Summary and outlook

Modeling of Fluid Dynamic in the Czochralski Growth of Semiconductor Crystals (Kakimoto)
1. Introduction
2. Effects of internal and external forces
2.1. Effects of temperature and of crystal and crucible rotations
2.2. Effects of steady electromagnetic forces
2.3. Effects of dynamic electromagnetic forces
2.4. Vertical magnetic fields
2.5. Transverse magnetic fields
3. Parallel computing
4. Visualization method
5. Summary

Molecular Simulations of Crystal Growth Processes (J.P.J.M. van der Eerden)
1. Introduction
2. Computer simulation vs computer experiment
3. Generic crystal growth models: Kossel and Lennard-Jones
3.1. The Kossel model, for growth from vapour and from solution
3.2. The Lennard-Jones model, for growth from a melt
4. Basic statistical thermodynamics
5. Molecular dynamics and Monte Carlo simulation
5.1. Measuring macroscopic quantities
5.2. Molecular dynamics simulation
5.3. Monte Carlo simulation
5.4. Comparison of molecular dynamics and Monte Carlo
6. Generic crystal morphology theories
6.1. Classical morphology rules
6.2. Lattice models
6.3. Lennard-Jones morphology
7. Smart choice of models and experiments
7.1. Choosing a smart model: striped phases in biomembranes
7.2. Choosing a smart experiment: double-pulse nucleation study
8. Smart approximations for models and dynamics
8.1. Coarsening the temporal resolution: DPD simulation
8.2. Coarsening the spatial resolution: continuum dynamics
8.3. Modifying the interaction potential: Umbrella Sampling
8.4. Modifying the state generation method: Configuration Bias Monte Carlo
8.5. Using only successes: Transition Path Sampling
9. Characterizing atomic scale structure
9.1. Definition and characterization of the neighbourhood of a particle
9.2. Structure assessment by Ensemble of Force Networks
10. Estimating free energies and supersaturation
10.1. Virtual particle insertion and removal
10.2. Thermodynamic integration methods
10.3. Example: Ice and water phase diagram for rigid H2O models
11. Conclusion

Dislocation Patterns in Crystalline Solids – Phenomenology and Modeling (Zaiser)
1. Introduction
2. Dislocation dynamics: fundamentals
2.1. Forces and interactions in dislocation systems
2.2. Dislocation motion and plastic flow
3. Discrete dislocation dynamics (DDD) simulations
3.1. DDD simulation of 3-dimensional dislocation systems
3.2. DDD simulation of 2-dimensional dislocation systems
4. Continuum dislocation dynamics approaches
4.1. Linear irreversible thermodynamics and energy minimization
4.2. Synergetic models
5. Stochastic approaches
5.1. Discrete stochastic dislocation dynamics
5.2. Continuum stochastic dislocation dynamics
6. Conclusions

Chapter 3: Crystal Growth Technology

Silicon Crystal Growth (W. von Ammon)
1. General aspects of silicon crystal growth
2. Technological relevance of crystal defects
3. Thermophysical properties of intrinsic point defects
4. Aggregates of intrinsic point defects
4.1. Experimental observations
4.2. Theoretical model: Incorporation of intrinsic point defects
4.3. Theoretical model: Aggregation of intrinsic point defects
4.4. Effect of impurities on intrinsic point defect aggregation
5. Formation of OSF Ring
6. Czochralski crystal growth
7. Floating zone crystal growth
8. Summary/Outlook

Microchannel Epitaxy – Physics of Lateral and Vertical Growth and its Applications (T. Nishinaga)
1. Introduction
2. Concept of microchannel epitaxy
3. MCE experiments by LPE
3.1. Si
3.2. GaAs
3.3. InP and GaP
3.4. Coalescence of MCE layers
4. Microchannel epitaxy of GaAs by MBE
4.1. Vertical microchannel epitaxy(V-MCE) of GaAs
4.2. Microchannel epitaxy of GaAs by low angle incidence MBE
5. Conclusions

Epitaxial Technologies for Short Wavelength Optoelectronic Devices (S. Figge, C. Kruse, T. Paskova, D. Hommel)
1. Introduction
2. Molecular beam epitaxy
2.1. In-situ characterization methods
2.2. Growth of ZnSe-based devices
3. Metalorganic vapor phase epitaxy
3.1. Gas system and precursors
3.2. Reaction kinetics
3.3. Reactor
3.4. Reflectometry and nucleation scheme
4. Hydride vapor phase epitaxy
4.1. Basic principles of HVPE
4.2. Material characterization
5. Conclusions

Solution Growth Methods at Low and High Temperatures (J. Zaccaro, B. Menaert, D. Balitsky, A. Ibanez)
Abstract

Materials and Crystal Growth for Photovoltaics (Th. Surek)
Abstract

Chapter 4: Crystal Defects and Characterization

Point Defects in Compound Semiconductors (D.T.J. Hurle)
1. Introduction
2. Some experimental techniques for the determination of native point defect concentrations and their charge states
2.1. Coulometric Titration
2.2. Density/lattice parameter measurements
2.3. Positron Annihilation
2.4. X-ray quasi-forbidden reflection
2.5. Diffusion studies
2.6. Scanning Tunnelling Microscopy
2.7. Spectroscopic Techniques
2.8. Carrier concentration and mobility measurements
2.9. Thermodynamic modelling of dopant solubility data
3. Theoretical modelling of native point defect configurations and their formation and ionisation energies
3.1. Introduction
3.2. Neutral species
3.3. Charged native point defects and electroneutrality
4. Isolated native point defects
4.1. Vacancies
4.2. Self interstitials
4.3. Antisite defects
5. The cooling crystal
6. Phase extent
7. Doping
7.1. The donor-cation vacancy complex
7.2. Acceptor-anion vacancy complexes
7.3. Cation vacancy under-saturation during cooling of n+ crystals
8. Annealing
9. Self diffusion in GaAs
9.1. Radio-tracer self diffusion measurements
9.2. Gallium sub-lattice diffusion
9.3. Arsenic sub-lattice diffusion
10. Dopant Diffusion in GaAs
10.1. As-sub-lattice diffusion
10.2. Ga sub-lattice diffusion
11. Conclusion

Synchrotron Radiation X-Ray Imaging: a Tool for Crystal Growth (J. Baruchel)
1. Introduction
2. Absorption and phase imaging
2.1. Absorption radiography
2.2. Microtomography
2.3. Phase imaging
3. Microbeam-based X-ray imaging
4. Bragg diffraction imaging (“X-ray topography”)
4.1. Basic principles of X-ray diffraction topography
4.2. Some results of dynamical diffraction theory
4.3. Effect of imperfections: contrast mechanisms
4.4. Diffraction topographic techniques
4.5. Simulation of X-ray topographs
5. Examples of application of synchrotron radiation imaging techniques to crystal growth
5.1. Propagation of defects from the seed to the growing crystal
5.2 Simultaneous phase and diffraction imaging of porosity in quasicrystals
5.3. Real time investigation of the growth of metallic alloys
5.4. Bragg diffraction imaging using a coherent beam
6. Conclusion

Macromolecular Crystals – Growth and Characterization (J.M. Garcia-Ruiz,
J. Otálora)
1. Introduction
2. Crystallization Techniques of biological macromolecules
3. X-ray Characterization techniques
3.1. Rocking curves
3.2. Reciprocal Space Mapping
3.3. Topography
3.4. Combining methods
4. Crystal quality for structural analysis
5. Other characterization techniques
5.1. Optical microscopy
5.2. Atomic Force Microscopy
5.3. Electron microscopy and electron diffraction

In-Situ Analysis of Thin Film Growth Using STM (U. Köhler, V. Dorna, C. Jensen, M. Kneppe, G. Piaszenski, K. Reshöft, C. Wolf)
1. Introduction
2. Experimental
3. Examples illustrating epitaxial growth
3.1. Surface diffusion
3.2. Nucleation and island growth
3.3. Layer-by-layer-growth and kinetic roughening
3.4. Inhomogeneous nucleation
3.5. Relaxation processes after growth
3.6. Alloy formation
4. Conclusion