Crystal Growth for Beginners
by I. Markov
CONTENTS OF THE SECOND EDITION
1. CRYSTAL - AMBIENT PHASE EQUILIBRIUM
1.1. Equilibrium of Infinitely Large Phases
1.2. Supersaturation
1.3. Equilibrium of finite phases
1.3.1. Equation of Laplace
1.3.2. Equation of Thomson-Gibbs
1.4. Equilibrium Shape of Crystals
1.4.1. Theorem of Gibbs - Curie - Wulff
1.4.1.1. Crystal in a Three-Dimensional Medium
1.4.1.2. Crystal on a Surface
1.4.1.2.1. Relation of Dupre
1.4.1.2.2. Equilibrium Shape
1.4.2. Polar Diagram of the Surface Energy
1.4.3. Herring's formula
1.4.4. Stability of Crystal Surfaces
1.5. Atomistic Views on Crystal Growth
1.5.1. Equilibrium of infinitely large crystal with the ambient phase - The concept of half-crystal position
1.5.2. Equilibrium finite crystal - ambient phase -- The concept of mean separation work
1.5.3. Equilibrium 2D Crystal -- ambient phase
1.5.4. Equilibrium shape of crystals -- Atomistic approach
1.5.5. Equilibrium vapor pressure of a 2D crystal on a foreign substrate
1.6. Equilibrium Structure of Crystal Surfaces
1.6.1. Classification of crystal surfaces
1.6.2. Equilibrium Structure of a Step
1.6.3. Equilibrium Structure of F Faces
1.6.3.1. Model of Jackson
1.6.3.2. Model of Temkin
1.6.3.3. Criterion of Fisher and Weeks
1.6.4. Kinetic Roughness
2. NUCLEATION
2.1. Thermodynamics
2.1.1. Homogeneous formation of nuclei
2.1.2. Heterogeneous formation of 3D nuclei
2.1.3. Heterogeneous formation of elastically strained 3D nuclei
2.1.4. Formation of 2D Nuclei
2.1.5. Mode of Nucleation on a Foreign Substrate
2.2. Rate of Nucleation
2.2.1. General Formulation
2.2.2. The Equilibrium State
2.2.3. Steady State Nucleation Rate
2.2.4. Nucleation of Liquids from Vapors
2.2.5. Statistical Contributions
2.2.6. Nucleation from Solutions and Melts
2.2.7. Rate of Heterogeneous Nucleation
2.2.8. Rate of 2D Nucleation
2.2.8.1. Rate of 2D Nucleation from Vapors
2.2.8.2. Rate of 2D Nucleation from Solutions
2.2.8.3. Rate of 2D Nucleation in Melts
2.2.9. Atomistic Theory of Nucleation
2.2.9.1. The Equilibrium State
2.2.9.2. Steady State Nucleation Rate
2.2.10. Nonsteady state nucleation
2.2.11. Mass Crystallization and Saturation Nucleus Density
2.2.12. Ostwald's Step Rule
3. CRYSTAL GROWTH
3.1. Normal Growth of Rough Crystal Faces
3.2. Layer Growth of Flat Faces
3.2.1. Rate of Advance of Steps
3.2.1.1. Growth from Vapor Phase
3.2.1.1.1. Elementary Processes on Crystal Surfaces
3.2.1.1.2. Kinetic Coefficient of a Step
3.2.1.1.3. Rate of Advance of a Single Step
3.2.1.1.4. Rate of Advance of a Train of Parallel Steps
3.2.1.1.5. Rate of Advance of Curved Steps
3.2.1.2. Growth from Solutions
3.2.1.2.1. Rate of Advance of a Single Step
3.2.1.2.2. Rate of Advance of a Step in a Train of Steps
3.2.1.3. Growth from Melts
3.2.2. Spiral Growth of F Faces
3.2.2.1. Shape of the Growth Spiral
3.2.2.2. Growth from a Vapor Phase
3.2.2.2.1. The Back Stress Effect
3.2.2.3. Growth in Solutions
3.2.2.4. Growth in Melts
3.2.3. Growth by 2D nucleation
3.2.3.1. Constant Rates of Nucleation and Step Advance
3.2.3.1.1. Layer-by-layer Growth
3.2.3.1.2. Multilayer Growth
3.2.3.2. Time Dependent Rates of Nucleation and Step Advance
3.2.3.2.1. Multinuclear Layer-by-layer Growth
3.2.3.2.2. Simultaneous Growth of Two Monolayers
3.2.3.2.3. Simultaneous Growth of Arbitrary Number of Monolayers
3.2.4. Influence of Surface Anisotropy -- Growth of Si(001) Vicinal Surface
3.2.4.1. Dimer's Structure
3.2.4.2. Structure and Energy of Steps
3.2.4.3. Ground State of Vicinal Si(100) Surfaces
3.2.4.4. Anisotropy of Surface Diffusion Coefficient
3.2.4.5. Theory of 1D Nucleation
3.2.4.6. Rate of Step Advance by 1D Nucleation
3.2.4.7. Growth of Si(001) Vicinal by Step Flow
3.2.5. Ehrlich-Schwoebel Barrier and its Consequences
3.2.5.1. Ehrlich-Schwoebel Effect on Step-Flow
3.2.5.1.1. Bunching and Debunching of Steps
3.2.5.1.2. Bales-Zangwill Instability
3.2.5.2. Ehrlich-Schwoebel Effect on 2D Nucleation
3.2.5.2.1. Second Layer Nucleation
3.2.5.2.2. Step Kinetics
3.3. Kinematic Theory of Crystal Growth
3.4. A Classical Experiment in Crystal Growth
4. EPITAXIAL GROWTH
4.1. Basic Concepts and Definitions
4.2. Structure and Energy of Epitaxial Interfaces
4.2.1. Boundary Region
4.2.2. Models of Epitaxial Interfaces
4.2.3. Misfit Dislocations
4.2.4. Frank - van der Merwe Model of Thin Overlayer
4.2.4.1. Interatomic Potentials
4.2.4.2. Interfacial Interactions
4.2.4.3. 1D Model of Epitaxial Interface
4.2.4.3.1. Single Dislocations
4.2.4.3.2. Sequence of Dislocations
4.2.4.4. 2D Model of Frank and van der Merwe
4.2.4.5. Comparison of 2D and 1D Models
4.2.4.6. Application of 1D Model to Thickening Overlayer
4.2.5. 1D Model with non-Hookean Interatomic Forces
4.2.6. van der Merwe Model of Thick Overgrowth
4.2.7. Thickening Overgrowth
4.2.8. The Volterra Approach
4.3. Mechanism of Growth of Epitaxial Films
4.3.1. Classification of the Growth Modes
4.3.2. Experimental Evidence
4.3.2.1. Metals on Insulators
4.3.2.2. Metals on Metals
4.3.2.3. Metals on Semiconductors
4.3.2.4. Semiconductors on Semiconductors
4.3.2.4.1. Effect of Surfactants
4.3.3. General Tendencies
4.3.4. Thermodynamics of Epitaxy
4.3.4.1. Wetting and Clustering
4.3.4.2. Relation of Dupre for Misfitting Crystals
4.3.4.3. Thickness Variation of Chemical Potential
4.3.4.4. Thermodynamic Criterion of the Growth Mode
4.3.5. Kinetics of Growth of Thin Epitaxial Films
4.3.5.1. Mechanism of 2D-3D transformation
4.3.5.2. Kinetics of 2D-3D transformation
4.3.5.3. Critical Temperature for 2D-3D Transition
4.3.5.4. Cross Hatch Patterns
4.3.6. Surfactants in Epitaxial Growth
4.3.6.1. Thermodynamic considerations
4.3.6.1.1. Chemical Potential of a Bulk Crystal
4.3.6.1.2. Chemical Potential of a Thin Film
4.3.6.1.3. Thermodynamic Effect of Surfactants
4.3.6.2. Kinetics
4.3.6.2.1. Effect of Surfactant on 2D Nucleation
4.3.6.2.2. Attachment -- Detachment Kinetics
4.3.6.2.3. Exchange--De-exchange Kinetics
