Structure and Dynamics of Surfaces II

Structural and dynamical properties of surfaces are of considerable importance for the elucidation of surface phenomena. For example, the adsorption of particles and chemical reactions at surfaces are influenced by these properties. Also, the electronic surface states of electronic device materials (e.g., Schottky barrier diodes and metal-insulator-semiconductor devices) depend critically on the structure of the semiconductor surface and the overlayers. As in Structure and Dynamics of Surfaces I, this Topics volume considers the problems at the mircoscopic level. It deals with ordered and disordered as well as harmonic and anharmonic surface effects. Novel experimental techniques and theoretical developments which have been applied successfully during the last decade are integrated. The contributions of this volume also include the background of the subject, typical results, and, in most cases, trends of future developments.

1. Introduction: Surface Phenomena and Their Analysis by Scattering Experiments.- 1.1 Surface Phenomena.- 1.1.1 Reconstruction and Relaxation.- 1.1.2 Phase Transitions.- 1.1.3 Defects.- 1.1.4 Phonons and Mean Vibrational Amplitudes.- 1.1.5 Bound Resonant States.- 1.1.6 Vibrations of Adsorbed Species.- 1.1.7 Diffusion, Adsorption and Desorption.- 1.1.8 Segregation.- 1.1.9 Interfaces and Superlattices.- 1.1.10 Magnetism and Electronic States.- 1.2 Scattering Methods for Surface Analysis.- 1.2.1 Electron Scattering.- 1.2.2 Scattering of He Atoms.- 1.2.3 Neutron Scattering.- 1.2.4 X-Ray Scattering.- 1.2.5 Scattering of Ions.- 1.2.6 Comparison of Different Scattering Methods.- 1.2.7 Conclusion and Outlook.- 1.3 On the Temperature-Dependence of Surface Properties.- 1.3.1 Pair Potentials at the Surface.- 1.3.2 Density-Functional Formalism for Nonzero Temperatures.- 1.3.3 Conclusions.- 1.4 Book Outline.- References.- Additional References with Titles.- 2. Study of Surface Phonons by Means of the Green’s Function Method.- 2.1 Introductory Remarks.- 2.2 The Time-Independent Green’s Function Method in Summary.- 2.3 The Green’s Function Method in Surface Dynamics.- 2.4 From a Slab to a Semiinfinite Lattice: Selfconsistent Definition of the Perturbation Matrix.- 2.5 The Electronic Contribution to Surface Dynamics in the Framework of Shell Models.- 2.6 Surface Vibrations in Alkali Halides.- 2.6.1 LiF and NaF.- 2.6.2 NaCl and NaI.- 2.6.3 Potassium Halides.- 2.7 Further Developments: The Study of Surface Phonon Anomalies.- References.- 3. Surface Diffusion and Layer Growth.- 3.1 Mass Transport and Growth Phenomena at Surfaces.- 3.2 Description of Surface Diffusion.- 3.3 Experimental Methods for the Study of Surface Diffusion and Typical Results.- 3.3.1 Direct Observation of Diffusing Atoms.- 3.3.2 The Study of Particle Correlations in Equilibrium Systems.- 3.3.3 Diffusion Studies in a Concentration Gradient.- 3.3.4 Anisotropy of Surface Diffusion.- 3.3.5 Surface Diffusion Near the Melting Point.- 3.4 Growth Modes.- 3.5 Layer-Growth Techniques.- 3.6 Methods for the Examination of Growth Processes and Typical Results.- 3.6.1 Detection of Growth Modes by Electron Spectroscopy.- 3.6.2 Observation of Layer Growth by Diffraction Experiments.- 3.6.3 Examination of Surface and Interface Layers by High-Energy Ion Scattering.- 3.6.4 The Growth of Metal Layers on Semiconductor Substrates.- 3.6.5 Examination of Superlattices.- 3.7 Model Calculations and Simulations.- 3.8 Conclusion and Outlook.- References.- Additional References with Titles.- 4. Phase Transitions on Single-Crystal Surfaces and in Chemisorbed Layers.- 4.1 Background.- 4.2 Theoretical Foundations.- 4.2.1 Phases in Two Dimensions.- 4.2.2 Origin of Surface Phases and Relation to Magnetic Models.- 4.2.3 Models and Nomenclature.- 4.2.4 Continuous Order-Disorder Transitions.- a) Critical Behaviour and Exponents, Universality and Scaling Laws.- b) Symmetry Analysis and Symmetric Lattice Models.- c) Asymmetric and Anisotropic Models.- 4.2.5 Order-Order Transitions.- 4.2.6 Commensurate-Incommensurate Transitions.- 4.2.7 Melting in Two Dimensions.- 4.2.8 Interface Delocalization Transitions in Two Dimensions.- 4.2.9 Systems with Long-Range Repulsive Interactions.- 4.2.10 Systems with Purely Attractive Interactions.- 4.3 Experimental Techniques.- 4.3.1 Diffraction Methods.- 4.3.2 Scattering Methods.- 4.3.3 Work Function Change Measurement.- 4.3.4 Thermal Desorption Methods.- 4.3.5 Electron Microscopy.- 4.3.6 Experimental Limitations.- 4.4 Results.- 4.4.1 Clean Surfaces.- a) The Si(111)-(7 × 7)?(1 × 1) Transition.- b) The Au(110)-(1 × 2)?(1 × 1) Transition.- c) W(100)-c(2 × 2)?(1 × 1) Transition.- d) Other Transitions on Clean Surfaces.- 4.4.2 Chemisorbed Layers with Repulsive Nearest-Neighbour Interactions.- a) Two-Dimensionally Densely Packed Surfaces.- b) One-Dimensionally Densely Packed Surfaces (p2mm).- c) Open Surfaces.- 4.4.3 Chemisorbed Layers with Attractive Nearest-Neighbour Interactions.- 4.5 Concluding Remarks and Outlook.- References.- Additional References with Titles.- 5. Solid and Liquid Surfaces Studied by Synchrotron X-Ray Diffraction.- 5.1 Reflectivity and Density Profile.- 5.1.1 Master Formula.- 5.1.2 Fresnel Reflectivity.- 5.1.3 Derivation of Master Formula.- 5.1.4 Traditional Calculation Scheme for R(Q).- 5.2 Experimental Reflectivity Set Up.- 5.2.1 General Wave-Vector Transfer.- 5.2.2 Resolution.- 5.3 Examples of Reflectivity Measurements.- 5.3.1 Thermal Roughness.- 5.3.2 Smectic Layering on Liquid Crystal Surfaces.- a) Smectic Layering in the Isotropic Phase.- b) Layer Penetration in the Nematic Phase.- c) Antiferroelectric Surface Layers.- 5.4 In-Plane Structures.- 5.4.1 Grazing Incidence Geometry.- a) Penetration Depth.- b) Field Strength.- c) Summary of Grazing Incidence.- 5.4.2 Principles of Surface Crystallography.- a) Bragg Scattering.- b) Unit Cell in Surface Geometry, InSb(111).- c) Reciprocal Lattice. Bragg Points.- d) Reconstructed (n × m) Surface Structure. Bragg Rods.- e) Bragg Rods from Termination at Surface.- f) Patterson Function.- 5.4.3 Reconstructed Surface of InSb(111)-(2 × 2).- a) Diffractometer Set Up.- b) Sample Preparation.- c) Results.- 5.4.4 Surface Structures Revealed by X-Ray Diffraction.- References.- 6. Statistical Mechanics of the Liquid Surface and the Effect of Premelting.- 6.1 The Structure of the Liquid Surface.- 6.1.1 General Remarks.- 6.1.2 Bulk Liquids.- 6.1.3 Liquid Surfaces.- a) Single-Particle Distribution Function.- b) The Two-Particle Distribution Function.- 6.1.4 Surface Thermodynamic Properties.- 6.1.5 Liquid Metals.- 6.2 Dynamics of the Liquid Surface.- 6.3 The Effect of Premelting. A Study for Krypton.- 6.3.1 Model.- 6.3.2 Results for the Distribution Functions.- a) Single-Particle Distribution Functions for Krypton.- b) Pair Correlation Function for Krypton.- 6.3.3 Discussion of the Results for the Distribution Functions.- a) Single-Particle Distribution Function for the Outermost Layer at T=7 K.- b) The Dynamics of the Particles of the Outermost Layer at T=102 K.- c) Melting Mechanism: Description at the Atomic Level.- 6.4 Final Remarks.- References.- Additional References with Titles.- 7. The Roughening Transition.- 7.1 Background.- 7.2 Macroscopic Description of Equilibrium Crystal Shapes.- 7.2.1 The Wulff Construction.- 7.2.2 Facets, Edges and Corners.- 7.2.3 The Roughening Transition and Other Phase Transitions.- 7.3 Microscopic Description of Crystal Surfaces.- 7.3.1 The Kossel Crystal, Lattice-Gas Models, Solid-on-Solid Models.- 7.3.2 Steps and Step Free Energies.- 7.3.3 Microscopic Characterization of Roughening Transitions.- 7.3.4 Equilibrium Shapes of Facets. General Criterium for Roughening.- 7.4 Statistical Mechanics of Interface Models.- 7.4.1 Renormalization-Group Results.- a) Roughening Temperature.- b) Surface Tension.- c) Step Free Energies.- d) Correlation Length.- e) Height-Height Correlation Function.- f) Jump in Curvature and Surface Stiffness.- 7.4.2 The BCSOS Model.- 7.4.3 The Terrace-Step-Kink Model.- 7.4.4 Universal Shape of Vicinal Areas.- 7.5 Discussion.- 7.5.1 Roughening Versus Surface Melting.- 7.5.2 Are All Roughening Transitions of Kosterlitz-Thouless Type?.- a) Inequivalent Layers.- b) Impurities and Lattice Faults.- c) First-Order Transitions.- 7.5.3 Multilayer Adsorption and Roughening.- Appendix 7.A: Surface Stiffness and Universal Jump in Curvature.- References.- Additional References with Titles.- 8. Structural and Dynamical Aspects of Adsorption and Desorption.- 8.1 General.- 8.2 Basic Experimental Facts.- 8.2.1 Elastic Scattering at Surfaces.- 8.2.2 Trapping and Sticking.- 8.2.3 Direct Inelastic Scattering.- 8.2.4 Desorption.- 8.3 Overview of the Different Theoretical Approaches.- 8.3.1 Classical and Classical-Stochastic Theories.- 8.3.2 Semiclassical Theories.- 8.3.3 Quantum Theories.- 8.4 Selected Problems.- 8.4.1 Structural and Dynamical Constraints.- 8.4.2 The Compensation Effect.- 8.4.3 The Sticking Coefficient — Definition and Zero Temperature/Zero Kinetic Energy Behaviour.- 8.4.4 Quantum Partitioning Techniques.- 8.4.5 Non-Adiabatic Adsorption and Desorption.- 8.5 Concluding Remarks.- References.- 9. Many-Body Description of Surface Elementary Excitations. Application to Semiconductors.- 9.1 Background.- 9.2 Elementary Excitations on Surfaces.- 9.2.1 Homogeneous Bethe-Salpeter Equations.- 9.2.2 Equation of Motion in the Local-Orbital Representation.- 9.2.3 Surface Density-Response Function.- 9.3 Surface Electromagnetic Response.- 9.3.1 Surface Macroscopic Dielectric Tensor.- 9.3.2 Microscopic Formulation of the Optical Response.- 9.3.3 Microscopic Theory of Surface Reflectivity.- 9.4 Electron-Phonon Interaction and Microscopic Theory of Lattice Dynamics on Surfaces.- 9.4.1 Surface Lattice Dynamics.- 9.5 Applications: Si(111).- 9.5.1 Electronic Instabilities in an Ideal Si(111) Slab.- 9.5.2 Microscopic Phonon Calculations for an Ideal Si(111)Slab.- 9.6 Summary and Perspectives.- References.