Mario P. Tosi - Böcker

This book has its origins in the 1982 Spring College held at the Interna­ tional Centre for Theoretical Physics, Miramare, Trieste. The primary aim is to give a broad coverage of liquids and amorphous solids, at a level suitable for graduate students and research workers in condensed-matter physics, physical chemistry, and materials science. The book is intended for experimental workers with interests in the basic theory. While the topics covered are many, it was planned to place special emphasis on both static structure and dynamics, including electronic transport. This emphasis is evident from the rather complete coverage of the determination of static structure from both diffraction experiments and, for amorphous solids especially, from model building. The theory of the structure of liquids and liquid mixtures is then dealt with from the standpoint of, first, basic statistical mechanics and, subsequently, pair potentials constructed from the electron theory of simple metals and their alloys. The discussion of static structure is completed in two chapters with rather different emphases on liquid surfaces and interfaces. The first deals with the basic statistical mechanics of neutral and charged interfaces, while the second is concerned with solvation and double-layer effects. Dynamic structure is introduced by a comprehensive discussion of single-particle motion in liquids. This is followed by the structure and dynamics of charged fluids, where again much basic statistical mechanics is developed.

This book is concerned primarily with the fundamental theory underlying the physical and chemical properties of crystalIine semiconductors. After basic introductory material on chemical bonding, electronic band structure, phonons, and electronic transport, some emphasis is placed on surface and interfacial properties, as weil as effects of doping with a variety of impurities. Against this background, the use of such materials in device physics is examined and aspects of materials preparation are discussed briefty. The level of presentation is suitable for postgraduate students and research workers in solid-state physics and chemistry, materials science, and electrical and electronic engineering. Finally, it may be of interest to note that this book originated in a College organized at the International Centre for Theoretical Physics, Trieste, in Spring 1984. P. N. Butcher N. H. March M. P. Tosi vii Contents 1. Bonds and Bands in Semiconductors 1 E. Mooser 1. 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. 2. The Semiconducting Bond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1. 3. Bond Approach Versus Band Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1. 4. Construction of the Localized X by Linear Combination of n Atomic Orbitals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1. 5. The General Octet Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1. 6. The Aufbau-Principle of the Crystal Structure of Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1. 7. A Building Principle for Polyanionic Structures . . . . . . . . . . . . . . . . . . . . . . 29 I. H. Structural Sorting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 1. 9. Chemical Bonds and Semiconductivity in Transition-Element Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 1. 10. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 2. Electronic Band Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 G. Grosso 2. 1. Two Different Strategies for Band-Structure Calculations . . . . . . . 55 2. 2. The Tight-Binding Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

This volume is concerned with the theoretical description of patterns and instabilities and their relevance to physics, chemistry, and biology. More specifically, the theme of the work is the theory of nonlinear physical systems with emphasis on the mechanisms leading to the appearance of regular patterns of ordered behavior and chaotic patterns of stochastic behavior. The aim is to present basic concepts and current problems from a variety of points of view. In spite of the emphasis on concepts, some effort has been made to bring together experimental observations and theoretical mechanisms to provide a basic understanding of the aspects of the behavior of nonlinear systems which have a measure of generality. Chaos theory has become a real challenge to physicists with very different interests and also in many other disciplines, of which astronomy, chemistry, medicine, meteorology, economics, and social theory are already embraced at the time of writing. The study of chaos-related phenomena has a truly interdisciplinary charac­ ter and makes use of important concepts and methods from other disciplines. As one important example, for the description of chaotic structures the branch of mathematics called fractal geometry (associated particularly with the name of Mandelbrot) has proved invaluable. For the discussion of the richness of ordered structures which appear, one relies on the theory of pattern recognition. It is relevant to mention that, to date, computer studies have greatly aided the analysis of theoretical models describing chaos.

Presenting the latest advances in artificial structures, this volume discusses in-depth the structure and electron transport mechanisms of quantum wells, superlattices, quantum wires, and quantum dots. It will serve as an invaluable reference and review for researchers and graduate students in solid-state physics, materials science, and electrical and electronic engineering.

This book deals with three related areas having both fundamental and technological interest. In the first part, the objective is to provide a bird's­ eye view on structure in polymeric solids. This is then complemented by a chapter, directly technological in its emphasis, dealing with the influence of processing on polymeric materials. In spite of the technological interest, this leads to some of the current fundamental theory. Part II, concerned with liquid crystals, starts with a discussion of the physics of the various types of material, and concludes with a treatment of optical applications. Again, aspects of the theory are stressed though this part is basically phenomenological in character. In Part III, an account is given first of the use of chemical-bonding arguments in understanding the electronic structure of low-dimensional solids, followed by a comprehensive treatment of the influence of dimen­ sionality on phase transitions. A brief summary of dielectric screening in low-dimensional solids follows. Space-charge layers are then treated, including semiconductor inversion layers. Effects of limited dimensionality on superconductivity are also emphasized. Part IV concludes the volume with two specialized topics: electronic structure of biopolymers, and topological defects and disordered systems. The Editors wish to acknowledge that this book had its origins in the material presented at a course organized by the International Centre for Theoretical Physics, Trieste.

There is considerable interest, both fundamental and technological, in the way atoms and molecules interact with solid surfaces. Thus the description of heterogeneous catalysis and other surface reactions requires a detailed understand­ ing of molecule-surface interactions. The primary aim of this volume is to provide fairly broad coverage of atoms and molecules in interaction with a variety of solid surfaces at a level suitable for graduate students and research workers in condensed matter physics, chemical physics, and materials science. The book is intended for experimental workers with interests in basic theory and concepts and had its origins in a Spring College held at the International Centre for Theoretical Physics, Miramare, Trieste. Valuable background reading can be found in the graduate-Ievel introduction to the physics of solid surfaces by ZangwilI(1) and in the earlier works by Garcia­ Moliner and F1ores(2) and Somorjai.(3) For specifically molecule-surface interac­ tions, additional background can be found in Rhodin and Ertl(4) and March.(S) V. Bortolani N. H. March M. P. Tosi References 1. A. Zangwill, Physics at Surfaces, Cambridge University Press, Cambridge (1988). 2. F. Garcia-Moliner and F. Flores, Introduction to the Theory of Solid Surfaces, Cambridge University Press, Cambridge (1979). 3. G. A. Somorjai, Chemistry in Two Dimensions: Surfaces, Cornell University Press, Ithaca, New York (1981). 4. T. N. Rhodin and G. Erd, The Nature of the Surface Chemical Bond, North-Holland, Amsterdam (1979). 5. N. H. March, Chemical Bonds outside Metal Surfaces, Plenum Press, New York (1986).

This book has its origins in the 1982 Spring College held at the Interna­ tional Centre for Theoretical Physics, Miramare, Trieste. The primary aim is to give a broad coverage of liquids and amorphous solids, at a level suitable for graduate students and research workers in condensed-matter physics, physical chemistry, and materials science. The book is intended for experimental workers with interests in the basic theory. While the topics covered are many, it was planned to place special emphasis on both static structure and dynamics, including electronic transport. This emphasis is evident from the rather complete coverage of the determination of static structure from both diffraction experiments and, for amorphous solids especially, from model building. The theory of the structure of liquids and liquid mixtures is then dealt with from the standpoint of, first, basic statistical mechanics and, subsequently, pair potentials constructed from the electron theory of simple metals and their alloys. The discussion of static structure is completed in two chapters with rather different emphases on liquid surfaces and interfaces. The first deals with the basic statistical mechanics of neutral and charged interfaces, while the second is concerned with solvation and double-layer effects. Dynamic structure is introduced by a comprehensive discussion of single-particle motion in liquids. This is followed by the structure and dynamics of charged fluids, where again much basic statistical mechanics is developed.

This book is concerned primarily with the fundamental theory underlying the physical and chemical properties of crystalIine semiconductors. After basic introductory material on chemical bonding, electronic band structure, phonons, and electronic transport, some emphasis is placed on surface and interfacial properties, as weil as effects of doping with a variety of impurities. Against this background, the use of such materials in device physics is examined and aspects of materials preparation are discussed briefty. The level of presentation is suitable for postgraduate students and research workers in solid-state physics and chemistry, materials science, and electrical and electronic engineering. Finally, it may be of interest to note that this book originated in a College organized at the International Centre for Theoretical Physics, Trieste, in Spring 1984. P. N. Butcher N. H. March M. P. Tosi vii Contents 1. Bonds and Bands in Semiconductors 1 E. Mooser 1. 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. 2. The Semiconducting Bond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1. 3. Bond Approach Versus Band Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1. 4. Construction of the Localized X by Linear Combination of n Atomic Orbitals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1. 5. The General Octet Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1. 6. The Aufbau-Principle of the Crystal Structure of Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1. 7. A Building Principle for Polyanionic Structures . . . . . . . . . . . . . . . . . . . . . . 29 I. H. Structural Sorting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 1. 9. Chemical Bonds and Semiconductivity in Transition-Element Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 1. 10. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 2. Electronic Band Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 G. Grosso 2. 1. Two Different Strategies for Band-Structure Calculations . . . . . . . 55 2. 2. The Tight-Binding Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

This volume is concerned with the theoretical description of patterns and instabilities and their relevance to physics, chemistry, and biology. More specifically, the theme of the work is the theory of nonlinear physical systems with emphasis on the mechanisms leading to the appearance of regular patterns of ordered behavior and chaotic patterns of stochastic behavior. The aim is to present basic concepts and current problems from a variety of points of view. In spite of the emphasis on concepts, some effort has been made to bring together experimental observations and theoretical mechanisms to provide a basic understanding of the aspects of the behavior of nonlinear systems which have a measure of generality. Chaos theory has become a real challenge to physicists with very different interests and also in many other disciplines, of which astronomy, chemistry, medicine, meteorology, economics, and social theory are already embraced at the time of writing. The study of chaos-related phenomena has a truly interdisciplinary charac­ ter and makes use of important concepts and methods from other disciplines. As one important example, for the description of chaotic structures the branch of mathematics called fractal geometry (associated particularly with the name of Mandelbrot) has proved invaluable. For the discussion of the richness of ordered structures which appear, one relies on the theory of pattern recognition. It is relevant to mention that, to date, computer studies have greatly aided the analysis of theoretical models describing chaos.

Presenting the latest advances in artificial structures, this volume discusses in-depth the structure and electron transport mechanisms of quantum wells, superlattices, quantum wires, and quantum dots. It will serve as an invaluable reference and review for researchers and graduate students in solid-state physics, materials science, and electrical and electronic engineering.

This volume of proceedings contains contributions which provide an overview of theoretical electrochemistry from a condensed matter physics point of view. Main attention is focused on developments in the theory of liquids and solutions, structure, adsorption and electric and optical properties of the electrochemical interface, kinetics of charge transfer reactions, fractal and superconducting electrodes, solar energy conversion and power sources.

This volume contains the Proceedings of the International Workshop on “Non-Equilibrium Phenomena in Supercooled Fluids, Glasses and Amorphous Materials”, held in Pisa in the early fall of 1995 as a joint initiative of the University of Pisa and of the Scuola Normale Superiore. The goal was to bring together liquid state physicists, chemists and engineers, to review current developments and comparatively discuss experimental facts and theoretical predictions in this vast scientific area. The core of the Workshop was a set of general lectures followed by more specific presentations on current issues in the main areas of the field. This structure has been maintained in this volume, in which a set of five overviews is followed by topically grouped contributions in the five areas of ionic glasses and glassy materials, the glass transition, viscous flow and microscopic relaxation, complex fluids, and polymers. The volume also preserves a record of the many short contributions given to the Workshop through posters, which are grouped in it under the subjects of inorganic glasses, organic glasses and complex fluids, polymers, and theoretical aspects.

An elementary act of charge transfer determines a variety of phenomena in physics, chemistry and biology. The study of charge transfer processes has developed together with general progress in theoretical physics and in fast high resolution spectroscopy, so that research deals now with a broad class of systems, materials and environmental conditions. The specific topics covered are: (1) the environment and reactant-environment interaction at bulk and interfaces; (2) the elementary act of electron and proton transfer; homogeneous and heterogeneous processes; (3) processes of ion and heavy group transfer; ion transport in complex systems; (4) artificially and naturally organized charge transfer in physics, chemistry and biology, technological applications (molecular electronics, sensors, modified electrodes, membrane transport).

This important book provides an introduction to the liquid state. A qualitative description of liquid properties is first given, followed by detailed chapters on thermodynamics, liquid structure in relation to interaction forces and transport properties such as diffusion and viscosity. Treatment of complex fluids such as anisotropic liquid crystals and polymers, and of technically important topics such as non-Newtonian and turbulent flows, is included. Surface properties and characteristics of the liquid-vapour critical point are also discussed. While the book focuses on classical liquids, the final chapter deals with quantal fluids.