Foreword A student that has attained a MSc degree in the physics of materials or electronics will have acquired an understanding of basic atomic physics and quantum mechanics. He or she will have a grounding in what is a vast realm: solid state theory and electronic properties of solids in particular. The aim of this book is to enable the step-by-step acquisition of the fundamentals, in particular the origin of the description of electronic energy bands. The reader is thus prepared for studying relaxation of electrons in bands and hence transport properties, or even coupling with radiance and thus optical properties, absorption and emission. The student is also equipped to use by him- or herself the classic works of taught solid state physics, for example, those of Kittel, and Ashcroft and Mermin This aim is reached by combining qualitative explanations with a detailed treatment of the mathematical arguments and techniques used. Valuably, in the final part the book looks at structures other than the macroscopic crystal, such as quantum wells, disordered materials, etc. towards more advanced problems including Peierls transition, Anderson localization and polarons. In this, the author's research specialization of conductors and conjugated polymers is discernable. There is no doubt that students will benefit from this well placed book that will be of continual use in their professional careers Michel Schott Emeritus Research Director(CNRS) Ex-Director of the Groupe de Physique des Solides(GPS), Pierre and Marie Curie University, Paris, France
Foreword A student that has attained a MSc degree in the physics of materials or electronics will have acquired an understanding of basic atomic physics and quantum mechanics. He or she will have a grounding in what is a vast realm: solid state theory and electronic properties of solids in particular. The aim of this book is to enable the step-by-step acquisition of the fundamentals, in particular the origin of the description of electronic energy bands. The reader is thus prepared for studying relaxation of electrons in bands and hence transport properties, or even coupling with radiance and thus optical properties, absorption and emission. The student is also equipped to use by him- or herself the classic works of taught solid state physics, for example, those of Kittel, and Ashcroft and Mermin. This aim is reached by combining qualitative explanations with a detailed treatment of the mathematical arguments and techniques used. Valuably, in the final part the book looks at structures other than the macroscopic crystal, such as quantum wells, disordered materials, etc., towards more advanced problems including Peierls transition, Anderson localization and polarons. In this, the author’s research specialization of conductors and conjugated polymers is discernable. There is no doubt that students will benefit from this well placed book that will be of continual use in their professional careers. Michel SCHOTT Emeritus Research Director (CNRS), Ex-Director of the Groupe de Physique des Solides (GPS), Pierre and Marie Curie University, Paris, France
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Introduction This volume proposes both course work and problems with detailed solutions. It is the result of many: es. It is written with device physics and electronics students in years'experience in teaching at MSc level in applied, materials and electronic phy mind. The book describes the fundamental physics of materials used in electronics This thorough comprehension of the physical properties of materials enables an understanding of the technological processes used in the fabrication of electronic and photonic devices The first six chapters are essentially a basic course in the rudiments of solid-state physics and the description of electronic states and energy levels in the simplest of cases. The last four chapters give more advanced theories that have been developed to account for electronic and optical behaviors of ordered and disordered material The book starts with a physical description of weak and strong electronic bonds in a lattice. The appearance of energy bands is then simplified by studying energy levels in rectangular potential wells that move closer to one another. Chapter 2 introduces the theory for free electrons where particular attention is paid to the relation between the nature of the physical solutions to the number of dimensions chosen for the system. Here, the important state density functions are also intr troduced. Chapter 3, covering semi-free electrons, is essentially given to the description of band theory for weak bonds based on the physical origin of permitted and forbidden bands. In Chapter 4, band theory is applied with respect to the electrical and electronic behaviors of the material in hand. be it insulator. semiconductor metal. From this, superlattice structures and their application in optoelectronics described. Chapter 5 focuses on ordered solid-state physics where direct lattices reciprocal lattices, Brillouin zones and Fermi surfaces are good representations of electronic states and levels in a perfect solid. Chapter 6 applies these representations respectively. An excursion into the preparation of alloys is also proposed nd silicon to metals and semiconductors using the archetypal examples of copper
Introduction This volume proposes both course work and problems with detailed solutions. It is the result of many years’ experience in teaching at MSc level in applied, materials and electronic physics. It is written with device physics and electronics students in mind. The book describes the fundamental physics of materials used in electronics. This thorough comprehension of the physical properties of materials enables an understanding of the technological processes used in the fabrication of electronic and photonic devices. The first six chapters are essentially a basic course in the rudiments of solid-state physics and the description of electronic states and energy levels in the simplest of cases. The last four chapters give more advanced theories that have been developed to account for electronic and optical behaviors of ordered and disordered materials. The book starts with a physical description of weak and strong electronic bonds in a lattice. The appearance of energy bands is then simplified by studying energy levels in rectangular potential wells that move closer to one another. Chapter 2 introduces the theory for free electrons where particular attention is paid to the relation between the nature of the physical solutions to the number of dimensions chosen for the system. Here, the important state density functions are also introduced. Chapter 3, covering semi-free electrons, is essentially given to the description of band theory for weak bonds based on the physical origin of permitted and forbidden bands. In Chapter 4, band theory is applied with respect to the electrical and electronic behaviors of the material in hand, be it insulator, semiconductor or metal. From this, superlattice structures and their application in optoelectronics is described. Chapter 5 focuses on ordered solid-state physics where direct lattices, reciprocal lattices, Brillouin zones and Fermi surfaces are good representations of electronic states and levels in a perfect solid. Chapter 6 applies these representations to metals and semiconductors using the archetypal examples of copper and silicon respectively. An excursion into the preparation of alloys is also proposed
xvi Solid-State Physics for Electronics The last four chapters touch on theories which are rather more complex. Chapter 7 is dedicated to the description of the strong bond in ID media. Floquet's theorem, which is a sort of physical analog for the Huckel's theorem that is so widely used physical chemistry, is established. These results are extended to 3D media in Chapter 8, along with a simplified presentation of silicon band theory. The huge gap between the discovery of the working transistor (1947) and the rigorous establishment of silicon band theory around 20 years later is highlighted. Chapter 9 is given over to the description of energy levels in real solids where defaults can generate localized levels. Amorphous materials are well covered, for example amorphous silicon is used in non-negligible applications such as photovoltaics Finally, Chapter 10 contains a description of the principal quasi-particles in solid state, electronic and optical physics. Phonons are thus covered in detail. Phonons are widely used in thermic; however, the coupling of this with electronic charges is at the origin of phonons in covalent materials. These polarons, which often determine the electronic transport properties of a material, are described in all their possible configurations. Excitons are also described with respect to their degree of extension and their presence in different materials. Finally, the coupling of an electromagnetic wave with electrons or with(vibrating) ions in a diatomic lattice is studied to give a classical description of quasi-particles such as plasmons and polaritons
xvi Solid-State Physics for Electronics The last four chapters touch on theories which are rather more complex. Chapter 7 is dedicated to the description of the strong bond in 1D media. Floquet’s theorem, which is a sort of physical analog for the Hückel’s theorem that is so widely used in physical chemistry, is established. These results are extended to 3D media in Chapter 8, along with a simplified presentation of silicon band theory. The huge gap between the discovery of the working transistor (1947) and the rigorous establishment of silicon band theory around 20 years later is highlighted. Chapter 9 is given over to the description of energy levels in real solids where defaults can generate localized levels. Amorphous materials are well covered, for example, amorphous silicon is used in non-negligible applications such as photovoltaics. Finally, Chapter 10 contains a description of the principal quasi-particles in solid state, electronic and optical physics. Phonons are thus covered in detail. Phonons are widely used in thermics; however, the coupling of this with electronic charges is at the origin of phonons in covalent materials. These polarons, which often determine the electronic transport properties of a material, are described in all their possible configurations. Excitons are also described with respect to their degree of extension and their presence in different materials. Finally, the coupling of an electromagnetic wave with electrons or with (vibrating) ions in a diatomic lattice is studied to give a classical description of quasi-particles such as plasmons and polaritons
Chapter 1 Introduction: Representations of Electron-Lattice Bonds 11. Introduction insulators and metals with equal consideration. In metals, conduction electrons are aurally more numerous and freer than in a dielectric material, in the sense that they are less localized around a specific atom Starting with the dual wave-particle theory, the propagation of a de Broglie wave interacting with the outermost electrons of atoms of a solid is first studied. It is this hat confers certain properties on solids, especially in terms of electronic and thermal transport. The most simple potential configuration will be laid out first Chapter 2). This involves the so-called flat-bottomed well within which free electrons are simply thought of as being imprisoned by potential walls at the extremities of a solid. No account is taken of their interactions with the constituents of the solid. Taking into account the fine interactions of electrons with atoms situated at nodes in a lattice means realizing that the electrons are no more than semi-free, or rather"quasi-free, within a solid. Their bonding is classed as either weak"or"strong" depending on the form and the intensity of the interaction of the electrons with the lattice. Using representations of weak and strong bonds in the following chapters, we will deduce the structure of the energy bands on which solid- state electronic physics is based
Chapter 1 Introduction: Representations of Electron-Lattice Bonds 1.1. Introduction This book studies the electrical and electronic behavior of semiconductors, insulators and metals with equal consideration. In metals, conduction electrons are naturally more numerous and freer than in a dielectric material, in the sense that they are less localized around a specific atom. Starting with the dual wave-particle theory, the propagation of a de Broglie wave interacting with the outermost electrons of atoms of a solid is first studied. It is this that confers certain properties on solids, especially in terms of electronic and thermal transport. The most simple potential configuration will be laid out first (Chapter 2). This involves the so-called flat-bottomed well within which free electrons are simply thought of as being imprisoned by potential walls at the extremities of a solid. No account is taken of their interactions with the constituents of the solid. Taking into account the fine interactions of electrons with atoms situated at nodes in a lattice means realizing that the electrons are no more than semi-free, or rather “quasi-free”, within a solid. Their bonding is classed as either “weak” or “strong” depending on the form and the intensity of the interaction of the electrons with the lattice. Using representations of weak and strong bonds in the following chapters, we will deduce the structure of the energy bands on which solidstate electronic physics is based