The theory of the inhomogeneous electron gas had its origin in the Thomas Fermi statistical theory, which is discussed in the first chapter of this book. This already leads to significant physical results for the binding energies of atomic ions, though because it leaves out shell structure the results of such a theory cannot reflect the richness of the Periodic Table. Therefore, for a long time, the earlier method proposed by Hartree, in which each electron is assigned its own personal wave function and energy, dominated atomic theory. The extension of the Hartree theory by Fock, to include exchange, had its parallel in the density description when Dirac showed how to incorporate exchange in the Thomas-Fermi theory. Considerably later, in 1951, Slater, in an important paper, showed how a result similar to but not identical with that of Dirac followed as a simplification of the Hartree-Fock method. It was Gombas and other workers who recognized that one could also incorporate electron correlation consistently into the Thomas-Fermi-Dirac theory by using uniform electron gas relations locally, and progress had been made along all these avenues by the 1950s.

The case of an inhomogeneous electron gas within which the density variation is significant over a spatial range of the order of a Fermi wave-length is considered in this report. It is seen that for most systems of physical interest, this sort of non-uniformity is a result of diffraction effects. This is a fundamentally different phenomenon than can reasonably be treated by the density gradient method of Kohn for slowly varying inhomogeneous electron gases. Several sample cases are treated. The first considerations are directed towards the problem of a weak periodic potential in an interacting electron gas. The momentum-dependent self-energy is calculated for an electron propagating in the many-body medium of an electron gas plus a periodic lattice pseudo-potential. This is the equivalent of a quasi-particle energy spectrum and thus an orthogonalized plane wave energy band. It does not appear that the lattice drastically changes qualitative aspects of plane wave many-body theory. A dielectric formulation for a general inhomogeneous electron gas is presented. By introducing a new image technique, the dielectric function within the random phase approximation, which is valid in the surface region of an electron gas, is obtained. A Green's function formalism is developed for treating the static dielectric screening of a point impurity in an electron gas. The surface dielectric function is used with the impurity screening formalism to treat the problem of impurity screening in the surface region. This is an idealized model of ionic adsorption on metal surface. Screening charge densities resulting from volume polarization effects are calculated. From these results, it is seen why unjustifiable application of classical image forces in previous adsorption theories has fortunately produced reasonable results. A new method for obtaining the appropriate plasmon contribution to the electron self-energy in the surface region is developed. With these results, the electron gas surface potentials calculated by Loucks and Cutler are then improved.

This book is a broad review of the electronic structure of metals and alloys. It emphasises the way in which the behavior of electrons in these materials governs the thermodynamic and other properties of these conducting materials. The theoretical treatment proceeds from a wave mechanics approach to more sophisticated techniques for the description of the properties of metals and alloys.

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Starting with the simplest semiclassical approaches and ending with the description of complex fully quantum-mechanical methods for quantum transport analysis of state-of-the-art devices, Computational Electronics: Semiclassical and Quantum Device Modeling and Simulation provides a comprehensive overview of the essential techniques and methods for effectively analyzing transport in semiconductor devices. With the transistor reaching its limits and new device designs and paradigms of operation being explored, this timely resource delivers the simulation methods needed to properly model state-of-the-art nanoscale devices. The first part examines semiclassical transport methods, including drift-diffusion, hydrodynamic, and Monte Carlo methods for solving the Boltzmann transport equation. Details regarding numerical implementation and sample codes are provided as templates for sophisticated simulation software. The second part introduces the density gradient method, quantum hydrodynamics, and the concept of effective potentials used to account for quantum-mechanical space quantization effects in particle-based simulators. Highlighting the need for quantum transport approaches, it describes various quantum effects that appear in current and future devices being mass-produced or fabricated as a proof of concept. In this context, it introduces the concept of effective potential used to approximately include quantum-mechanical space-quantization effects within the semiclassical particle-based device simulation scheme. Addressing the practical aspects of computational electronics, this authoritative resource concludes by addressing some of the open questions related to quantum transport not covered in most books. Complete with self-study problems and numerous examples throughout, this book supplies readers with the practical understanding required to create their own simulators.

Density Functional Theory is a rapidly developing branch of many-particle physics that has found applications in atomic, molecular, solid-state and nuclear physics. This book describes the conceptual framework of density functional theory and discusses in detail the derivation of explicit functionals from first principles as well as their application to Coulomb systems. Both non-relativistic and relativistic systems are treated. The connection of density functional theory with other many-body methods is highlighted. The presentation is self-contained; the book is, thus, well suited for a graduate course on density functional theory.

This book is a rigorous, unified account of the fundamental principles of the density-functional theory of the electronic structure of matter and its applications to atoms and molecules. Containing a detailed discussion of the chemical potential and its derivatives, it provides an understanding of the concepts of electronegativity, hardness and softness, and chemical reactivity. Both the Hohenberg-Kohn-Sham and the Levy-Lieb derivations of the basic theorems are presented, and extensive references to the literature are included. Two introductory chapters and several appendices provide all the background material necessary beyond a knowledge of elementary quantum theory. The book is intended for physicists, chemists, and advanced students in chemistry.