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Author: W. Kohn Publisher: ISBN: Category : Languages : en Pages : 6
Book Description
From a theory of Hohenberg and Kohn, approximation methods for treating an inhomogeneous system of interacting electrons are developed. They lead to selfconsistent equations analagous to the Hartree and HartreeFock equations, respectively. In these equations the exchange and correlation portions of the chemical potential of a uniform electron gas appear as corrections to the electrostatic potential. (Author).
Author: W. Kohn Publisher: ISBN: Category : Languages : en Pages : 6
Book Description
From a theory of Hohenberg and Kohn, approximation methods for treating an inhomogeneous system of interacting electrons are developed. They lead to selfconsistent equations analagous to the Hartree and HartreeFock equations, respectively. In these equations the exchange and correlation portions of the chemical potential of a uniform electron gas appear as corrections to the electrostatic potential. (Author).
Author: Stig Lundqvist Publisher: Springer Science & Business Media ISBN: 1489904158 Category : Science Languages : en Pages : 405
Book Description
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.
Author: John William Gadzuk Publisher: ISBN: Category : Electron gas Languages : en Pages : 100
Book Description
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.
Author: Walter Kohn Publisher: ISBN: Category : Languages : en Pages : 23
Book Description
From a theory of Hohenberg and Kohn, approximation methods for treating an inhomogeneous system of interacting electrons are developed. These methods are exact for systems of slowly varying or high density. For the ground state, they lead to self-consistent equations analogous to the Hartree and Hartree-Fock equations, respectively. In these equations the exchange and correlation portions of the chemical potential of a uniform electron gas appear as additional effective potentials. (The exchange portion of our effective potential differs from that due to Slater by a factor of 2/3.) Electronic systems at finite temperatures and in magnetic fields are also treated by similar methods. An appendix deals with a further correction for systems with short wavelength density oscillations. (Author).
Author: Dragica Vasileska Publisher: CRC Press ISBN: 1351834886 Category : Technology & Engineering Languages : en Pages : 866
Book Description
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.
Author: Publisher: ISBN: Category : Aeronautics Languages : en Pages : 936
Book Description
Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Author: A. Gonis Publisher: Springer Science & Business Media ISBN: 1475737602 Category : Science Languages : en Pages : 413
Book Description
This is the second in a series of "International Workshops on Electron Correlations and Materials Properties. " The aim of this series of workshops is to provide a periodic (triennial) and in-depth assessment of advances in the study and understanding of the effects that electron-electron interactions in solids have on the determination of measurable properties of materials. The workshop is structured to include exposure to experimental work, to phenomenology, and to ab initio theory. Since correlation effects are pervasive the workshop aims to concentrate on the identification of promising developing methodology, experimental and theoretical, addressing the most critical frontier issues of electron correlations on the properties of materials. This series of workshops is distinguished from other topical meetings and conferences in that it strongly promotes an interdisciplinary approach to the study of correlations, involving the fields of quantum chemistry, physics, and materials science. The First Workshop was held June 28-July 3, 1998, and a proceedings of the workshop was published by KluwerlPlenum. The Second Workshop was held June 24- 29,2001, and this volume contains the proceedings of that scientific meeting. Through the publications of proceedings, the workshop attempts to disseminate the information gathered during the discussions held at the Workshop to the wider scientific community, and to establish a record of advances in the field.
Author: Massimo V. Fischetti Publisher: Springer ISBN: 3319011014 Category : Technology & Engineering Languages : en Pages : 481
Book Description
This textbook is aimed at second-year graduate students in Physics, Electrical Engineering, or Materials Science. It presents a rigorous introduction to electronic transport in solids, especially at the nanometer scale.Understanding electronic transport in solids requires some basic knowledge of Hamiltonian Classical Mechanics, Quantum Mechanics, Condensed Matter Theory, and Statistical Mechanics. Hence, this book discusses those sub-topics which are required to deal with electronic transport in a single, self-contained course. This will be useful for students who intend to work in academia or the nano/ micro-electronics industry.Further topics covered include: the theory of energy bands in crystals, of second quantization and elementary excitations in solids, of the dielectric properties of semiconductors with an emphasis on dielectric screening and coupled interfacial modes, of electron scattering with phonons, plasmons, electrons and photons, of the derivation of transport equations in semiconductors and semiconductor nanostructures somewhat at the quantum level, but mainly at the semi-classical level. The text presents examples relevant to current research, thus not only about Si, but also about III-V compound semiconductors, nanowires, graphene and graphene nanoribbons. In particular, the text gives major emphasis to plane-wave methods applied to the electronic structure of solids, both DFT and empirical pseudopotentials, always paying attention to their effects on electronic transport and its numerical treatment. The core of the text is electronic transport, with ample discussions of the transport equations derived both in the quantum picture (the Liouville-von Neumann equation) and semi-classically (the Boltzmann transport equation, BTE). An advanced chapter, Chapter 18, is strictly related to the ‘tricky’ transition from the time-reversible Liouville-von Neumann equation to the time-irreversible Green’s functions, to the density-matrix formalism and, classically, to the Boltzmann transport equation. Finally, several methods for solving the BTE are also reviewed, including the method of moments, iterative methods, direct matrix inversion, Cellular Automata and Monte Carlo. Four appendices complete the text.
Author: J.T. Golab Publisher: Springer Science & Business Media ISBN: 148991319X Category : Science Languages : en Pages : 249
Book Description
Many chemical processes that are important to society take place at boundaries between phases. Understanding these processes is critical in order for them to be subject to human control. The building of theoretical or computational models of them puts them into a theoretical framework in terms of which the behavior of the system can be understood on a detailed level. Theoretical and computational models are often capable of giving descriptions of interfacial phenomena that are more detailed, on a molecular level, than can be obtained through experimental observation. Advances in computer hardware have also made possible the treatment of larger and chemically more interesting systems. The study of interfacial phenomena is a multi-disciplinary endeavor which requires collaboration and communication among researchers in different fields and across different types of institutions. Because there are many important problems in this field much effort is being expended to understand these processes by industrial laboratories as well as by groups at universities. Our conference titled "Theoretical and Computational Approaches to Interface Phenomena" held at South Dakota State University, August 2-4, 1993 brought together over thirty scientists from industry and academia and three countries in the western hemisphere to discuss the modeling of interfacial phenomena.
Author: W. Kohn
Author: W. Kohn
Author: Stig Lundqvist
Author: John William Gadzuk
Author: Walter Kohn
Author: 
Author: Dragica Vasileska
Author: 
Author: A. Gonis
Author: Massimo V. Fischetti
Author: J.T. Golab