A Deterministic Particle Method For The Simulation Of The Boltzmann Transport Equation Of Semiconductors
Download A Deterministic Particle Method For The Simulation Of The Boltzmann Transport Equation Of Semiconductors full books in PDF, epub, and Kindle. Read online free A Deterministic Particle Method For The Simulation Of The Boltzmann Transport Equation Of Semiconductors ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
| Author | : Randolph Bank |
| Publisher | : Birkhäuser |
| Total Pages | : 314 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034885288 |
Progress in today's high-technology industries is strongly associated with the development of new mathematical tools. A typical illustration of this partnership is the mathematical modelling and numerical simulation of electric circuits and semiconductor devices. At the second Oberwolfach conference devoted to this important and timely field, scientists from around the world, mainly applied mathematicians and electrical engineers from industry and universities, presented their new results. Their contributions, forming the body of this work, cover electric circuit simulation, device simulation and process simulation. Discussions on experiences with standard software packages and improvements of such packages are included. In the semiconductor area special lectures were given on new modelling approaches, numerical techniques and existence and uniqueness results. In this connection, mention is made, for example, of mixed finite element methods, an extension of the Baliga-Patankar technique for a three dimensional simulation, and the connection between semiconductor equations and the Boltzmann equations.
| Author | : Massimo V. Fischetti |
| Publisher | : Springer |
| Total Pages | : 481 |
| Release | : 2016-05-20 |
| Genre | : Technology & Engineering |
| ISBN | : 3319011014 |
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 | : R. Glowinski |
| Publisher | : SIAM |
| Total Pages | : 464 |
| Release | : 1990-01-01 |
| Genre | : Science |
| ISBN | : 9780898712643 |
"Proceedings of the Ninth International Conference on Computing Methods in Applied Sciences and Engineering, Paris, France, January 29-February 2, 1990"--T.p. verso.
| Author | : Randolph E. Bank |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 206 |
| Release | : 1990-02-15 |
| Genre | : Technology & Engineering |
| ISBN | : 9780821896938 |
Numerical simulation is rapidly becoming an important part of the VLSI design process, allowing the engineer to test, evaluate, and optimize various aspects of chip design without resorting to the costly and time-consuming process of fabricating prototypes. This procedure not only accelerates the design process, but also improves the end product, since it is economically feasible to numerically simulate many more options than might otherwise be considered. With the enhanced computing power of today's computers, more sophisticated models are now being developed. This volume contains the proceedings of the AMS-SIAM Summer Seminar on Computational Aspects of VLSI Design, held at the Institute for Mathematics and Its Applications at the University of Minnesota, in the spring of 1987. The seminar featured presentations by some of the top experts working in this area. Their contributions to this volume form an excellent overview of the mathematical and computational problems arising in this area.
| Author | : Joseph W. Jerome |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 177 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642799876 |
This book addresses the mathematical aspects of semiconductor modeling, with particular attention focused on the drift-diffusion model. The aim is to provide a rigorous basis for those models which are actually employed in practice, and to analyze the approximation properties of discretization procedures. The book is intended for applied and computational mathematicians, and for mathematically literate engineers, who wish to gain an understanding of the mathematical framework that is pertinent to device modeling. The latter audience will welcome the introduction of hydrodynamic and energy transport models in Chap. 3. Solutions of the nonlinear steady-state systems are analyzed as the fixed points of a mapping T, or better, a family of such mappings, distinguished by system decoupling. Significant attention is paid to questions related to the mathematical properties of this mapping, termed the Gummel map. Compu tational aspects of this fixed point mapping for analysis of discretizations are discussed as well. We present a novel nonlinear approximation theory, termed the Kras nosel'skii operator calculus, which we develop in Chap. 6 as an appropriate extension of the Babuska-Aziz inf-sup linear saddle point theory. It is shown in Chap. 5 how this applies to the semiconductor model. We also present in Chap. 4 a thorough study of various realizations of the Gummel map, which includes non-uniformly elliptic systems and variational inequalities. In Chap.
| Author | : Heiner Ryssel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 515 |
| Release | : 2012-12-06 |
| Genre | : Computers |
| ISBN | : 3709166195 |
SISDEP ’95 provides an international forum for the presentation of state-of-the-art research and development results in the area of numerical process and device simulation. Continuously shrinking device dimensions, the use of new materials, and advanced processing steps in the manufacturing of semiconductor devices require new and improved software. The trend towards increasing complexity in structures and process technology demands advanced models describing all basic effects and sophisticated two and three dimensional tools for almost arbitrarily designed geometries. The book contains the latest results obtained by scientists from more than 20 countries on process simulation and modeling, simulation of process equipment, device modeling and simulation of novel devices, power semiconductors, and sensors, on device simulation and parameter extraction for circuit models, practical application of simulation, numerical methods, and software.
| Author | : Martin Galler |
| Publisher | : World Scientific |
| Total Pages | : 247 |
| Release | : 2005 |
| Genre | : Philosophy |
| ISBN | : 9812563555 |
Deterministic simulation of the particle transport in semiconductor devices is an interesting alternative to the common Monte Carlo approach. In this book, a state-of-the-art technique called the multigroup approach is presented and applied to a variety of transport problems in bulk semiconductors and semiconductor devices. High-field effects as well as hot-phonon phenomena in polar semiconductors are studied in detail. The mathematical properties of the presented numerical method are studied, and the method is applied to simulating the transport of a two-dimensional electron gas formed at a semiconductor heterostructure. Concerning semiconductor device simulation, several diodes and transistors fabricated of silicon and gallium arsenide are investigated. For all of these simulations, the numerical techniques employed are discussed in detail.This unique study of the application of direct methods for semiconductor device simulation provides the interested reader with an indispensable reference on this growing research area.
| Author | : |
| Publisher | : |
| Total Pages | : 712 |
| Release | : 2006 |
| Genre | : Electronic journals |
| ISBN | : |
| Author | : R. Bank |
| Publisher | : Birkhäuser |
| Total Pages | : 298 |
| Release | : 2013-11-22 |
| Genre | : Science |
| ISBN | : 3034856989 |
Numerical simulation and modelling of electric circuits and semiconductor devices are of primal interest in today's high technology industries. At the Oberwolfach Conference more than forty scientists from around the world, in cluding applied mathematicians and electrical engineers from industry and universities, presented new results in this area of growing importance. The contributions to this conference are presented in these proceedings. They include contributions on special topics of current interest in circuit and device simulation, as well as contributions that present an overview of the field. In the semiconductor area special lectures were given on mixed finite element methods and iterative procedures for the solution of large linear systems. For three dimensional models new discretization procedures including software packages were presented. Con nections between semiconductor equations and the Boltzmann equation were shown as well as relations to the quantum transport equation. Other issues discussed in this area include the design of simulation programs for semiconductors, vectorcomputers, and interface problems in several dimensions. Topics discussed in the area of circuit simulation include the index classification of differential-algebraic systems, connections with ill-posed problems, and regularization techniques. Split discretization procedures were given for the efficient calculation of periodic solutions of circuits taking into acount the latency. Homotopy methods and new numerical techniques for differential-algebraic systems were presented, and im provements of special numerical methods for standard software packages were sug gested. The editors VII Table of Contents Circuit Simulation Merten K.
| Author | : Peter A. Markowich |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 261 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3709169615 |
In recent years the mathematical modeling of charge transport in semi conductors has become a thriving area in applied mathematics. The drift diffusion equations, which constitute the most popular model for the simula tion of the electrical behavior of semiconductor devices, are by now mathe matically quite well understood. As a consequence numerical methods have been developed, which allow for reasonably efficient computer simulations in many cases of practical relevance. Nowadays, research on the drift diffu sion model is of a highly specialized nature. It concentrates on the explora tion of possibly more efficient discretization methods (e.g. mixed finite elements, streamline diffusion), on the improvement of the performance of nonlinear iteration and linear equation solvers, and on three dimensional applications. The ongoing miniaturization of semiconductor devices has prompted a shift of the focus of the modeling research lately, since the drift diffusion model does not account well for charge transport in ultra integrated devices. Extensions of the drift diffusion model (so called hydrodynamic models) are under investigation for the modeling of hot electron effects in submicron MOS-transistors, and supercomputer technology has made it possible to employ kinetic models (semiclassical Boltzmann-Poisson and Wigner Poisson equations) for the simulation of certain highly integrated devices.
