Download or read book The Stationary Semiconductor Device Equations written by P.A. Markowich and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last two decades semiconductor device simulation has become a research area, which thrives on a cooperation of physicists, electrical engineers and mathe maticians. In this book the static semiconductor device problem is presented and analysed from an applied mathematician's point of view. I shall derive the device equations - as obtained for the first time by Van Roosbroeck in 1950 - from physical principles, present a mathematical analysis, discuss their numerical solu tion by discretisation techniques and report on selected device simulation runs. To me personally the most fascinating aspect of mathematical device analysis is that an interplay of abstract mathematics, perturbation theory, numerical analysis and device physics is prompting the design and development of new technology. I very much hope to convey to the reader the importance of applied mathematics for technological progress. Each chapter of this book is designed to be as selfcontained as possible, however, the mathematical analysis of the device problem requires tools which cannot be presented completely here. Those readers who are not interested in the mathemati cal methodology and rigor can extract the desired information by simply ignoring details and proofs of theorems. Also, at the beginning of each chapter I refer to textbooks which introduce the interested reader to the required mathematical concepts.
Download or read book The Stationary Semiconductor Device Equations written by Peter A. Markowich and published by Springer Verlag. This book was released on 1986 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Semiconductor Equations written by Peter A. Markowich and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Analysis of Mathematical Models of Semiconductor Devices written by Michael Stephen Mock and published by . This book was released on 1983 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computational Aspects of VLSI Design with an Emphasis on Semiconductor Device Simulation written by Randolph E. Bank and published by American Mathematical Soc.. This book was released on 1990-02-15 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Quasi hydrodynamic Semiconductor Equations written by Ansgar Jüngel and published by Springer Science & Business Media. This book was released on 2001-02-01 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a hierarchy of macroscopic models for semiconductor devices, studying three classes of models in detail: isentropic drift-diffusion equations, energy-transport models, and quantum hydrodynamic equations. The derivation of each, including physical discussions, is shown. Numerical simulations for modern semiconductor devices are performed, showing the particular features of each. The author develops modern analytical techniques, such as positive solution methods, local energy methods for free-boundary problems and entropy methods.
Download or read book Mathematical Modelling and Simulation of Electrical Circuits and Semiconductor Devices written by Randolph Bank and published by Birkhäuser. This book was released on 2012-12-06 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Semiconductor Devices written by Kevin M. Kramer and published by Prentice Hall. This book was released on 1997 with total page 746 pages. Available in PDF, EPUB and Kindle. Book excerpt: CD-ROM contains: "Win32 version of SGFramework and the simulations contains in the book."
Download or read book Transport Equations for Semiconductors written by Ansgar Jüngel and published by Springer. This book was released on 2009-04-20 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Semiconductor devices are ubiquitous in the modern computer and telecommunications industry. A precise knowledge of the transport equations for electron flow in semiconductors when a voltage is applied is therefore of paramount importance for further technological breakthroughs. In the present work, the author tackles their derivation in a systematic and rigorous way, depending on certain key parameters such as the number of free electrons in the device, the mean free path of the carriers, the device dimensions and the ambient temperature. Accordingly a hierarchy of models is examined which is reflected in the structure of the book: first the microscopic and macroscopic semi-classical approaches followed by their quantum-mechanical counterparts.
Download or read book Springer Handbook of Semiconductor Devices written by Massimo Rudan and published by Springer Nature. This book was released on 2022-11-10 with total page 1680 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Springer Handbook comprehensively covers the topic of semiconductor devices, embracing all aspects from theoretical background to fabrication, modeling, and applications. Nearly 100 leading scientists from industry and academia were selected to write the handbook's chapters, which were conceived for professionals and practitioners, material scientists, physicists and electrical engineers working at universities, industrial R&D, and manufacturers. Starting from the description of the relevant technological aspects and fabrication steps, the handbook proceeds with a section fully devoted to the main conventional semiconductor devices like, e.g., bipolar transistors and MOS capacitors and transistors, used in the production of the standard integrated circuits, and the corresponding physical models. In the subsequent chapters, the scaling issues of the semiconductor-device technology are addressed, followed by the description of novel concept-based semiconductor devices. The last section illustrates the numerical simulation methods ranging from the fabrication processes to the device performances. Each chapter is self-contained, and refers to related topics treated in other chapters when necessary, so that the reader interested in a specific subject can easily identify a personal reading path through the vast contents of the handbook.
Download or read book Advanced Semiconductor Device Physics and Modeling written by Juin J. Liou and published by Artech House on Demand. This book was released on 1994-01-01 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference provides detailed information on semiconductor physics and modelling.
Download or read book Introduction to Partial Differential Equations and Hilbert Space Methods written by Karl E. Gustafson and published by Courier Corporation. This book was released on 2012-04-26 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Easy-to-use text examines principal method of solving partial differential equations, 1st-order systems, computation methods, and much more. Over 600 exercises, with answers for many. Ideal for a 1-semester or full-year course.
Download or read book Applied and Industrial Mathematics in Italy II written by Vincenzo Cutello and published by World Scientific. This book was released on 2007 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt: Industrial mathematics is evolving into an important branch of mathematics. Mathematicians, in particular in Italy, are becoming increasingly aware of this new trend and are engaged in bridging the gap between highly specialized mathematical research and the emerging demand for innovation from industry. The contributions in this volume provide both R&D workers in industry with a general view of existing skills, and academics with state-of-the-art applications of mathematics to real-world problems, which may also be incorporated in advanced courses.
Download or read book Mathematical Problems in Semiconductor Physics written by Angelo Marcello Anile and published by Springer Science & Business Media. This book was released on 2003-09-16 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: On the the mathematical aspects of the theory of carrier transport in semiconductor devices. The subjects covered include hydrodynamical models for semiconductors based on the maximum entropy principle of extended thermodynamics, mathematical theory of drift-diffusion equations with applications, and the methods of asymptotic analysis.
Download or read book Mathematical Modelling and Simulation of Electrical Circuits and Semiconductor Devices written by R. Bank and published by Birkhäuser. This book was released on 2013-11-22 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Intrinsic Point Defects Impurities and Their Diffusion in Silicon written by Peter Pichler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the first comprehensive review of intrinsic point defects, impurities and their complexes in silicon. Besides compiling the structures, energetic properties, identified electrical levels and spectroscopic signatures, and the diffusion behaviour from investigations, it gives a comprehensive introduction into the relevant fundamental concepts.
Download or read book Semiconductors written by W.M. Jr. Coughran and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications SEMICONDUCTORS, PART II is based on the proceedings of the IMA summer program "Semiconductors." Our goal was to foster interaction in this interdisciplinary field which involves electrical engineers, computer scientists, semiconductor physicists and mathematicians, from both university and industry. In particular, the program was meant to encourage the participation of numerical and mathematical analysts with backgrounds in ordinary and partial differential equations, to help get them involved in the mathematical as pects of semiconductor models and circuits. We are grateful to W.M. Coughran, Jr., Julian Cole, Peter Lloyd, and Jacob White for helping Farouk Odeh organize this activity and trust that the proceedings will provide a fitting memorial to Farouk. We also take this opportunity to thank those agencies whose financial support made the program possible: the Air Force Office of Scientific Research, the Army Research Office, the National Science Foundation, and the Office of Naval Research. A vner Friedman Willard Miller, J r. Preface to Part II Semiconductor and integrated-circuit modeling are an important part of the high technology "chip" industry, whose high-performance, low-cost microprocessors and high-density memory designs form the basis for supercomputers, engineering work stations, laptop computers, and other modern information appliances. There are a variety of differential equation problems that must be solved to facilitate such mod eling.
