Semiconductor Equations
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Semiconductor Equations
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Author : Peter A. Markowich
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Semiconductor Equations written by Peter A. Markowich and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Transport Equations For Semiconductors
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Author : Ansgar Jüngel
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-03-17
Transport Equations For Semiconductors written by Ansgar Jüngel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-17 with Science categories.
This volume presents a systematic and mathematically accurate description and derivation of transport equations in solid state physics, in particular semiconductor devices.
The Stationary Semiconductor Device Equations
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Author : P.A. Markowich
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
The Stationary Semiconductor Device Equations written by P.A. Markowich and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Technology & Engineering categories.
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.
Rate Equations In Semiconductor Electronics
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Author : John E. Carroll
language : en
Publisher: Cambridge University Press
Release Date : 1990-03-30
Rate Equations In Semiconductor Electronics written by John E. Carroll and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-03-30 with Science categories.
This book presents a novel approach to the teaching of dynamic aspects of the operation of semiconductor and opto-electronic devices. Such dynamic aspects often determine the steady state conditions. Also, the dynamical operation of such devices is of increasing importance as modern methods of communicating data and information require electronic devices that switch electrical or optical signals at ever faster rates. The author discusses the rates at which electrons and holes can reach equilibrium, the rates at which transistors and diodes can switch, and the rates at which electrons and holes can interact with photons, and with protons. He also applies the rate equations in a unified way to models of light-emitting diodes, injection lasers and photodiodes. Finally, the author discusses more-advanced topics on the photon statistics of injection lasers, mode-locking and the application of rate equations and Maxwell's equations to opto-electronic devices.
Quasi Hydrodynamic Semiconductor Equations
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Author : Ansgar Jüngel
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-02-01
Quasi Hydrodynamic Semiconductor Equations written by Ansgar Jüngel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-02-01 with Mathematics categories.
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.
Mathematical Problems In Semiconductor Physics
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Author : Angelo Marcello Anile
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-09-16
Mathematical Problems In Semiconductor Physics written by Angelo Marcello Anile and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-09-16 with Science categories.
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.
Analysis And Simulation Of Semiconductor Devices
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Author : S. Selberherr
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Analysis And Simulation Of Semiconductor Devices written by S. Selberherr and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
The invention of semiconductor devices is a fairly recent one, considering classical time scales in human life. The bipolar transistor was announced in 1947, and the MOS transistor, in a practically usable manner, was demonstrated in 1960. From these beginnings the semiconductor device field has grown rapidly. The first integrated circuits, which contained just a few devices, became commercially available in the early 1960s. Immediately thereafter an evolution has taken place so that today, less than 25 years later, the manufacture of integrated circuits with over 400.000 devices per single chip is possible. Coincident with the growth in semiconductor device development, the literature concerning semiconductor device and technology issues has literally exploded. In the last decade about 50.000 papers have been published on these subjects. The advent of so called Very-Large-Scale-Integration (VLSI) has certainly revealed the need for a better understanding of basic device behavior. The miniaturization of the single transistor, which is the major prerequisite for VLSI, nearly led to a breakdown of the classical models of semiconductor devices.
Hierarchy Of Semiconductor Equations Relaxation Limits With Initial Layers For Large Initial Data
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Author : Shinya Nishibata
language : en
Publisher: World Scientific
Release Date : 2011-07
Hierarchy Of Semiconductor Equations Relaxation Limits With Initial Layers For Large Initial Data written by Shinya Nishibata and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07 with Mathematics categories.
This volume provides a recent study of mathematical research on semiconductor equations. With recent developments in semiconductor technology, several mathematical models have been established to analyze and to simulate the behavior of electron flow in semiconductor devices. Among them, a hydrodynamic, an energy-transport and a drift-diffusion models are frequently used for the device simulation with the suitable choice, depending on the purpose of the device usage. Hence, it is interesting and important not only in mathematics but also in engineering to study a model hierarchy, relations among these models. The model hierarchy has been formally understood by relaxation limits letting the physical parameters, called relaxation times, tend to zero. The main concern of this volume is the mathematical justification of the relaxation limits. Precisely, we show that the time global solution for the hydrodynamic model converges to that for the energy-transport model as a momentum relaxation time tends to zero. Moreover, it is shown that the solution for the energy-transport model converges to that for the drift-diffusion model as an energy relaxation time tends to zero. For beginners' help, this volume also presents the physical background of the semiconductor devices, the derivation of the models, and the basic mathematical results such as the unique existence of time local solutions.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets
Physics Of Semiconductor Devices
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Author : J.-P. Colinge
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-08
Physics Of Semiconductor Devices written by J.-P. Colinge and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-08 with Technology & Engineering categories.
Physics of Semiconductor Devices covers both basic classic topics such as energy band theory and the gradual-channel model of the MOSFET as well as advanced concepts and devices such as MOSFET short-channel effects, low-dimensional devices and single-electron transistors. Concepts are introduced to the reader in a simple way, often using comparisons to everyday-life experiences such as simple fluid mechanics. They are then explained in depth and mathematical developments are fully described. Physics of Semiconductor Devices contains a list of problems that can be used as homework assignments or can be solved in class to exemplify the theory. Many of these problems make use of Matlab and are aimed at illustrating theoretical concepts in a graphical manner.
Balance Equation Approach To Electron Transport In Semiconductors
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Author : Xiaolin Lei
language : en
Publisher: World Scientific
Release Date : 2008
Balance Equation Approach To Electron Transport In Semiconductors written by Xiaolin Lei and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Technology & Engineering categories.
This book presents a systematic, comprehensive and up-to-date description of the physical basis of the balance equation transport theory and its applications in bulk and low-dimensional semiconductors. The different aspects of the balance equation method, originally proposed by C S Ting and the author of the present book, were reviewed in the volume entitled Physics of Hot Electron Transport in Semiconductors (edited by C S Ting, World Scientific, 1992). Since then, this method has been extensively developed and applied to various new fields, such as transport in nonparabolic systems, spatially nonuniform systems and semiconductor devices, miniband conduction of superlattices, hot-electron magnetotransport, effects of impact ionization in transport, microwave-induced magnetoresistance oscillation, radiation-driven transport and electron cooling, etc. Due to its simplicity and effectiveness, the balance equation approach has become a useful tool to tackle the many transport phenomena in semiconductors, and provides a reliable basis for developing theories, modeling devices and explaining experiments.The book may be used as a textbook by graduate students. It will also benefit researchers in the field by helping them grasp the basic principles and techniques of the method, without having to spend a lot of time digging out the information from widespread literature covering a period of 30 years.