Analysis Of Mathematical Models Of Semiconductor Devices
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Analysis Of Mathematical Models Of Semiconductor Devices
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Author : Michael Stephen Mock
language : en
Publisher:
Release Date : 1983
Analysis Of Mathematical Models Of Semiconductor Devices written by Michael Stephen Mock and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Semiconductors categories.
Analysis Of Charge Transport
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Author : Joseph W. Jerome
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Analysis Of Charge Transport written by Joseph W. Jerome 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.
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.
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.
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.
Introduction To Semiconductor Device Modelling
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Author : Christopher M. Snowden
language : en
Publisher: World Scientific
Release Date : 1998
Introduction To Semiconductor Device Modelling written by Christopher M. Snowden and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Science categories.
This book deals mainly with physical device models which are developed from the carrier transport physics and device geometry considerations. The text concentrates on silicon and gallium arsenide devices and includes models of silicon bipolar junction transistors, junction field effect transistors (JFETs), MESFETs, silicon and GaAs MESFETs, transferred electron devices, pn junction diodes and Schottky varactor diodes. The modelling techniques of more recent devices such as the heterojunction bipolar transistors (HBT) and the high electron mobility transistors are discussed. This book contains details of models for both equilibrium and non-equilibrium transport conditions. The modelling Technique of Small-scale devices is discussed and techniques applicable to submicron-dimensioned devices are included. A section on modern quantum transport analysis techniques is included. Details of essential numerical schemes are given and a variety of device models are used to illustrate the application of these techniques in various fields.
The Stationary Semiconductor Device Equations
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Author : Peter A. Markowich
language : en
Publisher: Springer Verlag
Release Date : 1986
The Stationary Semiconductor Device Equations written by Peter A. Markowich and has been published by Springer Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Technology & Engineering categories.
Mathematical Modelling And Simulation Of Electrical Circuits And Semiconductor Devices
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Author : Randolph Bank
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Mathematical Modelling And Simulation Of Electrical Circuits And Semiconductor Devices written by Randolph Bank and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
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.
Mathematical Problems In Semiconductor Physics
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Author : Angelo Marcello Anile
language : en
Publisher: Springer
Release Date : 2003-12-15
Mathematical Problems In Semiconductor Physics written by Angelo Marcello Anile and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-15 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.
Infinite Dimensional Algebras And Quantum Integrable Systems
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Author : Petr P. Kulish
language : en
Publisher:
Release Date : 2005
Infinite Dimensional Algebras And Quantum Integrable Systems written by Petr P. Kulish and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Curves categories.