Download or read book Mathematical and Numerical Modelling of Heterostructure Semiconductor Devices From Theory to Programming written by E.A.B. Cole and published by Springer Science & Business Media. This book was released on 2009-11-28 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part of my lecturing work in the School of Mathematics at the University of Leeds involved teaching quantum mechanics and statistical mechanics to mathematics undergraduates, and also mathematical methods to undergraduate students in the School of Electronic and Electrical Engineering at the University. The subject of this book has arisen as a result of research collaboration on device modelling with members of the School of Electronic and Electrical Engineering. I wanted to write a book which would be of practical help to those wishing to learn more about the mathematical and numerical methods involved in heteroju- tion device modelling. I have introduced only a comparatively small number of t- ics, and the reader may think that other important topics should have been included. But of the topics which I have introduced, I hope that I have given the reader some practical advice concerning the implementation of the methods which are discussed. This practical advice includes demonstrating how the implementation of the me- ods may be tailored to the speci?c device being modelled, and also includes some sections of computer code to illustrate this implementation. I have also included some background theory regarding the origins of the routines.
Download or read book Stochastic Geometry Spatial Statistics and Random Fields written by Volker Schmidt and published by Springer. This book was released on 2014-10-24 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an attempt to provide a graduate level introduction to various aspects of stochastic geometry, spatial statistics and random fields, with special emphasis placed on fundamental classes of models and algorithms as well as on their applications, e.g. in materials science, biology and genetics. This book has a strong focus on simulations and includes extensive codes in Matlab and R which are widely used in the mathematical community. It can be seen as a continuation of the recent volume 2068 of Lecture Notes in Mathematics, where other issues of stochastic geometry, spatial statistics and random fields were considered with a focus on asymptotic methods.
Download or read book Mathematical Modelling and Simulation of Electrical Circuits and Semiconductor Devices written by Randolph E. Bank and published by Springer Science & Business Media. This book was released on 1994 with total page 806 pages. Available in PDF, EPUB and Kindle. Book excerpt: Circuit Simulation.- A new efficient numerical integration scheme for highly oscillatory electric circuits.- Numerische Lösung von hierarchisch strukturierten Systemen von Algebro-Differentialgleichungen.- Partitioning and multirate strategies in latent electric circuits.- Circuit simulation - an application for parallel ODE solvers?.- Numerical stability criteria for differential-algebraic systems.- Analysis of linear time-invariant networks in the frequency domain.- Limit cycle computation of oscillating electric circuits.- Timestep control for charge conserving integration in circuit simulation.- Ein Zusammenhang zwischen Waveformrelaxation und Iterationsverfahren für nichtlinear gestörte Gleichungen.- Multilevel-Newton-Verfahren in der Transientenanalyse elektrischer Netzwerke.- Transientensimulation elektrischer Netwerke mit TRBDF.- The transient behavior of an oscillator.- Device Simulation.- Numerical simulation of the carrier transport in semiconductor devices on the base of an energy model.- On uniqueness of solutions to the drift-diffusion-model of semiconductor devices.- On restrictions for discretizations of the simplified linearized van Roosbroeck's equations.- Mixed finite element discretization of continuity equations arising in semiconductor device simulation.- A piecewise linear Petrov-Galerkin analysis of the box-method.- Stability analysis of thermocapillary convection in semiconductor crystal growth.- The method of Baliga-Patankar and 3-D device simulation.- A mass conserving moving grid method for dopant simulation.- Numerical approaches to the kinetic semiconductor equations.- The non-stationary semiconductor model with bounded convective velocity and generation/recombination term.
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 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 Analysis of Charge Transport written by Joseph W. Jerome and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 Introduction To Semiconductor Device Modelling written by Christopher M Snowden and published by World Scientific. This book was released on 1998-09-29 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Circuit Device and Process Simulation written by Graham F. Carey and published by . This book was released on 1996-06-19 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents for the first time a unified treatment of the physical processes, mathematical models and numerical techniques for circuit, device and process simulation. At the macroscopic level linear and nonlinear circuit elements are introduced to yield a mathematical model of an integrated circuit. Numerical techniques used to solve this coupled system of ODEs are described. Microscopically, current flow within a transistor is modeled using the drift-diffusion and hydrodynamic PDE systems. Finite difference and finite element methods for spatial discretizations are treated, as are grid generation and refinement, upwinding, and multilevel schemes. At the fabrication level, physical processes such as diffusion, oxidation, and crystal growth are modeled using reaction-diffusion-convection equations. These models require multistep integration techniques and Krylov projection methods for successful implementation. Exercises, programming assignments, and an extensive bibliography are included to reinforce and extend the treatment.
Download or read book Mathematical Problems in Semiconductor Physics written by Angelo Marcello Anile and published by Springer. This book was released on 2003-12-15 with total page 152 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 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 Fundamental Research on the Numerical Modelling of Semiconductor Devices and Processes written by John J. H. Miller and published by . This book was released on 1987 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Simulations written by Lutz Angermann and published by BoD – Books on Demand. This book was released on 2011-01-30 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book will interest researchers, scientists, engineers and graduate students in many disciplines, who make use of mathematical modeling and computer simulation. Although it represents only a small sample of the research activity on numerical simulations, the book will certainly serve as a valuable tool for researchers interested in getting involved in this multidisciplinary field. It will be useful to encourage further experimental and theoretical researches in the above mentioned areas of numerical simulation.
Download or read book Modeling Simulation and Optimization of Integrated Circuits written by K. Antreich and published by Birkhäuser. This book was released on 2012-12-06 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: The third Conference on Mathematical Models and Numerical Simulation in Electronic Industry brought together researchers in mathematics, electrical engineering and scientists working in industry. The contributions to this volume try to bridge the gap between basic and applied mathematics, research in electrical engineering and the needs of industry.
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 with total page 208 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.
Download or read book Analysis and Simulation of Semiconductor Devices written by S. Selberherr and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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."
