Numerical Investigation of the Hydrodynamic Model Equations for Charge Transport in Semiconductors PDF Download
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Author: A. M. Blochin
Publisher:
ISBN:
Category :
Languages : en
Pages : 52
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Book Description
Author: A. M. Blochin
Publisher:
ISBN:
Category :
Languages : en
Pages : 52
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Book Description
Author: Peter A. Markowich
Publisher: Springer Science & Business Media
ISBN: 3709169615
Category : Mathematics
Languages : en
Pages : 261
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Book Description
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.
Author: Vito Dario Camiola
Publisher: Springer Nature
ISBN: 303035993X
Category : Science
Languages : en
Pages : 344
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Book Description
This book offers, from both a theoretical and a computational perspective, an analysis of macroscopic mathematical models for description of charge transport in electronic devices, in particular in the presence of confining effects, such as in the double gate MOSFET. The models are derived from the semiclassical Boltzmann equation by means of the moment method and are closed by resorting to the maximum entropy principle. In the case of confinement, electrons are treated as waves in the confining direction by solving a one-dimensional Schrödinger equation obtaining subbands, while the longitudinal transport of subband electrons is described semiclassically. Limiting energy-transport and drift-diffusion models are also obtained by using suitable scaling procedures. An entire chapter in the book is dedicated to a promising new material like graphene. The models appear to be sound and sufficiently accurate for systematic use in computer-aided design simulators for complex electron devices. The book is addressed to applied mathematicians, physicists, and electronic engineers. It is written for graduate or PhD readers but the opening chapter contains a modicum of semiconductor physics, making it self-consistent and useful also for undergraduate students.
Author: Aleksandr Mikhaĭlovich Blokhin
Publisher:
ISBN: 9781617617911
Category : Hydrodynamics
Languages : en
Pages : 0
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Book Description
For the last decades mathematical simulation of physical phenomena in semiconductor devices becomes an actual and rapidly developing area of applied mathematics. Progress in microelectronic technologies enables constructing semiconductor devices of extremely small size such that simplified analytic models can hardly be used for analysis and design of modern semiconductor devices. The reason is that traditional simplifying assumptions which form the background of such models may be essentially broken in modern components of integral schemes. This book discusses the dynamics in this process.
Author: Aleksandr Mikhaĭlovich Blokhin
Publisher:
ISBN: 9781611222166
Category : SCIENCE
Languages : en
Pages : 181
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Book Description
For the last decades mathematical simulation of physical phenomena in semiconductor devices becomes an actual and rapidly developing area of applied mathematics. Progress in microelectronic technologies enables constructing semiconductor devices of extremely small size such that simplified analytic models can hardly be used for analysis and design of modern semiconductor devices. The reason is that traditional simplifying assumptions which form the background of such models may be essentially broken in modern components of integral schemes. This book discusses the dynamics in this process. (Imprint: Nova)
Author: Ansgar Jüngel
Publisher: Springer
ISBN: 3540895264
Category : Science
Languages : en
Pages : 326
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Book Description
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.
Author:
Publisher:
ISBN:
Category : Mathematical statistics
Languages : en
Pages : 1196
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Book Description
Author: Ansgar Jüngel
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 312
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Book Description
Author: Joseph W. Jerome
Publisher: Springer Science & Business Media
ISBN: 3642799876
Category : Mathematics
Languages : en
Pages : 177
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Book Description
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: W.H.A. SCHILDERS
Publisher: Elsevier
ISBN: 0080459153
Category : Mathematics
Languages : en
Pages : 930
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Book Description
This special volume provides a broad overview and insight in the way numerical methods are being used to solve the wide variety of problems in the electronics industry. Furthermore its aim is to give researchers from other fields of application the opportunity to benefit from the results wich have been obtained in the electronics industry.* Complete survey of numerical methods used in the electronic industry* Each chapter is selfcontained* Presents state-of-the-art applications and methods* Internationally recognised authors
