Overview

In this book a hierarchy of macroscopic models for semiconductor devices is presented. Three classes of models are studied in detail: isentropic drift-diffusion equations, energy-transport models, and quantum hydrodynamic equations. The derivation of each of the models is shown, including physical discussions. Furthermore, the corresponding mathematical problems are analyzed, using modern techniques for nonlinear partial differential equations. The equations are discretized employing mixed finite-element methods. Also, numerical simulations for modern semiconductor devices are performed, showing the particular features of the models. Modern analytical techniques have been used and further developed, such as positive solution methods, local energy methods for free-boundary problems and entropy methods. The book is aimed at applied mathematicians and physicists interested in mathematics, as well as graduate and postdoc students and researchers in these fields.

Full Product Details

Author:   Ansgar Jüngel
Publisher:   Birkhauser Verlag AG
Imprint:   Birkhauser Verlag AG
Edition:   Softcover reprint of the original 1st ed. 2001
Volume:   41
Dimensions:   Width: 15.50cm , Height: 1.60cm , Length: 23.50cm
Weight:   0.474kg
ISBN:  

9783034895217

ISBN 10:   3034895216
Pages:   293
Publication Date:   21 October 2012
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

1 Introduction.- 1.1 A hierarchy of semiconductor models.- 1.2 Quasi-hydrodynamic semiconductor models.- 2 Basic Semiconductor Physics.- 2.1 Homogeneous semiconductors.- 2.2 Inhomogeneous semiconductors.- 3 The Isentropic Drift-diffusion Model.- 3.1 Derivation of the model.- 3.2 Existence of transient solutions.- 3.3 Uniqueness of transient solutions.- 3.4 Localization of vacuum solutions.- 3.5 Numerical approximation.- 3.6 Current-voltage characteristics.- 4 The Energy-transport Model.- 4.1 Derivation of the model.- 4.2 Symmetrization and entropy function.- 4.3 Existence of transient solutions.- 4.4 Long-time behavior of the transient solution.- 4.5 Regularity and uniqueness.- 4.6 Existence of steady-state solutions.- 4.7 Uniqueness of steady-state solutions.- 4.8 Numerical approximation.- 5 The Quantum Hydrodynamic Model.- 5.1 Derivation of the model.- 5.2 Existence and positivity.- 5.3 Uniqueness of steady-state solutions.- 5.4 A non-existence result.- 5.5 The classical limit.- 5.6 Current-voltage characteristics.- 5.7 A positivity-preserving numerical scheme.- References.

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