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ISBN: 9783642799877
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 mod… Mehr…
Joseph W. Jerome:
Analysis of Charge Transport - neues BuchISBN: 9783642799877
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 mo… Mehr…
Analysis of Charge Transport - neues Buch
ISBN: 9783642799877
*Analysis of Charge Transport* - A Mathematical Study of Semiconductor Devices / pdf eBook für 53.49 € / Aus dem Bereich: eBooks, Sachthemen & Ratgeber, Technik Medien > Bücher nein eBook… Mehr…
Analysis of Charge Transport - neues Buch
ISBN: 9783642799877
Analysis of Charge Transport - A Mathematical Study of Semiconductor Devices: ab 53.49 € eBooks > Sachthemen & Ratgeber > Technik Springer Berlin Heidelberg eBook als pdf, Springer Berlin… Mehr…
Analysis of Charge Transport - neues Buch
ISBN: 9783642799877
Analysis of Charge Transport - A Mathematical Study of Semiconductor Devices: ab 79.99 € eBooks > Sachthemen & Ratgeber > Technik Springer Berlin Heidelberg eBook als pdf, Springer Berlin… Mehr…
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Detailangaben zum Buch - Analysis of Charge Transport
EAN (ISBN-13): 9783642799877
Herausgeber: Springer Berlin Heidelberg
Buch in der Datenbank seit 2017-01-05T18:22:41+01:00 (Zurich)
Detailseite zuletzt geändert am 2023-05-23T15:23:05+02:00 (Zurich)
ISBN/EAN: 9783642799877
ISBN - alternative Schreibweisen:
978-3-642-79987-7
Alternative Schreibweisen und verwandte Suchbegriffe:
Autor des Buches: jerome jerome
Titel des Buches: mathematical analysis, analysis transport
Daten vom Verlag:
Autor/in: Joseph W. Jerome
Titel: Analysis of Charge Transport - A Mathematical Study of Semiconductor Devices
Verlag: Springer; Springer Berlin
167 Seiten
Erscheinungsjahr: 2012-12-06
Berlin; Heidelberg; DE
Sprache: Englisch
53,49 € (DE)
55,00 € (AT)
59,00 CHF (CH)
Available
XI, 167 p.
EA; E107; eBook; Nonbooks, PBS / Mathematik/Analysis; Mathematische Analysis, allgemein; Verstehen; Abweichungs-Diffusionssystem; Boltzmann transport equation; Boltzmann-Transportmodell; Drift-diffusion system; Energie; Gummel Iteration; Scharfetter-Gummel discretization; System decoupling; calculus; differential equation; energy transport model; finite element method; inf-sup Theorie; linearization; mixed boundary value problem; nichtlineare finite Elemente-Konvergenz-Theorie; nonlinear finite element convergence theory; numerical fixed point map; p/n Junktion; transistor; C; Analysis; Numerical Analysis; Electronics and Microelectronics, Instrumentation; Theoretical, Mathematical and Computational Physics; Analysis; Numerical Analysis; Electronics and Microelectronics, Instrumentation; Theoretical, Mathematical and Computational Physics; Mathematics and Statistics; Numerische Mathematik; Elektronik; Mathematische Physik; BB
1. Introduction.- 1.1 Modeling.- 1.2 Computational Foundations.- 1.3 Mathematical Theory.- 1.4 Summary.- I. Modeling of Semiconductor Devices.- 2. Development of Drift-Diffusion Models.- 2.1 Descriptive Background.- 2.2 Modeling Overview.- 2.3 Scaling and Junction Width Estimation.- 2.3.1 System and Scalings.- 2.3.2 Example and Heuristic Analysis.- 2.4 The Scharfetter-Gummel Discretization.- 2.4.1 Variational Calculus.- 2.4.2 Piecewise Constant Flux.- 2.5 A Model for Drift-Diffusion.- 2.5.1 The Mobility Relations.- 2.5.2 Boundary Conditions and Current-Voltage Relations.- 3. Moment Models: Microscopic to Macroscopic.- 3.1 The Hydrodynamic Model.- 3.1.1 Charge, Momentum and Energy Transport Equations.- 3.1.2 Moment Closure and Relaxation Relations.- 3.2 Calibration with the Mechanics of Charged Fluids.- 3.2.1 Conservation of Mass and Energy.- 3.2.2 The Momentum Subsystem.- 3.3 Subsonic Linearization Analysis in One Dimension.- 3.4 Energy Transport Models and Stokes’ Flow.- 3.4.1 The Steady-State System.- 3.4.2 Exponential Variables in One Dimension.- 3.4.3 Maximum Principles.- 3.4.4 The Fixed Point Map.- 3.5 Modeling Issues.- 3.5.1 Regimes Defined by Damping.- 3.6 A Glimpse of the Quantum Hydrodynamic Model.- II. Computational Foundations.- 4. A Family of Solution Fixed Point Maps: Partial Decoupling.- 4.1 Contraction Property of the Gummel Map in Two Dimensions.- 4.1.1 A Framework for the Gummel Map.- 4.1.2 The Principal Result.- 4.1.3 The Supporting Lemmas and Hypotheses.- 4.2 General Case: A Framework of Weighted Spaces.- 4.3 Existence and Maximum Principles for Uf.- 4.4 Admissible Lag and the Mapping VW f.- 4.4.1 Admissible Lagging of the Continuity Subsystem.- 4.4.2 Uniqueness and Definition of the Map VWf.- 4.5 A Variational Inequality for the Current Continuity Subsystem.- 4.5.1 Abstract Inequality Formulation.- 4.5.2 The Concrete Variational Inequality.- 4.6 Equivalence with the Current Continuity Subsystem.- 4.7 Compactness and Continuity of VWf and Fixed Points of Tf.- 4.7.1 Compactness.- 4.7.2 Continuity.- 4.7.3 The Gummel Map and its Fixed Points.- 4.8 Technical Properties of Norms and Mappings.- 4.8.1 Norm Equivalence.- 4.8.2 Enhanced Continuity for the Subsystem Map.- 5. Nonlinear Convergence Theory for Finite Elements.- 5.1 Definitions of the Composite Mappings of T.- 5.2 The Numerical Map Tn.- 5.2.1 The Composite Finite Element Maps.- 5.2.2 The Discrete Maximum Principles.- 5.2.3 The Numerical Fixed Point Map.- 5.3 Approximation Theory in Energy Norms and Pointwise Norms.- 5.3.1 Approximation Theory for Gradient Equations.- 5.3.2 Convergence Properties of Tn in Energy Norms.- 5.3.3 Convergence Properties of Tn in the Pointwise Norm.- 5.4 A Calculus for the System Mappings.- 5.4.1 The Map U: Differentiability Properties.- 5.4.2 The Mappings V and W: Differentiability Properties.- 5.5 The Mappings Uh, Vh, and Wh.- 5.5.1 The Mapping Uh.- 5.5.2 The Mappings Vh and Wh.- 5.6 Summary of Results for T and Tn.- 5.7 Verification of the General Hypotheses.- 5.7.1 Verification of the ‘A Priori’ Estimates.- 5.7.2 Verification of the ‘A Posteriori’ Estimates.- 5.8 Final Convergence Results.- III. Mathematical Theory.- 6. Numerical Fixed Point Approximation in Banach Space.- 6.1 Linear Theory: Staircase to the Nonlinear Theory.- 6.2 Nonlinear Estimation and the Operator Calculus.- 6.2.1 ‘A Priori’ Estimates and Asymptotic Linearity.- 6.2.2 ‘A Posteriori’ Estimates.- 6.3 Approximate Fixed Points via Newton’s Method.- 6.4 The Inf-Sup Theory As a Special Case.- 7. Construction of the Discrete Approximation Sequence.- 7.1 The Fixed Point Map as Smoother.- 7.1.1 Solution of the Central Approximation Problem.- 7.2 Smoothing for Newton Iteration: Differential Maps.- 7.2.1 Framework for the Postconditioning Iteration.- 7.2.2 The Superlinear Convergence Theorem.- References.Charge transport is a very active and quickly developing research field with a rich tradition going back into the last century. The author is one of the leading experts working on the mathematical theory and approximation of semiconductor models. During the last 15 years, he has made important contributions to this area.
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