Stochastic approaches to electron transport in micro- and nanostructures / / Mihail Nedjalkov, Ivan Dimov, Siegfried Selberherr

• Autore: Nedjalkov Mihail
• Pubblicazione: Cham, Switzerland : , : Birkhäuser, , [2021]; ©2021
• Descrizione fisica: 1 online resource (xvi, 214 pages) : illustrations
• Disciplina: 574.192
• Soggetto topico: Electron transport - Mathematical models; Microelectronics - Mathematical models; Nanoelectronics - Mathematical models; Charge carrier processes; Transport d'electrons; Microelectrònica; Nanoelectrònica; Models matemàtics
• Soggetto genere / forma: Llibres electrònics
• Persona (resp. second.): DimovIvan <1963->; SelberherrSiegfried <1955->
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Intro -- Preface -- Introduction to the Parts -- Contents -- Part I Aspects of Electron Transport Modeling -- 1 Concepts of Device Modeling -- 1.1 About Microelectronics -- 1.2 The Role of Modeling -- 1.3 Modeling of Semiconductor Devices -- 1.3.1 Basic Modules -- 1.3.2 Transport Models -- 1.3.3 Device Modeling: Aspects -- 2 The Semiconductor Model: Fundamentals -- 2.1 Crystal Lattice Electrons -- 2.1.1 Band Structure -- 2.1.2 Carrier Dynamics -- 2.1.3 Charge Transport -- 2.2 Lattice Imperfections -- 2.2.1 Phonons -- 2.2.2 Phonon Scattering -- 3 Transport Theories in Phase Space -- 3.1 Classical Transport: Boltzmann Equation -- 3.1.1 Phenomenological Derivation -- 3.1.2 Parametrization -- 3.1.3 Classical Distribution Function -- 3.2 Quantum Transport: Wigner Equation -- 3.2.1 Operator Mechanics -- 3.2.2 Quantum Mechanics in Phase Space -- 3.2.3 Derivation of the Wigner Equation -- 3.2.4 Properties of the Wigner Equation -- 3.2.5 Classical Limit of the Wigner Equation -- 4 Monte Carlo Computing -- 4.1 The Monte Carlo Method for Solving Integrals -- 4.2 The Monte Carlo Method for Solving Integral Equations -- 4.3 Monte Carlo Integration and Variance Analysis -- Part II Stochastic Algorithms for Boltzmann Transport -- 5 Homogeneous Transport: Empirical Approach -- 5.1 Single-Particle Algorithm -- 5.1.1 Single-Particle Trajectory -- 5.1.2 Mean Values -- 5.1.3 Concept of Self-Scattering -- 5.1.4 Boundary Conditions -- 5.2 Ensemble Algorithm -- 5.3 Algorithms for Statistical Enhancement -- 6 Homogeneous Transport: Stochastic Approach -- 6.1 Trajectory Integral Algorithm -- 6.2 Backward Algorithm -- 6.3 Iteration Approach -- 6.3.1 Derivation of the Backward Algorithm -- 6.3.2 Derivation of Empirical Algorithms -- 6.3.3 Featured Applications -- 7 Small Signal Analysis -- 7.1 Empirical Approach -- 7.1.1 Stationary Algorithms. ; 7.1.2 Time Dependent Algorithms -- 7.2 Iteration Approach: Stochastic Model -- 7.3 Iteration Approach: Generalizing the Empirical Algorithms -- 7.3.1 Derivation of Finite Difference Algorithms -- 7.3.2 Derivation of Collinear Perturbation Algorithms -- 8 Inhomogeneous Stationary Transport -- 8.1 Stationary Conditions -- 8.2 Iteration Approach: Forward Stochastic Model -- 8.2.1 Adjoint Equation -- 8.2.2 Boundary Conditions -- 8.3 Iteration Approach: Single-Particle Algorithm and Ergodicity -- 8.3.1 Averaging on Before-Scattering States -- 8.3.2 Averaging in Time: Ergodicity -- 8.3.3 The Choice of Boundary -- 8.4 Iteration Approach: Trajectory Splitting Algorithm -- 8.5 Iteration Approach: Modified Backward Algorithm -- 8.6 A Comparison of Forward and Backward Approaches -- 9 General Transport: Self-Consistent Mixed Problem -- 9.1 Formulation of the Problem -- 9.2 The Adjoint Equation -- 9.3 Initial and Boundary Conditions -- 9.3.1 Initial Condition -- 9.3.2 Boundary Conditions -- 9.3.3 Carrier Number Fluctuations -- 9.4 Stochastic Device Modeling: Features -- 10 Event Biasing -- 10.1 Biasing of Initial and Boundary Conditions -- 10.1.1 Initial Condition -- 10.1.2 Boundary Conditions -- 10.2 Biasing of the Natural Evolution -- 10.2.1 Free Flight -- 10.2.2 Phonon Scattering -- 10.3 Self-Consistent Event Biasing -- Part III Stochastic Algorithms for Quantum Transport -- 11 Wigner Function Modeling -- 12 Evolution in a Quantum Wire -- 12.1 Formulation of the Problem -- 12.2 Generalized Wigner Equation -- 12.3 Equation of Motion of the Diagonal Elements -- 12.4 Closure at First-Off-Diagonal Level -- 12.5 Closure at Second-Off-Diagonal Level -- 12.5.1 Approximation of the fFOD+ Equation -- 12.5.1.1 Contribution from fSOD++, -- 12.5.1.2 Contribution from fSOD+,- -- 12.5.1.3 Correction from fSOD+-, -- 12.5.1.4 Correction from fSOD+,+.
• Titolo autorizzato: Stochastic approaches to electron transport in micro- and nanostructures
• ISBN: 3-030-67917-9
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 996466553703316
• Lo trovi qui: Univ. di Salerno
• Serie: Modeling and simulation in science, engineering & technology.