LEADER 05947nam 2200661 450 001 996466553703316 005 20220603154924.0 010 $a3-030-67917-9 035 $a(CKB)4100000011867306 035 $a(MiAaPQ)EBC6534963 035 $a(Au-PeEL)EBL6534963 035 $a(OCoLC)1246581143 035 $a(PPN)255290039 035 $a(EXLCZ)994100000011867306 100 $a20211021d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aStochastic approaches to electron transport in micro- and nanostructures /$fMihail Nedjalkov, Ivan Dimov, Siegfried Selberherr 210 1$aCham, Switzerland :$cBirkha?user,$d[2021] 210 4$d©2021 215 $a1 online resource (xvi, 214 pages) $cillustrations 225 1 $aModeling and simulation in science, engineering & technology 311 $a3-030-67916-0 320 $aIncludes bibliographical references. 327 $aIntro -- 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. 327 $a7.1.2 Time Dependent Algorithms -- 7.2 Iteration Approach: Stochastic Model -- 7.3 Iteration Approach: Generalizing the Empirical Algorithms -- 7.3.1 Derivation of Finite Difference Algorithms -- 7.3.2 Derivation of Collinear Perturbation Algorithms -- 8 Inhomogeneous Stationary Transport -- 8.1 Stationary Conditions -- 8.2 Iteration Approach: Forward Stochastic Model -- 8.2.1 Adjoint Equation -- 8.2.2 Boundary Conditions -- 8.3 Iteration Approach: Single-Particle Algorithm and Ergodicity -- 8.3.1 Averaging on Before-Scattering States -- 8.3.2 Averaging in Time: Ergodicity -- 8.3.3 The Choice of Boundary -- 8.4 Iteration Approach: Trajectory Splitting Algorithm -- 8.5 Iteration Approach: Modified Backward Algorithm -- 8.6 A Comparison of Forward and Backward Approaches -- 9 General Transport: Self-Consistent Mixed Problem -- 9.1 Formulation of the Problem -- 9.2 The Adjoint Equation -- 9.3 Initial and Boundary Conditions -- 9.3.1 Initial Condition -- 9.3.2 Boundary Conditions -- 9.3.3 Carrier Number Fluctuations -- 9.4 Stochastic Device Modeling: Features -- 10 Event Biasing -- 10.1 Biasing of Initial and Boundary Conditions -- 10.1.1 Initial Condition -- 10.1.2 Boundary Conditions -- 10.2 Biasing of the Natural Evolution -- 10.2.1 Free Flight -- 10.2.2 Phonon Scattering -- 10.3 Self-Consistent Event Biasing -- Part III Stochastic Algorithms for Quantum Transport -- 11 Wigner Function Modeling -- 12 Evolution in a Quantum Wire -- 12.1 Formulation of the Problem -- 12.2 Generalized Wigner Equation -- 12.3 Equation of Motion of the Diagonal Elements -- 12.4 Closure at First-Off-Diagonal Level -- 12.5 Closure at Second-Off-Diagonal Level -- 12.5.1 Approximation of the fFOD+ Equation -- 12.5.1.1 Contribution from fSOD++, -- 12.5.1.2 Contribution from fSOD+,- -- 12.5.1.3 Correction from fSOD+-, -- 12.5.1.4 Correction from fSOD+,+. 410 0$aModeling and simulation in science, engineering & technology. 606 $aElectron transport$xMathematical models 606 $aMicroelectronics$xMathematical models 606 $aNanoelectronics$xMathematical models 606 $aCharge carrier processes 606 $aTransport d'electrons$2thub 606 $aMicroelectrònica$2thub 606 $aNanoelectrònica$2thub 606 $aModels matemàtics$2thub 608 $aLlibres electrònics$2thub 615 0$aElectron transport$xMathematical models. 615 0$aMicroelectronics$xMathematical models. 615 0$aNanoelectronics$xMathematical models. 615 0$aCharge carrier processes. 615 7$aTransport d'electrons 615 7$aMicroelectrònica 615 7$aNanoelectrònica 615 7$aModels matemàtics 676 $a574.192 700 $aNedjalkov$b Mihail$01221186 702 $aDimov$b Ivan$f1963- 702 $aSelberherr$b Siegfried$f1955- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466553703316 996 $aStochastic approaches to electron transport in micro- and nanostructures$92831548 997 $aUNISA