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Table of Contents
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
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