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Table of Contents
Intro
Acknowledgements
Author biographies
David K Ferry
Xavier Oriols
Josef Weinbub
Chapter Introduction
1.1 Particles in classical transport
1.2 The quantum mechanical view of particles
1.2.1 Heisenberg and quantization
1.2.2 De Broglie and Schrödinger
1.2.3 The hydrodynamic or Bohmian view
1.2.4 Consistent histories
1.3 Electronic devices as complex systems
1.3.1 Electronic devices as open systems
1.3.2 Electronic devices as nonequilibrium systems
1.4 Probability and particles
1.4.1 Probability
1.4.2 Particles in quantum field theory
1.5 Various approaches for semiconductor devices
1.5.1 Basic beginnings
1.5.2 Landauer and beyond
1.5.3 Wigner functions
1.5.4 Green's functions
1.6 An outline of this book
Appendix A On quantization and second quantization
A.1 The harmonic oscillator
A.2 The operator approach to the harmonic oscillator
A.3 Field operators
References
Chapter The microscopic world and microscopic properties
2.1 The measurement problem in quantum mechanics
2.2 Measurements and the environment
2.2.1 Drain-induced barrier lowering
2.2.2 Light emission
2.3 Landauer and contacts
2.3.1 The Landauer formula
2.3.2 Charge and contacts
2.3.3 Casting the MOSFET in Landauer form
2.4 Microscopic properties and the measurement of classical systems
2.5 Microscopic properties and the measurement of quantum systems
2.5.1 Measurements according to quantum theories with observers
2.5.2 Measurements according to quantum theories without observers
2.5.3 What physical reality says about measurements
2.6 Single-time measurements
2.7 Multi-time measurements
2.8 Displacement current
Appendix A Weak and strong measurements
A.1 Von Neumann's strong measurements
A.2 Von Neumann's weak or indirect measurements.
References
Chapter Many-body open systems outside thermodynamic equilibrium
3.1 The many-body problem in quantum mechanics
3.1.1 The Born-Oppenheimer approximation
3.1.2 Quantum statistics
3.1.3 Quantum effects in scattering
3.2 Open systems-interaction with the environment
3.2.1 Interaction with the environment
3.2.2 An example of pointer states
3.2.3 Environment-induced states
3.3 Wave functions for open systems
3.3.1 The scattering matrix approach
3.3.2 An introduction to scattering
3.3.3 The simulation of a small MOSFET
3.3.4 Simulation with particles
3.4 Microscopic equations of motion for particles
3.4.1 Bohmian conditional wave functions
3.4.2 The reduced density matrix and the statistical density matrix
3.4.3 Thermalization, decoherence, and pointer states
3.4.4 Markovian and non-Markovian open systems
3.5 The macroscopic world and thermodynamics
References
Chapter An overview of semiconductor devices
4.1 Introduction
4.1.1 An example-the evolution of the FET
4.1.2 How does quantum transport arise?
4.1.3 How do quantum transport and classical transport differ?
4.2 Diodes and bipolar junction transistors
4.3 The MOSFET
4.3.1 Inversion layers
4.3.2 Strain
4.3.3 Discrete impurities
4.4 MESFETs
4.4.1 The Schottky barrier
4.4.2 The MESFET
4.5 The high-electron-mobility transistor
4.6 Other interesting devices
4.6.1 Tunnel diodes
4.6.2 Tunnel FETs
4.6.3 SpinFETs
4.6.4 Single-atom transistors
4.7 Ballistic transport
4.8 Optical devices
References
Chapter What is needed from quantum mechanics
5.1 Space- and timescales
5.2 Entanglement
5.2.1 Schrödinger's cat
5.2.2 Further thoughts
5.3 Particles in quantum transport
5.4 Current approaches
5.4.1 The density matrix
5.4.2 Quantum kinetic equations.
5.4.3 Wigner functions
5.4.4 Green's functions
5.5 Tunneling with particles
5.6 Spin
5.7 Time dependence
Appendix A Classical and quantum brackets
Appendix B Spin and second quantization for fermions
B.1 Spin and antisymmetry
B.2 Second quantization for fermions
References
Chapter Electron-atom interaction: band structure
6.1 The basics of energy bands
6.1.1 Potentials and pseudopotentials
6.1.2 A diatomic lattice
6.1.3 The complex band structure
6.2 Real-space approaches
6.3 Momentum-space approaches
6.4 The k·p approximation
6.4.1 The energy bands
6.4.2 Anisotropic valence bands
6.5 Broadening of the band edges
6.6 The effective-mass approximation
6.7 Strain
6.8 Connecting transport to the band structure
6.9 Phonons: beyond the Born-Oppenheimer approximation
6.9.1 Nonequilibrium phonons
6.9.2 Treating phonons as particles
References
Chapter Electron interactions with fields: the electrostatic approximation
7.1 Poisson's equation and charge distributions
7.2 The self-consistency of the transport equation
7.2.1 The drift-diffusion transport model
7.2.2 Monte Carlo models
7.3 Apportioning the charge
7.4 Boundary conditions
7.5 Not always so simple
References
Chapter Beyond the electrostatic approximation
8.1 Maxwell's equations and the gauge
8.2 Cutoff frequencies
8.3 Circuit effects
8.4 Finite-difference time-domain analysis
8.4.1 Finite-difference time-domain and ensemble Monte Carlo methods for devices
8.4.2 The finite-difference time-domain method and optics
8.5 Electromagnetic field quantization
8.6 Electron-photon interactions
8.6.1 Electron-photon scattering
8.6.2 Free-carrier absorption
8.6.3 Electron-hole creation
8.7 Electron-electron scattering
8.7.1 Electron-plasmon scattering.
8.7.2 Single-particle scattering
8.7.3 Treating the interaction in real space
8.8 The quantization of electrons and radiation
8.8.1 Maxwell's equations in terms of transverse and longitudinal fields
8.8.2 A Hamiltonian for electrons interacting with the electromagnetic field
8.8.3 Canonical variables for the description of one mode of the electromagnetic fields
8.8.4 The classical solution for matter-light interaction
8.8.5 The semiclassical solution for matter-light interaction
8.8.6 The quantum solution for matter-light interaction
8.8.7 The quantum solution with particles and fields
References
Chapter The Monte Carlo method
9.1 The path integral
9.2 Free-flight generation
9.3 Scattering
9.4 Rejection techniques
9.4.1 State filling and degeneracy
9.4.2 Nonequilibrium phonons
9.4.3 An example
9.5 Full-band approaches
References
Chapter Effective potentials and Bohmian trajectories
10.1 On the role of particle size
10.1.1 Simply the size
10.1.2 The effective potential
10.1.3 An example
10.2 The Bohm potential
10.2.1 Trajectories
10.2.2 The two-slit experiment
10.2.3 Optical confirmation
10.2.4 Semiconductor devices
10.3 The Wigner potential
10.4 Feynman's effective potentials
10.5 Determining effective potentials using Bohmian conditional wave functions
10.5.1 Quantum transport based on Bohmian trajectories and conditional wave functions
10.5.2 Application to resonant-tunneling diodes
10.5.3 Final remarks
Appendix A Empirical and theoretical definitions of weak values
References
Chapter Wigner functions
11.1 Some properties of the Wigner function
11.1.1 The Moyal star product and the equation of motion
11.1.2 Initial conditions
11.1.3 Wigner-Weyl methods
11.2 Generalizing the Wigner function.
11.2.1 The general Weyl operator and the Wigner function
11.2.2 General uses of the characteristic function
11.3 The use of particles with the Wigner function
11.3.1 Weighted Monte Carlo
11.3.2 The affinity parameter
11.3.3 Signed particles
11.3.4 Spectral methods
11.4 Particles in Wigner optics
11.4.1 The optical waveguide
11.4.2 The ring resonator
11.4.3 Monte Carlo methods
11.5 Scattering with Wigner functions
11.6 Device simulation with Wigner particles
References
Chapter Why not Green's functions?
12.1 Equations of motion
12.1.1 The retarded Green's function
12.1.2 The 'less-than' function
12.1.3 The solution of the quantum Boltzmann equation
12.2 A high-field solution
12.2.1 The Airy transform
12.2.2 The retarded Green's function
12.2.3 The 'less-than' function
12.3 The limitations of NEGFs
12.4 NEGFs in devices
12.4.1 MOSFETs
12.4.2 Other materials and devices
12.5 The use of particles in NEGFs
12.5.1 The silicon model
12.5.2 The Monte Carlo sequence
12.5.3 Results
References.
Acknowledgements
Author biographies
David K Ferry
Xavier Oriols
Josef Weinbub
Chapter Introduction
1.1 Particles in classical transport
1.2 The quantum mechanical view of particles
1.2.1 Heisenberg and quantization
1.2.2 De Broglie and Schrödinger
1.2.3 The hydrodynamic or Bohmian view
1.2.4 Consistent histories
1.3 Electronic devices as complex systems
1.3.1 Electronic devices as open systems
1.3.2 Electronic devices as nonequilibrium systems
1.4 Probability and particles
1.4.1 Probability
1.4.2 Particles in quantum field theory
1.5 Various approaches for semiconductor devices
1.5.1 Basic beginnings
1.5.2 Landauer and beyond
1.5.3 Wigner functions
1.5.4 Green's functions
1.6 An outline of this book
Appendix A On quantization and second quantization
A.1 The harmonic oscillator
A.2 The operator approach to the harmonic oscillator
A.3 Field operators
References
Chapter The microscopic world and microscopic properties
2.1 The measurement problem in quantum mechanics
2.2 Measurements and the environment
2.2.1 Drain-induced barrier lowering
2.2.2 Light emission
2.3 Landauer and contacts
2.3.1 The Landauer formula
2.3.2 Charge and contacts
2.3.3 Casting the MOSFET in Landauer form
2.4 Microscopic properties and the measurement of classical systems
2.5 Microscopic properties and the measurement of quantum systems
2.5.1 Measurements according to quantum theories with observers
2.5.2 Measurements according to quantum theories without observers
2.5.3 What physical reality says about measurements
2.6 Single-time measurements
2.7 Multi-time measurements
2.8 Displacement current
Appendix A Weak and strong measurements
A.1 Von Neumann's strong measurements
A.2 Von Neumann's weak or indirect measurements.
References
Chapter Many-body open systems outside thermodynamic equilibrium
3.1 The many-body problem in quantum mechanics
3.1.1 The Born-Oppenheimer approximation
3.1.2 Quantum statistics
3.1.3 Quantum effects in scattering
3.2 Open systems-interaction with the environment
3.2.1 Interaction with the environment
3.2.2 An example of pointer states
3.2.3 Environment-induced states
3.3 Wave functions for open systems
3.3.1 The scattering matrix approach
3.3.2 An introduction to scattering
3.3.3 The simulation of a small MOSFET
3.3.4 Simulation with particles
3.4 Microscopic equations of motion for particles
3.4.1 Bohmian conditional wave functions
3.4.2 The reduced density matrix and the statistical density matrix
3.4.3 Thermalization, decoherence, and pointer states
3.4.4 Markovian and non-Markovian open systems
3.5 The macroscopic world and thermodynamics
References
Chapter An overview of semiconductor devices
4.1 Introduction
4.1.1 An example-the evolution of the FET
4.1.2 How does quantum transport arise?
4.1.3 How do quantum transport and classical transport differ?
4.2 Diodes and bipolar junction transistors
4.3 The MOSFET
4.3.1 Inversion layers
4.3.2 Strain
4.3.3 Discrete impurities
4.4 MESFETs
4.4.1 The Schottky barrier
4.4.2 The MESFET
4.5 The high-electron-mobility transistor
4.6 Other interesting devices
4.6.1 Tunnel diodes
4.6.2 Tunnel FETs
4.6.3 SpinFETs
4.6.4 Single-atom transistors
4.7 Ballistic transport
4.8 Optical devices
References
Chapter What is needed from quantum mechanics
5.1 Space- and timescales
5.2 Entanglement
5.2.1 Schrödinger's cat
5.2.2 Further thoughts
5.3 Particles in quantum transport
5.4 Current approaches
5.4.1 The density matrix
5.4.2 Quantum kinetic equations.
5.4.3 Wigner functions
5.4.4 Green's functions
5.5 Tunneling with particles
5.6 Spin
5.7 Time dependence
Appendix A Classical and quantum brackets
Appendix B Spin and second quantization for fermions
B.1 Spin and antisymmetry
B.2 Second quantization for fermions
References
Chapter Electron-atom interaction: band structure
6.1 The basics of energy bands
6.1.1 Potentials and pseudopotentials
6.1.2 A diatomic lattice
6.1.3 The complex band structure
6.2 Real-space approaches
6.3 Momentum-space approaches
6.4 The k·p approximation
6.4.1 The energy bands
6.4.2 Anisotropic valence bands
6.5 Broadening of the band edges
6.6 The effective-mass approximation
6.7 Strain
6.8 Connecting transport to the band structure
6.9 Phonons: beyond the Born-Oppenheimer approximation
6.9.1 Nonequilibrium phonons
6.9.2 Treating phonons as particles
References
Chapter Electron interactions with fields: the electrostatic approximation
7.1 Poisson's equation and charge distributions
7.2 The self-consistency of the transport equation
7.2.1 The drift-diffusion transport model
7.2.2 Monte Carlo models
7.3 Apportioning the charge
7.4 Boundary conditions
7.5 Not always so simple
References
Chapter Beyond the electrostatic approximation
8.1 Maxwell's equations and the gauge
8.2 Cutoff frequencies
8.3 Circuit effects
8.4 Finite-difference time-domain analysis
8.4.1 Finite-difference time-domain and ensemble Monte Carlo methods for devices
8.4.2 The finite-difference time-domain method and optics
8.5 Electromagnetic field quantization
8.6 Electron-photon interactions
8.6.1 Electron-photon scattering
8.6.2 Free-carrier absorption
8.6.3 Electron-hole creation
8.7 Electron-electron scattering
8.7.1 Electron-plasmon scattering.
8.7.2 Single-particle scattering
8.7.3 Treating the interaction in real space
8.8 The quantization of electrons and radiation
8.8.1 Maxwell's equations in terms of transverse and longitudinal fields
8.8.2 A Hamiltonian for electrons interacting with the electromagnetic field
8.8.3 Canonical variables for the description of one mode of the electromagnetic fields
8.8.4 The classical solution for matter-light interaction
8.8.5 The semiclassical solution for matter-light interaction
8.8.6 The quantum solution for matter-light interaction
8.8.7 The quantum solution with particles and fields
References
Chapter The Monte Carlo method
9.1 The path integral
9.2 Free-flight generation
9.3 Scattering
9.4 Rejection techniques
9.4.1 State filling and degeneracy
9.4.2 Nonequilibrium phonons
9.4.3 An example
9.5 Full-band approaches
References
Chapter Effective potentials and Bohmian trajectories
10.1 On the role of particle size
10.1.1 Simply the size
10.1.2 The effective potential
10.1.3 An example
10.2 The Bohm potential
10.2.1 Trajectories
10.2.2 The two-slit experiment
10.2.3 Optical confirmation
10.2.4 Semiconductor devices
10.3 The Wigner potential
10.4 Feynman's effective potentials
10.5 Determining effective potentials using Bohmian conditional wave functions
10.5.1 Quantum transport based on Bohmian trajectories and conditional wave functions
10.5.2 Application to resonant-tunneling diodes
10.5.3 Final remarks
Appendix A Empirical and theoretical definitions of weak values
References
Chapter Wigner functions
11.1 Some properties of the Wigner function
11.1.1 The Moyal star product and the equation of motion
11.1.2 Initial conditions
11.1.3 Wigner-Weyl methods
11.2 Generalizing the Wigner function.
11.2.1 The general Weyl operator and the Wigner function
11.2.2 General uses of the characteristic function
11.3 The use of particles with the Wigner function
11.3.1 Weighted Monte Carlo
11.3.2 The affinity parameter
11.3.3 Signed particles
11.3.4 Spectral methods
11.4 Particles in Wigner optics
11.4.1 The optical waveguide
11.4.2 The ring resonator
11.4.3 Monte Carlo methods
11.5 Scattering with Wigner functions
11.6 Device simulation with Wigner particles
References
Chapter Why not Green's functions?
12.1 Equations of motion
12.1.1 The retarded Green's function
12.1.2 The 'less-than' function
12.1.3 The solution of the quantum Boltzmann equation
12.2 A high-field solution
12.2.1 The Airy transform
12.2.2 The retarded Green's function
12.2.3 The 'less-than' function
12.3 The limitations of NEGFs
12.4 NEGFs in devices
12.4.1 MOSFETs
12.4.2 Other materials and devices
12.5 The use of particles in NEGFs
12.5.1 The silicon model
12.5.2 The Monte Carlo sequence
12.5.3 Results
References.