Contents

• 1. Introduction
• 2. Fundamentals of Carbon Nanotubes
  • 2.1 Historical Overview
  • 2.2 Theoretical Background
  • 2.3 Nanotube Growth Methods
    • 2.3.1 Arc-Discharge and Laser Ablation
    • 2.3.2 Chemical Vapor Deposition
  • 2.4 Electronic Structure
    • 2.4.1 Electronic Band Structure of Graphene
    • 2.4.2 Electronic Band Structure of SW-CNTs
  • 2.5 Phonon Properties
    • 2.5.1 Phonon Dispersion Relations of Graphene
    • 2.5.2 Phonon Dispersion Relations of SW-CNTs
  • 2.6 Electron-Phonon Interaction
    • 2.6.1 Electron-Phonon Matrix Elements
  • 2.7 Transport Properties
    • 2.7.1 Ballistic Transport
    • 2.7.2 Diffusive Transport
  • 2.8 CNTs in Electronics
    • 2.8.1 Fabrication and Performance of CNT-FETs
    • 2.8.2 SCHOTTKY Barrier Model of CNT-FET Operation
    • 2.8.3 Environmental Influences on the Performance of CNT-FETs
    • 2.8.4 Prototype CNT-FET Circuits
  
  
• 3. Quantum Transport Models
  • 3.1 Equilibrium Zero Temperature GREEN's Function
    • 3.1.1 Definition of the GREEN's Function
  • 3.2 Equilibrium Finite Temperature GREEN's Function
    • 3.2.1 Equilibrium Ensemble Average
    • 3.2.2 MATSUBARA GREEN's Function
  • 3.3 Non-Equilibrium GREEN's Functions
    • 3.3.1 Non-Equilibrium Ensemble Average
    • 3.3.2 Contour-Ordered GREEN's Function
    • 3.3.3 KELDYSH Contour
  • 3.4 Perturbation Expansion of the GREEN's Function
    • 3.4.1 WICK Theorem
    • 3.4.2 First-Order Perturbation Expansion
  • 3.5 DYSON Equation
  • 3.6 Approximation of the Self-Energy
    • 3.6.1 Elecron-Electron Interaction
    • 3.6.2 Electron-Phonon Interaction
  • 3.7 Analytical Continuation
    • 3.7.1 Real Time Formalism
    • 3.7.2 LANGRETH Theorem
  • 3.8 Quantum Kinetic Equations
    • 3.8.1 The KADANOFF-BAYM Formulation
    • 3.8.2 KELDYSH Formulation
    • 3.8.3 Steady-State Kinetic Equations
  • 3.9 Relation to Observables
    • 3.9.1 Electron and Hole Density
    • 3.9.2 Spectral Function and Local Density of States
    • 3.9.3 Current Density
    • 3.9.4 Current Conservation
  • 3.10 Comparison of Transport Models
    • 3.10.1 Non-Equilibrium GREEN's Function
    • 3.10.2 Master Equation for the Density Matrix
    • 3.10.3 The WIGNER Distribution Function
  
  
• 4. Implementation
  • 4.1 Electrostatic Potential and the POISSON Equation
    • 4.1.1 Discretization of the POISSON Equation
    • 4.1.2 Boundary Conditions
    • 4.1.3 Interface Conditions
  • 4.2 Basis Functions and Matrix Representation
  • 4.3 Tight-Binding HAMILTONian
  • 4.4 Mode-Space Transformation
  • 4.5 Contact Self-Energies
    • 4.5.1 Semi-Infinite CNT Contacts
    • 4.5.2 SCHOTTKY Type Metal-CNT Contacts
  • 4.6 Scattering Self-Energies
    • 4.6.1 Scattering with Optical Phonons
    • 4.6.2 Scattering with Acoustic Phonons
  • 4.7 Evaluation of Observables
    • 4.7.1 Carrier Density
    • 4.7.2 Current
    • 4.7.3 Discussion
  • 4.8 Selection of the Energy Grid
    • 4.8.1 Confined States
    • 4.8.2 Non-adaptive Energy Grid
    • 4.8.3 Adaptive Energy Grid
  • 4.9 Self-Consistent Simulations
    • 4.9.1 Self-Consistent Iteration Scheme
    • 4.9.2 Convergence of the Self-Consistant Simulations
  
  
• 5. Applications
  • 5.1 Double-Gate Design
    • 5.1.1 Ambipolar Conduction
    • 5.1.2 Double-Gate CNT-FET
  • 5.2 Asymmetric Single-Gate Design
    • 5.2.1 Gate-Source Spacer Length
    • 5.2.2 Gate-Drain Spacer Length
  • 5.3 Device Optimization
    • 5.3.1 Gate-Delay Time of CNT-FETs
    • 5.3.2 Optimized Spacer Length
  • 5.4 Tunneling CNT-FETs
    • 5.4.1 Symmetric and Asymmetric Doping
  • 5.5 The Effect of Electron-Phonon Interaction
    • 5.5.1 Electron-Phonon Coupling Strength
    • 5.5.2 Phonon Energy
    • 5.5.3 Diffusive Limit
    • 5.5.4 Discussion
  
  
• 6. Summary and Conclusions
• A. First and Second Quantization
• B. Time Evolution Pictures
  • B.1 SCHRÖDINGER Picture
  • B.2 Interaction Picture
  • B.3 HEISENBERG Picture
  • B.4 The Evolution Operator
  • B.5 Imaginary Time Operators
  
  
• C. Review of Thermodynamics and Statistical Mechanics
  • C.1 FERMI-DIRAC Statistics
  • C.2 Bose-EINSTEIN Statistics
  
  
• D. Non-Interacting GREEN's Functions
  • D.1 Non-Interacting FERMIons
  • D.2 Non-Interacting Bosons
  
  
• E. FEYNMAN Diagrams
• F. Variational Derivation of Self-Energies
  • F.1 Electron-Electron Interaction
    • F.1.1 Screened Interaction, Polarization, and Vertex Function
  • F.2 Electron-Phonon Interaction
    • F.2.1 The Phonon GREEN's Function
    • F.2.2 The Phonon Self-Energy
  • F.3 Approximation of the Self-Energy
  
  
• G. Treatment of Contacts
  • G.1 Matrix Truncation
  • G.2 Contact Self-Energies
  • G.3 Surface GREEN's Function
  
  
• H. Recursive GREEN's Function Method
  • H.1 Recursive Algorithm to Calculate
  • H.2 Recursive Algorithm to Calculate
  
  
• Bibliography
• Own Publications

M. Pourfath: Numerical Study of Quantum Transport in Carbon Nanotube-Based Transistors