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4.7 Comparison with Monte
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Dissertation R. Kosik
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Introduction to Part III
III. On the Road Beyond 2010: Simulation of Emerging Research Devices
Subsections
Introduction to Part III
5. A Test Case for NanoTCAD: Resonant Tunneling Structures
5.1 Physics of Resonant Tunneling
5.2 Resonant Tunneling Diode Structure
5.3 Coherent Tunneling
5.4 Influence of Scattering Events
6. Mathematical Formulations of Quantum Mechanics
6.1 Quantum Mechanics in Configuration Space
6.1.1 Wave Mechanics
6.1.1.1 Schrödinger Equation
6.1.1.2 Von Neumann Equation
6.1.2 Hydrodynamical Formulation
6.1.3 The Riccati and Prüfer Equation
6.2 Quantum Mechanics in Phase Space
6.2.1 Phase Space Distribution Functions
6.2.2 Definition of Wigner Function
6.2.3 Operator-Theoretic Structure
6.2.4 Probabilistic Structure
6.2.5 A Caveat on Marginal Distributions
6.2.6 A Feasible Phase Space Distribution
6.2.7 Quantum Propagators and Trajectories
7. Schrödinger and von Neumann Equation
7.1 Single Particle Transport
7.1.1 Open Quantum Systems
7.1.2 Absorbing Boundary Conditions
7.1.2.1 Schrödinger: Transparent BCs
7.1.2.2 Riccati and Prüfer: Dirichlet BCs
7.1.3 Comparison: Schrödinger, Riccati & Prüfer Equation
7.2 The Open Von Neumann-Poisson Equation
7.2.1 Separation of Neumann Equation
7.2.2 Open System
7.2.3 Self Consistency
7.2.4 A Brute Force Approach: Parallelization with MPI
7.2.5 Existence But Non-Uniqueness
7.2.6 Scattering in the QTBM
7.2.6.1 Schrödinger Equation with an Imaginary Potential
7.2.6.2 Relaxation-Time-Like Models
8. Finite Difference Wigner Function Method
8.1 Wigner Equation
8.2 Discrete Wigner Transform
8.3 Conservation of Mass
8.3.1 Continuity Equation
8.3.2 Meshing Constraints
8.4 Discretization
8.4.1 Free Term
8.4.2 Drift Term
8.4.3 Relaxation Time Scattering
8.4.4 Boundary Conditions
8.5 Remarks on Implementation
9. Stochastic Methods and Monte Carlo
9.1 Quantum Electron-Phonon Scattering
9.2 Boltzmann-Type Scattering
9.3 A Scattering Interpretation of the Potential Operator
9.4 The Negative Sign Problem
10. Evaluation of Quantum Simulation Approaches
10.1 Comparison of Simulation Results
10.1.1 I-V curves
10.1.2 Current Density
10.1.3 Carrier Density
10.2 Discussion of Discrepancy
10.2.1 Coherence Length
10.2.2 Mesh Size
10.2.3 Boundary Conditions
10.2.4 Effective Mass Model
10.2.5 Discretization
Previous:
4.7 Comparison with Monte
Up:
Dissertation R. Kosik
Next:
Introduction to Part III
R. Kosik: Numerical Challenges on the Road to NanoTCAD
Previous: 4.7 Comparison with Monte
Up: Dissertation R. Kosik
Next: Introduction to Part III
Previous: 4.7 Comparison with Monte
Up: Dissertation R. Kosik
Next: Introduction to Part III