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1.4.2 Quantum TCAD
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Dissertation R. Kosik
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Introduction to Part II
II. On the Road Through 2010: Ultimate Nanoscale CMOS Simulation Capability
Subsections
Introduction to Part II
2. A Six Moments Model for the Boltzmann Equation
2.1 The Boltzmann Poisson System
2.1.1 The Boltzmann Equation for Parabolic Energy Bands
2.1.2 Poisson Equation
2.1.3 Dimensional Reduction
2.1.4 Distribution Function Models
2.2 The Method of Moments
2.2.1 Macroscopic Observables
2.2.1.1 Sets of Moments
2.2.1.2 Physical Quantities
2.2.2 Hierarchy of Moment Equations
2.2.2.1 Even Moments
2.2.2.2 Odd Moments
2.2.2.3 Non-Parabolicity Corrections
2.2.3 Closure Problem
2.2.4 Boundary Conditions
2.3 Closure Relations for the Scattering Operator
2.3.1 Even Moments: Relaxation Times
2.3.2 Odd Moments: Mobilities
2.3.3 Analytical Mobility and Relaxation Times
2.3.4 Consistency with Bulk Monte Carlo Results
2.3.5 Hierarchy of Equations
3. Highest Order Moment Closure
3.1 Cumulant Closure
3.2 Maximum Entropy Closure
3.2.1 Distribution Families
3.2.2 Critique and Modifications
3.2.3 Diffusion Closure
3.3 Higher Order Statistics
3.4 Gaussian Invariant Closure
4. Tuning of the Nonlinear Solver
4.1 Discretization
4.1.1 Variants of the Scharfetter Gummel Discretization
4.1.2 Double Grid Discretization
4.1.3 Discussion
4.2 Consistent Highest Order Moment Closure
4.3 Choice of Residual Function
4.4 Linesearch
4.5 Initial Values and Stepping Methods
4.6 Variations of the Newton Method
4.7 Comparison with Monte Carlo
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1.4.2 Quantum TCAD
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Dissertation R. Kosik
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Introduction to Part II
R. Kosik: Numerical Challenges on the Road to NanoTCAD
Previous: 1.4.2 Quantum TCAD
Up: Dissertation R. Kosik
Next: Introduction to Part II
Previous: 1.4.2 Quantum TCAD
Up: Dissertation R. Kosik
Next: Introduction to Part II