Contents

• Abstract
• Kurzfassung
• Acknowledgements
• 1 Introduction
  • 1.1 Motivation
  • 1.2 Approach and Outline
• 2 Ion Implantation
  • 2.1 Physically Based Modeling
    • 2.1.1 Monte Carlo Simulation
    • 2.1.2 Boltzmann Transport Equation Method
    • 2.1.3 LSS-Theory
  • 2.2 One-Dimensional Distribution Functions
    • 2.2.1 Vertical Distribution Function
    • 2.2.2 Lateral Distribution Function
    • 2.2.3 Getting the Range Parameters
    • 2.2.4 Multilayered Structures
  • 2.3 Two-Dimensional Profiles
    • 2.3.1 Two-Dimensional Point Response
    • 2.3.2 Profiles in Arbitrary Structures
    • 2.3.3 Grid Generation and Adaption
  • 2.4 Model Library
  • 2.5 Applications
    • 2.5.1 Analytical Ion Implantation - Monte Carlo Ion Implantation
    • 2.5.2 Knock-in Implantation - A Feasibility Study for the Production of Ultra Shallow Profiles
• 3 Diffusion
  • 3.1 Governing Physical Equations
  • 3.2 Model Library
    • 3.2.1 Coupled/Uncoupled Diffusion (Models DIFC and DIFN)
      • Model Equations for Electric Field Coupled Diffusion (Model DIFC)
      • Simplifications for Uncoupled Diffusion (Model DIFN)
      • Model Parameters
    • 3.2.2 High Concentration Effects (Models DIFSCL and DIFDCL)
      • Dynamic Clustering (Model DIFDCL)
      • Static Clustering (Model DIFSCL)
      • Model Parameters
    • 3.2.3 Oxidation Enhanced/Retarded Diffusion (Models OEDS and OED)
      • Analytical Point Defect Model for OED/ORD (Model OEDS)
      • Coupled Point Defect and Impurity Diffusion Model for OED/ORD
        (Model OED)
    • 3.2.4 Rapid Thermal Annealing (Model RTA)
      • Basic Assumptions
      • RTA Peculiarities
      • Model Parameters
  • 3.3 Transformation Method
    • 3.3.1 Reference Mapping Strategy
    • 3.3.2 Differential Geometric Notation
      • Mapping Operator
      • Base Vectors
      • Area, Arc and Surface Elements
    • 3.3.3 Generation of Curvilinear Coordinate Systems
      • Distribution of Boundary Points
      • Algebraic Methods
      • Elliptic Methods
      • Variational Methods
    • 3.3.4 Transformation of Differential Operators
      • Gradient and Divergence
      • Time Derivatives and Moving Grid
      • Boundary Conditions
    • 3.3.5 Transformed Physical Equations
  • 3.4 Discretization of the PDEs
    • 3.4.1 Divided Differences
    • 3.4.2 Fluxes
      • Diffusion Fluxes
      • Convection Fluxes
      • Diffusion and Convection Fluxes
    • 3.4.3 Divergence Operator
    • 3.4.4 Recombination
    • 3.4.5 Time Derivatives
    • 3.4.6 Boundary Conditions
  • 3.5 Solving the Nonlinear System
    • 3.5.1 Modified Newton Method
    • 3.5.2 Fréchet Derivative (Jacobian Matrix)
    • 3.5.3 Automatic Local Scaling
    • 3.5.4 Solving the Linear System
  • 3.6 Transient Integration Algorithm
    • 3.6.1 Time Step Adaption
    • 3.6.2 Adaption of the Spatial Grid
      • Dose Conservation Criterion
      • Gradient Resolution Criterion
      • Regularity of Grid Spacing
  • 3.7 Applications
    • 3.7.1 Trench Isolation
    • 3.7.2 LDD P-Channel Transistor Design
    • 3.7.3 Field Oxide Isolation
    • 3.7.4 RTA-Experiments
• 4 Oxidation
  • 4.1 Oxide Growth Model
  • 4.2 Applications
• 5 Future Work
• References
• List of Publications
• Curriculum Vitae
• About this document ...