Contents

• 1. Introduction
  • 1.1 Grid Requirements for Numerical Discretization Methods
  • 1.2 Influence of the Simulation Grid on the Solution
  
  
• 2. Grid Types
  • 2.1 Ortho Grids
    • 2.1.1 Mixed Grids
    • 2.1.2 Providing Attributes
  • 2.2 Tetrahedral Grids
  • 2.3 Grid Requirements
  • 2.4 Demands for the Box Integration Method
    • 2.4.1 Voronoi Tessellation -- Delaunay Mesh
    • 2.4.2 Two-Dimensional Criterion
    • 2.4.3 Three-Dimensional Criterion
  • 2.5 Demands for Finite Elements
    • 2.5.1 Two-Dimensional Criterion
  • 2.6 Grid Refinement -- Adaptive Meshes
    • 2.6.1 Hierarchical Refinement
    • 2.6.2 Moving Boundaries
    • 2.6.3 Cellular Data
  
  
• 3. The Box Integration Method
  • 3.1 The Poisson Equation
    • 3.1.1 Approximation of and
    • 3.1.2 Continuation of the Discretization
    • 3.1.3 Boundary Conditions
  • 3.2 The Diffusion Equation
    • 3.2.1 Initial Conditions
  • 3.3 The Basic Semiconductor Equations
  
  
• 4. An Alternative Approach for Diffusion Simulation
  • 4.1 Diffusion and Green's Functions
  • 4.2 Prerequisites for Applying the Green's Functions Method
  • 4.3 Advantages of the Green's Functions Method
  • 4.4 Device Optimization by Three-Dimensional Diffusion Simulation
    • 4.4.1 Simulated Structure
    • 4.4.2 Comparison of Simulation Approaches
    • 4.4.3 Calibration and Evaluation
    • 4.4.4 Results
  
  
• 5. Grid Generation for Device Simulation
  • 5.1 Grid Requirements for Device Simulation
  • 5.2 Adapted Grid Generation
  • 5.3 Potential-Based Grid Generation
    • 5.3.1 Two-Dimensional Behavior
    • 5.3.2 Extension to Three Dimensions
    • 5.3.3 Calculating the Equipotential Surfaces of the Capacitor
    • 5.3.4 Topological Cuboids
    • 5.3.5 Proof of the Two-Dimensional Duality
    • 5.3.6 The Three-Dimensional Capacitor Model
    • 5.3.7 Evaluation of the Electric Potential of the Capacitor
  • 5.4 Alternative Approaches for the Potential Method
  • 5.5 Example for the Potential Method and the Electrode Placement
  
  
• 6. Applications of the Potential Based Method
  • 6.1 Device Simulation of a FinFET
  • 6.2 Development of an EEPROM Memory-Cell
    • 6.2.1 Process Simulation of the Memory-Cell
    • 6.2.2 Electrical Analysis of the Device
  
  
• 7. Conclusion and Outlook
• Bibliography
• List of Figures
• List of Tables
• List of Publications