Contents

• List of Tables
• List of Figures
• 1. Preface
• 2. Overview of Tools for Numerical Analysis of Electromagnetic Fields in Microelectronics
  • 2.1 Ansoft
  • 2.2 The COMSOL Group
  • 2.3 CST
  • 2.4 Magwel
  • 2.5 Remcom
  • 2.6 Synopsys
  • 2.7 Institute for Microelectronics at the TU Wien
  
  
• 3. Introduction to the Finite Element Method
  • 3.1 Boundary-Value Problems
  • 3.2 The Weighted Residual Method
  • 3.3 Galerkin's Method
    • 3.3.1 Galerkin's Method for the Scalar Differential Operator
    • 3.3.2 Galerkin's Method for the Vector Differential Operator
  
  
• 4. The Scalar Finite Element Method
  • 4.1 Two-Dimensional Scalar Finite Element Method
    • 4.1.1 Domain Discretization
    • 4.1.2 Linear Shape Functions on Triangular Elements
    • 4.1.3 Introduction of Triangle Barycentric Coordinates
    • 4.1.4 Assembling
    • 4.1.5 Neumann Boundary Condition
  • 4.2 Three-Dimensional Scalar Finite Element Method
    • 4.2.1 Linear Shape Functions on Tetrahedral Elements
    • 4.2.2 Tetrahedron Barycentric Coordinates
    • 4.2.3 Assembling
  
  
• 5. The Vector Finite Element Method
  • 5.1 Edge Elements Applications
    • 5.1.1 The Wave Equation for the Electric Field
    • 5.1.2 Equations for the Electrodynamic Potentials
    • 5.1.3 Quasi-Magnetostatics
  • 5.2 Three-Dimensional Vector Finite Element Method
    • 5.2.1 Domain Discretization
    • 5.2.2 Linear Vector Shape Functions on Tetrahedral Elements
    • 5.2.3 Assembling
  • 5.3 Two-Dimensional Vector Finite Element Method
    • 5.3.1 Linear Vector Shape Functions on a Triangular Elements
    • 5.3.2 Assembling
  
  
• 6. Applications
  • 6.1 Inductance and Resistance of a Coaxial Structure
    • 6.1.1 Analytical Inductance and Resistance Calculation
    • 6.1.2 Numerical Inductance and Resistance Extraction
    • 6.1.3 Simulated Fields Visualization and Results Comparison
  • 6.2 Inductance and Resistance of On-Chip Inductors
    • 6.2.1 Boundary Conditions
    • 6.2.2 Domain Discretization
    • 6.2.3 Examples and Results
  • 6.3 Periodic Boundaries
    • 6.3.1 Mesh Generation
    • 6.3.2 Simulation Results
  
  
• 7. Outlook
• A. Integral Domain Transformation
• B. Two-Dimensional Neumann Boundary Term
  • B.1 Neumann Boundary for the Rotor-Rotor-Operator
  • B.2 Neumann Boundary for Gauß's Law of Magnetism
    • B.2.1 For the Scalar Function
    • B.2.2 For the Vector Function
  
  
• C. Three-Dimensional Neumann Boundary Term Assembling
  • C.1 The Neumann Boundary for the Rotor-Rotor-Operator
  • C.2 Neumann Boundary for Gauß's Law of Magnetism
    • C.2.1 For the Scalar Function
    • C.2.2 For the Vector Function
  
  
• Bibliography