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Abstract
Contents
Abstract
Kurzfassung
Acknowledgment
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
Own Publications
Curriculum Vitae
A. Nentchev: Numerical Analysis and Simulation in Microelectronics by Vector Finite Elements
