Computational Electrodynamics
A Gauge Approach with Applications in Microelectronics

Cloth: 978 87 93519 84 8 / $100.00
Published: June 2017  

Publisher: River Publishers
450 pp., 6 1/8" x 9 1/5"
Series: River Publishers Series in Electronic Materials and Devices
Computational electrodynamics is a vast research field with a wide variety of tools. In physics, the principle of gauge invariance plays a pivotal role as a guide towards a sensible formulation of the laws of nature as well as for computing the properties of elementary particles using the lattice formulation of gauge theories. However, the gauge principle has played a much less pronounced role in performing computation in classical electrodynamics.

In this work, the author demonstrates that starting from the gauge formulation of electrodynamics using the electromagnetic potentials leads to computational tools that can very well compete with the conventional electromagnetic field-based tools. Once accepting the formulation based on gauge fields, the computational code is very transparent due to the mimetic mapping of the electrodynamic variables on the computational grid. Although the illustrations and applications originate from microelectronic engineering, the method has a much larger range of applicability. Therefore this book will be useful to everyone having interest in computational electrodynamics.

The volume is organized as follows: In part 1, a detailed introduction and overview is presented of the Maxwell equations as well as the derivation of the current and charge densities in different materials. Semiconductors are responding to electromagnetic fields in a non-linear way, and the induced complications are discussed in detail. Part 2, using the gauge potentials, presents the transition of electrodynamics theory to a formulation that can serve as the gateway to computational code. In part 3, a collection of microelectronic device designs demonstrate the feasibility and success of the methods in Part 2. Part 4 focuses on a set of topical themes that brings the reader to the frontier of research in building the simulation tools, using the gauge principle in computational electrodynamics.

Technical topics discussed in the book include:
- Electromagnetic Field Equations
- Constitutive Relations
- Discretization and Numerical Analysis
- Finite Element and Finite Volume Methods
- Design of Integrated Passive Components

Table of Contents:
List of Symbols

PART1: Introduction
The Microscopic Maxwell Equations
The microscopic Maxwell equations in integral and differential form
Conservation laws
Potentials and Fields and the Lagrangian
The scalar and vector potential
Gauge invariance
Lagrangian for an electromagnetic field interacting with charges and currents
The Macroscopic Maxwell Equations
Constitutive equations
Boltzmann transport equation
Currents in metals
Charges in metals
Currents in semiconductors
Dielectric and Magnetic media
Wave Guides and Transmission Lines
Transmission line theory
Classical Ghosts Fields
Energy Calculations and the Poynting Vector
The Geometry of Electrodynamics
Integral Theorems
Vector identities

PART 2: The Finite Difference Method
The Finite Element Method
The Finite Volume Method and Finite Surface Method
Finite Volume Method and the Transient Regime

PART 3: Simple Test Cases
Evaluation of Coupled Inductors
Coupled Electromagnetic-TCAD Simulation for High Frequencies
EM-TCAD Solving from 0-100 THz
Large Signal Simulation of Integrated Inductors on Semi-Conducting Substrates
Inclusion of Lorentz Force Effects in TCAD Simulations
Self-Induced Magnetic Field Effects, the Lorentz Force and Fast-Transient Phenomena
EM Analysis of ESD Protection for Advanced CMOS Technology
Coupled Electromagnetic-TCAD Simulation for Fast-Transient Systems
A Fast Time-Domain EM-TCAD Coupled Simulation Framework via Matrix Exponential with Stiffness Reduction

PART 4: Surface-Impedance Approximation to Solve RF Design Problems
Using the Ghost Method for Floating Domains in Electromagnetic Field Solvers
Integrating Factors for the Discretized Maxwell-Ampere Equation
Stability Analysis of the Transient Field Solver
Summary of the Numerical Techniques