Computational Electrodynamics: A Gauge Approach with Applications in Microelectronics

ISBN-13: 9788793519848 / Angielski / Twarda / 2017 / 450 str.

Wim Schoenmaker

Opis

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

Spis treści

• Preface
• 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 metalsCharges 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

O autorze

Wim Schoenmaker