Computational electrodynamics : a gauge approach with applications in microelectronics / Wim Schoenmaker.

Format:

Book

Author/Creator:

Schoenmaker, Wim, author.

Series:

River Publishers series in electronic materials and devices.

River Publishers Series in Electronic Materials and Devices

Language:

English

Subjects (All):

Electromagnetism.

Physical Description:

1 online resource (xlvii, 595 pages) : illustrations

Edition:

1st ed.

Place of Publication:

Gistrup, Denmark ; Delft, Netherlands : River Publishers, 2017.

Summary:

Annotation 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.

Contents:

Cover

Half Title

Series Page

Title Page

Copyright Page

Table of Contents

Preface

Acknowledgments

List of Figures

List of Tables

List of Symbols

List of Abbreviations

Part I: Introduction to Electromagnetism

1: Introduction

2: The Microscopic Maxwell Equations

2.1 Definition of the Electric Field

2.2 Definition of the Magnetic Field

2.3 The Microscopic Maxwell Equations in Integral and Differential Form

2.4 Conservation Laws

2.4.1 Conservation of Charge - The Continuity Equation

2.4.2 Conservation of Energy - Poynting's Theorem

2.4.3 Conservation of Linear Momentum - The Electromagnetic Field Tensor

2.4.4 Angular Momentum Conservation

3: Potentials and Fields and the Lagrangian

3.1 The Scalar and Vector Potential

3.2 Gauge Invariance

3.3 Lagrangian for an Electromagnetic Field Interacting with Charges and Currents

4: The Macroscopic Maxwell Equations

4.1 Constitutive Equations

4.2 Boltzmann Transport Equation

4.3 Currents in Metals

4.4 Charges in Metals

4.5 Semiconductors

4.6 Currents in Semiconductors

4.7 Insulators

4.8 Dielectric Media

4.9 Magnetic Media

5: Wave Guides and Transmission Lines

5.1 TEM Modes

5.2 TM Modes

5.3 TE Modes

5.4 Transmission Line Theory - S Parameters

5.5 Classical Ghosts Fields

5.6 The Static Approach and Dynamic Parts

5.7 Interface Conditions

5.8 Boundary Conditions

6: Energy Calculations and the Poynting Vector

6.1 Static Case

6.2 High-Frequency Case

7: From Macroscopic Field Theory to Electric Circuits

7.1 Kirchhoff's Laws

7.2 Circuit Rules

7.3 Inclusion of Time Dependence

8: Gauge Conditions

8.1 The Coulomb Gauge

8.2 The Lorenz Gauge

8.3 The Landau Gauge

8.4 The Temporal Gauge

8.5 The Axial Gauge

8.6 The 't Hooft Gauge.

9: The Geometry of Electrodynamics

9.1 Gravity as a Gauge Theory

9.2 The Geometrical Interpretation of Electrodynamics

10: Integral Theorems

10.1 Vector Identities

Part II: Discretization Methods for Sources and Fields

11: The Finite Difference Method

12: The Finite Element Method

12.1 Trial Solutions

12.2 The Element Concept

13: The Finite Volume Method and Finite Surface Method

13.1 Differential Operators in Cartesian Grids

13.2 Discretized Equations

13.3 The No-Ghost Approach

13.4 Current Continuity Equation

13.5 Computational Details of the Hole Transport Equation

13.5.1 Scaling

13.6 Computational Details of the Electron Transport Equation

13.6.1 Couplings

13.7 The Poisson Equation

13.8 Maxwell-Ampere Equation

13.9 Using Gauge Conditions to Decrease Matrix Fill-In

13.9.1 Poisson System

13.9.2 Metals

13.9.3 Dielectrics

13.9.4 Maxwell-Ampere System

13.9.5 "Standard" Implementation

13.9.6 Decoupling Implementation

13.10 The Generalized Coulomb Gauge

13.10.1 Implementation Details of the Ampere-Maxwell System

13.11 The EV Solver

13.11.1 Boundary Conditions for the EV System

13.11.2 Implementation Details of the EV System

13.11.3 Solution Strategy of the EV System

13.12 The Scharfetter-Gummel Discretization

13.12.1 The Static and Dynamic Parts

13.13 Using Unstructured Grids

14: Finite Volume Method and the Transient Regime

14.1 The Electromagnetic Drift-Diffusion Solver in the Time Domain

14.2 Gauge Conditions

14.3 Semiconductor Treatment

14.4 Implementation of Numerical Methods for Solving the Equations

14.5 Spatial Discretization

14.6 Discretization of Gauss' Law

14.7 Boundary Conditions for Gauss' Discretized Law

14.8 Discretization of the Maxwell-Ampere System.

14.9 Boundary Conditions for the Maxwell-Ampere Equation

14.10 Generalized Boundary Conditions for the Maxwell-Ampere Equation

14.11 Discretization of the Gauge Condition

14.12 Temporal Discretization

14.13 BDF for DAEs

14.14 State-Space Matrices and Linking Harmonic to Transient Analysis

14.15 A Technical Detail: Link Orientations

14.16 Scaling

14.16.1 Scaling the Poisson Equation

14.16.2 Scaling the Current-Continuity Equations

14.16.3 Scaling the Maxwell-Ampere Equation

Summary

Part III: Applications

15: Simple Test Cases

15.1 Examples

15.1.1 Crossing Wires

15.1.2 Square Coaxial Cable

15.1.3 Spiral Inductor

15.2 S-Parameters, Y-Parameters, Z-Parameters

15.3 A Simple Conductive Rod

15.4 Strip Line above a Conductive Plate

15.4.1 Finite tM Results

15.5 Running the Adapter

15.6 Simulations with Opera - VectorFields

15.7 Coax Configuration

15.8 Inductor with Grounded Guard Ring

15.9 Inductor with Narrow Winding above a Patterned Semiconductor Layer

16: Evaluation of Coupled Inductors

16.1 Scaling Rules for the Maxwell Equations

16.2 Discretization

16.3 The EV Solver

16.3.1 Boundary Conditions

16.4 Scattering Parameters

16.5 Application to Compute the Coupling of Inductors

17: Coupled Electromagnetic-TCAD Simulation for High Frequencies

17.1 Review of A-V Formulation

17.1.1 A-V Formulation of the Coupled System

17.2 Origin of the High-Frequency Breakdown of the A-V Solver

17.3 E-V Formulation

17.3.1 Redundancy in Coupled System

17.3.2 Issues of Material Properties

17.3.3 Boundary Conditions

17.3.4 Implementation Details

17.3.5 Matrix Permutation

17.4 Numerical Results

17.4.1 Accuracy of E-V Solver

17.4.2 Spectral Analyses

17.4.3 Performance Comparisons

18: EM-TCAD Solving from 0-100 THz.

18.1 From AV to EV

18.2 Discretization

18.3 Simplified EV Schemes

18.4 Combination of AV and EV Solvers

18.5 Numerical Experiments

18.6 Best Practices for Iterative Solving

19: Large Signal Simulation of Integrated Inductors on Semi-Conducting Substrates

19.1 Need for Mimetic Formulation

19.2 Field Equations

19.3 Application to An Octa-Shaped Inductor

20: Inclusion of Lorentz Force Effects in TCAD Simulations

20.1 Steady-State Equations

20.2 Discretization of the Lorentz Current Densities

20.3 Static Skin Effects in Conducting Wires

20.4 Self-Induced Lorentz Force Effects in Metallic Wires

20.5 Self-Induced Lorentz Force Effects in Silicon Wires

20.6 External Fields

21: Self-Induced Magnetic Field Effects, the Lorentz Force and Fast-Transient Phenomena

21.1 Time-Domain Formulation of EM-TCAD Problem

21.2 Inclusion of the Lorentz Force

21.3 Discretization of the Lorentz Current Densities

21.4 Applications

22: EM Analysis of ESD Protection for Advanced CMOS Technology

22.1 Simulation of a Metallic Wire

22.2 In-depth Simulation of the Full ESD Structure

22.3 Negative Stress with Active Diode

22.4 Diode SCR

22.5 Comparison with TLP Measurements

23: Coupled Electromagnetic-TCAD Simulation for Fast-Transient Systems

23.1 Time-Domain A-V Formulation

23.2 Analysis of Fast-Transient Breakdown

23.3 Time-Domain E-V Formulation

23.4 Numerical Results

24: A Fast Time-Domain EM-TCAD Coupled Simulation Framework via Matrix Exponential with Stiffness Reduction

24.1 Time-Domain Formulation of EM-TCAD Problem

24.2 Time-Domain Simulation with Matrix Exponential Method

24.3 Error Control and Adaptivity

24.4 E-V Formulation of EM-TCAD for MEXP Method

24.5 Numerical Results.

24.6 Validity Proof of Regularization with Differentiated Gauss' Law

24.7 Fast Computation of Mx in E-V Formulation

Part IV: Advanced Topics

25: Surface-Impedance Approximation to Solve RF Design Problems

25.1 Surface Impedance Approximation

25.2 Formulation of the BISC in Potentials

25.3 Scaling Considerations

25.4 One-Dimensional Test Example

26: Using the Ghost Method for Floating Domains in Electromagnetic Field Solvers

26.1 Problem Description

26.2 Proposed Solution

26.3 Example 1: Metal Blocks Embedded in Insulator

26.4 Example 2: A Transformer System

26.5 Initial Guess

26.6 High-Frequency Problems

26.7 Floating Semiconductor Regions

27: Integrating Factors for Discretizing the Maxwell-Ampere Equation

27.1 Review of the Scharfetter-Gummel Discretization

27.2 Observations

27.3 Maxwell Equations

27.4 Discretization of the Curl-Curl Operator

27.5 Discretization of the Divergence Operator

27.6 Discretization of Poisson-Type Operators

27.7 Equivalence

27.8 High-Frequency Maxwell Equations

27.9 Integrating Factors for Unstructured Grids

27.10 Implementation Details

27.11 Effect of the Inclusion of the Integrating Factor

27.12 Simulation Set Up and Results

28: Stability Analysis of the Transient Field Solver

28.1 Impact of the Gauge Condition

28.2 Magnetic Neumann Boundary Conditions

28.3 Results for Larger Values of the Conductance

28.4 Yet Another Experiment

28.5 Inductor Experiments

28.6 Results for a Metal Loop

28.7 Results for a Twisted Bar

28.8 Corner Example

28.9 Returning to the Original Problem

28.10 Revisiting the Equations

28.11 Redoing the Corner Structure

28.12 Simple Test Structure for the Stability Problem

28.13 Results for a Single Line

28.14 Some Theoretical Considerations.

28.15 The Impact of the Meshing.

Notes:

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (ebrary, viewed July 17, 2017).

ISBN:

9781000799408

1000799409

9781003337669

100333766X

9781000799262

1000799263

9788793519831

8793519834

OCLC:

992577138