| Description |
1 online resource (xlvii, 595 pages) : illustrations. |
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text file |
| Series |
River Publishers Series in Electronic Materials and Devices
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River Publishers series in electronic materials and devices.
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| Bibliography |
Includes bibliographical references and index. |
| 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 |
Preface xv Acknowledgments xix -- List of Figures xxi -- List of Tables xxxix -- List of Symbols xli List of Abbreviations xlv PART I: Introduction to Electromagnetism 1 Introduction 3 -- 2 The Microscopic Maxwell Equations 7 -- 2.1 Definition of the Electric Field 7 -- 2.2 Definition of the Magnetic Field 8 -- 2.3 The Microscopic Maxwell Equations in Integral and Differential Form 9 -- 2.4 Conservation Laws 12 -- 2.4.1 Conservation of Charge -- The Continuity Equation 12 -- 2.4.2 Conservation of Energy -- Poynting's Theorem 13 -- 2.4.3 Conservation of Linear Momentum -- The Electromagnetic Field Tensor 14 -- 2.4.4 Angular Momentum Conservation 15 -- 3 Potentials and Fields and the Lagrangian 17 -- 3.1 The Scalar and Vector Potential 17 -- 3.2 Gauge Invariance 19 -- 3.3 Lagrangian for an Electromagnetic Field Interacting with Charges and Currents 19 -- 4 The Macroscopic Maxwell Equations 23 -- 4.1 Constitutive Equations 23 -- 4.2 Boltzmann Transport Equation 24 -- 4.3 Currents in Metals 26 -- 4.4 Charges in Metals 29 -- 4.5 Semiconductors 30 -- 4.6 Currents in Semiconductors 31 -- 4.7 Insulators 36 -- 4.8 Dielectric Media 37 -- 4.9 Magnetic Media 41 -- 5 Wave Guides and Transmission Lines 45 -- 5.1 TEM Modes 47 -- 5.2 TM Modes 49 -- 5.3 TE Modes 49 -- 5.4 Transmission Line Theory -- S Parameters 50 -- 5.5 Classical Ghosts Fields 54 -- 5.6 The Static Approach and Dynamic Parts 56 -- 5.7 Interface Conditions 58 -- 5.8 Boundary Conditions 59 -- 6 Energy Calculations and the Poynting Vector 69 -- 6.1 Static Case 69 -- 6.2 High-Frequency Case 70 -- 7 From Macroscopic Field Theory to Electric Circuits 73 -- 7.1 Kirchhoff's Laws 73 -- 7.2 Circuit Rules 78 -- 7.3 Inclusion of Time Dependence 80 -- 8 Gauge Conditions 87 -- 8.1 The Coulomb Gauge 89 -- 8.2 The Lorenz Gauge 90 -- 8.3 The Landau Gauge 91 -- 8.4 The Temporal Gauge 94 -- 8.5 The Axial Gauge 95 -- 8.6 The 't Hooft Gauge 95 -- 9 The Geometry of Electrodynamics 97 -- 9.1 Gravity as a Gauge Theory 98 -- 9.2 The Geometrical Interpretation of Electrodynamics 104. |
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10 Integral Theorems 107 -- 10.1 Vector Identities 113 PART II: Discretization Methods for Sources and Fields 11 The Finite Difference Method 117 -- 12 The Finite Element Method 121 -- 12.1 Trial Solutions 121 -- 12.2 The Element Concept 122 -- 13 The Finite Volume Method and Finite Surface Method 129 -- 13.1 Differential Operators in Cartesian Grids 132 -- 13.2 Discretized Equations 134 -- 13.3 The No-Ghost Approach 134 -- 13.4 Current Continuity Equation 139 -- 13.5 Computational Details of the Hole Transport Equation 141 -- 13.5.1 Scaling 144 -- 13.6 Computational Details of the Electron Transport Equation 151 -- 13.6.1 Couplings 152 -- 13.7 The Poisson Equation 156 -- 13.8 Maxwell-Ampere Equation 162 -- 13.9 Using Gauge Conditions to Decrease Matrix Fill-In 164 -- 13.9.1 Poisson System 165 -- 13.9.2 Metals 166 -- 13.9.3 Dielectrics 168 -- 13.9.4 Maxwell-Ampere System 170 -- 13.9.5 "Standard" Implementation 171 -- 13.9.6 Decoupling Implementation 171 -- 13.10 The Generalized Coulomb Gauge 172 -- 13.10.1 Implementation Details of the Ampere-Maxwell System 173 -- 13.11 The EV Solver 174 -- 13.11.1 Boundary Conditions for the EV System 176 -- 13.11.2 Implementation Details of the EV System 177 -- 13.11.3 Solution Strategy of the EV System 179 -- 13.12 The Scharfetter-Gummel Discretization 179 -- 13.12.1 The Static and Dynamic Parts 181 -- 13.13 Using Unstructured Grids 183 -- 14 Finite Volume Method and the Transient Regime 187 -- 14.1 The Electromagnetic Drift-Diffusion Solver in the Time Domain 188 -- 14.2 Gauge Conditions 191 -- 14.3 Semiconductor Treatment 194 -- 14.4 Implementation of Numerical Methods for Solving the Equations 197 -- 14.5 Spatial Discretization 197 -- 14.6 Discretization of Gauss' Law 198 -- 14.7 Boundary Conditions for Gauss' Discretized Law 199 -- 14.8 Discretization of the Maxwell-Ampere System 202 -- 14.9 Boundary Conditions for the Maxwell-Ampere Equation 207 -- 14.10 Generalized Boundary Conditions for the Maxwell-Ampere Equation 211. |
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14.11 Discretization of the Gauge Condition 213 -- 14.12 Temporal Discretization 214 -- 14.13 BDF for DAEs 215 -- 14.14 State-Space Matrices and Linking Harmonic to Transient Analysis 216 -- 14.15 A Technical Detail: Link Orientations 221 -- 14.16 Scaling 222 -- 14.16.1 Scaling the Poisson Equation 222 -- 14.16.2 Scaling the Current-Continuity Equations 223 -- 14.16.3 Scaling the Maxwell-Ampere Equation 224 Summary 226 PART III: Applications 15 Simple Test Cases 229 -- 15.1 Examples 229 -- 15.1.1 Crossing Wires 229 -- 15.1.2 Square Coaxial Cable 229 -- 15.1.3 Spiral Inductor 231 -- 15.2 S-Parameters, Y-Parameters, Z-Parameters 233 -- 15.3 A Simple Conductive Rod 235 -- 15.4 Strip Line above a Conductive Plate 239 -- 15.4.1 Finite tM Results 246 -- 15.5 Running the Adapter 247 -- 15.6 Simulations with Opera -- VectorFields 247 -- 15.7 Coax Configuration 256 -- 15.8 Inductor with Grounded Guard Ring 258 -- 15.9 Inductor with Narrow Winding above a Patterned Semiconductor Layer 265 Summary 280 -- 16 Evaluation of Coupled Inductors 281 -- 16.1 Scaling Rules for the Maxwell Equations 282 -- 16.2 Discretization 283 -- 16.3 The EV Solver 285 -- 16.3.1 Boundary Conditions 287 -- 16.4 Scattering Parameters 288 -- 16.5 Application to Compute the Coupling of Inductors 290 -- 17 Coupled Electromagnetic-TCAD Simulation for High Frequencies 295 -- 17.1 Review of A-V Formulation 298 -- 17.1.1 A-V Formulation of the Coupled System 298 -- 17.2 Origin of the High-Frequency Breakdown of the A-V Solver 300 -- 17.3 E-V Formulation 301 -- 17.3.1 Redundancy in Coupled System 303 -- 17.3.2 Issues of Material Properties 304 -- 17.3.3 Boundary Conditions 305 -- 17.3.4 Implementation Details 306 -- 17.3.5 Matrix Permutation 307 -- 17.4 Numerical Results 308 -- 17.4.1 Accuracy of E-V Solver 308 -- 17.4.2 Spectral Analyses 311 -- 17.4.3 Performance Comparisons 314 Summary 316 -- 18 EM-TCAD Solving from 0-100 THz 317 -- 18.1 From AV to EV 317 -- 18.2 Discretization 319 -- 18.3 Simplified EV Schemes 320. |
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18.4 Combination of AV and EV Solvers 321 -- 18.5 Numerical Experiments 321 -- 18.6 Best Practices for Iterative Solving 325 -- 19 Large Signal Simulation of Integrated Inductors on Semi-Conducting Substrates 327 -- 19.1 Need for Mimetic Formulation 328 -- 19.2 Field Equations 329 -- 19.3 Application to An Octa-Shaped Inductor 332 Summary 339 -- 20 Inclusion of Lorentz Force Effects in TCAD Simulations 341 -- 20.1 Steady-State Equations 342 -- 20.2 Discretization of the Lorentz Current Densities 344 -- 20.3 Static Skin Effects in Conducting Wires 347 -- 20.4 Self-Induced Lorentz Force Effects in Metallic Wires 348 -- 20.5 Self-Induced Lorentz Force Effects in Silicon Wires 349 -- 20.6 External Fields 349 Summary 351 -- 21 Self-Induced Magnetic Field Effects, the Lorentz Force and Fast-Transient Phenomena 353 -- 21.1 Time-Domain Formulation of EM-TCAD Problem 356 -- 21.2 Inclusion of the Lorentz Force 358 -- 21.3 Discretization of the Lorentz Current Densities 360 -- 21.4 Applications 366 Summary 377 -- 22 EM Analysis of ESD Protection for Advanced CMOS Technology 379 -- 22.1 Simulation of a Metallic Wire 380 -- 22.2 In-depth Simulation of the Full ESD Structure 383 -- 22.3 Negative Stress with Active Diode 387 -- 22.4 Diode SCR 389 -- 22.5 Comparison with TLP Measurements 391 Summary 392 -- 23 Coupled Electromagnetic-TCAD Simulation for Fast-Transient Systems 395 -- 23.1 Time-Domain A-V formulation 397 -- 23.2 Analysis of Fast-Transient Breakdown 400 -- 23.3 Time-Domain E-V Formulation 402 -- 23.4 Numerical Results 404 Summary 407 -- 24 A Fast Time-Domain EM-TCAD Coupled Simulation Framework via Matrix Exponential with Stiffness Reduction 409 -- 24.1 Time-Domain Formulation of EM-TCAD Problem 411 -- 24.2 Time-Domain Simulation with Matrix Exponential Method 415 -- 24.3 Error Control and Adaptivity 420 -- 24.4 E-V Formulation of EM-TCAD for MEXP Method 421 -- 24.5 Numerical Results 424 -- 24.6 Validity Proof of Regularization with Differentiated Gauss' Law 431 -- 24.7 Fast Computation of M x in E-V Formulation 432 Summary 433 PART IV: Advanced Topics 25 Surface-Impedance Approximation to Solve RF Design Problems 437. |
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25.1 Surface Impedance Approximation 437 -- 25.2 Formulation of the BISC in Potentials 440 -- 25.3 Scaling Considerations 442 -- 25.4 One-Dimensional Test Example 444 -- 26 Using the Ghost Method for Floating Domains in Electromagnetic Field Solvers 455 -- 26.1 Problem Description 456 -- 26.2 Proposed Solution 458 -- 26.3 Example 1: Metal Blocks Embedded in Insulator 459 -- 26.4 Example 2: A Transformer System 460 -- 26.5 Initial Guess 462 -- 26.6 High-Frequency Problems 462 -- 26.7 Floating Semiconductor Regions 468 -- 27 Integrating Factors for Discretizing the Maxwell-Ampere Equation 477 -- 27.1 Review of the Scharfetter-Gummel Discretization 478 -- 27.2 Observations 479 -- 27.3 Maxwell Equations 481 -- 27.4 Discretization of the Curl-Curl Operator 482 -- 27.5 Discretization of the Divergence Operator 484 -- 27.6 Discretization of Poisson-Type Operators 489 -- 27.7. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Electrodynamics -- Mathematical models.
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Electrodynamics -- Mathematical models. |
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Electrodynamics. |
| Genre/Form |
Electronic books.
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Electronic books.
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| Other Form: |
Print version: Schoenmaker, Wim. Computational Electrodynamics : A Gauge Approach with Applications in Microelectronics. Aalborg : River Publishers, ©2017 9788793519848 |
| ISBN |
9788793519831 |
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8793519834 |
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9788793609938 (electronic book) |
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8793609930 (electronic book) |
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8793519842 |
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9788793519848 |
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