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Computational electrodynamics : a gauge approach with applications in microelectronics /
Annotation
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Aalborg :
River Publishers,
©2017.
|
| Colección: | River Publishers series in electronic materials and devices.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.
- 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.
- 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.
- 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.
- 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.