Foreword xi
Preface xiii
1. Introduction 1
1.1 Introduction of Electronic Package Integration 1
1.2 Review of Modeling Technologies 6
1.3 Organization of the Book 10
References 11
2. Macromodeling of Complex Interconnects in 3D Integration 16
2.1 Introduction 16
2.1.1 Scope of macromodeling 18
2.1.2 Macromodeling in the picture of electrical modeling of interconnects 19
2.2 Network Parameters: Impedance Admittance and Scattering Matrices 19
2.2.1 Impedance matrix 21
2.2.2 Admittance matrix 22
2.2.3 Scattering matrix 23
2.2.4 Conversion between Z Y and S matrices 24
2.3 Rational Function Approximation with Partial Fractions 25
2.3.1 Introduction 25
2.3.2 Iterative weighted linear least-squares estimator 27
2.4 Vector Fitting (VF) Method 29
2.4.1 Two steps in vector fitting method 29
2.4.2 Fitting vectors with common poles 35
2.4.3 Selection of initial poles 37
2.4.4 Enhancement to the original vector fitting method 38
2.5 Macromodel Synthesis 41
2.5.1 Jordan canonical method for macromodel synthesis 42
2.5.2 Equivalent circuits 46
2.6 Stability Causality and Passivity of Macromodel 48
2.6.1 Stability 48
2.6.2 Causality 50
2.6.3 Passivity assessment 54
2.6.4 Passivity enforcement 58
2.6.5 Other issues 78
2.7 Macromodeling Applied to High-Speed Interconnects and Circuits 79
2.7.1 A lumped circuit with nonlinear components 79
2.7.2 Vertically natural capacitors (VNCAPs) 83
2.7.3 Stripline-to-microstrip line transition with vias 87
2.8 Conclusion 91
References 92
3. 2.5D Simulation Method for 3D Integrated Systems 97
3.1 Introduction 97
3.2 Multiple Scattering Method for Electronic Package Modeling with Open Boundary Problems 98
3.2.1 Modal expansion of fields in a parallel-plate waveguide (PPWG) 98
3.2.2 Multiple scattering coefficients among cylindrical PEC and perfect magnetic conductor (PMC) vias 101
3.2.3 Excitation source and network parameter extraction 109
3.2.4 Implementation of effective matrix-vector multiplication (MVM) in linear equations 117
3.2.5 Numerical examples for single-layer power-ground planes 121
3.3 Novel Boundary Modeling Method for Simulation of Finite-Domain Power-Ground Planes 127
3.3.1 Perfect magnetic conductor (PMC) boundary 128
3.3.2 Frequency-dependent cylinder layer (FDCL) 128
3.3.3 Validations of FDCL 131
3.4 Numerical Simulations for Finite Structures 133
3.4.1 Extended scattering matrix method (SMM) algorithm for finite structure simulation 133
3.4.2 Modeling of arbitrarily shaped boundary structures 139
Contents vii
3.5 Modeling of 3D Electronic Package Structure 142
3.5.1 Modal expansions and boundary conditions 143
3.5.2 Mode matching in PPWGs 150
3.5.3 Generalized T-matrix for two-layer problem 158
3.5.4 Formulae summary for two-layer problem 164
3.5.5 Formulae summary for 3D structure problem 169
3.5.6 Numerical simulations for multilayered power-ground planes with multiple vias 176
3.6 Conclusion 182
References 183
4. Hybrid Integral Equation Modeling Methods for 3D Integration 185
4.1 Introduction 185
4.2 2D Integral Equation Equivalent Circuit (IEEC) Method 186
4.2.1 Overview of the algorithm 186
4.2.2 Modal decoupling inside the power distribution network (PDN) 187
4.2.3 2D integral equation solution of parallel plate mode in power-ground planes (PGPs) 189
4.2.4 Combinations of transmission and parallel plate modes 194
4.2.5 Cascade connections of equivalent networks 205
4.2.6 Simulation results 214
4.3 3D Hybrid Integral Equation Method 220
4.3.1 Overview of the algorithm 220
4.3.2 Equivalent electromagnetic currents and dyadic greenâs functions 224
4.3.3 Simulation results 231
4.4 Conclusion 238
References 238
5. Systematic Microwave Network Analysis for 3D Integrated Systems 241
5.1 Intrinsic Via Circuit Model for Multiple Vias in an Irregular Plate Pair 242
5.1.1 Introduction 242
5.1.2 Segmentation of vias and a plate pair 245
5.1.3 An intrinsic 3-port via circuit model 248
5.1.4 Determination of the virtual via boundary 263
5.1.5 Complete model for multiple vias in an irregular plate pair 267
5.1.6 Validation and measurements 269
5.1.7 Conclusion 280
5.2 Parallel Plane Pair Model 281
5.2.1 Introduction 281
5.2.2 Overview of two conventional Z pp definitions 283
5.2.3 New Z pp definition using the zero-order parallel plate waves 285
5.2.4 Analytical formula for radial scattering matrix S pp in a circular plate pair 290
5.2.5 BIE method to evaluate S R pp for an irregular plate pair 292
5.2.6 Numerical examples and measurements 296
5.2.7 Conclusion 303
5.3 Cascaded Multiport Network Analysis of Multilayer Structure with Multiple Vias 305
5.3.1 Introduction 305
5.3.2 Multilayer PCB with vias and decoupling capacitors 307
5.3.3 Systematic microwave network method 308
5.3.4 Validations and discussion 316
5.3.5 Conclusion 324
Appendix: Properties of the Auxiliary Function W mn (x y) 326
References 327
6. Modeling of Through-Silicon Vias (TSV) in 3D Integration 331
6.1 Introduction 331
6.1.1 Overview of process and fabrication of TSV 332
6.1.2 Modeling of TSV 335
6.2 Equivalent Circuit Model for TSV 336
6.2.1 Overview 337
6.2.2 Problem statement: Two-TSV configuration 338
6.2.3 Wideband Pi-type equivalent-circuit model 339
6.2.4 Rigorous closed-form formulae for resistance and inductance 341
6.2.5 Scattering parameters of two-TSV system 345
6.2.6 Results and discussion 346
6.3 MOS Capacitance Effect of TSV 351
6.3.1 MOS capacitance effect 351
6.3.2 Bias voltage-dependent MOS capacitance of TSVs 351
6.3.3 Results and analysis 355
6.4 Conclusion 356
References 358
Index 361
