Electrical Modeling and Design for 3D System Integration

ER-PING LI, PhD, holds an appointment as Chair Professor at Zhejiang University, China, and has also been a principal scientist and director at the Institute of High Performance Computing, Singapore. He is a Fellow of the IEEE and a Fellow of the Electromagnetics Academy. He has received numerous awards and honors in recognition of his professional work from the IEEE and other professional bodies. Dr. Li is a pioneer in the modeling and simulation for signal/power and EMC in integrated circuits and electronic systems packaging. He has chaired or spoken at numerous international conferences and universities, and has also served as editor to several IEEE Transactions.

• Foreword xiPreface xiii1. Introduction 11.1 Introduction of Electronic Package Integration 11.2 Review of Modeling Technologies 61.3 Organization of the Book 10References 112. Macromodeling of Complex Interconnects in 3D Integration 162.1 Introduction 162.1.1 Scope of macromodeling 182.1.2 Macromodeling in the picture of electrical modeling of interconnects 192.2 Network Parameters: Impedance Admittance and Scattering Matrices 192.2.1 Impedance matrix 212.2.2 Admittance matrix 222.2.3 Scattering matrix 232.2.4 Conversion between Z Y and S matrices 242.3 Rational Function Approximation with Partial Fractions 252.3.1 Introduction 252.3.2 Iterative weighted linear least-squares estimator 272.4 Vector Fitting (VF) Method 292.4.1 Two steps in vector fitting method 292.4.2 Fitting vectors with common poles 352.4.3 Selection of initial poles 372.4.4 Enhancement to the original vector fitting method 382.5 Macromodel Synthesis 412.5.1 Jordan canonical method for macromodel synthesis 422.5.2 Equivalent circuits 462.6 Stability Causality and Passivity of Macromodel 482.6.1 Stability 482.6.2 Causality 502.6.3 Passivity assessment 542.6.4 Passivity enforcement 582.6.5 Other issues 782.7 Macromodeling Applied to High-Speed Interconnects and Circuits 792.7.1 A lumped circuit with nonlinear components 792.7.2 Vertically natural capacitors (VNCAPs) 832.7.3 Stripline-to-microstrip line transition with vias 872.8 Conclusion 91References 923. 2.5D Simulation Method for 3D Integrated Systems 973.1 Introduction 973.2 Multiple Scattering Method for Electronic Package Modeling with Open Boundary Problems 983.2.1 Modal expansion of fields in a parallel-plate waveguide (PPWG) 983.2.2 Multiple scattering coefficients among cylindrical PEC and perfect magnetic conductor (PMC) vias 1013.2.3 Excitation source and network parameter extraction 1093.2.4 Implementation of effective matrix-vector multiplication (MVM) in linear equations 1173.2.5 Numerical examples for single-layer power-ground planes 1213.3 Novel Boundary Modeling Method for Simulation of Finite-Domain Power-Ground Planes 1273.3.1 Perfect magnetic conductor (PMC) boundary 1283.3.2 Frequency-dependent cylinder layer (FDCL) 1283.3.3 Validations of FDCL 1313.4 Numerical Simulations for Finite Structures 1333.4.1 Extended scattering matrix method (SMM) algorithm for finite structure simulation 1333.4.2 Modeling of arbitrarily shaped boundary structures 139Contents vii3.5 Modeling of 3D Electronic Package Structure 1423.5.1 Modal expansions and boundary conditions 1433.5.2 Mode matching in PPWGs 1503.5.3 Generalized T-matrix for two-layer problem 1583.5.4 Formulae summary for two-layer problem 1643.5.5 Formulae summary for 3D structure problem 1693.5.6 Numerical simulations for multilayered power-ground planes with multiple vias 1763.6 Conclusion 182References 1834. Hybrid Integral Equation Modeling Methods for 3D Integration 1854.1 Introduction 1854.2 2D Integral Equation Equivalent Circuit (IEEC) Method 1864.2.1 Overview of the algorithm 1864.2.2 Modal decoupling inside the power distribution network (PDN) 1874.2.3 2D integral equation solution of parallel plate mode in power-ground planes (PGPs) 1894.2.4 Combinations of transmission and parallel plate modes 1944.2.5 Cascade connections of equivalent networks 2054.2.6 Simulation results 2144.3 3D Hybrid Integral Equation Method 2204.3.1 Overview of the algorithm 2204.3.2 Equivalent electromagnetic currents and dyadic green’s functions 2244.3.3 Simulation results 2314.4 Conclusion 238References 2385. Systematic Microwave Network Analysis for 3D Integrated Systems 2415.1 Intrinsic Via Circuit Model for Multiple Vias in an Irregular Plate Pair 2425.1.1 Introduction 2425.1.2 Segmentation of vias and a plate pair 2455.1.3 An intrinsic 3-port via circuit model 2485.1.4 Determination of the virtual via boundary 2635.1.5 Complete model for multiple vias in an irregular plate pair 2675.1.6 Validation and measurements 2695.1.7 Conclusion 2805.2 Parallel Plane Pair Model 2815.2.1 Introduction 2815.2.2 Overview of two conventional Z pp definitions 2835.2.3 New Z pp definition using the zero-order parallel plate waves 2855.2.4 Analytical formula for radial scattering matrix S pp in a circular plate pair 2905.2.5 BIE method to evaluate S R pp for an irregular plate pair 2925.2.6 Numerical examples and measurements 2965.2.7 Conclusion 3035.3 Cascaded Multiport Network Analysis of Multilayer Structure with Multiple Vias 3055.3.1 Introduction 3055.3.2 Multilayer PCB with vias and decoupling capacitors 3075.3.3 Systematic microwave network method 3085.3.4 Validations and discussion 3165.3.5 Conclusion 324Appendix: Properties of the Auxiliary Function W mn (x y) 326References 3276. Modeling of Through-Silicon Vias (TSV) in 3D Integration 3316.1 Introduction 3316.1.1 Overview of process and fabrication of TSV 3326.1.2 Modeling of TSV 3356.2 Equivalent Circuit Model for TSV 3366.2.1 Overview 3376.2.2 Problem statement: Two-TSV configuration 3386.2.3 Wideband Pi-type equivalent-circuit model 3396.2.4 Rigorous closed-form formulae for resistance and inductance 3416.2.5 Scattering parameters of two-TSV system 3456.2.6 Results and discussion 3466.3 MOS Capacitance Effect of TSV 3516.3.1 MOS capacitance effect 3516.3.2 Bias voltage-dependent MOS capacitance of TSVs 3516.3.3 Results and analysis 3556.4 Conclusion 356References 358Index 361