Foreword |
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xi | |
Preface |
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xiii | |
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1 | (15) |
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1.1 Introduction of Electronic Package Integration |
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1 | (5) |
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1.2 Review of Modeling Technologies |
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6 | (4) |
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1.3 Organization of the Book |
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10 | (6) |
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11 | (5) |
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2 Macromodeling of Complex Interconnects in 3D Integration |
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16 | (81) |
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16 | (3) |
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2.1.1 Scope of macromodeling |
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18 | (1) |
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2.1.2 Macromodeling in the picture of electrical modeling of interconnects |
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19 | (1) |
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2.2 Network Parameters: Impedance, Admittance, and Scattering Matrices |
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19 | (6) |
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21 | (1) |
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22 | (1) |
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23 | (1) |
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2.2.4 Conversion between Z, Y, and S matrices |
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24 | (1) |
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2.3 Rational Function Approximation with Partial Fractions |
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25 | (4) |
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25 | (2) |
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2.3.2 Iterative weighted linear least-squares estimator |
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27 | (2) |
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2.4 Vector Fitting (VF) Method |
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29 | (12) |
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2.4.1 Two steps in vector fitting method |
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29 | (6) |
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2.4.2 Fitting vectors with common poles |
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35 | (2) |
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2.4.3 Selection of initial poles |
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37 | (1) |
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2.4.4 Enhancement to the original vector fitting method |
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38 | (3) |
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41 | (7) |
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2.5.1 Jordan canonical method for macromodel synthesis |
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42 | (4) |
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2.5.2 Equivalent circuits |
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46 | (2) |
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2.6 Stability, Causality, and Passivity of Macromodel |
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48 | (31) |
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48 | (2) |
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50 | (4) |
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2.6.3 Passivity assessment |
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54 | (4) |
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2.6.4 Passivity enforcement |
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58 | (20) |
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78 | (1) |
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2.7 Macromodeling Applied to High-Speed Interconnects and Circuits |
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79 | (12) |
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2.7.1 A lumped circuit with nonlinear components |
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79 | (4) |
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2.7.2 Vertically natural capacitors (VNCAPs) |
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83 | (4) |
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2.7.3 Stripline-to-microstrip line transition with vias |
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87 | (4) |
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91 | (6) |
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92 | (5) |
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3 2.5D Simulation Method for 3D Integrated Systems |
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97 | (88) |
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97 | (1) |
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3.2 Multiple Scattering Method for Electronic Package Modeling with Open Boundary Problems |
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98 | (29) |
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3.2.1 Modal expansion of fields in a parallel-plate waveguide (PPWG) |
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98 | (3) |
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3.2.2 Multiple scattering coefficients among cylindrical PEC and perfect magnetic conductor (PMC) vias |
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101 | (8) |
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3.2.3 Excitation source and network parameter extraction |
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109 | (8) |
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3.2.4 Implementation of effective matrix-vector multiplication (MVM) in linear equations |
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117 | (4) |
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3.2.5 Numerical examples for single-layer power-ground planes |
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121 | (6) |
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3.3 Novel Boundary Modeling Method for Simulation of Finite-Domain Power-Ground Planes |
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127 | (6) |
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3.3.1 Perfect magnetic conductor (PMC) boundary |
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128 | (1) |
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3.3.2 Frequency-dependent cylinder layer (FDCL) |
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128 | (3) |
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3.3.3 Validations of FDCL |
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131 | (2) |
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3.4 Numerical Simulations for Finite Structures |
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133 | (9) |
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3.4.1 Extended scattering matrix method (SMM) algorithm for finite structure simulation |
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133 | (6) |
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3.4.2 Modeling of arbitrarily shaped boundary structures |
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139 | (3) |
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3.5 Modeling of 3D Electronic Package Structure |
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142 | (40) |
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3.5.1 Modal expansions and boundary conditions |
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143 | (7) |
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3.5.2 Mode matching in PPWGs |
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150 | (8) |
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3.5.3 Generalized T-matrix for two-layer problem |
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158 | (6) |
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3.5.4 Formulae summary for two-layer problem |
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164 | (5) |
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3.5.5 Formulae summary for 3D structure problem |
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169 | (7) |
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3.5.6 Numerical simulations for multilayered power-ground planes with multiple vias |
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176 | (6) |
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182 | (3) |
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183 | (2) |
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4 Hybrid Integral Equation Modeling Methods for 3D Integration |
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185 | (56) |
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185 | (1) |
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4.2 2D Integral Equation Equivalent Circuit (IEEC) Method |
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186 | (34) |
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4.2.1 Overview of the algorithm |
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186 | (1) |
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4.2.2 Modal decoupling inside the power distribution network (PDN) |
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187 | (2) |
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4.2.3 2D integral equation solution of parallel plate mode in power-ground planes (PGPs) |
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189 | (5) |
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4.2.4 Combinations of transmission and parallel plate modes |
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194 | (11) |
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4.2.5 Cascade connections of equivalent networks |
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205 | (9) |
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214 | (6) |
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4.3 3D Hybrid Integral Equation Method |
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220 | (18) |
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4.3.1 Overview of the algorithm |
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220 | (4) |
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4.3.2 Equivalent electromagnetic currents and dyadic green's functions |
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224 | (7) |
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231 | (7) |
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238 | (3) |
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238 | (3) |
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5 Systematic Microwave Network Analysis for 3D Integrated Systems |
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241 | (90) |
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5.1 Intrinsic Via Circuit Model for Multiple Vias in an Irregular Plate Pair |
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242 | (39) |
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242 | (3) |
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5.1.2 Segmentation of vias and a plate pair |
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245 | (3) |
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5.1.3 An intrinsic 3-port via circuit model |
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248 | (15) |
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5.1.4 Determination of the virtual via boundary |
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263 | (4) |
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5.1.5 Complete model for multiple vias in an irregular plate pair |
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267 | (2) |
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5.1.6 Validation and measurements |
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269 | (11) |
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280 | (1) |
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5.2 Parallel Plane Pair Model |
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281 | (24) |
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281 | (2) |
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5.2.2 Overview of two conventional Zpp definitions |
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283 | (2) |
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5.2.3 New Zpp definition using the zero-order parallel plate waves |
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285 | (5) |
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5.2.4 Analytical formula for radial scattering matrix SRpp in a circular plate pair |
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290 | (2) |
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5.2.5 BIE method to evaluate SRpp for an irregular plate pair |
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292 | (4) |
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5.2.6 Numerical examples and measurements |
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296 | (7) |
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303 | (2) |
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5.3 Cascaded Multiport Network Analysis of Multilayer Structure with Multiple Vias |
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305 | (26) |
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305 | (2) |
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5.3.2 Multilayer PCB with vias and decoupling capacitors |
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307 | (1) |
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5.3.3 Systematic microwave network method |
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308 | (8) |
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5.3.4 Validations and discussion |
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316 | (8) |
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324 | (2) |
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Appendix: Properties of the Auxiliary Function Wmn(x, y) |
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326 | (1) |
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327 | (4) |
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6 Modeling of Through-Silicon Vias (TSV) in 3D Integration |
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331 | (30) |
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331 | (5) |
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6.1.1 Overview of process and fabrication of TSV |
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332 | (3) |
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335 | (1) |
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6.2 Equivalent Circuit Model for TSV |
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336 | (15) |
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337 | (1) |
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6.2.2 Problem statement: Two-TSV configuration |
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338 | (1) |
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6.2.3 Wideband Pi-type equivalent-circuit model |
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339 | (2) |
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6.2.4 Rigorous closed-form formulae for resistance and inductance |
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341 | (4) |
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6.2.5 Scattering parameters of two-TSV system |
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345 | (1) |
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6.2.6 Results and discussion |
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346 | (5) |
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6.3 MOS Capacitance Effect of TSV |
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351 | (5) |
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6.3.1 MOS capacitance effect |
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351 | (1) |
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6.3.2 Bias voltage-dependent MOS capacitance of TSVs |
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351 | (4) |
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6.3.3 Results and analysis |
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355 | (1) |
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356 | (5) |
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358 | (3) |
Index |
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361 | |