1 Introduction
1.1 The Need for Parasitic Extraction
1.2 The Methods for RC Extraction and Field Solver
1.3 Book Outline
1.4 Summary
2 Basic Field-Solver Techniques for RC Extraction
2.1 Problem Formulation
2.2 Overview of the Numerical Methods
2.3 Indirect Boundary Element Method
2.4 Direct Boundary Element Method
2.5 Floating Random Walk Method
2.6 Summary
3 Fast Boundary Element Methods for Capacitance
Extraction I
3.1 Basics of Indirect Boundary Element Methods
3.2 Fast Multipole Methods
3.2.1 Introduction
3.2.2 Multipole Expansions
3.2.3 Local Expansions
3.2.4 Fast Multipole Algorithm
3.3 Low-Rank Matrix Compression-Based Fast Iterative Solvers
3.3.1 Why Compression?
3.3.2 Matrix Compression Can Reduce the Complexity to Linear
3.3.3 Compression Possible?
3.3.4 Basics of Matrix Compression Using SVD and QR
3.3.5 Compression Without Building Entire Matrix Beforehand
3.4 Matrix Compression by Adaptive Cross Approximation
3.4.1 Adaptive Cross Approximation ACA
3.4.2 Recompression of Adaptive Cross Approximation
3.5 Summary
4 Fast Boundary Element Methods for Capacitance
Extraction II
4.1 Direct Boundary Element Method for Multi-dielectric Capacitance Extraction
4.2 The Quasi-multiple Medium Approach
4.2.1 Basic Idea
4.2.2 Decomposition of Dielectrics and Boundary Element Partition
4.2.3 Algorithm Description and Analysis
4.3 Equation Organization and Solving Techniques
4.3.1 Organization of the Coefficient Matrix
4.3.2 Extended Jacobi and MN Preconditioners
4.4 Numerical Results
4.4.1 The Comparison with GIMEI
4.4.2 The Comparison with ODDM
4.4.3 The Results for Structures from Real Design
4.4.4 The Comparison with FastCap
4.5 Efficient Techniques for Handling Floating Metal Fills
4.5.1 Basic Idea
4.5.2 Equation Formation and Solution
4.5.3 Numerical Results
4.6 Summary
5 Resistance Extraction of Complex 3-D Interconnects
5.1 Analytical Resistance Formulation
5.2 Field Solver for Interconnect Resistance
5.2.1 Resistance Network of Multiterminal Regions
5.2.2 Resistance Calculation Using Direct BEM
5.3 Fast BEM Solver Using Linear Boundary Elements
5.3.1 Physics-Based Nonuniform Virtual Cutting
5.3.2 Discarding Conductors Not in the Path of Direct Current
5.3.3 Dividing Elements Only in One Direction When Possible
5.3.4 Linear Boundary Elements for Straight Conductors
5.3.5 Efficiency Summary
5.4 Analytical QBEM Extraction
5.4. l General Analytical QBEM Algorithm
5.4.2 Distinguish Between Regular and Irregular Subregions
……
6 Slbstrate Resistance Extraction with Boundary Element Method
7 Extracting Frequency-Dependent Substrate Parasitics
8 Process Variation-Aware Capacitance Extraction
9 Statistical Capacitance Extraction Based on Continuous-Surface Geometric Model
10 Fast Floating Random Walk Method for Capacitance Extraction
11 FRW-Based Solver for Chip-Scale Large Structures
References
Index
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