By Wenjian Yu, Xiren Wang (auth.)
Resistance and capacitance (RC) extraction is an important step in modeling the interconnection wires and substrate coupling influence in nanometer-technology built-in circuits (IC). The field-solver suggestions for RC extraction warrantly the accuracy of modeling, and have gotten more and more vital in assembly the call for for exact modeling and simulation of VLSI designs. Advanced Field-Solver recommendations for RC Extraction of built-in Circuits offers a scientific creation to, and remedy of, the main field-solver tools for RC extraction of VLSI interconnects and substrate coupling in mixed-signal ICs. a variety of field-solver concepts are defined intimately, with real-world examples to demonstrate the benefits and drawbacks of every algorithm.
This ebook will gain graduate scholars and researchers within the box of electric and computing device engineering in addition to engineers operating within the IC layout and layout automation industries.
Dr. Wenjian Yu is an affiliate Professor on the division of machine technology and expertise at Tsinghua college in China; Dr. Xiren Wang is a R&D Engineer at Cadence layout structures within the USA.
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Extra info for Advanced Field-Solver Techniques for RC Extraction of Integrated Circuits
3, the technical details of fast multipole method and low-rank matrix compression in the indirect BEM capacitance solvers will be presented. 4 Direct Boundary Element Method The direct BEM is based on the direct boundary integral equation (direct BIE) and suitable for solving 3-D Laplace equation with various boundary conditions . Specifically, the direct BEM is very efficient for handling the finite-domain model of capacitance extraction. Within the finite domain that is involved in capacitance extraction (see Fig.
Source points), one for an element, the discretized BIEs for the ith dielectric are achieved: 1 The early version of Q3DTM of Ansoft Corp. 1 Direct Boundary Element Method for Multi-dielectric Capacitance Extraction Fig. 1 The trapezoid element P1 P2 P3 P4 , whose hemlines are parallel to the X-axis Z P4(x4, y2, z2) 41 P3(x3, y2, z2) Y P1(x1, y1, z1) P2(x2, y1, z1) O ck uk C ! k/ d uj D X ! 4) where Ni is the number of the boundary elements in dielectric i and j is the jth element. 4) costs a major part of the computational time of boundary element algorithms, in particular for 3-D analysis [25, 46].
Level-1 squares don’t have far fields. Let’s see the level-3 square in gray. It has 8 near-field neighbors, each of which shares at least a common boundary point. Its parent box (in dashed line) also has 8 near-field neighbors; the nine level-2 boxes (including itself) have 36 level-3 squares. Among these 36 squares, apart from the gray box itself and its near-field neighbors, the left 27 squares are the far fields. 26 3 Fast Boundary Element Methods for Capacitance Extraction (I) Multipole Expansion Local Expansion Charges Potential Fig.