Download e-book for kindle: Advanced Field-Solver Techniques for RC Extraction of by Wenjian Yu, Xiren Wang (auth.)
By Wenjian Yu, Xiren Wang (auth.)
Resistance and capacitance (RC) extraction is an important step in modeling the interconnection wires and substrate coupling impact 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 actual modeling and simulation of VLSI designs. Advanced Field-Solver options for RC Extraction of built-in Circuits offers a scientific advent to, and remedy of, the most important field-solver equipment for RC extraction of VLSI interconnects and substrate coupling in mixed-signal ICs. numerous field-solver options are defined intimately, with real-world examples to demonstrate the benefits and drawbacks of every algorithm.
This e-book will gain graduate scholars and researchers within the box of electric and machine 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 desktop technology and expertise at Tsinghua college in China; Dr. Xiren Wang is a R&D Engineer at Cadence layout platforms within the USA.
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Extra info for Advanced Field-Solver Techniques for RC Extraction of Integrated Circuits
Within the finite domain that is involved in capacitance extraction (see Fig. 10) stands for the space possessed by the ith dielectric. u stands for the Dirichlet boundary (conductor surfaces), where is known as the bias voltages; q represents the Neumann boundary (outer boundary of the simulated region), where electric flux q is supposed to be zero. Here n denotes the unit vector outward normal to the boundary. 9) holds. 11) i where uis stands for the electric potential at collocation point s (in dielectric region i) and cs is a constant dependent on the boundary geometry near to the point s.
2 Schematic fast multipole algorithm. ” Sources map their charges to fine-level centers, which will in turn map the collected “charges” to upper level. The upper level conducts electrical potential on upper-level evaluation centers, which then pass the potential to fine-level evaluations However, fast multipole method can reduce the interaction computation to order O(m C n). A schematic diagram is in Fig. 2. In order to get product Px, it takes x as electrical charges and Px correspondingly as the electrical potential resulted from these charges.
This is why it is called squared complexity. By contrary, O(m C n) only increases 10x, so it’s called linear complexity, meaning its increasing is linear to m and n. Suppose we can solve a problem with 100 unknowns in 1 day. 1 lists the time request for problem of larger sizes. For simplicity, it’s assumed that m D n. This table tells us that if the problem size increases 100x to 10,000, O(mn) algorithms will require 27 years, while linear O(m C n) algorithms only request in less than 4 months.
Advanced Field-Solver Techniques for RC Extraction of Integrated Circuits by Wenjian Yu, Xiren Wang (auth.)