By Wenjian Yu, Xiren Wang (auth.)
Resistance and capacitance (RC) extraction is a necessary step in modeling the interconnection wires and substrate coupling impression in nanometer-technology built-in circuits (IC). The field-solver thoughts 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 recommendations for RC Extraction of built-in Circuits offers a scientific creation to, and therapy of, the most important field-solver equipment for RC extraction of VLSI interconnects and substrate coupling in mixed-signal ICs. a number of field-solver recommendations are defined intimately, with real-world examples to demonstrate the benefits and downsides of every algorithm.
This e-book will profit 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 desktop technological know-how and expertise at Tsinghua collage in China; Dr. Xiren Wang is a R&D Engineer at Cadence layout platforms within the USA.
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Extra resources for Advanced Field-Solver Techniques for RC Extraction of Integrated Circuits
Let’s see the approximations and error distributions with rank 30, rank 10, and rank 4, in Figs. 12. These figures tell us that rank-30 approximation is almost the same as the original matrix, without any visual discrepancy. 2 Singular values of a 1/r matrix with random charge and evaluation points 31 No. 01 100 0 100 80 60 40 20 0 0 20 40 60 80 100 50 0 0 20 40 60 80 100 Fig. 01 100 0 100 80 80 60 40 20 0 0 20 40 60 50 0 0 Fig. 01 100 0 100 80 60 40 20 0 0 20 40 60 80 100 50 0 0 20 40 60 80 100 Fig.
The QMM approach has been applied in the extraction of actual 3-D multilayered interconnect capacitance. It produces the overall coefficient matrix with much sparsity.
1 Adaptive Cross Approximation (ACA) This algorithm is to find appropriate U and V, so that Pm n Um k VTn k , where rank k is much smaller than m and n. 26), until kU(:, k)kF kV(:, k)kF Ä 2 kAk kF . W; k/k2F : Note that only a small number of rows and columns are involved in the above procedure, and the computation is simply multiplication and addition. Therefore, the complexity is also linear O(m C n). An interesting property of ACA is that matrix UVT is exact at the selected columns and rows, (UVT )(ik C 1 , :) D A(ik C 1 , :), (UVT )(:, jk C 1 ) D A(:, jk C 1 ).
Advanced Field-Solver Techniques for RC Extraction of Integrated Circuits by Wenjian Yu, Xiren Wang (auth.)