By Wenjian Yu, Xiren Wang (auth.)

ISBN-10: 3642542972

ISBN-13: 9783642542978

ISBN-10: 3642542980

ISBN-13: 9783642542985

ISBN-10: 7302351511

ISBN-13: 9787302351511

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**

**Example text**

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.)

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