Efficient 3-d capacitance extraction considering lossy substrate with multilayered green´s function

An efficient algorithm for extraction of three-dimensional (3-D) capacitance on multilayered and lossy substrates is presented. The new algorithm presents a major improvement over the quasi-3-D approach used in a Green´s function-based solver and takes into consideration the sidewalls of 3-D conductors. To improve the efficiency of the computation and the transformation of the Green´s function, a nonuniform grid is adopted. The most computationally intensive part in the transformation of the Green´s function is computed separately as technology-independent matrices Tk foremost. Once computed, Tk can be stored and used for any technology, thus the storage requirement and computational complexity are reduced from O (S²) and O (S² log S²), respectively, to just O [(log S_max)²]. Extensive tests have been performed to verify the new algorithm, and its accuracy has been established by comparing with other programs.