Substrate model extraction using finite differences and parallel multigrid

Substrate noise in integrated circuits is one of the most important problems in high-frequency mixed-signal designs, such as communication, biomedical and analog signal processing circuits and systems. Fast-switching digital blocks inject noise into the common substrate, hindering the performance of high-precision sensible analog circuitry. Miniaturization trends require increasing the accuracy in substrate coupling simulation environments. However, model extraction and evaluation times should not increase, which demands for fast and still accurate substrate model extraction tools.In this work, a three-dimensional finite difference extraction methodology is presented. The resulting three-dimensional mesh is efficiently reduced to a circuit-level contact-based model by means of a fast multigrid-based algorithm. Moreover, this contact-based model extraction is shown to be efficiently computed in a parallel environment, resulting in extremely useful extraction speedups. Extraction results prove the proposed method to be very efficient, providing linear time and space complexity, and a constant number of iterations, outperforming competing algorithms.