Multigrid-based substrate coupling model extraction

Substrate noise is one of the most eminent 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 common substrate hindering the performance of high precision sensible analog circuitry. Miniaturization effects on IC's complexity, inevitably make the accuracy requirements for substrate coupling simulation increase. However, model extraction and evaluation should not increase, leading to the need for fast and accurate substrate model extraction tools. We propose an extraction methodology based on a 3D finite difference formulation. The resulting 3D mesh is efficiently reduced to a circuit-level contact-based model by means of a fast multilevel algorithm. Extraction results show the proposed method to be very efficient, achieving linear complexity independently of accuracy and discretization and outperforming competing algorithms that show quadratic complexity.