Modeling magnetic coupling for on-chip interconnect

As advances in IC technologies and operating frequencies make the modeling of on-chip magnetic interactions a necessity, it is apparent that extension of traditional inductance extraction approaches to full-chip scale problems is impractical. There are primarily two obstacles to performing inductance extraction with the same efficacy as full-chip capacitance extraction: (1) neglecting far-away coupling terms can generate an unstable inductance matrix approximation; and (2) the penetrating nature of inductance makes localized extraction via windowing extremely difficult. In this paper we propose and contrast three new options for stable and accurate window-based extraction of large-scale magnetic coupling. We analyze the required window sizes to consider the possibilities for pattern-matching style solutions, and propose three schemes for determining coupling values and window sizing for extraction via on-the-fly field solution.