Eecient Formulation and Model-order Reduction for the Transient Simulation of Three-dimensional Vlsi Interconnect

Accurately accounting for three dimensional geometry and distributed RC eeects in on-chip interconnect is important for predicting crosstalk in memory cells, analog circuits, and regions of congested routing in digital circuits. In this paper we describe a multipole-accelerated, mixed surface-volume formulation and a preconditioned model-order reduction algorithm for distributed RC, or electroquasistatic, simulation of three-dimensional integrated circuit interconnect. The diiculties arising from the ill-conditioning inherent in the dynamic problem is eeectively resolved by a combined surface-volume approach. Results are presented to demonstrate that the computational cost for extracting a complete reduced-order model is order N, where N is the number of surface unknowns. Finally, the multipole-accelerated code is used to investigate the accuracy of the one-dimensional diiusion equation for long RC lines.