Efficient reduced-order modeling for the transient simulation of three-dimensional interconnect

Multipole-accelerated surface-volume methods have proved to be very efficient techniques for delay and cross-talk simulation of three-dimensional integrated circuit interconnect. However, to be efficiently combined with transistor circuitry in a SPICE-level simulation, reduced-order models which have accurate low-frequency behavior must be constructed. Asymptotic Waveform Evaluation (AWE) or Pade-via-Lanczos (PVL) algorithms can not be used directly to construct the reduced-order models from the surface-volume formulation, because the formulation generates dense matrices which are too expensive to factor. In this paper we describe a two-level approach to efficiently generating reduced-order models with accurate low frequency behavior. First, reduced-order models which match Taylor series terms at s=/spl infin/ are efficiently generated from the surface-volume formulation using an Arnoldi method, and then these fairly high-order models are used to efficiently construct lower-order models which snatch Taylor series terms at s=0. Examples are given to demonstrate the accuracy of the resultant low-order model.