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

ABSTRACT

Abstract: 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.

REFERENCES

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INDEX TERMS

Primary Classification:
  B. Hardware
  B.7 INTEGRATED CIRCUITS
      B.7.2 Design Aids
          Subjects: Simulation

General Terms:
Algorithms, Theory

Keywords:
Arnoldi method, SPICE-level simulation, Taylor series terms, circuit analysis computing, integrated circuit interconnect, integrated circuit interconnections, reduced-order modeling, reduced-order models, series (mathematics), surface-volume methods, three-dimensional interconnect, transient analysis, transient simulation