Accurate modeling of noise coupling effects due to crosstalk via the substrate is an increasingly important concern for the design and verification of mixed analog-digital systems. In this paper we present a technique to accelerate the model computation using BEM methods that can be used for accurate and efficient extraction of substrate coupling parameters in mixed-signal designs.

Industry trends aimed at integrating higher levels of circuit functionality have triggered a proliferation of mixed analog-digital systems. Magnified noise coupling through the common chip substrate has made the design and verification of such systems an increasingly difficult task. In this paper we present a fast eigendecomposition technique that accelerates operator application in BEM methods and avoids the dense-matrix storage while taking all of the substrate boundary effects into account explicitly. This technique can be used for accurate and efficient modeling of substrate coupling effects in mixed-signal integrated circuits.

The extraction of substrate coupling resistances can be formulated as a first-kind integral equation, which requires only discretization of the two-dimensional contacts. However, the result is a dense matrix problem which is too expensive to store or to factor directly. Instead, we present a novel, multigrid iterative method which converges more rapidly than previously applied Krylov-subspace methods. At each level in the multigrid hierarchy, we avoid dense matrix-vector multiplication by using moment-matching approximations and a sparsification algorithm based on eigendecomposition. Results on realistic examples demonstrate that the combined approach is up to an order of magnitude faster than a Krylov-subspace method with sparsification, and orders of magnitude faster than not using sparsification at all.

Industry trends aimed at integrating higher levels of circuit functionality have triggered a proliferation of mixed analog-digital systems. Magnified noise coupling through the common chip substrate has made the design and verification of such systems an increasingly difficult task. In this paper we present a fast eigen-decomposition technique that accelerates operator application in BEM methods and avoids the dense-matrix storage while taking all of the substrate boundary effects into account explicitly. This technique can be used for accurate and efficient modeling of substrate coupling effects in mixed-signal integrated circuits.

Accurately accounting for three-dimensional (3-D) geometry and distributed RC effects 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 3-D integrated circuit interconnect. The difficulties arising from the ill conditioning inherent in the dynamic problem is effectively 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 diffusion equation for long RC lines.

It has recently been shown that the boundaryelement method can be used to perform accurate cross-talk simulations of three-dimensional integrated circuit interconnect. However, the computational complexity grows as , where is the number of surface unknowns. Straightforward application of the fast-multipole algorithm reduces the computational complexity to order , but produces magnified errors due to the ill-conditioning of the steady-state problem. We present a mixed surface-volume approach and prove that the formulation results in the exact steadystate solution, independent of the multipole approximations. Numerical experiments are presented to demonstrate the accuracy and efficiency of this technique. On a realistic example, the new method runs fifteen times faster than using dense-matrix iterative methods.

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.