Optimization-based Wideband Basis Functions for Efficient Interconnect Extraction

Abstract

This paper introduces a technique for the numerical generation of basis functions that are capable of parameterizing the frequency-variant nature of cross-sectional conductor current distributions. Hence skin and proximity effects can be captured utilizing much fewer basis functions in comparison to the prevalently-used piecewise-constant basis functions. One important characteristic of these basis functions is that they only need to be pre-computed once for a frequency range of interest per unique conductor cross-sectional geometry, and they can be stored off-line with a minimal associated cost. In addition, the robustness of these frequency-independent basis functions is enforced using an optimization routine. It has been demonstrated that the cost of solving a complex interconnect system can be reduced by a factor of 170 when compared to the use of piecewise-constant basis functions over a wide range of operating frequencies