An Algorithm to Calculate Correlation Coefficients between Interconnect Delays for Use in Statistical Timing Analysis

Shuji TSUKIYAMA  Masahiko TOMITA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E89-A   No.2   pp.535-543
Publication Date: 2006/02/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.2.535
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: VLSI Design Technology and CAD
correlation coefficient,  interconnect delay,  Elmore delay,  statistical timing analysis,  Gaussian distribution,  

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As process technologies decrease below a hundred nanometers, the variability of circuit parameters increases, and statistical timing analysis, which analyzes the distribution of the critical delay of a circuit, is receiving a great deal of attention. In such statistical approaches, correlations between random variables are important to the accuracy of analysis. Since interconnect delays dominate in recent technology, their correlations are of primary concern in statistical timing analysis. In this paper, we propose an efficient algorithm for calculating correlation coefficients between Elmore interconnect delays with the use of Gaussian distributions. Our algorithm is efficient and yields reasonable results for correlations between interconnect delays of different nets. In order to evaluate the performance of the proposed algorithm, we show experimental results compared against Monte-Carlo simulations using SPICE.