Statistical Analysis of Circuit Timing Using Majorization. - Orshansky, Michael; Wei-Shen Wang (Communications of the ACM, 2009)
Future miniaturization of silicon transistors following Moore's Law may be in jeopardy as it becomes harder to precisely define the behavior and shape of nanoscale transistors. One fundamental challenge is overcoming the variability in key integrated circuit parameters. In this paper, we discuss the development of electronic design automation tools that predict the impact of process variability on circuit behavior, with particular emphasis on verifying timing correctness. We present a new analytical technique for solving the central mathematical challenge of the statistical formulation of timing analysis which is the computation of the circuit delay distribution when delays of circuit elements are correlated. Our approach derives the bounds for the exact distribution using the theory of stochastic majorization. Across the benchmarks, the root-mean-square difference between the exact distribution and the bounds is 1.7-4.5% for the lower bound and 0.9-6.2% for the upper bound.