A unified framework for statistical timing analysis with coupling and multiple input switching

As technology scales to smaller dimensions, increasing process variations, coupling induced delay variations and multiple input switching effects make timing verification extremely challenging. In this paper, we establish a theoretical framework for statistical timing analysis with coupling and multiple input switching. We prove the convergence of our proposed iterative approach and discuss implementation issues under the assumption of a Gaussian distribution for the parameters of variation. A statistical timer based on our proposed approach is developed and experimental results are presented for the IS-CAS benchmarks. We juxtapose our timer with a single pass, non iterative statistical timer that does not consider the mutual dependence of coupling with timing and another statistical timer that handles coupling deterministically. Monte Carlo simulations reveal a distinct gain (up to 24%) in accuracy by our approach in comparison to the others mentioned.