Exploiting correlation kernels for efficient handling of intra-die spatial correlation, with application to statistical timing

Intra-die manufacturing variations are unavoidable in nanoscale processes. These variations often exhibit strong spatial correlation. Standard grid-based models assume model parameters (grid-size, regularity) in an ad hoc manner and can have high measurement cost. The random £eld model overcomes these issues. However, no general algorithm has been proposed for the practical use of this model in statistical CAD tools. In this paper, we propose a robust and ef£cient numerical method, based on the Galerkin technique and Karhunen Loéve Expansion, that enables effective use of the model. We test the effectiveness of the technique using a Monte Carlo-based Statistical Static Timing Analysis algorithm, and see errors less than 0.7%, while reducing the number of random variables from thousands to 25, resulting in speedups of up to 100x.