Modeling of Intra-die Process Variations for Accurate Analysis and Optimization of Nanoscale

This paper proposes the use of Karhunen-Loève Expansion (KLE) for accurate and efficient modeling of intra-die correlations in the semiconductor manufacturing process. We demonstrate that the KLE provides a significantly more accurate representation of the underlying stochastic process compared to the traditional approach of dividing the layout into grids and applying Principal Component Analysis (PCA). By comparing the results of leakage analysis using both KLE and the existing approaches, we show that using KLE can provide up to 4 − 5× reduction in the variability space (number of random variables) while maintaining the same accuracy. We also propose an efficient leakage minimization algorithm that maximizes the leakage yield while satisfying probabilistic constraints on the delay.