Timing Yield-Aware Color Reassignment and Detailed Placement Perturbation for Bimodal CD Distribution in Double Patterning Lithography

Abstract

Double patterning lithography (DPL) is in current production for memory products, and is widely viewed as inevitable for logic products at the 32 nm node. DPL decomposes and prints the shapes of a critical-layer layout in two exposures. In traditional single-exposure lithography, adjacent identical layout features will have identical mean critical dimension (CD), and spatially correlated CD variations. However, with DPL, adjacent features can have distinct mean CDs, and uncorrelated CD variations. This introduces a new set of “bimodal” challenges for timing analysis and optimization. We assess the potential impact of bimodal CD distribution on timing analysis and guardbanding, and find that the traditional “unimodal” characterization and analysis framework may not be viable for DPL. We propose new bimodal-aware timing analysis and optimization methods to improve timing yield of standard-cell based designs that are manufactured using DPL. Our first contribution is a DPL-aware approach to timing modeling, based on detailed analysis of cell layouts. Our second contribution is an integer linear programming-based maximization of “alternate” mask coloring of instances in timing-critical paths, to minimize harmful covariance and performance variation. Third, we propose a dynamic programming-based detailed placement algorithm that solves mask coloring conflicts and can be used to ensure “double patterning correctness” after placement or even after detailed routing, while minimizing the displacement of timing-critical cells with manageable engineering change order (ECO) impact. With a 45 nm library and open-source design testcases, our timing-aware recoloring and placement optimization together achieve up to 271 ps (respectively, 55.75 ns) reduction in worst (respectively, total) negative slack, and 70% (respectively, 72%) reduction in worst (respectively, total) negative slack variation, respectively.