Timing Analysis and Optimization Implications of Bimodal CD Distribution in Double Patterning Lithography

Double patterning lithography (DPL) is in current production for memory products, and is widely viewed as inevitable for logic products at the 32nm 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 DPL on timing analysis error and guardbanding, and find that the traditional 'unimodal' characterization and analysis framework may not be viable for DPL. For example, using 45nm models, we find that different DPL mask layout solutions can cause 50ps skew in clock distribution that is unseen by traditional analyses. Different mask layouts can also result in 20% or more change in timing path delays. Such results lead to insights into physical design optimizations for clock and data path placement and mask coloring that can help mitigate the error and guardband costs of DPL.