An MILP-based wire spreading algorithm for PSM-aware layout modification

Abstract

Phase shifting mask (PSM) is a promising resolution enhancement technique, which is used in the deep sub-wavelength lithography of the VLSI fabrication process. However, applying the PSM technique requires the layout to be free of phase conflicts. In this paper, we present a mixed integer linear programming (MILP) based layout modification algorithm which solves the phase conflict problem by wire spreading. Unlike existing layout modification methods which first solve the phase conflict problem by removing edges from the layout-associated conflict graphs and then try to revise the layout to match the resultant conflict graphs, our algorithm simultaneously considers the phase conflict problem and the feasibility of modifying the layout. The experimental results indicate that without increasing the chip size, the phase conflict problem can be well tackled with minimal perturbation to the layout.