OPTIMAL PHASE CONFLICT REMOVAL FOR LAYOUT OF ALTERNATING PHASE-SHIFTING MASKS
Method for resolving phase conflict for dark-field and bright-field alternating phase-shifting mask technologies is disclosed. For the dark-field masks, the method consists of a new 2-coloring and compaction approach that simultaneously optimizes layout and phase assignment which is based on planar embedding of an associated phase conflict graph; optimal and fast algorithms minimizing the number of phase conflicts that must be removed to ensure 2-colorability of the phase conflict graph; and fast gadget-based algorithms solving optimally the corresponding T-join problem. For the bright-field masks, the method consists of a new 2-coloring and compaction approach that simultaneously optimizes layout and phase assignment which is based on planar embedding of an associated feature graph, wherein the feature graph incorporates two types of layout modifications: increasing spacing and changing the width of critical thin features; optimal fast algorithms minimizing the number of phase conflicts that must be removed by increasing spacing; and approximate fast algorithms minimizing the number of phase conflicts that must be removed by both types of layout modifications.