Triple/quadruple patterning layout decomposition via linear programming and iterative rounding

As the feature size of the semiconductor technology scales down to 10 nm and beyond, multiple patterning lithography (MPL) has become one of the most practical candidates for lithography, along with other emerging technologies, such as extreme ultraviolet lithography (EUVL), e-beam lithography (EBL), and directed self-assembly. Due to the delay of EUVL and EBL, triple and even quadruple patterning is considered to be used for lower metal and contact layers with tight pitches. In the process of MPL, layout decomposition is the key design stage, where a layout is split into various parts and each part is manufactured through a separate mask. For metal layers, stitching may be allowed to resolve conflicts, whereas it is forbidden for contact and via layers. We focus on the application of layout decomposition where stitching is not allowed, such as for contact and via layers. We propose a linear programming (LP) and iterative rounding solving technique to reduce the number of nonintegers in the LP relaxation problem. Experimental results show that the proposed algorithms can provide high quality decomposition solutions efficiently while introducing as few conflicts as possible.