Throughput optimization for SADP and e-beam based manufacturing of 1D layout

Due to the resolution limitations of optical lithography equipment, 1D gridded layout design is gaining steam. Self-aligned double patterning (SADP) is a mature technology for printing 1D layouts. However, for 20nm and beyond, SADP using a single trim mask becomes insufficient for printing all 1D layouts. A viable solution is to complement SADP with e-beam lithography. In this paper, in order to increase the throughput of printing a 1D layout, we consider the problem of e-beam shot count minimization subject to bounded line end extension constraints. Two different approaches of utilizing the trim mask and e-beam to print a layout are considered. The first approach is under the assumption that the trim mask and e-beam are used for end cutting. The second is under the assumption that the trim mask and e-beam are used to rid of all unnecessary portions. We propose elegant ILP formulations for both approaches. Experimental results show that both ILP formulations can be solved efficiently. The pros and cons of the two approaches for manufacturing 1D layout are discussed.