Two-Stage Layout Decomposition for Hybrid E-Beam and Triple Patterning Lithography

Abstract

Hybrid e-beam lithography (EBL) and triple patterning lithography (TPL) are advanced technologies for the manufacture of integrated circuits. We propose a technology that combines the advantages of EBL and TPL, which is more promising for the pattern product industry. Layout decomposition is a crucial step in this technology. In this article, we propose a two-stage decomposition flow for the hybrid e-beam and triple patterning lithography of the general layout decomposition (HETLD) problem. At the first stage, we formulate two optimization problems: the e-beam and stitch-aware TPL mask assignment (ESTMA) problem and the extended minimum weight dominating set for R 4 mask assignment (MDS R 4 MA) problem. Binary linear program formulations of the two problems are solved by the cutting plane approach. At the second stage, solutions of the first stage problems are legalized to feasible solutions of the HETLD problem by stitch insertion and e-beam shot. To speed up decomposition, we reduce the problem size by removing some vertices and some minor conflict edges before decomposition. Experimental results show the effectiveness of our decomposition methods based on ESTMA and MDS R 4 MA.