Novel Guiding Template and Mask Assignment for DSA-MP Hybrid Lithography Using Multiple BCP Materials

Abstract

Directed self-assembly (DSA) is one of the leading candidates for extending the resolution of optical lithography to sub-7 nm and beyond. By incorporating DSA in multiple patterning lithography (DSA-MP), the flexibility and resolution of contact/via patterning can be further enhanced by using multiple block copolymer (BCP) materials. Prior work faces the dilemma between solution quality and efficiency and is unable to handle 2-D templates. In this article, we capture the essence of template and mask assignment in DSA-MP by a new graph model and a new problem reduction: Our graph model explicitly represents spacing conflict edges and template hyperedges; thus, extra enumeration and manipulation of incompatible via grouping edges can be avoided, and arbitrary 1-D/2-D templates can be natively handled. We further reduce the assignment problem to exact cover, which is encoded by a sparse matrix. Our concise integer linear programming (ILP) formulation and fast backtracking heuristic achieve substantially superior solution quality and efficiency to the state-of-the-art work. Moreover, our problem and graph modelling is flexible and extensible to utilize dummy vias to improve manufacturability. To narrow down the search region of dummy vias, we devise a conflict core finding technique, which is general and applicable to conflict core analysis of exact cover and other multiple patterning layout decomposition problems. Experimental results show the effectiveness and efficiency of our approach.