Directed self-assembly of block copolymers has been used for fabricating various nanoscale patterns, ranging from periodic lines to simple bends. However, assemblies of dense bends, junctions and line segments in a single pattern have not been achieved by using sparse templates, because no systematic template design methods for achieving such complex patterns existed. To direct a complex pattern by using a sparse template, the template needs to encode the key information contained in the final pattern, without being a simple copy of the pattern. Here we develop a set of topographic template tiles consisting of square lattices of posts with a restricted range of geometric features. The block copolymer patterns resulting from all tile arrangements are determined. By combining tiles in different ways, it is possible to predict a relatively simple template that will direct the formation of non-trivial block copolymer patterns, providing a new template design method for a complex block copolymer pattern.
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