Enhancing commensurability using cylinder-forming block copolymer-homopolymer ternary blends on spotted chemical patterns

Self-assembly of block copolymers can be directed by underlying chemical patterns to create well-defined nanostructures with registration and a high degree of order, and is extremely useful for multiplying feature density from the pattern, if the pattern spacing and surface chemistry are carefully selected. Best hexagonal order of cylinder-forming pure polystyrene-\textit{block}-poly(methyl methacrylate) (bulk inter-cylinder spacing $L_{0})$ on spotted chemical pattern (inter-spot spacing $L_{S})$ is typically achieved within the range of 0.96$L_{0} \quad \le \quad L_{S} \quad \le $ 1.06$L_{0}$ of the pattern and even narrower range for the density multiplication technique. Using ternary blends of block copolymer and low molecular weight homopolymers increase the range of $L_{S}$ for which direct hexagonal cylinders with registration on the spot patterns, up to $\pm $ 10{\%} from $L_{0}$, although the blends have similar $L_{0}$ with pure block copolymer. Additionally, inclusion of homopolymers relaxes the commensurability requirements for multiplying the cylinder density on the spot patterns.