Directed Assembly of Block Copolymers by Sparsely Patterned Substrates

Self-consistent field theory and dissipative particle dynamics simulations are used to demonstrate the controlled positioning and alignment of cylindrical domains by chemical surface patterns in an asymmetric slit. Self-assembly of the copolymer melt is simulated near dense and sparse surface patterns, both with one and two characteristic length scales. In particular, we compare the effect of a hexagonal pattern, sparse rectangular pattern, and triangle pattern. The parallel alignment of microdomains between preferentially attractive homogeneous surfaces is shown to transform into the stable perpendicular hexagonal phase in the case of the substrate patterns, which commensurate with the hexagonal morphology in the bulk. For the sparse rectangular pattern, when two different length scales of interactions are involved, and for the sparse hexagonal pattern, we observe that the self-assembly of diblocks multiplies the density of the surface patterns by a factor of 2 and 4, respectively. A 2-fold resolution enhancement was found for sparse triangle pattern with two characteristic length scales. The analysis of the circularly averaged structure factor allowed us to distinguish the structure orientation in a film. Additional peak in the region of small lateral wave numbers is attributed to undulational deformations of cylinder domains under preferable film boundaries. This theoretical work serves to rationalize modern nanolithographic fabrication of high-spatial-frequency arrays using lower-spatial-frequency templates.