Roles of chemical pattern period and film thickness in directed self-assembly of diblock copolymers

We develop a new numerical self-consistent field theory (SCFT) scheme for examining thin film nanostructures of cylinder-forming AB diblock copolymers on a chemically patterned substrate. Using this, we make a systematic analysis to achieve a fundamental understanding of the model system, and the conditions to create various novel film morphologies are scrutinized by varying the pattern period and film thickness. At a fixed pattern period, eight candidate phases which are divided into two groups according to the film thickness are found, and then their free energies are compared to identify the stable morphology. Among the thinner film morphologies, a crossed cylinder geometry is found to be stable with a comfortable margin. While for the thicker film morphologies, the stability of the phases depends strongly on both the pattern period and film thickness. In addition, we identify an unstable phase capable of thinning the films and consequently providing instability for the ordering of the thicker film nanostructures. A qualitative agreement is found between our theory and previously reported experimental results.