Calculations of the free energy of dislocation defects in lamellae forming diblock copolymers using thermodynamic integration

Abstract. State-of-the-art directed self-assembly (DSA) of block copolymer (BCP) methods still yield defect densities orders of magnitude higher than is necessary in semiconductor fabrication. The defect free energy of a dislocation pair or jog defect, one of the most common defects found in BCP-DSA, is calculated via thermodynamic integration using a coarse-grained molecular dynamics model as a function of χ and the degree of polymerization (N). It is found that χN is not the best predictor of defect free energy and that a single χN value can yield vastly different free energies when χ and N are different. Defect free energy was highly dependent on defect location relative to the underlayer, and free energy differences ∼100  kT were found among the three possible defect locations on a 1:3 guiding pattern. It was found that increasing molar mass dispersity (Ð) significantly reduced defect free energy. Extrapolating from Ð up to 1.5 suggests that the defect will occur in equal proportions to the defect free state at a Ð of around 1.6 for this system. It was found that long chains tended to concentrate near the defect and stabilize the defect.

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