Out-of-plane Block Copolymer Microdomains in High Aspect-Ratio Templates

Directed self-assembly DSA of block copolymers BCP proved to be a power approach for nanoscale fabrication. In addition, BCP with highly incompatible blocks (high Flory-Huggins interaction parameter ($\chi ))$ offer improvement in resolution of the BCP patterns. Unfortunately, high-$\chi $ BCPs usually exhibit large differences in surface affinity between the two blocks, forming a surface layer of the lower surface energy block and favoring in-plane orientation of lamellae or cylindrical microdomains. Here, we explore the conditions under which a high $\chi $ BCP creates an out-of-plane lamellar structure using high aspect ratio trenches with preferential walls. We employ self-consistent field theory SCFT and single mode expansion of Ginzburg-Landau free energy expression in the weak segregation limit to analytically construct a phase diagram of the in- and out-of-plane lamellae as a function of aspect ratio and surface affinity. It is found that achieving an out of plane lamellar structure necessitates a coupling between aspect ratio and surface functionality. In particular, strong side wall attraction results in out-of-plane lamellae when the trench aspect ratio is greater than unity. The results are validated for a polystyrene-block-polydimethylsiloxane (PS-b-PDMS) system within trenches made using interference lithography.