Conditions for the directed assembly of thick block copolymer films on chemically nano-patterned surfaces

The extent to which a lamellae forming block copolymer (bulk period, $L_{0}$ = 48 nm) can be directed to assemble on chemically nano-patterned striped surfaces (period $L_{S})$ with domains registered to and extending vertically away from the underlying pattern with few defects was studied as a function of film thickness, commensurability between $L_{S}$ and $L_{0}$, and temperature. The thickness through which low defect assembly could be achieved increased as $L_{S}$ and $L_{0}$ became more commensurate and as the temperature increased from 190 \r{ }C to 230 \r{ }C. Under certain conditions ($L_{S} \quad \approx \quad L_{0}$, 230 \r{ }C), block copolymer films approaching 750 nm (aspect ratio $\approx $ 30) in thickness still exhibited low levels of defectivity. These results were interpreted in terms of a phenomenological model and minimization of free energy including surface and interfacial energies and chain configuration entropy.