Design of surface patterns with optimized thermodynamic driving forces for the directed self-assembly of block copolymers in lithographic applications

It is well established by theory and experiment that lamella-forming block copolymers with characteristic periodicity, L-0, can assemble into lines-and-spaces over carefully crafted chemically patterned substrates composed of stripes of width W that repeat with period L-S. While previous works measured the efficacy of pattern designs for self-assembly through visual inspection of experimental images or examination of morphologies obtained from simulations, here we combine visual inspection over a large number of processing conditions with a new theoretical strategy that quantitatively measures the thermodynamic driving force of chemical patterns to produce a single grain of lines-and-spaces. The metric we use to describe the thermodynamic driving force is defined by the free-energy difference between the desired assembly of lines-and-spaces and the grain orientation with the lowest energy, referred to as the most competitive assembly. Visualization of experimental systems using SEM imaging provides a first-order approximation of the process windows in pattern design space in regard to W and the chemical contrast of the stripes and the background region, where the thermodynamic driving force is large enough to eliminate competitive grains. The strategy proposed in this work then uses complementary molecular simulations to elucidate which combination of these pattern parameters provides the largest driving force through free-energy calculations obtained by thermodynamic integration and attempts to identify which pattern designs minimize the probability of assembling lamellae that are stabilized at undesired angles to the patterned stripes. The combination of experiment and theory shows that narrow guiding stripes with width 0.4 <= W/L-0 <= 0.8 that are highly preferential for one of the blocks are best for obtaining a directed self-assembly process flow with the highest probability of assembling a desired grain orientation.