A Computational Method for Inverse Design Problem in Directed Self-Assembly of Block Copolymers

Directed Self-Assembly is an important process used in the semi-conductor industry. It uses confinement masks to drive the self-assembly of block copolymers towards targeted nano-templates for subsequent optical or e-beam lithography. The shape of such confinement masks must be carefully designed as it is one of the primary factors determining the final polymeric structures. In this talk, we present a computational approach, within the self-consistent field theory framework, for finding confinement shapes that lead to a-priori chosen self-assembled structures of block copolymers. The method is based on a constrained optimization formulation described by partial differential equations: we define a cost functional that measures the discrepancy between the target and the actual self-assembled configurations, and analytically derive the sensitivity of the functional to changes in shape, which in turn enables an efficient minimization of the functional with respect to the confinement shape. We provide simulation results that demonstrate the ability of our approach to design mask geometries that successfully guide the self-assembly to the desired targets.