A Non-parametric Gradient-Based Shape Optimization Approach for Solving Inverse Problems in Directed Self-Assembly of Block Copolymers

We consider the inverse problem of finding guiding pattern shapes that result in desired self-assembly morphologies of block copolymer melts. Specifically, we model polymer self-assembly using the self-consistent field theory and derive, in a non-parametric setting, the sensitivity of the dissimilarity between the desired and the actual morphologies to arbitrary perturbations in the guiding pattern shape. The sensitivity is then used for the optimization of the confining pattern shapes such that the dissimilarity between the desired and the actual morphologies is minimized. The efficiency and robustness of the proposed gradient-based algorithm are demonstrated in a number of examples related to templating vertical interconnect accesses (VIA).