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

作　　者：Daniil Bochkov Frederic Gibou 

机构地区：[1]Department of Mechanical Engineering,University of California,Santa Barbara,Santa Barbara,CA93106,USA [2]Department of Computer Science,University of California,Santa Barbara,Santa Barbara,CA 93106 USA

出　　处：《Communications on Applied Mathematics and Computation》2024年第2期1472-1489,共18页应用数学与计算数学学报（英文）

基　　金：supported by the NSF DMS 1620471.

摘　　要：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 selfassembly 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).

关 键 词：Block copolymers Directed self-assembly Inverse design Shape optimization Vertical interconnect accesses(VIA) 

分 类 号：O24[理学—计算数学] O29[理学—数学]