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

doi:10.1007/s42967-024-00394-x

Communications on Applied Mathematics and Computation ›› 2024, Vol. 6 ›› Issue (2): 1472-1489.doi: 10.1007/s42967-024-00394-x

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

Daniil Bochkov¹, Frederic Gibou^1,2

1. Department of Mechanical Engineering, University of California, Santa Barbara, Santa Barbara, CA 93106, USA;
2. Department of Computer Science, University of California, Santa Barbara, Santa Barbara, CA 93106, USA

收稿日期:2023-02-17 修回日期:2024-02-08 接受日期:2024-02-11 出版日期:2024-05-02 发布日期:2024-05-02
通讯作者: Daniil Bochkov,E-mail:bochkov.ds@gmail.com;Frederic Gibou,E-mail:fgibou@ucsb.edu E-mail:bochkov.ds@gmail.com;fgibou@ucsb.edu
基金资助:
This research was supported by the NSF DMS 1620471.

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

Daniil Bochkov¹, Frederic Gibou^1,2

1. Department of Mechanical Engineering, University of California, Santa Barbara, Santa Barbara, CA 93106, USA;
2. Department of Computer Science, University of California, Santa Barbara, Santa Barbara, CA 93106, USA

Received:2023-02-17 Revised:2024-02-08 Accepted:2024-02-11 Online:2024-05-02 Published:2024-05-02
Contact: Daniil Bochkov,E-mail:bochkov.ds@gmail.com;Frederic Gibou,E-mail:fgibou@ucsb.edu E-mail:bochkov.ds@gmail.com;fgibou@ucsb.edu
Supported by:
This research was supported by the NSF DMS 1620471.

摘要/Abstract

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 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).

关键词: Block copolymers, Directed self-assembly, Inverse design, Shape optimization, Vertical interconnect accesses(VIA)

Abstract: 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).

Key words: Block copolymers, Directed self-assembly, Inverse design, Shape optimization, Vertical interconnect accesses(VIA)

Daniil Bochkov, Frederic Gibou. A Non-parametric Gradient-Based Shape Optimization Approach for Solving Inverse Problems in Directed Self-Assembly of Block Copolymers[J]. Communications on Applied Mathematics and Computation, 2024, 6(2): 1472-1489.

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

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

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