Optimal design of chemoepitaxial guideposts for the directed self-assembly of block copolymer systems using an inexact Newton algorithm
Optimal design of chemoepitaxial guideposts for the directed self-assembly of block copolymer systems using an inexact Newton algorithm
复制标题
DOI：
10.1016/j.jcp.2023.112101
复制
发表时间：
2023-04-12
影响因子：
4.1
通讯作者：
Oden，Tinsley
中科院分区：
文献类型：
--
作者：
Luo，Dingcheng;Cao，Lianghao;Oden，Tinsley
嵌段共聚物（BCP）的定向自组装（DSA）是纳米级器件经济高效生产中最有前途的发展之一。该工艺利用了 BCP 熔体在相分离时形成纳米级结构的自然趋势。可以通过使用化学图案化基底来引导相分离，以促进半导体器件生产所必需的形态的形成。此外，基板图案的设计可以表述为一个优化问题，我们寻求有效产生给定目标形貌的最佳基板设计。在本文中，我们采用基于Ohta-Kawasaki自由能最小化的非局部Cahn-Hilliard偏微分方程（PDE）给出的相场模型，并为优化设计问题提出了一个有效的PDE约束优化框架。设计变量是用于模拟基材化学图案的圆形或条形导柱的位置。为了解决随后的优化问题，我们提出了针对该问题量身定制的不精确牛顿共轭梯度算法的变体。我们在跨越一系列目标形态的数值示例上证明了我们的计算策略的有效性。由于我们的二阶优化器和快速状态求解器，数值结果表明计算成本比之前的工作降低了五个数量级。我们框架的效率和优化算法的快速收敛使我们不仅能够在两个空间维度上，而且在三个空间维度上快速解决最优设计问题。
Directed self-assembly (DSA) of block copolymers (BCPs) is one of the most promising developments in the cost-effective production of nanoscale devices. The process makes use of the natural tendency for BCP melts to form nanoscale structures upon phase separation. The phase separation can be directed through the use of chemically patterned substrates to promote the formation of morphologies that are essential to the production of semiconductor devices. Moreover, the design of substrate pattern can be formulated as an optimization problem for which we seek optimal substrate designs that effectively produce given target morphologies.In this paper, we adopt a phase field model given by a nonlocal Cahn–Hilliard partial differential equation (PDE) based on the minimization of the Ohta–Kawasaki free energy, and present an efficient PDE-constrained optimization framework for the optimal design problem. The design variables are the locations of circular- or strip-shaped guiding posts that are used to model the substrate chemical pattern. To solve the ensuing optimization problem, we propose a variant of an inexact Newton conjugate gradient algorithm tailored to this problem. We demonstrate the effectiveness of our computational strategy on numerical examples that span a range of target morphologies. Owing to our second-order optimizer and fast state solver, the numerical results demonstrate five orders of magnitude reduction in computational cost over previous work. The efficiency of our framework and the fast convergence of our optimization algorithm enable us to rapidly solve the optimal design problem in not only two, but also three spatial dimensions.