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具有非均匀粘度分布的聚甲基丙烯酸甲酯结构的热回流模拟

Thermal Reflow Simulation for PMMA Structures with Nonuniform Viscosity Profile.

作者信息

Sidorov Fedor, Rogozhin Alexander

机构信息

Valiev Institute of Physics and Technology, Russian Academy of Sciences, 117218 Moscow, Russia.

出版信息

Polymers (Basel). 2023 Sep 11;15(18):3731. doi: 10.3390/polym15183731.

DOI:10.3390/polym15183731
PMID:37765585
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC10534791/
Abstract

This paper presents a new approach to the simulation of the thermal reflow of e-beam-exposed polymethyl methacrylate (PMMA) taking into account its nonuniform viscosity profile. This approach is based on numerical "soapfilm" modeling of the surface evolution, processed by the free software "Surface Evolver" in area normalization mode. The PMMA viscosity profile is calculated via the simulation of the exposed PMMA number average molecular weight distribution using the Monte-Carlo method and empirical formulas. The relation between the PMMA viscosity and the mobility of PMMA surface vertices was determined via the thermal reflow simulation for uniform PMMA gratings using analytical and numerical approaches in a wide viscosity range. The agreement between reflowed profiles simulated with these two approaches emphasizes the applicability of "soapfilm" modeling in the simulation of polymer thermal reflow. The inverse mobility of PMMA surface vertices appeared to be proportional to the PMMA viscosity with a high precision. The developed approach enables thermal reflow simulations for complex nonuniform structures, which allows the use of predictable reflow as a stage of 3D microfabrication.

摘要

本文提出了一种新的方法来模拟电子束曝光聚甲基丙烯酸甲酯（PMMA）的热回流，同时考虑其非均匀粘度分布。该方法基于表面演化的数值“皂膜”建模，由免费软件“Surface Evolver”在面积归一化模式下处理。通过使用蒙特卡罗方法和经验公式模拟曝光PMMA的数均分子量分布来计算PMMA粘度分布。在很宽的粘度范围内，采用解析和数值方法对均匀PMMA光栅进行热回流模拟，确定了PMMA粘度与PMMA表面顶点迁移率之间的关系。用这两种方法模拟的回流轮廓之间的一致性强调了“皂膜”建模在聚合物热回流模拟中的适用性。PMMA表面顶点的反向迁移率似乎与PMMA粘度高度成比例。所开发的方法能够对复杂的非均匀结构进行热回流模拟，这使得可预测的回流作为3D微加工的一个阶段得以应用。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/d56c/10534791/619d4cdc2a2c/polymers-15-03731-g009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/d56c/10534791/41cb1ad50124/polymers-15-03731-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/d56c/10534791/558b8e8f71f2/polymers-15-03731-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/d56c/10534791/038cd1145591/polymers-15-03731-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/d56c/10534791/063eda8f43c0/polymers-15-03731-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/d56c/10534791/4870fd0c3f56/polymers-15-03731-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/d56c/10534791/46b4e2389f8b/polymers-15-03731-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/d56c/10534791/22c740bc5c41/polymers-15-03731-g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/d56c/10534791/5649c72b7a82/polymers-15-03731-g008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/d56c/10534791/619d4cdc2a2c/polymers-15-03731-g009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/d56c/10534791/41cb1ad50124/polymers-15-03731-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/d56c/10534791/558b8e8f71f2/polymers-15-03731-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/d56c/10534791/038cd1145591/polymers-15-03731-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/d56c/10534791/063eda8f43c0/polymers-15-03731-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/d56c/10534791/4870fd0c3f56/polymers-15-03731-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/d56c/10534791/46b4e2389f8b/polymers-15-03731-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/d56c/10534791/22c740bc5c41/polymers-15-03731-g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/d56c/10534791/5649c72b7a82/polymers-15-03731-g008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/d56c/10534791/619d4cdc2a2c/polymers-15-03731-g009.jpg

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本文引用的文献

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Nanoimprinting reflow modified moth-eye structures in chalcogenide glass for enhanced broadband antireflection in the mid-infrared.纳米压印回流法对硫系玻璃中的蛾眼结构进行改性，以增强中红外波段的宽带减反射性能。
Opt Lett. 2019 Sep 1;44(17):4383-4386. doi: 10.1364/OL.44.004383.
2
Asymmetric optical microstructures driven by geometry-guided resist reflow.由几何引导的光刻胶回流驱动的非对称光学微结构。
Opt Express. 2014 Sep 8;22(18):22089-94. doi: 10.1364/OE.22.022089.
3
Optical loss reduction in high-index-contrast chalcogenide glass waveguides via thermal reflow.
通过热回流降低高折射率对比硫系玻璃波导中的光学损耗。
Opt Express. 2010 Jan 18;18(2):1469-78. doi: 10.1364/OE.18.001469.
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Using the Surface Evolver to model droplet formation processes in membrane emulsification.使用表面演化器对膜乳化中的液滴形成过程进行建模。
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