Mao Qingyuan, Zhu Jingyuan, Cheng Xinbin, Wang Zhanshan
Institute of Precision Optical Engineering, School of Physics Science and Engineering, Tongji University, Shanghai, 200092, China.
MOE Key Laboratory of Advanced Micro-Structured Materials, Shanghai, 200092, China.
Discov Nano. 2025 May 19;20(1):84. doi: 10.1186/s11671-025-04264-0.
The proximity effect induced by electron scattering is one of the main factors limiting the development of high-resolution electron beam lithography (EBL) technology. Existing proximity effect correction (PEC) methods often face challenges related to either high computational demands or insufficient accuracy when calculating the point spread function (PSF) of electron scattering. This paper presents a composite model that combines a power function with a Gaussian function to calculate the PSF, where the forward scattering component is described by a power function and the backscattering component is represented by a Gaussian function. This approach ensures high accuracy of the PSF while simultaneously reducing computational complexity. Experimental validation was conducted using the commercial software BEAMER developed by GenISys GmbH, where the PSF curve obtained from this model was employed for PEC, resulting in a well-defined hydrogen silsesquioxane (HSQ) zone plate structure with an outer ring width of 30 nm. Comparative experiments showed that the composite model outperforms traditional Monte Carlo and double Gaussian models in terms of correction performance for the zone plate structure. Moreover, this model not only optimizes the computational efficiency of PSF calculations but also demonstrates greater potential for applications in the exposure of complex structures such as meta-surface and meta-lens.
电子散射引起的邻近效应是限制高分辨率电子束光刻（EBL）技术发展的主要因素之一。现有的邻近效应校正（PEC）方法在计算电子散射的点扩散函数（PSF）时，常常面临计算需求高或精度不足的挑战。本文提出了一种将幂函数与高斯函数相结合来计算PSF的复合模型，其中前向散射分量由幂函数描述，后向散射分量由高斯函数表示。这种方法在确保PSF高精度的同时，还降低了计算复杂度。使用GenISys GmbH开发的商业软件BEAMER进行了实验验证，其中从该模型获得的PSF曲线用于PEC，得到了外环宽度为30 nm的清晰定义的氢倍半硅氧烷（HSQ）波带片结构。对比实验表明，在波带片结构的校正性能方面，复合模型优于传统的蒙特卡罗模型和双高斯模型。此外，该模型不仅优化了PSF计算的计算效率，还在诸如超表面和超透镜等复杂结构的曝光应用中显示出更大的潜力。
