In electron beam lithography (EBL), the proximity effect seriously influences pattern resolution under high-precision conditions. Mainstream proximity effect correction (PEC) methods based on 2-D fast Fourier transform (2D-FFT) calculate a large number of unexposed points; thus, it may suffer from low efficiency especially when the exposure layout is unevenly distributed. This article proposes an efficient unequally spaced grid PEC method for EBL based on the fast multipole method (FMM). FMM in PEC just calculates the interaction between all the exposure points, and thus, it gets rid of the limitation of the equally spaced grid. Compared to the state-of-the-art PEC method based on 2D-FFT, the calculation speed of FMM will exceed the current fastest 2D-FFT convolution when the layout exposure density is below a certain proportion (approximately 80% under the 10-thread CPU parallel computing conditions). For the application of integrated circuit (IC) mask industry, the error of FMM is within the acceptable range of PEC. The PEC method in this article has been applied to a free software via software as a service (SaaS) mode, and a Windows-based EBL simulation and optimization software toolkit “HNU-EBL,” which is freely available at http://www.ebeam.com.cn .

中文翻译：

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使用具有不等间距网格的快速多极方法对电子束光刻进行高效邻近效应校正

在电子束光刻 (EBL) 中，邻近效应严重影响高精度条件下的图案分辨率。基于二维快速傅立叶变换（2D-FFT）的主流邻近效应校正（PEC）方法计算了大量未曝光点；因此，它可能会效率低下，尤其是当曝光布局分布不均匀时。本文提出了一种基于快速多极子方法（FMM）的高效EBL不等距网格PEC方法。PEC中的FMM只是计算所有曝光点之间的相互作用，从而摆脱了等距网格的限制。与最先进的基于 2D-FFT 的 PEC 方法相比，当布局曝光密度低于一定比例（10线程CPU并行计算条件下约80%）时，FMM的计算速度将超过目前最快的2D-FFT卷积。对于集成电路（IC）掩模行业的应用，FMM的误差在PEC的可接受范围内。本文中的 PEC 方法已通过软件即服务 (SaaS) 模式应用于免费软件，以及基于 Windows 的 EBL 仿真和优化软件工具包“HNU-EBL”，可在以下位置免费获得http://www.ebeam.com.cn .