Efficient Proximity Effect Correction Using Fast Multipole Method With Unequally Spaced Grid for Electron Beam Lithography

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.