Proximity effect correction in electron beam lithography using a composite function model of electron scattering energy distribution

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.