Analytic study of exposure contrast over feature edge in electron-beam lithography

In electron-beam (e-beam) lithography, the location of a feature edge may vary with experiment due to the stochastic nature of the e-beam exposure and resist-development processes. From the viewpoint of consistent reproducibility of a circuit pattern, it is essential to enhance the stability of a feature edge in the e-beam lithographic process. A fundamental metric affecting the stability is the exposure contrast over the feature edge, and therefore, it is important to understand the dependency of exposure contrast on significant parameters. However, the computer simulation for the dependency analysis is time-consuming and needs to be repeated. In this study, a new method has been developed by deriving closed-form mathematical expressions of exposure contrast for the cases of a single feature and a uniform pattern of multiple features. The mathematical expressions enable the fast analysis of exposure contrast without simulation, and therefore, can serve as a useful tool in e-beam lithography.