Analytic estimation of line edge roughness for large-scale uniform patterns in electron-beam lithography

Abstract

As the feature size continues to be reduced well below nanoscale, the line edge roughness (LER) will eventually become a resolution-limiting factor in the electron-beam (e-beam) lithography since the LER does not scale with the feature size. Therefore, to achieve the highest resolution possible by the e-beam lithography, the LER needs to be minimized. A simulation-based or experimental approach for estimating and minimizing the LER normally requires a great deal of effort to analyze the relationship between the LER and e-beam parameters and thus is time-consuming. Previously, an analytic method for estimating and minimizing the LER was developed for the case of a single line. In this paper, an extension of the estimation method for large-scale uniform patterns is described. In a large pattern, the exposure distribution over a feature varies with the location within the pattern, and the location dependency is due to the global exposure. The analytic expression of LER derived for a single line is adjusted depending on the location. The amount of adjustment for each of the critical locations is determined by the stochastic information on the global exposure at that location. The LER at a location is obtained through an interpolation using the LERs at the critical locations. The LER evaluated by the analytic expression of LER has been compared with that obtained through simulation.