Analysis of three-dimensional proximity effect in electron-beam lithography

In most of the proximity effect correction schemes, a two-dimensional model of proximity effect is employed by ignoring or averaging the variation of exposure along the depth dimension in the resist. However, as the feature size continues to decrease, the relative variation becomes significant so that it may need to be taken into account in proximity effect correction. In this study, the three-dimensional (3-D) proximity effect is analyzed in detail through computer simulation as a first step toward developing a 3-D proximity effect correction scheme. Effects of the parameters such as beam energy, resist thickness, feature size, developing threshold, etc., on the 3-D spatial distribution of exposure in the resist, in particular, depth-dependent proximity effect, are considered in the analysis. Results from the extensive simulation are presented in this paper.