Effects of stochastic exposure on critical dimension in electron-beam lithography

The computational lithography is a common approach to various optimizations of the electron-beam lithographic process. An essential step in most of the optimization problems is to estimate the exposure distribution in the resist, which is typically done through the convolution of the dose distribution of a circuit pattern with a point spread function (PSF). Although most of the computational lithographic methods employ a deterministic PSF, a PSF is stochastic in reality due to the shot noise and electron scattering. The feature size estimated from the stochastic exposure can be substantially different from that of the corresponding deterministic exposure. This difference stems from the fact that the rough development-front caused by the stochastic exposure makes the developing rate effectively larger. In this study, the effects of stochastic exposure on the critical dimension (linewidth) and their dependency on the lithographic parameters are analyzed in detail. Results obtained through an extensive simulation are presented and thoroughly discussed in this paper.