Space-charge-induced aberrations

Abstract

The effect of Coulomb interactions in electron-beam lithography systems are usually described in terms of the blur induced by stochastic electron–electron interactions. Here, we show both by an efficient Monte Carlo simulation and by a global space-charge model, that the aberrations induced by the lensing action of global space charge can be equally significant. For a 4:1 telecentric reduction projection optics operating at 100 kV beam energy and 25 μA total current, we obtain about 150 nm blur independent of any stochastic effects. The global space-charge model requires less than 5 min computation on a 450 MHz workstation. The aberration coefficients of the global space-charge-induced lens can be evaluated, and because they scale directly with the perveance of the beam, can be used to evaluate the global space-charge effect over a wide variety of conditions. When the Monte Carlo and global space-charge models are used together, the stochastic-only portion of the beam blur can be extracted.