Trajectory displacement effect in particle projection lithography systems: Modifications to the extended two-particle theory and Monte Carlo simulation technique

Abstract

The extended two-particle model for statistical interactions in particle beams, developed by Jansen [Coulomb Interactions in Particle Beams (Academic, Boston, 1990)], has been refined to improve the accuracy of the predictions of the trajectory displacement effect in particle beam projection systems. The original theory was developed for probe forming systems, such as electron and ion scanning microscopes and Gaussian or shaped beam lithography systems. Fit functions are used within the theory to express part of the numerical output into explicit analytical prescriptions. These functions were found to become inaccurate for the relatively wide beams typically used in the more recently developed projection type lithography systems. New fit functions are presented which extend the applicability of the theory to the wide beams and doublet configurations used in projection systems. The Monte Carlo program MONTEC, used to verify the results of the analytical theory, has been modified as well to account for the first order space charge magnification effect. This effect could be ignored for the relatively small spots of Gaussian and shaped beam systems, but would yield a significant overestimation of the trajectory displacement effect—assumed to be identical to the remaining blur after refocusing—for the wide images used in projection type of systems. The refined analytical theory and the modified MONTEC program have been used to evaluate the impact of statistical interactions on the performance of the SCALPEL electron projection system and a hypothetical ion projection lithography system, representing a simplified model of the IMS ALG-1000 (He+) system. The analytical predictions are in good agreement with the Monte Carlo results. An estimate of the total system resolution, determined by the combined effect of statistical interactions and geometrical aberrations, indicates that maximum attainable beam current for a 0.18 μm design rule is about 25 μA for the SCALPEL and 0.2–0.3 μA for the ion projection system, leading to an ∼10× higher throughput for the former taking the difference in resist sensitivities for electrons and ions into account.