Short-range and long-range scattering in electron beam lithography

In this paper a novel modelling of electron scattering trajectories is presented. The scattering is discussed in terms of short and long range components and a comparison is made with the conventional approach considering forward and back-scattering. The usual analysis is shown to uncorrectly take as representative of short-range effects the forward scattering component, which instead contains, besides a high-density localized central term, a long-range tail spread out over larger distances. A different parametrization of the scattering is introduced and, in particular, a generalized n{long right leg} is defined in place of the usual backscattering coefficient. The behaviour of the scattering components is studied by Monte Carlo simulation in a freestanding PMMA resist layer, 1.5 μm thick. Further results are shown, relative to some cases of practical interest, by considering a quite general system for master-mask fabrication. The limits of the conventional approach are demonstrated.