A Monte Carlo study of the extent of proximity effects in e-beam and p-beam writing of PMMA

The generation of secondary electrons (or δ-rays) represent a significant mode of energy loss and energy delocalisation in the penetration of a charged particle into matter. Owing to the large mass disparity between electrons and protons, (1) the trajectories of penetrating protons are essentially straight while those of electrons are tortuous and (2) the fractional energy transferred to secondary electrons by protons are much less than with electrons. Although, these suggest that protons are fundamentally capable of exhibiting superior proximity effects over electrons when used in lithography, no supporting evidence has yet been presented. In the present study we utilise the Hansen–Kocbach–Stolterfoht model for proton induced secondary electron emission to develop a Monte Carlo model capable of recreating the energy deposition profiles resulting from the creation and propagation of δ-rays produced by the passage of MeV protons in PMMA. We show that protons possess more confined energy deposition profiles than electrons.