Simulation of the spatial distribution and molecular weight of polymethylmethacrylate fragments in electron beam lithography exposures

摘要

We report a three-dimensional (3D) simulation model based on the kinetic transport theory for calculating the distribution of PMMA fragments after an exposure to electron impact. The conditions employed for the modeling were chosen to resemble a typical electron beam lithography exposure. The model accounts for inelastic collisions of electrons in PMMA and resulting random main-chain scissions. We have considered gratings composed of parallel lines distanced by 10-50 nm and exposed to electrons with energies of 10-60 keV. By the model simulations, we have generated and analyzed the detailed 3D distributions of small PMMA fragments (one to ten monomers) that are soluble at the development stage and thus are responsible for the clearance in the gratings. In terms of the spatial distributions of soluble fragments, we have formulated the criteria that define the total clearance as well as the local grating development and investigated their dependence on the grating period, electron dose, and energy.