Energy dissipation in a thin polymer film by electron beam scattering

Monte Carlo calculations have been performed to determine the spatial distribution of energy dissipated in a 4000-Å-thick film of polymethyl methacrylate (PMMA), due to an incident electron beam. The calculations were performed for 5-, 10-, and 20-keV electrons on a silicon substrate and also for 20-keV electrons on copper and gold substrates. The effect of varying the beam diameter from 250 to 3000 Å was evaluated. A detailed comparison is made between the Monte Carlo results and analytic models used to predict the energy dissipated. The plural scattering model is found to be in good agreement with the Monte Carlo calculations, whereas discrepancies are found with the multiple scattering model. The large-angle backscattering model is found to have several important limitations. Energy dissipation is calculated for the exposure of dots, isolated lines, and arrays of closely spaced lines—geometries that are of significance in electron beam lithography.