Monte Carlo calculations of fast secondary electron production have been performed with a hybrid model for the discrete and continuous energy-loss processes. The Moller theory was adopted for the differential inelastic scattering cross-section which determines the production rate of fast secondary electrons. The calculations were made for both a bulk polymethyl methacrylate (PMMA) sample and 4000-Å-thin films of PMMA (with and without a silicon substrate) at 10 and 20 keV. The new model is discussed and comparison made with results obtained from the old model, which is based on the continuous slowing down approximation of Bethe for energy loss and the screened Rutherford equation for elastic angular scattering. The new model predicts a larger absorbed energy density than the old model for an isolated line source exposure on a resist film. The consequences of this fast secondary electron contribution on the ultimate limit in electron lithography is discussed.