This work uses a single-scattering Monte Carlo simulation of electron-solid interactions to predict the effects of electron beam lithography on the gate oxide of metal-oxide-silicon field-effect transistors (MOSFET). Both 20 and 50 keV electron energies are examined. Electron radiation can cause significant disorder in the gate oxide and this paper discusses possible solutions to minimize the electron damage. One solution examined in detail is the effect of a high-density material incorporated in the MOSFET. The paper also explores the generation of x rays by the electron lithography. X-ray damage to the gate oxide is calculated to be small.