A mathematical model of extreme ultraviolet (EUV)-induced oxidation of a ruthenium (Ru)-coated EUV optic is presented. The model describes the key processes that contribute to the growth of the oxide within the optic when exposed to EUV radiation in the presence of water vapor. These processes include the adsorption and thermal desorption of water to and from the Ru surface, molecular diffusion of water across the optic surface, and the dissociation of the water by both direct EUV ionization and secondary electron excitation. Oxygen produced by dissociation may associatively desorb from the surface or may diffuse into the Ru subsurface where it can react to form an oxide. The presence of oxygen in the Ru coating, whether as oxide or atomic oxygen, reduces the reflectivity of the optic and the overall throughput of the EUV lithographic system. The model predicts oxide thickness over time, which may later be used to estimate the reflectively loss attributable to the oxide in any given EUV environment. Model predictions for EUV-induced oxide growth provide a good description of the oxide growth observed in available electron-beam experiments. The model is also used to estimate oxygen penetration into the Ru. coating under various conditions of water partial pressure, EUV power, and temperature. The model predicts reduced oxidation with higher temperatures and for substrates that bind water less tightly than ruthenium. (c) 2006 American Vacuum Society.