In order to estimate and predict the carbonaceous contamination of extreme ultraviolet (EUV) multilayer optical element surfaces caused by EUV irradiation in the presence of residual hydrocarbon gases, a comprehensive model of radiation-induced carbon growth on EUV optic surfaces is presented. The model describes the transport of residual hydrocarbons to the irradiated area and the subsequent dissociation of the hydrocarbon by both EUV ionization and secondary electron excitation. The dissociated hydrocarbons are reactive and form a carbonaceous film. Model predictions fit experimental data quite well. Theoretical analysis indicates that the primary cause of hydrocarbon dissociation is bond breaking by direct photon absorption rather than by secondary electrons. Calculations also demonstrate that the growth of carbon film depends on various conditions of hydrocarbon partial pressure and EUV power. The model successfully predicts that light hydrocarbons (<～100 amu) pose a negligible risk to EUV optics and modest increases in substrate temperature (~30 ℃), which will substantially reduce optic contamination by increasing hydrocarbon desorption from the surface.