A comprehensive model of radiation-induced carbon contamination of extreme ultraviolet (EUV) optics is presented. The mathematical model describes the key processes that contribute to the deposition of a carbon film on a multilayer optic when the optic is exposed to EUV radiation in the presence of residual hydrocarbons. These processes include the transport of residual hydrocarbons to the irradiated area, molecular diffusion across the optic surface, and the subsequent dissociation or "cracking" of the hydrocarbon by both direct EUV ionization and secondary electron excitation. Model predictions of carbon growth are compared to measurements taken on optics exposed to EUV in the presence of residual hydrocarbons. Model estimates of hydrocarbon film growth under various conditions of hydrocarbon partial pressures and EUV power demonstrate the sensitivity of film growth to varying operating conditions. Both the model and experimental data indicate that the predominant cause of hydrocarbon dissociation is bond breaking by direct photon absorption, rather than by dissociation processes caused by exposure to secondary electrons. Detailed predictions for carbon deposition for a variety of conditions of EUV power and hydrocarbon pressure are reported. The model successfully predicts that light hydrocarbons (< similar to 100 amu) pose a negligible risk to EUV optics, in general agreement with the experiment. Calculations also predict that modest increases in substrate temperature, on the order of 30 degrees C, will substantially reduce optic contamination by increasing hydrocarbon desorption from the surface. Model investigation of surface diffusion indicates that, while surface diffusion is an important surface phenomenon for light gases, for the heavier hydrocarbons that contribute substantially to contamination, surface diffusion is not an important transport phenomenon. (c) 2006 American Vacuum Society.