A mathematical model is used to describe the processes that contribute to the deposition of a carbon film on EUV multilayer optics when the optic is exposed to EUV radiation in the presence of residual hydrocarbon gases. The key physical and chemical processes taken into account within the model 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. The dissociated hydrocarbons are reactive and form a carbonaceous film that reduces the reflectivity of the optic and the overall throughput of the EUV lithographic system. The model, which provides estimates of hydrocarbon film growth under various conditions of hydrocarbon partial pressures and EUV power, is validated by predicting the carbon thickness associated with a series of EUV exposures performed in the laboratory. The model is then used to evaluate the effects of hydrocarbon partial pressure, EUV power, hydrocarbon mass, and temperature on the growth of the carbonaceous contaminate layer.