Reflectivity degradation of grazing-incident extreme ultraviolet (EUV) mirror samples by EUV exposure was investigated in a commercial XTS 13-35 EUV source. The roughness of EUV exposed samples increases with an increase in exposure time due to the erosion of sample surface by ions and neutrals, or deposition of contaminant such as carbon on the sample surface. While energetic debris certainly affects mirror reflectivity, the loss in reflectivity observed in EUV exposed samples surpassed that which would be attributable simply to induced surface roughness through sputtering. Surface analysis of the EUV mirror sample surface after exposure confirmed that carbon contamination was present. Experimentally measured reflectivity of EUV mirrors showed degradation after EUV exposure due to the carbon contamination present in the investigated system. The measured reflectivity data were fitted by changing the carbon film thickness using a bi-layer mirror model in the CXRO simulator. The experimentally measured values of reflectivity are in good agreement with the simulation results. The contamination rate was found to be dependent on the carbon contamination thickness. The contamination rate is fast (7x10^-^5nm/shot) in the beginning of contamination growth whereas it gets slower (2x10^-^5nm/shot) as carbon builds up on the Ru mirror surface. An analytical model taking the sputtering by ions into account was developed to understand the variation of carbon contaminant deposition rate with exposure time. In our model, the fast contamination rate in the beginning of carbon buildup is explained by the interplay of photo electron emission and the varying sputtering yield of the growing carbon layer on the EUV mirror.
