Extreme ultraviolet (EUV) projection lithography has been proposed to achieve features as small asL=180 nm to 70 nm for 1 G to 16 G DRAMs. Application will require high‐sensitivity resists and pattern fluctuation control to less than 10% of nominal linewidth. To evaluate low‐dose, resist material, and resist process dependent resist roughness limits in EUV lithography, a roughness model originally by Neureuther and Wilson is extended, and a new model for chemical amplification resists is presented and applied to EUV lithography. Analyses of molecular scale simulation and EUV exposures of novolac negative chemical amplification resists complete the study. For 13 nm exposure wavelengths, 180 nm lithography with positive chain‐scission resists requires at least 0.69 mJ/cm2, which scales to 54.3 mJ/cm2for 70 nm features, accounting for both intrinsic resist polymer roughness and absorption in 100 nm PMMA. At 4.5 nm exposure, the dose minima are 15.9 mJ/cm2and 1254 mJ/cm2, for 1 G and 16 G respectively. Novolac negative chemical amplification resists have a theoretical minimum linewidth of 115 nm, dependent on postexposure bake conditions and resist composition. Printability criteria limit the extent to which process variation can improve roughness. Existing novolac‐based negative chemical amplification resists are not suitable for EUV lithography in the 16 G regime, but may be suitable for the 4 G regime under certain conditions.