We have studied the lithographic performance of high-performance diamond-like carbon (DLC) membrane masks by demonstrating exposure experiments using Nikon's electron beam stepper, NSR-EB1A. We estimated the inelastic mean free path of 100 keV electrons in a membrane analytically using the measurement results of zero-loss electron transmittance and found it to be about 50 nm. We then used this value to find the relationship between membrane thickness and zero-loss electron transmittance. The resolution for high-performance membrane masks is equivalent to that of a stencil mask and was not deteriorated by chromatic aberration due to inelastic electron scattering. Electrons undergoing inelastic scattering did not appear to affect resolution. The nominal exposure dose was proportional to the inverse of zero-loss electron transmittance. We also discussed the optimum membrane thickness in terms of throughput and electron inelastic scattering, focusing on plasmon excitation.