We present theoretically derived design rules for an absorbingresonance antireflection coating for the spectral range of 100−400 nm, appliedhere on top of a molybdenum-silicon multilayer mirror (Mo/Si MLM)as commonly used in extreme ultraviolet lithography. The design rules foroptimal suppression are found to be strongly dependent on the thicknessand optical constants of the coating. For wavelengths below λ ∼ 230 nm,absorbing thin films can be used to generate an additional phase shift andcomplement the propagational phase shift, enabling full suppression alreadywith film thicknesses far below the quarter-wave limit. Above λ ∼ 230 nm,minimal absorption (k < 0.2) is necessary for low reflectance and the minimumrequired layer thickness increases with increasing wavelength slowlyconverging towards the quarter-wave limit.As a proof of principle, SixCyNz thin films were deposited that exhibitoptical constants close to the design rules for suppression around 285nm. The thin films were deposited by electron beam co-deposition ofsilicon and carbon, with N+ ion implantation during growth and analyzedwith variable angle spectroscopic ellipsometry to characterize the opticalconstants. We report a reduction of reflectance at λ = 285 nm, from 58%to 0.3% for a Mo/Si MLM coated with a 20 nm thin film of Si0.52C0.16N0.29.