Influence of surface and interface roughness on X-ray and extreme ultraviolet reflectance: A comparative numerical study

The influence of surface and interface roughness on X-ray and extreme ultraviolet (EUV) reflectometry is becoming increasingly important as layer thicknesses decrease to a few nanometers in next-generation nanodevices and multilayer optics. Here we simulate two different approaches for numerically modeling roughness, the Névot-Croce factor and the graded-interface method, in the Parratt formalism of calculating the complex reflectance of multilayer systems. The simulations were carried out at wavelengths relevant to widely used metrology techniques, including 0.154 nm for X-ray reflectometry and 13.5 nm for EUV lithography. A large discrepancy is observed between the two approaches in several situations: when the roughness is large with respect to the wavelength, for interfaces with large changes in refractive index across the boundary, as well as around reflectance peaks due to interference effects. Caution is thus required when using either approach to model roughness in these situations.