Multilayer roughness evaluated by X-ray reflectivity

A crystal diffraction theory has been developed and compared with experimental measurements in order to model the integrated reflectivity of multilayer structures. This study shows that the most important defect reducing the integrated reflectivities of the multilayer structures studied was correlated roughness (root mean square value about 7 Å). The theory describes correlated roughness as a probability distribution of the substrate surface displacement. A computer simulation and an analytical solution have been used to calculate the reflectivity of multilayer structures. The calculations using a rectangular distribution of correlated displacement result in a good first-order approximation of the experimental data. A Gaussian probability distribution for the substrate surface displacement results in calculations inconsistent with the measured reflectivities, although such a distribution has been assumed in other studies. Although other defects were studied, only roughness could explain the experimental data.