Characterisation of multilayers by X-ray reflection

The inclusion of refraction effects in kinematic scattering theory provides a powerful tool for describing diffuse scattering by X-ray reflectivity. The theory is applied to multilayers with roughened interfaces. Islands and miscut-induced steps as well as randomly oriented roughness are included in the theory. The interfacial roughness leads to a broad, diffuse intensity distribution around the multilayer Bragg reflections. From the line shape, the morphology of the interfaces can be deduced. The calculated profiles are compared with experimental data from a 4×(Si/GexSi1-x) multilayer with vicinal interfaces. Clear side peaks are observed from which the mean island size and the average step height are deduced, which are consistent with AFM images.