X-ray reflectivity has become an invaluable tool for studying the structure and the organization of materials that are grown layer by layer using the bottom-up approach in thin films and hetero-structures at the submicronic and atomic scales [STO 99, BOW 93, VAN 94, DIE 95, DEU 98, ROB 92]. In thin-film material research, the trend is to design solid films of increasing complexity having specific properties for technical applications. The perfection of layered super-structures can be defined by the quality of the interfaces, the control of the thickness, crystallinity, voids or various defects that may appear during the growing process. In particular, the roughness of the interfaces is of crucial importance for many technological applications and it is a parameter that must be determined to appreciate the quality of the interfaces. In addition, it is also of fundamental interest to discriminate between a morphological roughness and a composition gradient at the interface.
8.1.1. Definition of the reflectivity
Reflectivity is conventionally defined as the ratio:
where I(θ) is the intensity reflected along the direction θ from the surface and I0 (Figure 8.1) the intensity of the incident beam at θ from the surface.
8.1.2. Specular and off-specular reflectivity
In specular reflectivity (SXR), the scattered beam is detected for ...