Angular Distribution of Specularly Reflected X Rays from Thin Films

Abstract

The angular distribution of specularly reflected x rays from thin films has been studied. For incident angles ${\Theta }_i$ larger than the critical angle ${\Theta }_c$ the reflected radiation consists of three distinct parts: (1) the specular beam itself; (2) an anomalous beam near ${\Theta }_c$; (3) a low-intensity interference pattern extending from about ${\Theta }_c$ through the specular beam to higher angles. The two latter contributions can be attributed to small-angle scattering originating at the film surface and at the film-substrate interface. The shape of the specular beam varies periodically as a function of ${\Theta }_i$. This phenomenon is due to interference between truly specular components and scattered components. The scattered radiation accompanying specularly reflected x rays and its effect on the specular beam are sensitive indicators of the smoothness of both the film surface and the film-substrate interface.