X-Ray Reflectometry

An absolute and highly accurate method for thickness determination is X-ray reflectometry (XRR). In this technique, the reflectance of the sample is measured as a function of the grazing incidence angle of X-rays. Due to interference effects of radiation reflected on the layer surface and radiation reflected on the layer/substrate interface, oscillations occur in the reflectance curve which can be fitted according to the Fresnel equations. While the oscillation amplitude at fixed photon energy depends on the densities and the surface and interface roughness, the oscillation period is mainly determined by the layer thickness. In commercial instruments, Cu Kα radiation with an energy of 8048 eV is used. For some technologically important systems like thin SiO₂ films on silicon, this radiation is not well suited because the optical constants of Si and SiO₂ are very similar at this energy so that the reflection at the layer/substrate interface, and therefore also the oscillations, are very weak. With synchrotron radiation, any photon energy can be selected. It has been shown that pronounced oscillations occur at 1841 eV, just above the Si K absorption edge in pure Si, because the chemical bonding in the oxide causes a shift of the edge. Pronounced oscillations also occur at the oxygen K-edge around 530 eV. Here, steep incidence angles up to 50˚ can be used, enabling the application on strongly curved surfaces (e.g. on the silicon sphere for the Avogadro Project). The tunability of the photon energy can also be used to distinguish individual layers in double layer systems. Relative uncertainties of about 1 % can be achieved for the layer thickness.