X-ray reflectivity

X-ray reflectivity (sometimes known as X-ray specular reflectivity, X-ray reflectometry, or XRR) is a surface-sensitive analytical technique used in chemistry, physics, and materials science to characterize surfaces, thin films and multilayers. It is a form of reflectometry based on the use of X-rays and is related to the techniques of neutron reflectometry and ellipsometry. The basic principle of X-ray reflectivity is to reflect a beam of X-rays from a flat surface and to then measure the intensity of X-rays reflected in the specular direction (reflected angle equal to incident angle). If the interface is not perfectly sharp and smooth then the reflected intensity will deviate from that predicted by the law of Fresnel reflectivity. The deviations can then be analyzed to obtain the density profile of the interface normal to the surface. The technique appears to have first been applied to X-rays by Lyman G. Parratt in 1954. Parratt's initial work explored the surface of copper-coated glass, but since that time the technique has been extended to a wide range of both solid and liquid interfaces. When an interface is not perfectly sharp, but has an average electron density profile given by , then the X-ray reflectivity can be approximated by: Here is the reflectivity, , is the X-ray wavelength (typically copper's K-alpha peak at 0.154056 nm), is the density deep within the material and is the angle of incidence. Below the critical angle (derived from Snell's law), 100% of incident radiation is reflected through total external reflection, . For , . Typically one can then use this formula to compare parameterized models of the average density profile in the z-direction with the measured X-ray reflectivity and then vary the parameters until the theoretical profile matches the measurement. For films with multiple layers, X-ray reflectivity may show oscillations with Q (angle/wavelength), analogous to the Fabry-Pérot effect, here called Kiessig fringes.