# X-ray reflectivity

The X-ray reflectometry (English X -ray reflectometry XRR, and grazing incidence X -ray reflectometry GIXR ) is a surface-sensitive method of measurement. It is used, among others, in analytical chemistry, physics and materials science for the characterization of surfaces, thin films and multi- layer systems. It is related to similar methods, such as neutron and ellipsometry, which use a different type of radiation or a different wavelength of electromagnetic radiation.

## Principle

The basic idea of this analytical method is at a shallow incidence angle X-ray on a flat surface and (angle of incidence angle of reflection equal ) to measure the intensity of the specular reflection in the reflected X- rays. If the surface is not perfectly smooth, then deviates from the intensity of the reflected radiation from the predicted by the Fresnel equations intensity. These deviations can be used to obtain a density profile of the interface perpendicular to the surface.

This well-known from other areas of technology seems to have been applied by Professor Lyman G. Parratt from Cornell University in the early 1950s with the first time. In Parratts first publication on this subject he explored the surface of a copper-coated glass. Since then the technology has been extended to the analysis of a wide variety of liquid and solid interfaces.

The basic mathematical relationship that describes the directed ( specular ) reflection is fairly straightforward. If an interface is not perfectly sharp, but an average electron density profile has, then the X-ray reflectivity can be described by the following equation approximation.:

Here, the reflectivity as a function of the wavelength and the incident angle of X-rays used, and the density of the material away from the interface. Typically one can use this formula to compare parametric models of the average density in the z direction with the measured X-ray reflectance with parameter variation, and a compensation calculation, to the theoretical profile corresponding to the measurement result.

In X-ray reflection of multilayer systems vibrations having a wavelength similar to the Fabry -Perot effect (see Fabry -Perot interferometer ) may occur. Similarly as in the optical system, these vibrations can be used to derive the layer thicknesses and other properties, for example using the Abeles matrix formalism.