X-ray reflectometry

The X-ray reflectometry ( English X-ray reflectometry , XRR , or grazing incidence X-ray reflectometry GIXR) is a surface sensitive measurement method. It is used, among other things, in analytical chemistry , physics and materials science for the characterization of surfaces, thin films and multilayer systems. It is related to comparable methods such as neutron reflectometry 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 to reflect X-rays at a flat angle of incidence on a flat surface and to measure the intensity of the X-rays reflected in directional reflection (angle of reflection equals angle of incidence). If the surface is not perfectly smooth, the intensity of the reflected radiation will deviate from the intensity predicted by the Fresnel equations . This deviation can be used to obtain a density profile of the interface perpendicular to the surface.

This technique, known from other areas, appears to have been used for the first time in the early 1950s by Professor Lyman G. Parratt from Cornell University . In Parratt's first publication on the subject, he explored the surface of a copper-coated glass. Since then, the technique has expanded to include the analysis of a wide variety of solid and liquid interfaces.

Schematic representation of the directional reflection of X-rays

The basic mathematical relationship that describes directional (specular) reflection is quite straightforward. If an interface is not perfectly sharp, but has an average electron density profile, then the X-ray reflectance can be approximated by the following equation: ${\displaystyle \rho _{e}(z)}$

${\displaystyle {\frac {R(Q)}{R_{F}(Q)}}=\left|{\frac {1}{\rho _{\infty }}}{\int \limits _{-\infty }^{\infty }{e^{iQz}\left({\frac {\mathrm {d} \rho _{e}}{\mathrm {d} z}}\right)\mathrm {d} z}}\right|^{2}}$

Here, the reflectance as a function of , the wavelength and the incident angle of X-rays used, and the density of the material away from the interface. As a rule, this formula can be used to compare parameterized models of the mean density in the z-direction with the measured X-ray reflectance by means of parameter variation and a compensation calculation until the theoretical profile corresponds to the measurement result. ${\displaystyle R(Q)}$ ${\displaystyle Q={\frac {4\pi \sin(\theta )}{\lambda }}}$ ${\displaystyle \lambda }$ ${\displaystyle \theta }$ ${\displaystyle \rho _{\infty }}$

In the case of X-ray reflection on multilayer systems, vibrations with a wavelength analogous to the Fabry-Pérot effect (cf. Fabry-Pérot interferometer ) can occur. Similar to optics, these vibrations can be used to derive the layer thicknesses and other properties, for example using the Abelès matrix formalism .

literature

• Michael Krumrey, Michael Hoffmann, Michael Kolbe: Layer thickness determination with X-ray reflectometry . In: PTB-Mitteilungen . tape 115 , no. 3 , 2005, p. 38-40 ( online [PDF]).

Individual evidence

1. ↑ V. Holy', J. Kuběna, I. Ohli'dal, K. Lischka, W. Plotz: X-ray reflection from rough layered system . In: Physical Review B . tape 47 , no. 23 , June 15, 1993, pp. 15896–15903 , doi : 10.1103 / PhysRevB.47.15896 .
2. ↑ Jens Als-Nielsen, Des McMorrow: Elements of Modern X-Ray Physics . 1st edition. John Wiley & Sons, 2000, ISBN 0-471-49858-0 .
3. ↑ Jean Daillant, Alain Gibaud: X-ray and neutron Reflectivity: Principles and Applications . 1st edition. Springer, Berlin / Heidelberg 2009, ISBN 3-642-10017-1 .
4. ^ Metin Tolan: X-Ray Scattering from Soft-Matter Thin Films: Materials Science and Basic Research . 1st edition. Springer, Berlin / Heidelberg 1998, ISBN 3-540-65182-9 .
5. ^ LG Parratt: Surface Studies of Solids by Total Reflection of X-Rays . In: Physical Review . tape 95 , no. 2 , July 15, 1954, p. 359-369 , doi : 10.1103 / PhysRev.95.359 .
6. ↑ Jens Als-Nielsen, Des McMorrow: Elements of Modern X-Ray Physics . 1st edition. John Wiley & Sons, 2000, ISBN 0-471-49858-0 , pp. 83 .
7. ↑ cf. Florin Abelès: La théorie générale des couches minces . In: Journal de Physique et le Radium . tape 11 , no. 7 , 1950, pp. 307-309 , doi : 10.1051 / jphysrad: 01950001107030700 .