X-ray reflectivity

X-ray reflectivity sometimes known as X-ray Specular Reflectivity, X-ray Reflectometry, or XRR for short, is a surface-sensitive analytical technique used in chemistry, physics, and materials science to characterize surfaces, thin films and multilayers. [ Holy, V. et al. Phys. Rev. B. 47, 15896 (1993).] [ Jens Als-Nielsen, "Elements of Modern X-Ray Physics", Wiley, New York, (2001).] [ J.Daillant, A.Gibaud, "X-Ray and Neutron Reflectivity:Principles and Applications". Springer, (1999).] [ M.Tolan, "X-Ray Scattering from Soft-Matter Thin Films", Springer, (1999)] It is related to the complementary techniques of Neutron Reflectometry and Ellipsometry.

The basic idea behind the technique 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 Professor Lyman G. Parratt of Cornell University in an article published in the physical review in 1954 [ L. G. Parratt, Phys. Rev. "95", 359 (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.

The basic mathematical relationship which describes specular reflectivity is fairly straightforward. When an interface is not perfectly sharp, but has an average electron density profile given by $ho\_e(z)$, then the x-ray reflectivity can be approximated by:

$R(Q)/R\_F(Q)\; =\; left|frac\{1\}\{\; ho\; \_infty\}\; \{intlimits\_\{\; -\; infty\; \}^infty\; \{e^\{iQz\}\; ho\; \_e\; left(\; z\; ight)dz\}\; \}\; ight|^2$

Here $R(Q)$ is the reflectivity, $Q\; =\; 4\; pi\; sin\; (\; heta\; )\; /\; lambda$, $lambda$ is the x-ray wavelength, $ho\; \_infty$ is the density deep within the material and $heta$ is the angle of incidence. Typically one can then use this formula to compare parametrized 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.

Manufacturers of XRR apparatus

* [http://www.bede.co.uk Bede] Bede has been acquired by Jordan Valley on April 14, 2008
* [http://www.jvsemi.com Jordan Valley]
* [http://www.bruker-axs.com Bruker AXS]
* [http://www.panalytical.com Panalytical (formerly Philips)]
* [http://www.rigaku.com/index_world.html Rigaku]

References