Powder x-ray diffraction from multilayer in a grazing-incidence non-coplanar geometry

L. Horák and V. Holý

Department of Electronic Structures, Charles University, Prague, Czech Republic
e-mail: Lukas.horak@napismi.cz

X-ray powder diffraction in a non-coplanar grazing-incidence geometry makes it possible to determine lateral grain sizes and strains in polycrystalline multilayers. The depth profile of these quantities can be also determined using a standing x-ray wave generated in the multilayer by the interference of the primary and specularly reflected beams [1].

The grains of a polycrystalline layer are irradiated by the standing wave so that the intensity of the diffracted beam is modulated by the standing wave pattern. Similarly, the radiation diffracted by the polycrystalline grains reflects specularly from the interfaces in the multilayer and another standing wave pattern results, which affects the diffracted intensity as well.

Changing the incidence angle, we move the positions of the antinodes of the standing-wave pattern so that this method makes it possible to study the vertical profile of the parameters of the polycrystalline layer because total intensity are mostly given by the contribution of grains near antinodes.

We use this concept for the investigation of polycrystalline single layers and periodic multilayers. For both sample types, we have measured the distribution in the diffracted intensity in the angular (a_i,2Q) plane; the measurements have been carried out using a conventional laboratory diffractometer allowing for a non-coplanar scattering geometry equipped with a polycapillary optics and a secondary flat monochromator, intensity was integrated over a_f in a range given by detector’s window. We have measured these samples using a synchrotron radiation and in this case we have used several wavelengths (for example near absorption edge) and position sensitive detector so the intensity has been measured in a_f axis too.

The measured intensity distributions we have compared with simulations based on the distorted-wave Born approximation and kinematical scattering theory [1,2] to determine the grain sizes and their vertical profile. Parameters of the multilayers such as thickness and relative density we have obtained from x-ray reflectivity.

Whole these processes in sample we describe using distorted-wave Born approximation, the goal is to solve wave equation and we consider scattering potential divided to two potentials, undisturbed system without crystal lattice, this we are able to solve exactly using dynamic theory, this potential leads to wave field in sample [2]. The second potential is given by crystal lattice and it is a disturbance of the first potential. Assuming that grains are much smaller than extinction length and they diffract kinematically, we solve disturbance using kinematical theory and wave field given by undisturbed solution [1].

This method is suitable for probing multilayers and even single thin layer on a substrate. The greatest advantage is sensitivity to depth and ability to get information from thin layers, on the other hand there are strict requirements to roughness and lateral homogeneity, the sample has to be suitable for x-ray reflectivity measurement.

[1] P. F. Fewster, N. L. Andrew, V. Holý, and K. Barmak, Phys. Rev. B 72, 174105 (2005).

[2] U. Pietsch, V. Holý, and T. Baumbach, High Resolution X-Ray Scattering - From Thin Films to Lateral Nanostructures (Springer, 2004).