Research Article: Grazing-incidence small-angle X-ray scattering study of correlated lateral density fluctuations in W/Si multilayers

Date Published: March 01, 2019

Publisher: International Union of Crystallography

Author(s): K. V. Nikolaev, S. N. Yakunin, I. A. Makhotkin, J. de la Rie, R. V. Medvedev, A. V. Rogachev, I. N. Trunckin, A. L. Vasiliev, C. P. Hendrikx, M. Gateshki, R. W. E. van de Kruijs, F. Bijkerk.


An inhomogeneity of material in W/Si multilayer structures was studied with grazing-incidence small-angle X-ray scattering. The experimental study revealed lateral density fluctuations in the Si spacer layers.

Partial Text

Thin film periodic multilayer reflective coatings are used in spectroscopy and optical instruments in the photon energy range of a few tens of eV up to a few keV, i.e. from the extreme UV (XUV) to the soft X-ray range (Fewster, 1996 ▸; Louis et al., 2011 ▸). Depending on the application, various aspects of the structural quality of reflective coatings should be prioritized during the coating development process. As an example, often the reflectivity should be maximized over a certain bandwidth around a particular wavelength. However, for some applications like X-ray focusing optics the minimization of the off-specular diffuse scattering can be more important than maximization of the reflectivity. Primarily, diffuse scattering in multilayers is caused by interface roughness. In specific cases, diffuse scattering in multilayers may also be caused by a 3D distribution of defects in the volume of the structure (Pietsch et al., 2013 ▸). Analysis of the diffuse scattering provides information about the growth process including defects (Siffalovic et al., 2011 ▸). Such information can indicate directions for further optimization of the reflective properties of the multilayers.

Calculations of diffuse X-ray scattering are performed using a perturbation theory (Sinha et al., 1988 ▸). A rigorous formulation of the second-order perturbation theory is given in Kaganer et al. (1996 ▸). There, the theory is formulated in terms of the reciprocity theorem of electrodynamics (Landau et al., 1984 ▸). In this theorem, the scattering length f of the diffuse scattering wave has the formwhere the function represents a deviation of the actual dielectric susceptibility of a structure from the value of an ideal structure. Equation (1) is written in a scalar approximation. This value is used in the calculation of the wavefields in the structure: the field is induced by the incident beam, and the field by the diffusely scattered wave. Equation (1) is commonly referred to as the distorted-wave Born approximation (DWBA). We have considered here s-polarized radiation, as this was used in the measurements. Therefore, the fields and are represented as scalar functions.

HAADF-STEM and GISAXS were used to study density fluctuations inside Si layers in periodic W/Si multilayers of nanoscale-thickness films. The fluctuations are ordered vertically with a dispersion of 0.11 nm and mean distance 4.5 nm which is equal to the period of the multilayer sample. In the lateral direction, i.e. within the Si layer, these density fluctuations have a mean mutual distance of 8 nm, while the dispersion in the lateral direction is 3.2 nm. The density fluctuations are strongly confined within the Si layers and have reduced density ( 0.26 g cm−3). This study exemplifies the level of detail on growth phenomena that can be found using a combination of STEM and GISAXS analysis.




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