A semi-analytical approach for the characterization of ordered 3D nanostructures using grazing-incidence X-ray fluorescence.

Following the recent demonstration of grazing-incidence X-ray fluorescence (GIXRF)-based characterization of the 3D atomic distribution of different elements and dimensional parameters of periodic nanoscale structures, this work presents a new computational scheme for the simulation of the angular-dependent fluorescence intensities from such periodic 2D and 3D nanoscale structures. The computational scheme is based on the dynamical diffraction theory in many-beam approximation, which allows a semi-analytical solution to the Sherman equation to be derived in a linear-algebraic form. The computational scheme has been used to analyze recently published GIXRF data measured on 2D Si3N4 lamellar gratings, as well as on periodically structured 3D Cr nanopillars. Both the dimensional and structural parameters of these nanostructures have been reconstructed by fitting numerical simulations to the experimental GIXRF data. Obtained results show good agreement with nominal parameters used in the manufacturing of the structures, as well as with reconstructed parameters based on the previously published finite-element-method simulations, in the case of the Si3N4 grating.

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

A structural characterization of W/Si multilayers using X-ray reflectivity (XRR), scanning transmission electron microscopy (STEM) and grazing-incidence small-angle X-ray scattering (GISAXS) is presented. STEM images revealed lateral, periodic density fluctuations in the Si layers, which were further analysed using GISAXS. Characteristic parameters of the fluctuations such as average distance between neighbouring fluctuations, average size and lateral distribution of their position were obtained by fitting numerical simulations to the measured scattering images, and these parameters are in good agreement with the STEM observations. For the numerical simulations the density fluctuations were approximated as a set of spheroids distributed inside the Si layers as a 3D paracrystal (a lattice of spheroids with short-range ordering but lacking any long-range order). From GISAXS, the density of the material inside the density fluctuations is calculated to be 2.07 g cm-3 which is 89% of the bulk value of the deposited layer (2.33 g cm-3).

Specular reflection intensity modulated by grazing-incidence diffraction in a wide angular range.

Grazing-incidence X-ray diffraction (GID) is a well known technique for the characterization of crystal surfaces. A theoretical study has been performed of the sensitivity of GID to the structure of a crystal surface and distorted nanometre-thin surface layers. To simulate GID from crystals that have a complex subsurface structure, a matrix formalism of the dynamical diffraction theory has been applied. It has been found that the azimuthal rocking curves of a crystal that has a distorted subsurface, measured over a wide angular range, show asymmetric thickness oscillations with two distinguishable sets of frequencies: one corresponding to the diffraction in the single-crystal subsurface layer and the second corresponding to the diffraction in the single-crystal substrate. Therefore, azimuthal rocking curves allow characterization of the subsurface structure of a single crystal. Furthermore, thickness oscillations induced by evanescent diffraction modulate the specular reflection intensity, showing high-intensity modulations. This will potentially allow implementation of subsurface crystal characterization using, for instance, a laboratory-scale X-ray diffractometer.

Combined EUV reflectance and X-ray reflectivity data analysis of periodic multilayer structures.

We present a way to analyze the chemical composition of periodical multilayer structures using the simultaneous analysis of grazing incidence hard X-Ray reflectivity (GIXR) and normal incidence extreme ultraviolet reflectance (EUVR). This allows to combine the high sensitivity of GIXR data to layer and interface thicknesses with the sensitivity of EUVR to the layer densities and atomic compositions. This method was applied to the reconstruction of the layered structure of a LaN/B multilayer mirror with 3.5 nm periodicity. We have compared profiles obtained by simultaneous EUVR and GIXR and GIXR-only data analysis, both reconstructed profiles result in a similar description of the layered structure. However, the simultaneous analysis of both EUVR and GIXR by a single algorithm lead to a ∼ 2x increased accuracy of the reconstructed layered model, or a more narrow range of solutions, as compared to the GIXR analysis only. It also explains the inherent difficulty of accurately predicting EUV reflectivity from a GIXR-only analysis.