Multi-dimensional analysis of nano-scale periodic structures using EUV and X-RAY characterization: theoretical concepts and applications

The research described in this thesis concerns X-ray and Extreme UV characterization of periodic nanoscale structures. Advances in this analysis range from characterization of 1D systems, like multilayer short-wavelength mirrors, to nanoscale systems with a 2D or 3D, complex architecture. We have drastically improved the accuracy of the multilayer structure characterization by combining the analysis of X-ray reflectivity data and EUV normal-incidence reflectivity data, as compared to the traditional, sole use of X-ray analysis. This was done by using an uncertainty analysis based on the covariation matrix of the combined goodness of fit criterion for data taken at both wavelengths. It shows that the X-ray data primarily contribute to the accuracy of the layer and interface thicknesses, while the EUV data are more sensitive to the layer densities and atomic compositions. Multilayer mirrors can have imperfections distributed in all three dimensions. In a W/Si multilayer system for instance, a 3D distribution of density fluctuations was observed in the Si layers. These fluctuations have been studied using grazing-incidence small-angle X-ray scattering. Assuming a 3D para-crystal-like fluctuation of the density distribution, the parameters reconstructed by numeric simulations were found to be in excellent agreement with independent observations by scanning transmission electron microscopy. Moreover, the density fluctuations were noted to affect the morphology of the interface roughness. In subsequent theoretical research using grazing-incidence X-ray diffraction, the surface structure of monocrystals was further assessed. The structures were considered as 2D objects, assessed by probing the distribution of atoms in depth of the sample and in a chosen set of planes parallel to the surface. Using advances in the dynamical diffraction theory, we predicted an interesting effect: a signature of the off-plane diffraction can be observed by measuring the specular reflectivity. Another interesting aspect is that the intensity of the specular reflection is significantly higher than that of the diffracted beam. This may allow the characterization of the crystal surface, the surface oxidation and the thin (epitaxial) layers, using a relatively moderate power, lab-scale X-ray metrology tool as opposed to a synchrotron-based facility conventionally used for these purposes. The dimensionality was also addressed in the X-ray standing wave technique. Although it allows the analysis of the atomic in-depth distribution of different species, information on the lateral direction is normally lost in this approach. We have derived equations based on the dynamical diffraction theory in a many-beam approximation, which allows the detailed analysis of the 3D atomic distribution in the structure. This has been verified on experimental data measured on a Si3N4 lamellar grating structure using an incident photon energy in the EUV range and on a 3D nano-column Cr structure in the hard X-ray range. The result of simulations using our mathematical model showed a good agreement with nominal structure parameters. In conclusion, this thesis includes several analytical approaches to extend the scope of current X-ray and EUV analysis. This notably concerns the broadening of the dimensionality of the analysis of nano-scale devices and structures, and methods to arrive at an enhanced precision by combining data from different wavelength ranges