Quantitative analysis of grazing incidence small-angle x-ray scattering: Pd/MgO(001) growth

The present paper focuses on the analysis of grazing incidence small-angle x-ray scattering (GISAXS) of islands on a substrate. Getting accurate morphological parameters relevant for the elaboration process, i.e., growth curves, island equilibrium shape, and interfacial energy, implies a quantitative data analysis. The emphasis is put on the island form factor, i.e., the Fourier transform of the island shape. It is shown that the island shape and size can be obtained through the island symmetry, the presence of island facets, the asymptotic behavior at high momentum transfer for large polydispersity, and the zeros or minima of the intensity for small polydispersity. The specificity brought by the grazing incidence scattering geometry is highlighted by a careful comparison between the Born approximation and the more accurate distorted wave Born approximation. The interplay between the form factor and the interference function is all the more important in the total scattering intensity when incoherent diffuse scattering comes into play at small momentum transfer for disordered systems. Getting rid of these interpretation difficulties requires accurate measurements of the scattered intensity far in the reciprocal space. This analysis methodology is illustrated through recently acquired GISAXS patterns during the in situ molecular beam epitaxy of Pd nanoislands on MgO(001) single crystals for different thicknesses and temperatures. The morphological parameters obtained agree very well with subsequent transmission electron microscopy-results. Finally, GISAXS diffuse scattering has been shown, originating from the growth-coalescence process and from the size dependence of the island capture area.