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Register a new userX-ray scattering from stepped and kinked surfaces: An approach with the paracrystal model
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Added by
Fr\\'ed\\'eric Leroy
Publication date
2007
fields
Physics
and research's language is
English
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A general formalism of X-ray scattering from different kinds of surface morphologies is described. Based on a description of the surface morphology at the atomic scale through the use of the paracrystal model and discrete distributions of distances, the scattered intensity by non-periodic surfaces is calculated over the whole reciprocal space. In one dimension, the scattered intensity by a vicinal surface, the two-level model, the N-level model, the faceted surface and the rough surface are addressed. In two dimensions, the previous results are generalized to the kinked vicinal surface, the two-level vicinal surface and the step meandering on a vicinal surface. The concept of crystal truncation rod is generalized considering also the truncation of a terrace by a step (yielding a terrace truncation rod) and a step by a kink (yielding a step truncation rod).
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We studied the resonant diffraction signal from stepped surfaces of SrTiO3 at the Ti 2p -> 3d (L2,3) resonance in comparison with x-ray absorption (XAS) and specular reflectivity data. The steps on the surface form an artificial superstructure suited as a model system for resonant soft x-ray diffraction. A small step density on the surface is sufficient to produce a well defined diffraction peak, showing the high sensitivity of the method. At larger incidence angles, the resonant diffraction spectrum from the steps on the surface resembles the spectrum for specular reflectivity. Both deviate from the XAS data in the relative peak intensities and positions of the peak maxima. We determined the optical parameters of the sample across the resonance and found that the differences between the XAS and scattering spectra reflect the different quantities probed in the different signals. When recorded at low incidence or detection angles, XAS and specular reflectivity spectra are distorted by the changes of the angle of total reflection with energy. Also the step peak spectra, though less affected, show an energy shift of the peak maxima in grazing incidence geometry.
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The theoretical formulation of x-ray resonant magnetic scattering from rough surfaces and interfaces is given for the diffuse (off-specular) scattering, and general expressions are derived in both the Born approximation (BA) and the distorted-wave Born approximation (DWBA) for both single and multiple interfaces. We also give in the BA the expression for off-specular magnetic scattering from magnetic domains. For this purpose, structural and magnetic interfaces are defined in terms of roughness parameters related to their height-height correlation functions and the correlations between them. The results are generalized to the case of multiple interfaces, as in the case of thin films or multilayers. Theoretical calculations for each of the cases are illustrated as numerical examples and compared with experimental data of mangetic diffuse scattering from a Gd/Fe multilayer.
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