Imaging interfacial topography with coherent x-ray reflectivity
The use of coherent x-ray reflectivity to image interfaces is illustrated using model calculations for three cases: a thin film, a semi-infinite substrate, and a coherently strained epitaxial thin film. The intensities and phases of the coherent scattering signals are calculated based on a fully atomistic model (where the phases are assumed to have been recovered by a phasing algorithm). Here, we describe the characteristics of the effective density that are obtained by direct inverse Fourier transformation of the complex structure factors, using a window function to define the data range. These effective densities include significant artifacts like oscillations and negative values derived from the finite vertical momentum transfer of the window function. Two approaches are described to extract the surface topography from the effective densities for three-dimensional visualization: (i) multiplying the effective density by a phase factor and (ii) analyzing the data as a hybrid structure factor F(x, Q z ). The explicit surface sensitivity and specificity of measurements is illustrated when the film or substrate Bragg peaks are excluded. These considerations show that images of interfacial topography can be obtained using currently available experimental capabilities with parameters corresponding to epitaxial thin films.