A model-independent Fourier-inversion method for imaging elemental profiles from multilayer and total-external reflection x-ray standing wave (XSW) data is developed for the purpose of understanding the assembly of atoms, ions, and molecules at well-defined interfaces in complex environments. The direct-method formalism is derived for the case of a long-period XSW generated by low-angle specular reflection in an attenuating overlayer medium. It is validated through comparison with simulated and experimental data to directly obtain an elemental distribution contained within the overlayer. We demonstrate this formalism by extracting the one-dimensional profile of Ti normal to the surface for a TiO2 /Si/Mo trilayer deposited on a Si substrate using the TiKα fluorescence yield measured in air and under an aqueous electrolyte. The model-independent results demonstrate reduced coherent fractions for the in situ results associated with an incoherency of the x-ray beam (which are attributed to fluorescence excitation by diffusely or incoherently scattered x-rays). The uniqueness and limitations of the approach are discussed.
|Original language||English (US)|
|Journal||Physical Review B - Condensed Matter and Materials Physics|
|State||Published - Feb 19 2010|
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics