X-ray Reflectometry of Planar Nanoheterostructures:a New Model-less Approach

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X-ray reflectometry is a highly sensitive non-destructive method of the electron density profile determination in multilayer nanostructures. To evaluate the density variation with depth from the reflectivity data one uses traditionally the least squares method. However, it is known that in this case the solution has no stability and no uniqueness. This talk is devoted to a new method of obtaining the concentration profile of elements from reflectivity data. Using the integral equation, which describes the relationship of the reflection coefficient with the electron density distribution, we have shown that it can be transformed into an equation relating the reflection coefficient with concentration profiles of elements. The proposed method has a number of features: (i) we have found a solution of the ill-posed problem for a Fredholm integral equation using the regularization method proposed by Tikhonov; (ii) we formulate the problem in terms of the “phase problem.” To find a phase we use the logarithmic dispersion relation proposed by Klibanov. We demonstrate the application of this new model-less method for multilayers of several types.

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Journal: TechConnect Briefs
Volume: 1, Nanotechnology 2014: Graphene, CNTs, Particles, Films & Composites
Published: June 15, 2014
Pages: 444 - 447
Industry sector: Advanced Materials & Manufacturing
Topic: Materials Characterization & Imaging
ISBN: 978-1-4822-5826-4