Abstract
An experimental depth-resolved method for analyzing the local atomic structure of low-contrast multilayered thin films is presented in this work. A combination of X-ray reflectometry and angle-resolved EXAFS spectroscopy is considered. The following methods for solving ill-posed inverse problems are used to determine structural characteristics: the Tikhonov regularization method (for linear integral equations) and the Levenberg–Marquardt algorithm (for nonlinear equations). The proposed algorithms do not require information on the studied system such as the interface width and shape, the thickness of layers of specific elements and the depth at which they are located, and the atomic structure. This allows one to retrieve data on the local atomic structure of individual interface layers and the surface. Model numerical experiments for a Cr/Fe/Cr/Fe/Cr sample were conducted to assess the potential of this method.
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REFERENCES
V. V. Ustinov, L. N. Romashev, M. A. Milayev, A. V. Korolev, T. P. Krinitsina, and A. M. Burkhanov, “Kondo-like effect in the resistivity of superparamagnetic cluster-layered Fe/Cr nanostructures,” J. Magn. Magn. Mater. 300, 148–152 (2006).
K. Amemiya, “Sub-nm resolution depth profiling of the chemical state and magnetic structure of thin films by a depth-resolved X-ray absorption spectroscopy technique,” Phys. Chem. Chem. Phys. 14, 10477 (2012).
Y. Kayser, J. Sá, and J. Szlachetko, “Depth-resolved X‑ray absorption spectroscopy by means of grazing emission X-ray fluorescence,” Anal. Chem. 87, 10815–10821 (2015).
S. M. Heald, E. V. Barrera, and H. Chen, “Structure of surfaces and interfaces as studied using Synchrotron Radiation,” Faraday Discuss. Chem. Soc. 89, 21 (1990).
B P. Borthen and H.-H. Strehblow, “X-ray-reflectivity fine structure and EXAFS,” Phys. Rev. B 52, 3017–3019 (1995).
N. M. Souza-Neto, A. Y. Ramos, H. C. N. Tolentino, A. Martins, and A. D. Santos, “Depth-dependent local structures in thin films unraveled by grazing-incidence X-ray absorption spectroscopy,” J. Appl. Cryst. 42, 1158–1164 (2009).
V. V. Vasin and A. L. Ageev, Ill-posed Problems with A Priori Information (VSP, Utrecht, 1995).
V. V. Vasin, “Irregular nonlinear operator equations: Tikhonov’s regularization and iterative approximation,” J. Inv. Ill-Posed Probl. 21, 109–123 (2013).
Y. Babanov, Y. Salamatov, and V. Ustinov, “A new interpretation of X-ray reflectivity in real space for low contrast multilayer systems I. Mathematical algorithm and numerical simulations,” Superlattices Microstruct. 74, 100–113 (2014).
J. M. Ziman, Models of Disorder : The Theoretical Physics of Homogeneously Disordered Systems (Cambridge University Press, Cambridge, 1979; Mir, Moscow, 1982).
Yu. A. Babanov, Yu. A. Salamatov, V. V. Ustinov, and E. Kh. Mukhamedzhanov, “Diagnostics of the atomic structure of multilayer metallic nanoheterostructures from reflectometry data: A new approach to low-contrast systems,” Phys. Solid State 56, 1904–1915 (2014).
Y. Babanov, Y. Salamatov, V. Vasin, and V. Ustinov, “The phase problem for X-ray specular reflectivity from thin films: A new approach,” Superlattices Microstruct. 82, 612–622 (2015).
C. H. Booth and F. Bridges, “Improved self-absorption correction for fluorescence measurements of extended X-ray absorption fine-structure,” Phys. Scr. 115, 202–204 (2005).
Yu. A. Babanov, Yu. A. Salamatov, and E. Kh. Mukhame-dzhanov, “Variable-angle XAFS study of multilayer nanostructure: Determination of selective concentration profile and depth-dependent partial atomic distributions,” J. Phys.: Conf. Ser. 190, 012030 (2009).
Yu. A. Babanov, V. V. Vasin, A. L. Ageev, and N. V. Ershov, “A new interpretation of EXAFS spectra in real space. I. General formalism,” Phys. Status Solidi B 105, 747–754 (1981).
Yu. A. Babanov, D. A. Ponomarev, V. V. Ustinov, A. N. Baranov, and Ya. V. Zubavichus, “Local atomic structure of solid solutions with overlapping shells by EXAFS: The regularization method,” J. Electron Spectrosc. Relat. Phenom. 211, 1–12 (2016).
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This study was supported by the Ministry of Science and Higher Education of the Russian Federation (project “Spin,” no. AAAA-A18-118020290104-2).
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Translated by D. Safin
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Babanov, Y.A., Vasin, V.V., Ponomarev, D.A. et al. Atomic Structure of Multilayered Low-Contrast Fe/Cr Thin Films: Mathematical Formalism and Numerical Experiments. Phys. Metals Metallogr. 120, 756–762 (2019). https://doi.org/10.1134/S0031918X19080039
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DOI: https://doi.org/10.1134/S0031918X19080039