Recent Developments in the X-ray Reflectivity Analysis
American Journal of Physics and Applications
Volume 4, Issue 2, March 2016, Pages: 27-49
Received: Feb. 8, 2016; Accepted: Feb. 16, 2016; Published: Mar. 17, 2016
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Yoshikazu Fujii, Center for Supports to Research and Education Activities, Kobe University, Nada, Kobe, Japan
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X-ray reflectivity (XRR) is a powerfull tool for investigations on surface and interface structures of multilayered thin film materials. In the conventional XRR analysis, the X-ray reflectivity has been calculated based on the Parratt formalism, accounting for the effect of roughness by the theory of Nevot-Croce conventionally. However, the calculated results have shown often strange behaviour where interference effects would increase at a rough surface. The strange result had its origin in a serious mistake that the diffuse scattering at the rough interface was not taken into account in the equation. Then we developed new improved formalism to correct this mistake. However, the estimated surface and interface roughnesses from the x-ray reflectivity measurements did not correspond to the TEM image observation results. For deriving more accurate formalism of XRR, we tried to compare the measurements of the surface roughness of the same sample by atomic force microscopy (AFM), high-resolution Rutherford backscattering spectroscopy (HRBS) and XRR. The results of analysis showed that the effective roughness measured by XRR might depend on the angle of incidence. Then we introduced the effective roughness with depending on the incidence angle of X-ray. The new improved XRR formalism derived more accurate surface and interface roughness with depending on the size of coherent X-rays probing area, and derived the roughness correlation function and the lateral correlation length. In this review, an improved XRR formalism, considering the diffuse scattering and the effective roughness, is presented. The formalism derives an accurate analysis of the x-ray reflectivity from a multilayer surface of thin film materials.
X-ray Reflectivity, Surface and Interface Roughness, Multilayered Thin Film, Buried Interface
To cite this article
Yoshikazu Fujii, Recent Developments in the X-ray Reflectivity Analysis, American Journal of Physics and Applications. Vol. 4, No. 2, 2016, pp. 27-49. doi: 10.11648/j.ajpa.20160402.12
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Parratt L. G., Phys. Rev. 95, 359-369 (1954).
Nevot L. and Croce P., Rev. Phys. Appl. 15 761-779 (1980).
Yoneda Y., Phys. Rev. 131, 2010 (1963).
Marra W. C., Eisenberger P., and Cho A. Y., J. Appl. Phys. 50 6927 (1979).
Vineyard G. H., Phys. Rev. B 50, 4146 (1982).
Robinson I. K., Phys. Rev. B 33 3830 (1986).
Sakurai K., and Iida A., Jpn. J. Appl. Phys. 31, L113 (1992).
Sakaida Y., Harada S., and Tanaka K., J. Soc. Mat. Sci. Japan 42-477, 641 (1993).
Fujii Y., Nakayama T., and Yoshida K., ISIJ International 44 1549-1553 (2004).
Fujii Y., Komai T., and Ikeda K.; Surf.Interface Anal. 37, 190-193 (2005).
Fujii Y., Yanase E., and Arai K., Applied Auface Science 244, 230 (2005).
Fujii Y., and Nakayama T., Surf. Interface Anal. 38, 1679 (2006).
Fujii Y., Yanase E., and Nishio K., J. Phys.: Conf. Ser., 83, 012008 (2007).
Fujii Y., Surf. Interface Anal. 40, 1722 (2008).
Holy V., Pietsch U., and Baumbach T., (Eds.) High-Resolution X-Ray Scattering from Thin Films and Multilayers, Springer, Berlin (1999).
Daillant J., and Gibaud A., (Eds.) X-ray and Neutron Reflectivity, Principles and Applications, Springer, Berlin (1999).
Shinha S. K., Sirota E. B., Garoff S., and Stanley H.B., Phys. Rev. B 38, 2297-2311 (1988).
Holy V., Kubena J., Ohlidal I., Lischka K., and Plotz W., Phys. Rev. B 47 15896-15903 (1993).
Slater C., and Frank N. H., (Eds.) Electromagnetism, McGraw-Hill, New York (1947).
Vidal B., and Vincent P., Applied Optics 23 1794-1801 (1984).
Boer D. K. G., Phys. Rev. B 49, 5817 (1994).
Boer D. K. G., Phys. Rev. B 51 5297-5305 (1995).
Boer D. K. G., and A. J. G. Leenaers, Physica B 221, 18 (1996).
N. Awaji, and S. Komiya, J. Vac. Sci. Tecnol. A 14, 971 (1996).
M. K. Sanyal, J. k. Basu, A. Datta, and S. Banerjee, Europhys. Lett. 36, 265 (1996).
M. K. Sanyal, S. Hazra, J. k. Basu, and A. Datta, Phys. Rev. B 58, R4258 (1998).
T. Hirano, K. Usami, and K. Ueda, Synchrotoron Rad. 5, 969 (1998).
M. Tolan, X-ray Scattering from Soft-Matter Thin Films (Springer, Berlin, 1999).
K. Stoev, and K. Sakurai, Spectrochim. Acta B 54, 41 (1999).
E. Smigiel and A. Cornet, J. Phys. D 33, 1757 (2000).
K. Ueda, Trans. MRS Japan 32, 223 (2007).
Sakurai K., (Ed.) Introduction to X-ray Reflectivity, Kodansha Scientific, Tokyo (2009).
Fujii Y., Surf. Interface Anal. 42 1642-1645 (2010).
Fujii Y., Mater. Sci. Eng. 24, 012008 (9pp) (2011).
Fujii Y., Mater. Sci. Eng. 24, 012009 (21pp) (2011).
Fujii, Y., Powder Diffraction 28 (2), 100-104 (2013).
Fujii, Y., Adv. Anal. Chem. 3(2), 9-14 (2013).
Fujii, Y., Japanese Journal of Applied Physics. 53, 05FH06 (2014).
Fujii, Y., Nakajima, K., Suzuki, M., and Kimura, K. Surf. Interface Anal. 46, 1208-1211 (2014).
Fujii, Y., Powder Diffraction 29 (3), 265-268 (2014).
Fujii, Y., American Journal of Physics and Applications 3(2), 21-24 (2015).
K. Nakajima, S. Joumori, M. Suzuki, K. Kimura, T. Osipowicz, K. L. Tok, J. Z. Zheng, A. See, B. C. Zhang, Appl. Phys. Lett. 83, 296 (2003).
K. Kimura, K. Ohshima, M. Mannami, Appl. Phys. Lett. 64, 2232 (1994).
K. Kimura, S. Joumori, Y. Oota, K. Nakajima, M. Suzuki, Nucl. Instrum. Meth. B220, 351 (2004).
Q. Yang, D. J. O’Connor and Z. Wang, Nucl. Instrum. Meth. B61, 149 (1991).
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