Improvement of X-Ray Reflectivity Analysis on Surface and Interface Roughness Estimation

Yoshikazu Fujii

doi:doi:10.11648/j.ajpa.20150302.12

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Improvement of X-Ray Reflectivity Analysis on Surface and Interface Roughness Estimation

Yoshikazu Fujii

Published in American Journal of Physics and Applications (Volume 3, Issue 2)

Received: 26 January 2015 Accepted: 19 February 2015 Published: 3 March 2015

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Abstract

X-ray reflectivity (XRR) is usefull tool to estimate surface and interface roughness. In the conventional XRR analysis, the reflectivity is calculated based on the Parratt formalism, accounting for the effect of roughness by the theory of Nevot-Croce. However, the calculated results have shown often strange behavior due to the fact 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. 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) and XRR. The results of analysis show that the effective roughness measured by xrrmay depend on the angle of incidence. In this paper, it shows that new improved XRR formalism which derives more accurate surface and interface roughness with depending on the size of the probing area of coherent X-rays.

Published in	American Journal of Physics and Applications (Volume 3, Issue 2)
DOI	10.11648/j.ajpa.20150302.12
Page(s)	21-24
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

X-Ray Reflectivity, Surface and Interface Roughness, Multilayer Surfaces, Buried Interface

References

[1]	Parratt, L. G. (1954). “Surface Studies of Solids by Total Reflection of X-Rays,” Phys. Rev. 95, 359-369.
[2]	Nevot, L. And Croce, P. (1980). “Caracterisation des surfaces par reflexion rasante de rayons X. Application a l’etude du polissage de quelques verres silicates,” Rev. Phys. Appl. 15, 761-779.
[3]	Vidal, B and Vincent, P. (1984). “Metallic multilayers for x rays using classical thin-film theory,” Applied Optics 23, 1794-1801.
[4]	Sinha, S. K., Sirota, E. B., Garoff, S., and Stanley, H. B. (1988) “X-ray and neutron scattering from rough surfaces,” Phys. Rev. B 38, 2297-2311.
[5]	Holy, V., Kubena, J., Ohlidal, I., Lischka, K., and Plotz, W. (1993). “X-ray reflection from rough layered systems,” Phys. Rev. B 47, 15896-15903.
[6]	Boer, D. K. G. (1995). “X-ray reflection and transmission by rough surfaces,” Phys. Rev. B 51, 5297-5305.
[7]	Daillant, J. And Gibaud, A. (Eds.) (1999). X-ray and Neutron Reflectivity, Principles and Applications (Berlin Springer).
[8]	Holy, V., Pietsch, U., and Baumbach, T. (Eds.) (1999). High-Resolution X-ray Scattering from Thin Films and Multilayers (Berlin Springer).
[9]	Fujii, Y., Nakayama, T., and Yoshida, K. (2004). “Roughness Estimation of Polycrystalline Iron Surface under High Temperature by Small Glancing Angle X-ray Scattering,” ISIJ International 44, 1549-1553.
[10]	Fujii, Y., Komai, T., and Ikeda, K. (2005). ” Depth profiling of polycrystalline layers under a surface using x-ray diffraction at small glancing angle of incidence,” Surf. Interface Anal. 37, 190-193.
[11]	Sakurai, K. (Ed.) (2009). Introduction to X-ray Reflectivity (Kodansha Scientific).
[12]	Fujii, Y. (2010). “Influence of surface roughness on near-surface depth analysis from X-ray reflectivity measurements,” Surf. Interface Anal. 42, 1642-1645.
[13]	Fujii, Y. (2011). “Improved x-ray reflectivity calculations for rough surfaces and interfaces,” Series: Materials Science and Engineering 24 012009-1-21.
[14]	Fujii, Y. (2013). “Improved x-ray reflectivity calculations onamultilayered surface,” Powder Diffraction28(2), 100-104.
[15]	Fujii, Y. (2014). “Improvement of surface and interface roughness estimation on X-ray reflectivity,” Powder Diffraction29(3), 265-268.

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APA Style

Yoshikazu Fujii. (2015). Improvement of X-Ray Reflectivity Analysis on Surface and Interface Roughness Estimation. American Journal of Physics and Applications, 3(2), 21-24. https://doi.org/10.11648/j.ajpa.20150302.12

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ACS Style

Yoshikazu Fujii. Improvement of X-Ray Reflectivity Analysis on Surface and Interface Roughness Estimation. Am. J. Phys. Appl. 2015, 3(2), 21-24. doi: 10.11648/j.ajpa.20150302.12

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AMA Style

Yoshikazu Fujii. Improvement of X-Ray Reflectivity Analysis on Surface and Interface Roughness Estimation. Am J Phys Appl. 2015;3(2):21-24. doi: 10.11648/j.ajpa.20150302.12

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@article{10.11648/j.ajpa.20150302.12,
  author = {Yoshikazu Fujii},
  title = {Improvement of X-Ray Reflectivity Analysis on Surface and Interface Roughness Estimation},
  journal = {American Journal of Physics and Applications},
  volume = {3},
  number = {2},
  pages = {21-24},
  doi = {10.11648/j.ajpa.20150302.12},
  url = {https://doi.org/10.11648/j.ajpa.20150302.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajpa.20150302.12},
  abstract = {X-ray reflectivity (XRR) is usefull tool to estimate surface and interface roughness. In the conventional XRR analysis, the reflectivity is calculated based on the Parratt formalism, accounting for the effect of roughness by the theory of Nevot-Croce. However, the calculated results have shown often strange behavior due to the fact 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. 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) and XRR. The results of analysis show that the effective roughness measured by xrrmay depend on the angle of incidence. In this paper, it shows that new improved XRR formalism which derives more accurate surface and interface roughness with depending on the size of the probing area of coherent X-rays.},
 year = {2015}
}

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TY  - JOUR
T1  - Improvement of X-Ray Reflectivity Analysis on Surface and Interface Roughness Estimation
AU  - Yoshikazu Fujii
Y1  - 2015/03/03
PY  - 2015
N1  - https://doi.org/10.11648/j.ajpa.20150302.12
DO  - 10.11648/j.ajpa.20150302.12
T2  - American Journal of Physics and Applications
JF  - American Journal of Physics and Applications
JO  - American Journal of Physics and Applications
SP  - 21
EP  - 24
PB  - Science Publishing Group
SN  - 2330-4308
UR  - https://doi.org/10.11648/j.ajpa.20150302.12
AB  - X-ray reflectivity (XRR) is usefull tool to estimate surface and interface roughness. In the conventional XRR analysis, the reflectivity is calculated based on the Parratt formalism, accounting for the effect of roughness by the theory of Nevot-Croce. However, the calculated results have shown often strange behavior due to the fact 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. 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) and XRR. The results of analysis show that the effective roughness measured by xrrmay depend on the angle of incidence. In this paper, it shows that new improved XRR formalism which derives more accurate surface and interface roughness with depending on the size of the probing area of coherent X-rays.
VL  - 3
IS  - 2
ER  -

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Author Information

Yoshikazu Fujii

Center for Supports to Research and Education Activities, Kobe University, Nada, Kobe, Japan

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APA Style

Yoshikazu Fujii. (2015). Improvement of X-Ray Reflectivity Analysis on Surface and Interface Roughness Estimation. American Journal of Physics and Applications, 3(2), 21-24. https://doi.org/10.11648/j.ajpa.20150302.12

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ACS Style

Yoshikazu Fujii. Improvement of X-Ray Reflectivity Analysis on Surface and Interface Roughness Estimation. Am. J. Phys. Appl. 2015, 3(2), 21-24. doi: 10.11648/j.ajpa.20150302.12

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AMA Style

Yoshikazu Fujii. Improvement of X-Ray Reflectivity Analysis on Surface and Interface Roughness Estimation. Am J Phys Appl. 2015;3(2):21-24. doi: 10.11648/j.ajpa.20150302.12

Copy | Download

@article{10.11648/j.ajpa.20150302.12,
  author = {Yoshikazu Fujii},
  title = {Improvement of X-Ray Reflectivity Analysis on Surface and Interface Roughness Estimation},
  journal = {American Journal of Physics and Applications},
  volume = {3},
  number = {2},
  pages = {21-24},
  doi = {10.11648/j.ajpa.20150302.12},
  url = {https://doi.org/10.11648/j.ajpa.20150302.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajpa.20150302.12},
  abstract = {X-ray reflectivity (XRR) is usefull tool to estimate surface and interface roughness. In the conventional XRR analysis, the reflectivity is calculated based on the Parratt formalism, accounting for the effect of roughness by the theory of Nevot-Croce. However, the calculated results have shown often strange behavior due to the fact 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. 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) and XRR. The results of analysis show that the effective roughness measured by xrrmay depend on the angle of incidence. In this paper, it shows that new improved XRR formalism which derives more accurate surface and interface roughness with depending on the size of the probing area of coherent X-rays.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Improvement of X-Ray Reflectivity Analysis on Surface and Interface Roughness Estimation
AU  - Yoshikazu Fujii
Y1  - 2015/03/03
PY  - 2015
N1  - https://doi.org/10.11648/j.ajpa.20150302.12
DO  - 10.11648/j.ajpa.20150302.12
T2  - American Journal of Physics and Applications
JF  - American Journal of Physics and Applications
JO  - American Journal of Physics and Applications
SP  - 21
EP  - 24
PB  - Science Publishing Group
SN  - 2330-4308
UR  - https://doi.org/10.11648/j.ajpa.20150302.12
AB  - X-ray reflectivity (XRR) is usefull tool to estimate surface and interface roughness. In the conventional XRR analysis, the reflectivity is calculated based on the Parratt formalism, accounting for the effect of roughness by the theory of Nevot-Croce. However, the calculated results have shown often strange behavior due to the fact 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. 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) and XRR. The results of analysis show that the effective roughness measured by xrrmay depend on the angle of incidence. In this paper, it shows that new improved XRR formalism which derives more accurate surface and interface roughness with depending on the size of the probing area of coherent X-rays.
VL  - 3
IS  - 2
ER  -

Copy | Download