X-ray standing waves

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The X-ray standing wave technique

The X-ray standing wave (XSW) technique can be used to study the structure of surfaces and interfaces with high spatial resolution and chemical selectivity. Pioneered by B.W. Batterman in the 1960s [2] the availability of synchrotron light has stimulated the application of this interferometric technique to a wide range of problems in surface science.[3][4]

Basic principles

Principle of X-ray standing wave measurements

An X-ray interference field created by Bragg reflection provides the length scale against which atomic distances can be measured. The spatial modulation of this field described by the dynamical theory of X-ray diffraction undergoes a pronounced change when the sample is scanned through the Bragg condition. Due to a relative phase variation between the incoming and the reflected beam the nodal planes of the XSW field shift by half a lattice constant.[5]

Depending on the position of the atoms within this wave field the element specific absorption of X-rays varies in a characteristic way. Therefore, measurement of the photo yield – via X-ray fluorescence or photoelectron spectroscopy – can reveal the position of the atoms relative to the lattice planes.

For a quantitative analysis the normalized photo yield Y_{p} is described by [3][4]

Y_{{p}}(\Omega )=1+R+2C{\sqrt {R}}f_{H}\cos(\nu -2\pi P_{H}),

where R is the reflectivity and \nu is the relative phase of the interfering beams. The characteristic shape of Y_{p} can be used to derive precise structural information about the surface atoms because the two parameters f_{H} (coherent fraction) and P_{H} (coherent position) are directly related to the Fourier representation of the atomic distribution function.

X-ray reflectivity from the ubiquitous phase problem of X-ray crystallography. Therefore, and with a sufficiently large number of Fourier components being measured, XSW data can be used to establish the distribution of the different atoms in the unit cell (XSW imaging) [1]

Selected applications

which require ultra-high vacuum conditions

which do not require ultra-high vacuum conditions

  • Langmuir-Blodgett films
  • Self-assembled monolayers
  • Buried interfaces

See also

  • List of surface analysis methods

References

  1. ↑ L. Cheng, P. Fenter, M. J. Bedzyk, and N. J. Sturchio, Fourier-Expansion Solution of Atom Distributions in a Crystal Using X-Ray Standing Waves, Phys. Rev. Lett. 90 (2003) 255503
  2. ↑ B. W. Batterman and H. Cole, Dynamical Diffraction of X Rays by Perfect Crystals, Rev. Mod. Phys. 36 (1964) 681
  3. ↑ 3.0 3.1 3.2 J. Zegenhagen, Surface structure determination with X-ray standing waves Surf. Sci. Rep. 18(7/8) (1993) 199
  4. ↑ 4.0 4.1 4.2 D. P. Woodruff, Surface structure determination using x-ray standing waves, Rep. Prog. Phys. 68(4) (2005) 743
  5. ↑ J. Als-Nielsen and D. McMorrow, Elements of Modern X-ray Physics, John Wiley & Sons, Ltd (2000)
  6. ↑ P. Hoenicke et al., Depth profile characterization of ultra shallow junction implants, Anal. Bioanal. Chem., 396 (8), 2825-2832 (2010)

Further reading

Zegenhagen, Jörg; Kazimirov, Alexander (2013). The X-Ray Standing Wave Technique. World Scientific. ISBN 978-981-2779-00-7. 

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