X-ray standing waves

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 ^[1] the availability of synchrotron light has stimulated the application of this interferometric technique to a wide range of problems in surface science.^[2][3]

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.^[4]

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 ^[2][3]

$Y_{p}(\Omega) = 1 + R + 2C \sqrt{R} f_H \cos (\nu - 2\pi P_H )$,

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) ^[5]

Selected applications

which require ultra-high vacuum conditions

• Physisorption and chemisorption studies ^[2][3]
• Diffusion of dopants in crystals ^[6]
• Superlattices and Quasi-crystal characterization

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. B. W. Batterman and H. Cole, Dynamical Diffraction of X Rays by Perfect Crystals, Rev. Mod. Phys. 36 (1964) 681
2. J. Zegenhagen, Surface structure determination with X-ray standing waves Surf. Sci. Rep. 18(7/8) (1993) 199
3. D. P. Woodruff, Surface structure determination using x-ray standing waves, Rep. Prog. Phys. 68(4) (2005) 743
4. J. Als-Nielsen and D. McMorrow, Elements of Modern X-ray Physics, John Wiley & Sons, Ltd. (2000)
5. 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
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.