Abstract
The following chapter describes the basics and some applications for the case that photoelectrons are emitted from a hard X-ray interference field instead of by a travelling wave. The dipole approximation holds astonishingly well even for hard X-rays as far as the magnitude of the transition matrix element is concerned. However, the forward-backward asymmetry caused by higher order multipole terms needs to be considered when the photoelectron is emitted by the coherent action of two X-ray waves travelling in different directions. This has implications on the chosen experimental set-up which will be briefly discussed together with other experimental aspects. Finally, some examples of X-ray standing wave analysis using hard X-ray photoelectron spectroscopy will be presented yielding the geometric and electronic structure of (crystalline) materials with pm resolution.
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Notes
- 1.
Note the difference between diffraction plane, i.e. the plane defined by k 0 and k h and diffraction planes, which are parallel to a corresponding set of Miller planes, for example (333), (444), (555), etc. which are all parallel to the (111) Miller planes. Diffraction planes are not necessarily atomic planes. Their spacing \(d_{hkl} /m\) is defined by Bragg’s law \(2d_{hkl} \sin \Theta = m\lambda\) where \(d_{hkl}\) is the spacing of the \((hkl)\) Miller planes.
- 2.
The electron yield \(I_{A}^{h}\) detected in an XSWs experiment is given by \(I_{A}^{h} = I_{A,0} Y_{A,T}^{h}\) where \(I_{A,0}\), called off-Bragg yield, is proportional to the number of sampled atoms and other parameter such as photoelectric cross section, solid angle, beam intensity and more.
- 3.
For details of how the parameters \(S_{R}\), \(S_{I}\) and \(\psi\) are calculated, the reader is referred to the original publication [24].
- 4.
A minor influence by a modified surface layer leading to \(P = \ne 0\) cannot be excluded.
- 5.
If a divergent beam with a wide bandpass is incident on a crystal the different wavelengths are reflected at different angles, they are dispersed. When this rainbow like x-ray beam is incident on a sample crystal, incident wavelengths and angles only match if the crystal has exactly the same diffraction plane spacing (see e.g. [30]).
- 6.
This can easily be understood from Bragg’s law \(2d\sin (\varTheta ) = m\lambda\); at \(\varTheta = 90^\circ\) the sine function is flat and a small change in \(\lambda\) necessitates a large change in \(\varTheta\).
- 7.
As Herbert Kroemer phrased it in his Nobel lecture, December 8, 2000: “Often it may be said that the interface is the device”.
- 8.
This surface distance should not be confused with the bond length.
- 9.
Utilizing additionally the cubic symmetry of the SrTiO3.
- 10.
The absorption probability, i.e. cross section also depends strongly on the shape of the electron wavefunction close to the core.
- 11.
In order to fit with the experimental partial yield, the calculated lpDOS had to be convoluted with a Gaussian significantly wider than given by the experimental resolution, in particular for oxygen.
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Zegenhagen, J., Lee, TL., Thiess, S. (2016). Photoelectron Emission Excited by a Hard X-ray Standing Wave. In: Woicik, J. (eds) Hard X-ray Photoelectron Spectroscopy (HAXPES). Springer Series in Surface Sciences, vol 59. Springer, Cham. https://doi.org/10.1007/978-3-319-24043-5_12
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