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The ANBF is a hard x-ray beamline installed at the 2.5 GeV Photon Factory synchrotron light source, located in Tsukuba Science City, Japan. The ANBF delivers monochromatic x-rays in the energy range 4.5 – 20 keV to two experimental stations in a single hutch. The first station is a vacuum diffractometer, while the second is used for EXAFS. The latter equipment is mounted on an optical table just behind the diffractometer. Figures

4-10 and 4-11 show a schematic of the ANBF and a photo of the optical table for EXAFS, respectively.

A ten element Ge photodetector is used to measure the number of fluorescent photons as a function of normalised incident photon flux and photon energy. Each detector element has an incoming count rate limit of approximately 100 000 photons/sec, which can be optimised by adjusting the solid angle, i.e. change the distance between sample and detector.

The monochromator in front of the hutch operates on the Bragg diffraction principle by using two parallel Si(111) crystals, Figure 4-12. The angle q is chosen according to the desired wavelength, using:

q q q sin 9771 . 1 sin 2 3986 . 12 sin 2 ) ( = @ keVAo = d d hc keV E

Figure 4-10: Schematic view of the ANBF beamline at the Photon Factory, Japan.

Figure 4-11: The optical table designed for EXAFS experiments at the ANBF at the Photon Factory, Japan. 10 element Ge fluorescence x- ray photodetector Incident beam ionisation chamber Transmitted beam ionisation chamber Position of sample

The monochromator can select energies between 4.5 to 20 keV, with a resolution of approximately 1 eV.

4.6.3 Extended x-ray absorption fine structure (EXAFS)

EXAFS is a powerful characterisation technique utilising synchrotron radiation. EXAFS spectroscopy measures the fine details of how x-rays are absorbed by materials at energies just above the core-level binding energy of a selected atom. EXAFS requires a highly intense, monochromatic x-ray beam tunable over a continuous range of photon energies. A conventional x-ray source do not satisfy such criteria, and SR is thus necessary.

The EXAFS measurements themselves are relatively straight forward. On the other hand, the interpretation and analysis of EXAFS is rather complex, and has been under continuous development over the last thirty years [51]. The objective of EXAFS measurements is to gain information regarding the local atomic structure in a sample material. This information includes characteristics such as bond lengths and number of neighbouring atoms surrounding the specific atom of interest.

4.6.3.1 X-ray absorption

At energies in the x-ray regime (~0.5 to 500 keV), light is primarily absorbed through the photoelectric effect. In this process, an x-ray is absorbed by an electron in a tightly bound core-level, such as the K shell, of an

atom. The process is shown schematically in Figure 4-13.

q Si(111)

Si(111) Incident polychromatic x- ray beam from synchrotron

Selected monochromatic x-ray beam allowed into hutch

Figure 4-12: Simplified schematic of the monochromator.

Figure 4-13: Schematic of the photoelectric effect in which an x-ray is absorbed and a core-level electron is ejected out of the atom.

In order for a particular core-level electron to participate in the process, the energy of the level must be less than that of the incident x-ray. The extra energy in the absorption process is given as kinetic energy to the photoelectron that is ejected from the atom. The absorption coefficient, m, gives the probability of x-rays to be absorbed according to [51]:

where I0is the incident x-ray intensity on the sample, t is the sample thickness, and I is the intensity transmitted through the sample.

When the incident x-ray has an energy equal to that of the binding energy of a core- level, there is consequently a sharp increase in the absorption. This is termed the absorption edge, and corresponds to an electron being excited from the atom21 (into the continuum). For EXAFS we are concerned with the intensity of m as a function of energy, just above the absorption edge for K or L shell electrons, see Figure 4-14.

4.6.3.2 The photoelectron

The photoelectron ejected by the atom during absorption can be considered as a spherically emitted wave22 propagating radially away from the core. The

photoelectron has a de Broglie wavelength l, and wave number:

where m is the electron mass, E is the energy above the absorption edge, E0 is the energy at the absorption edge, and _ is Planck’s constant (divided by 2!).

The photoelectron wave can be backscattered from neighbouring atoms, resulting in constructive/destructive interference with the outgoing wave at the position of the

21 _{At the absorption edge such an electron will have essentially zero kinetic energy.} Figure 4-14: Post-edge EXAFS oscillations in the

absorption coefficient m(E).

Absorption edge 2 0) ( 2 h E E m k= - t e I I -m = 0

absorbing atom. This interference will alter the absorption coefficient, and is the origin of the oscillations in the absorption spectra above the edge. Figure 4-15 illustrates the wave interference after ejection of a photoelectron.

As the interference, and hence m(E), is influenced by the number of, and distance to the neighbouring atoms, the analysis of EXAFS data will yield information regarding the short-range order of the element of interest. See appendix H for the theoretical EXAFS model.

4.6.3.3 X-ray fluorescence emission

There are two main mechanisms for the decay of the excited atomic state following an x-ray absorption event. Only one will be discussed here; the x-ray fluorescence, Figure 4-16. A higher energy electron fills the vacant position, ejecting an x-ray of well-defined energy (E=hn) in the process. This is called the fluorescence energy and is characteristic of the atom. In the hard x-ray regime the fluorescence mode is the most likely decay mechanism.

Incident x-ray Backscattering from neighbouring atoms Spherical wave of ejected photoelectron

Figure 4-15: Diagram illustrating the ejection of a photoelectron with a wavelike nature (solid red circles) due to an incident x-ray (green arrow) onto the atom of interest (solid red). The photoelectron wave travels radially out from the atom. The wave is scattered (dashed lines) by the 1st shell of neighbouring atoms (blue) and the 2nd _{shell (green). The result is constructive/destructive}

The energy dependence of the absorption coefficient m(E) can be measured by [51]:

where If is the monitored intensity of a fluorescence line, and I0 is the incident beam flux. The EXAFS fine-structure function _(E) is defined by [51]:

where m is the measured absorption coefficient, m0 is the smoothly varying portion of m past the absorption edge, and _m0 is the measured jump in the absorption m. These terms are explained by Figure 4-17.

4.6.3.4 Processing and analysis of EXAFS

Raw EXAFS data, such as shown in Figure 4-17, are processed through a number of steps until a Fourier-transformed EXAFS-spectrum in R-space23 may be presented. The steps are outlined and explained below. The EXAFS data analysis in this project was done utilising the XFIT and FEFF software packages. The theoretical aspects of EXAFS and various parameters are briefly outlined in Appendix H.

Step 1:

In general multiple scans are performed for each sample. Every scan is initially compared with an averaged scan. Any spectra which differ significantly from the average is discarded at this stage on the basis of (temporary) detector instabilities. After this step all processing is done upon the averaged, energy-calibrated scan.

Figure 4-16: x-ray fluorescence decay of the excited state.

Figure 4-17: m(E) shown with smooth background function m0(E) and the edge-

step _m0. 0 0 0 0 ) ( ) ( ) ( ) ( m m m m m m c D - = D - = E E E E 0 / ) (E µI_f I m

Step 2:

In order to isolate the post-edge EXAFS, the pre-edge data is subtracted. The pre-edge is extrapolated beyond the edge by a second-order polynomial spline, and fitted with a slope similar to the EXAFS region,

Figure 4-18. This pre-edge removal minimises contribution to the EXAFS from absorption due to alien elements in the system, and general instrumental background. Further the spectrum is normalised to avoid sample concentration dependencies when comparing different sample spectra.

Step 3:

Further work is done on the EXAFS-region. A number of splines (here four) are fitted to the region to remove the background signal, i.e. the absorption from an isolated atom, Figure 4-19.

Step 4:

The EXAFS is now isolated and mapped onto electron wave vector space by the wave number:

and weighted by k3 in order to enhance the signal in the higher k regions to compensate for reduced amplitude, Figure 4-20.

Figure 4-18: Pre-edge subtraction and normalisation.

Figure 4-19: Post-edge subtraction

Figure 4-20: Isolated EXAFS oscillations

2 1 2 0)/ ] ( 2 [ m E E _h k= -

Step 5:

A window is chosen in which the spectrum is Fourier transformed onto radial (R-) space. This is a plot of the magnitude of the Fourier-transformed EXAFS spectrum as a function of distance (Å). The absorbing atom is now located at the origin, while each pronounced peak corresponds to the 1st, 2nd, 3rd etc, nearest neighbour shells, respectively. Distortions due to atomic

disorder are measurable as the Debye- Waller factor. Notice that the first peak in Figure 4-21 occurs at 2.24 Å, while the nominal value for the distance to the nearest neighbours in Cu is ~2.55 Å. This is not an error, but is due to phase-shifts during scattering, and is taken into account during the steps that follow.

Step 6:

Each shell of atoms can now be modelled based on qualified estimates for a range of structural parameters (normally taken from the corresponding bulk sample), Figure 4-22. Parameters such as bond-length, Debye-Waller factor and coordination number may then be determined with high accuracy.

As a concluding remark, the combination of XRD, RBS, TEM and EXAFS can provide visual, qualitative and quantitative, and characterisation of nc formation induced by ion implantation and subsequent furnace annealing.

Figure 4-21: Fourier transformed EXAFS.

Figure 4-22: First-shell fitting to experimental EXAFS data.