EXAFS Studies of Semiconductor Microstructure
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are due to backscattering of the photoelectron from the neighboring atoms. If a given coordination shell is composed of a single atomic species, then the oscillations in the EXAFS signal are approximated by X(*) = 2 ^ T i
*
s[n{2kR 2
i
+
d {k))
i
2
• exp(-2fc cr, ) • exp(-2(R ; -A)A,(k))
(1)
where the sum is over coordination shells. The ;'th coordination shell has Nj atoms at an average distance Rj. The backscattering amplitude and electronic phase shift are represented by / and 8, respectively, which both vary slowly with electron wave number k = (2mE)m/h. The mean-square fluctuation in distances to atoms in a given shell is represented by a2, with contributions from thermal motion of the atoms, site-to-site variations, and possible static distortion of the site. Electronelectron interactions and the finite lifetime of the excited state contribute to the photoelectron mean-free path \ . The A(=fy) represents a "core radius" where the mean free path concept does not apply. As can be seen from this formula, the periods of the oscillations contain information about the distances between the excited and back-scattering atoms, while the amplitude of the oscillations is related to the number and types of neighbors and to vibrational motion of the atoms. The positions and types of atoms in the first, second, and sometimes third coordination shells may often be determined with the technique. By tuning to the absorption edge of a particular atomic species, the environment about the corresponding excited atoms in the structure may be probed.
Experimental Methods EXAFS measurements are often made with x-ray transmission experiments, but other configurations are possible. The same effect may be observed by monitoring x-ray fluorescence, Auger electron emission, or even optical luminescence as a function of incident x-ray energy. These different detection methods have advantages for particular experiments: for instance, fluorescence detection is advantageous for systems with dilute atomic species, such as occur in the study of impurities. In all cases, polycrystalline, amorphous, and glassy materials may be studied as easily as single-crystal samples. A major factor determining the detection mode is the atomic concentration of the element of interest. If the absorption due to the atomic species of interest is a significant fraction of the total absorption, transmission measurements are usually preferable because of experimental simplicity. When the absorption due to the element of interest is less than a few percent of the total absorption, advantages exist in using fluorescence detection. For studying surfaces or near-surface regions, techniques based on electron detection are sometimes useful.2 Transmission and fluorescence measurements are described below in more detail. Transmission Measurements. In transmission experiments, the incident and transmitted x-ray fluxes are monitored with ion chambers, and the absorption coefficient as a function of x-ray energy is determined. Experiments are typically conducted at
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