Structural determination of crystalline silicon by extended energy-loss fine-structure spectroscopy

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Abstract
We present recent structural results obtained through extended energy-loss fine-structure (EELFS) spectroscopy in the reflection mode above the silicon K edge. Although the electron-energy-loss technique is one of the most ancient tools for surface investigation, only recently has it been proved also to give local structural information. Thanks to an increased amount of experimental evidence, the physical process underlying the EELFS features, described in terms of a final-state interference effect similar to what happens in extended x-ray-absorption fine-structure (EXAFS) spectroscopy, seems to be well accepted now, although a deeper theoretical analysis is required. In this paper we compare EELFS and EXAFS features detected above the same edge in order to demonstrate that the dipole approximation can be applied with confidence even for a deep edge of ionization energy comparable with the primary beam energy. The good agreement between the structural parameters obtained by means of x rays and by low-energy primary electrons is theoretically explained in terms of a complete calculation of the inelastic-electron-scattering cross section. The most important result of this approach, based on the distorted-wave Born approximation, is the strong predominance of the dipole channel over the monopole and quadrupole contributions, at least for nodeless core initial wave functions. The present theory allows one to include in a manageable way multiple scattering and exchange effects.