Multiple-scattering effects in theK-edge x-ray-absorption near-edge structure of crystalline and amorphous silicon

We report the experimental extraction of the multiple-scattering contribution to the K-edge x-ray-absorption near-edge structure spectrum (XANES) of crystalline silicon. The multiple-scattering signal, is obtained by taking the difference ${\mathrm{\chi }}_{\mathrm{expt}}$(k)-${\mathrm{\chi }}_2$(k)=${\mathrm{\chi }}_{\mathrm{MS}}$(k)= where ${\chi }_{\mathrm{expt}\mathrm{}\left(\mathrm{k}\right)\mathrm{}}$ is defined as [α(k)-${\alpha }_0$(k)]/${\alpha }_0$(k), ${\chi }_2$ is the spherical-wave-calculated extended x-ray-absorption fine-structure (EXAFS) signal, and the ${\chi }_n$’s are the multiple-scattering contributions to the total absorption coefficient α(k) assumed to have the form α(k)=${\mathrm{\alpha }}_0$(k)[1+ over the full wave-vector range, ${\alpha }_0$(k) being the atomic absorption coefficient. The ${\chi }_2$ term has been calculated over the full energy range by using a spherical-wave formula and including mean-free-path and Debye-Waller effects. By using the subtraction procedure we find a ${\chi }_{\mathrm{MS}}$ oscillation of large amplitude in the first 70 eV of the spectrum. Comparison with the theoretical double scattering ${\chi }_3$(k) gives account of the main features of the ${\chi }_{\mathrm{MS}\left(\mathrm{k}\right)}$ spectrum. We show that the main ${\chi }_3$ contribution comes from the double scattering paths involving atoms of the first as well as of the second shell and that higher terms of the series (n>3) are damped by the finite core hole lifetime and the inelastic losses of the photoelectron in the final state. Finally we analyze the K-edge absorption spectra of amorphous silicon. We find that the ${\chi }_{\mathrm{MS}}$ signal, contrary to the crystalline case, is suppressed. Its suppression is assigned to the orientational disorder in bond angles in the amorphous phase.