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

Abstract

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 ${\mathrm{\ensuremath{\chi}}}_{\mathrm{expt}}$(k)-${\mathrm{\ensuremath{\chi}}}_{2}$(k)=${\mathrm{\ensuremath{\chi}}}_{\mathrm{MS}}$(k)= where ${\ensuremath{\chi}}_{\mathrm{expt}(\mathrm{k})}$ is defined as [\ensuremath{\alpha}(k)-${\ensuremath{\alpha}}_{0}$(k)]/${\ensuremath{\alpha}}_{0}$(k), ${\ensuremath{\chi}}_{2}$ is the spherical-wave-calculated extended x-ray-absorption fine-structure (EXAFS) signal, and the ${\ensuremath{\chi}}_{n}$'s are the multiple-scattering contributions to the total absorption coefficient \ensuremath{\alpha}(k) assumed to have the form \ensuremath{\alpha}(k)=${\mathrm{\ensuremath{\alpha}}}_{0}$(k)[1+ over the full wave-vector range, ${\ensuremath{\alpha}}_{0}$(k) being the atomic absorption coefficient. The ${\ensuremath{\chi}}_{2}$ 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 ${\ensuremath{\chi}}_{\mathrm{MS}}$ oscillation of large amplitude in the first 70 eV of the spectrum. Comparison with the theoretical double scattering ${\ensuremath{\chi}}_{3}$(k) gives account of the main features of the ${\ensuremath{\chi}}_{\mathrm{MS}(\mathrm{k})}$ spectrum. We show that the main ${\ensuremath{\chi}}_{3}$ 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 (ng3) 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 ${\ensuremath{\chi}}_{\mathrm{MS}}$ signal, contrary to the crystalline case, is suppressed. Its suppression is assigned to the orientational disorder in bond angles in the amorphous phase.