Incoherent and Thermal Small-Angle X-Ray Scattering in Silicon

Abstract

The intensity of small-angle x-ray scattering in single-crystal silicon has been measured with the scattering vector K oriented along each of the three symmetry directions. The scattering intensity extrapolates to zero angle in reasonable agreement with the thermal scattering, calculated from the velocity of sound in each direction. The thermal scattering is calculated from known phonon dispersion relations and subtracted from the total to obtain the incoherent, or Compton, scattering. The incoherent scattering is smaller than that calculated by Freeman from Hartree-Fock wave functions for the free atom. This conclusion agrees with previous approximate measurements at small $K$ on other crystals. Theoretical ideas about the source of the deficiency, apparently a solid-state effect, and about small-angle thermal scattering are outlined. The incoherent scattering shows little anisotropy and no sharp rise with increasing angle, which would suggest the onset of excitation of electrons across the forbidden band.