Interaction between specular reflection and back scattering

Institute for Solid State Physics, University of Tokyo* JASRI/SPring-8, Japan** KEK-PF, Japan***
â—‹Daisuke Arai* Shuji Kusano* Yousuke Nodumi* Mitsuhiro Hashimoto* Toshio Takahashi* Yasuhiko Imai** Yoshitaka Yoda** Keiichi Hirano*** Xiao-Wei Zhang***

We perform the experiment on the Bragg diffraction that the Bragg angle is nearly 90 degrees (back scattering) in the grazing incidence condition that X-rays are totally reflected, and we discuss the results based on the dynamical theory of diffraction. The total reflection occurs when the glancing angle of X-rays is smaller than the critical angle in the grazing incidence condition. Because X-rays penetrate only very little inside the crystal, the total reflection is used for the structure analysis on the surface layer. In the back scattering, because the angular width of the rocking curve becomes comparable to the critical angle, we expect to observe the interaction between the specularly reflected wave and the back scattered wave in the vicinity of the critical angle. Therefore this phenomenon might be applied to the structural analysis of the surface layer for various kinds of crystals in the future.
We think about the diffracting plane perpendicular to the crystal surface. If the glancing angle of incident X-rays on the crystal surface is smaller than the critical angle, the transmitted wave and the diffracted wave can hardly go into the crystal and are reflected outside the crystal. The sample used is a silicon single-crystal with Si(001) surface, and the lattice plane of Si(880) is adopted for back scattering. The glancing angle to the sample surface was changed to observe the rocking curves at each wavelength. The specular reflection and the back scattering were measured at the same time.
The interaction between the specularly reflected wave and the back scattered wave was observed under the grazing incidence conditions at various wavelengths. The experimental results agreed semi-quantitatively with the results calculated by the dynamical theory.