Diffraction from surfaces with randomly distributed structural defects

Abstract

Diffraction techniques are powerful tools to probe surfaces with respect to structural defects. Basing our calculation on the kinematic approximation valid for the analysis of spot profiles we present a general closed-form solution for the spot profile for surfaces with randomly displaced domains. Generally both lateral and vertical displacements of domains are considered. On the other hand within one domain all atoms are arranged perfectly with respect to each other. The spot profiles depend only on the distribution of displacements and domain sizes supposing that these are not correlated. From analyzing spot profiles at different scattering conditions (order of the spot and varying the vertical scattering condition) one can conclude the kind of defects, evaluate their distribution and the distribution of domain sizes. Finally, we present a detailed analysis of spot profiles for strongly distorted surfaces (all atoms are displaced) and for surfaces with grain boundaries. While for strongly distorted surfaces the spots vanish with increasing scattering vector for surfaces with grains, the spot profiles can be obtained from the incoherent interference of the grains for these scattering conditions.