Kinematical x-ray diffraction model with a new boundary condition for analysis of Bragg-peak profiles of layered crystals

Abstract

A new boundary condition is employed in the kinematical model analysis of Bragg-peak profiles of layered single crystals, which is the dynamical reflection amplitude of the substrate instead of the previously used dynamical intensity. It is shown that this boundary condition properly accounts for the angular shift effect in the Bragg-peak profile of very thin epitaxial layers and superlattices. A kinematical model simulates properly the interference profiles in the C-layer Bragg peak of C/A/C/sub-type samples, but not in the B-layer Bragg peak of the B/A/B-type samples. The simulated and experimental rocking curves for the thin single-layer AlGaAs/GaAs and GaInAs/InP samples and for an AlGaAs/GaAs superlattice sample are discussed. Rocking curves are simulated by using the dynamical diffraction theory and the kinematical model with the old or new boundary condition. A matrix method for the dynamical theory superlattice simulation is also presented. The superlattice simulation using this matrix method is found to be substantially faster than the conventional recursive formula approach.