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.

Bragg-Case X-ray Interference in Multilayered Structures. Comparison Between Kinematical Approximation and Dynamical Treatment

“…It is to be underlined that the present kinematical theory, unlike previously reported kinematical (or semikinematical) models (Kyutt, Petrashen & Sorokin, 1980;Speriosu, 1981;Wie & Kim, 1991), has led to a simple analytical expression for the intensity instead of the amplitude. This aspect as well as the more general character of this approach offer the advantages: (i) to treat embedded non-diffracting layers of any thickness in an extended angular range; (ii) to easily expand (7) into the relevant terms for the experimental interference pattern of a complex multilayered structure, as will be shown in the following; and (iii) to use interplanar spacings and not approximated expressions of strain with respect to the substrate.…”

“…However, we are well aware that considering all the layers (substrate included) as kinematically diffracting materials implies some discrepancies with respect to the experimental RCs. These difficulties cannot be fully overcome by combining kinematical diffraction from the layers and dynamical diffraction from the Substrate (Speriosu, 1981;Wie & Kim, 1991) but only by resorting to dynamical theory for all the structure.…”

“…Resorting to the kinematical approximation, which enables an easy analytical description of the diffraction phenomenon, has already been used not only in the case of multilayered heterostructures (Tapfer & Ploog, 1989;Wie, 1989;Holloway, 1990;Wie & Kim, 1991) but also in diffused and ion-implanted crystals (Afanas'ev, Koval'chuk, Kovev & Kohn, 1977;Speriosu, 1981). The main interest in this description relies on the possibility of clarifying the relative importance of the different structural parameters responsible for the complicated interference pattern experimentally observed in multilayered materials.…”

Direct measurements of multi-photon induced nonlinear lattice dynamics in semiconductors via time-resolved x-ray scattering

“…We note that there is a considerable difference between the penetration depths of the optical pump and x-ray probe pulses. In order to account for the penetration depth-mismatch, our numerical modelling utilizes dynamical theory of x-rays41 that simulates x-ray diffraction peaks for depth-dependent strain profiles as a function of the x-ray penetration depth (See TRXS Simulation in METHODS). Measured aggregate lattice displacements from equilibrium are shown in Fig.…”

Dynamical X-ray Diffraction from ZnS y Se1−y /GaAs (001) Multilayers and Superlattices with Dislocations

“…Dynamical [1][2][3][4][5][6] and kinematical [7][8][9][10][11] simulations have been used in conjunction with a curve-fitting procedure to extract the profiles of strain and composition, but are based on perfect, dislocation-free laminar crystals, and this renders the analysis inapplicable to mismatched structures with dislocation densities greater than 10 6 cm À2 . Krivoglaz and Ryaboshapka 12 and Levine and Thomson 13 have analyzed the line profiles of Bragg peaks from crystals containing straight, parallel screw dislocations with precisely known atomic displacements.…”