MROX 2.0: a software tool to explore quantum heterostructures by combining X-ray reflectivity and diffraction

Abstract

New software for the simulation and fitting of specular X-ray reflectivity (XRR) measurements has been developed. The novel software employs the recursive formalism of the dynamical theory of X-ray scattering and constitutes an extension of the Multiple Reflection Optimization package for X-ray diffraction (MROX). The software is used to determine the layer thicknesses, mass densities and roughnesses of quantum heterostructures of two sets of samples: Si/Ge bilayers with 1, 2, 3, 4 and 10 periods grown on Si buffer layers and (001) Si substrates, and a 50 period ZnO/Zn_1−xMg_xO layer grown on a m-ZnO substrate. For the case of the group IV elemental semiconductors, an increase in the interface roughness with an increasing number of periods is found. The evolution of the roughness with increasing layering complexity is suggested to be due to the decrease of the crystalline quality deduced via simulations of X-ray diffraction 004 2θ–ω scans. With respect to the superlattice grown on top of the wide bandgap II–VI semiconductor, XRR scans were performed for different azimuth directions, ϕ = {0°, 20°, 40°, 60°, 80°, 90°}. In perfect agreement with high-resolution transmission electron microscopy images, lower roughnesses are derived when the X-ray beam is perpendicular to the c-axis. Furthermore, in both systems, the derived thicknesses fully agree with the ones observed via imaging techniques. For the wurtzite one, the low averaged MgO content (∼10%) reduces the contrast between the binaries' refractive indices (mass densities) while a difference in the a-lattice parameter is still observed experimentally. The density of the Zn_1−xMg_xO compound is then determined as a linear interpolation between the binaries' densities weighted by the MgO content derived via XRD and used as input in the XRR simulations. The resulting XRR simulations agree perfectly with the experimental data. Thus, an approach combining reflectivity and diffraction presents substantial advantages over the single scattering mode.