Extraction of structural parameters and growth rates from symmetric (004) x-ray diffraction patterns of SiGe/GeSn superlattices

SiGeSn alloys offer widely tunable lattice constants and bandgaps, but their accessible composition range is limited by the low equilibrium solubility of Sn and the miscibility gap. Molecular beam epitaxy (MBE)-grown SiGe/GeSn superlattices (SLs) provide a promising route to increase Sn incorporation while enabling band-structure engineering. Because the electronic and structural properties of these SLs depend sensitively on the compositions and thicknesses of the constituent sublayers, accurate structural characterization is essential. Here, a physically constrained extraction method is developed within a theoretical framework for determining superlattice structures and compositions. The underdetermination of single-scan symmetric x-ray diffraction (XRD) is overcome by introducing physically motivated growth constraints across sample design and growth conditions. By combining the pseudomorphic growth assumption, elastic theory, Vegard's law, known shutter times, and controlled variation of growth conditions, the extraction of both SL structural parameters and MBE growth rates from symmetric (004) XRD measurements is experimentally demonstrated with a minimum set of two properly designed samples. The method, therefore, addresses the inherent underdetermination problem without relying on extensive characterization or full-spectrum fitting and provides an efficient, physically grounded route for extracting structural parameters and growth rates in SiGe/GeSn superlattices. It should also facilitate further band-structure engineering in SiGeSn systems.