Combining x-ray real and reciprocal space mapping techniques to explore the epitaxial growth of semiconductors

In the present work, the importance of determining the strain states of semiconductor compounds with high accuracy is demonstrated. For the matter in question, new software titled LAPAs, the acronym for LAttice PArameters is presented. The lattice parameters as well as the chemical composition of Al1-xInxN and Ge1-xSnx compounds grown on top of GaN- and Ge-buffered c-Al2O3 and (001) oriented Si substrates, respectively, are calculated via the real space Bond's method. The uncertainties in the lattice parameters and composition are derived, compared and discussed with the ones found via x-ray diffraction reciprocal space mapping. Broad peaks lead to increased centroid uncertainty and are found to constitute up to 99% of the total uncertainty in the lattice parameters. Refraction correction is included in the calculations and found to have an impact of 0.001 angstrom in the lattice parameters of both hexagonal and cubic crystallographic systems and below 0.01% in the quantification of the InN and Sn contents. Although the relaxation degrees of the nitride and tin compounds agree perfectly between the real and reciprocal-spaces methods, the uncertainty in the latter is found to be ten times higher. The impact of the findings may be substantial for the development of applications and devices as the intervals found for the lattice match the condition of Al1-xInxN grown on GaN templates vary between similar to 1.8% (0.1675-0.1859) and 0.04% (0.1708-0.1712) if derived via the real- and reciprocal spaces methods. This work was supported by the Portuguese Foundation for Science and Technology (FCT) in the framework of the Plurianual Strategic Funding UID/FIS/50010/2019. FO acknowledges the FCT PhD Grant and thanks the Institut fuer Halbleitertechnik, Universitaet Stuttgart for hospitality. The authors acknowledge Professor I Watson and Professor F Schulze from the Universities of Strathclyde, Scotland, United Kingdom, and Stuttgart, Germany for the growth of the nitrides and tin compounds, respectively.