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Description
Germanium and tin both belong to group IV of the periodic table, but exhibit different properties when it comes to electrical conductivity. Ge is a semiconductor, with a direct and indirect bandgap of 0.8 eV and 0.67 eV respectively, while 𝛼-Sn is a (semi)metal. When combined as an alloy, the bandgap of GeSn can be tuned from 0.67 eV to 0 eV by varying the Sn content making it a useful material in optoelectronics within the near infrared (IR) to mid-IR ranges. However, the realization of these alloys is difficult because of the low solubility equilibrium (<1%) of Sn in Ge and the large lattice mismatch (~15%) between Ge and Sn.
In this study, we employ the cluster expansion methodology implemented in the Alloy Theoretic Automated Toolkit to predict 17 of the ground state structures of Ge1-xSnx in the complete x =0-1 range and compute their formation energies. We computed the bandgaps of the structures using the many-body perturbation theory method, GW0 method. We examined the roles of Sn clustering, using the Warren-Cowley short-range order parameter on the bandgap of the alloys. A comprehensive validation against experimental data in the literature reveals that the methods employed in this study accurately reproduce experimental observations as well as give rigorous insights into the structure, electronic properties, and the role of Sn clustering on the stability and band structures of the alloys.