Composition and strain dependence of intrinsic and substitutional defect formation energies in Sn_xGe_1−x alloys

We present a density functional theory investigation of the formation energies of intrinsic and substitutional defects in Sn_xGe_1−x alloy as a function of both Sn composition and biaxial strain relevant to heteroepitaxial interface settings. Special quasi-random supercell structures (SQS) are used obtain the ground state energy of the initial and defect bearing Sn_xGe_1−x alloys. Intrinsic defects considered in this study include the vacancy and [110] split Ge interstitial, while substitutional defects include the analogous [110] split Sn interstitial, as well as substitutional Sn and P. The study focuses on Sn_xGe_1−x alloy compositions with 0%–25% Sn content and compressive and tensile strains up to 2%. The results reveal a complex coupling of strain and compositional dependence of formation energies among different types of defects. The formation energies of split [110] Ge interstitial and substitutional Sn defects decrease monotonically with increasing Sn content while the intrinsic vacancy, Sn split [110] interstitial, and substitutional P defects exhibit a minimum formation energy between 13%–19% Sn. Biaxial strain increases the formation energy of all defects by approximately 0.1 eV for an absolute strain of 1%.