Density Functional Theory Study of the Stress Impact on Formation Enthalpy of Intrinsic Point Defect around Dopant Atom in Ge Crystal

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During the last decade, the use of single crystal germanium (Ge) layers and structures in combination with silicon (Si) substrates has led to a revival of defect research on Ge. In Si crystals, dopants and stresses affect the intrinsic point defect (vacancy V and self-interstitial I) parameters and thus change the thermal equilibrium concentrations of V and I. However, the control of intrinsic point defect concentrations has not yet been realized at the same level in Ge crystals as in Si crystals due to the lack of experimental data. In this study, we have used density functional theory (DFT) calculations to evaluate the effect of isotropic internal/external stress (σin/σex) on the formation enthalpy (Hf) of neutral V and I around dopant (B, Ga, C, Sn, and Sb) atom in Ge and compared the results with those for Si. The results of the analysis are threefold. First, Hf of V (I) in perfect Ge is decreased (increased) by compressive σin while Hf of V (I) in perfect Ge is increased (decreased) by compressive σex, i.e., hydrostatic pressure. The stress impact for perfect Ge crystals is larger than that for perfect Si crystals. Second, Hf of V around Sn and Sb atoms decrease while Hf of I around B, Ga, and C atoms decrease in Ge crystals. The dopant impact for Ge crystals is smaller than that for Si crystals. Third, the compressive σin decreases (increases) Hf of V (I) around dopant atom in Ge crystals independent of the dopant type while the σex has a smaller effect on Hf of V and I in doped Ge crystals than the σin. The thermal equilibrium concentrations of total V and I at the melting point of doped Ge under the thermal stresses during the crystal growth were also evaluated.