Effects of magnitude and direction of the biaxial compressive strain on the formation and migration of a vacancy in Ge by using density functional theory

Abstract

The effects of the magnitude and direction of biaxial compressive strain on the formation and migration barrier of a neutral vacancy in germanium were studied using density functional theory. Bulk Ge cells with (100) and (111) planes under various in-plane biaxial compressive strains were investigated to model epitaxial Ge on Si(1-x)Ge(x) substrate. Biaxial compressive strain decreases the vacancy formation energy by 68% and 81% for the (100) and (111) supercells, respectively, when Ge is assumed to be epitaxially grown on Si. The biaxial compressive strain hardly affects the migration behavior of a vacancy in the (100) supercell. On the contrary, in the (111) supercell, the migration barrier energy shows anisotropic behavior; the migration along the perpendicular and virtually parallel directions with respect to the strain becomes distinctly more difficult and slightly easier, respectively. The effects of strain on the formation and migration of the vacancy were explained by the atomic relaxation around it and electron redistribution. By comparing the formation energy and migration barrier energy, vacancy formation was suggested to be dominant for vacancy-mediated diffusion in Ge. (C) 2011 American Institute of Physics. [doi:10.1063/1.3611076]