First-principles simulations of Si vacancy diffusion in erbium silicide

First-principles calculations are performed to explore the diffusion of excess Si vacancies in rare-earth silicide Er Si_2-x. Nudged elastic band calculations show that Si vacancies diffuse quickly within the Si planes via a site-exchange mechanism with neighboring Si atoms, with a barrier of 0.67 eV. The vacancy diffusion across Er planes is more difficult (the barrier height is nearly 4.4 times larger). This leads to a remarkable anisotropy in Si vacancy diffusion in these two directions. When Er Si_2-x is grown heteroepitaxially on Si(001), the formation energy of a Si vacancy decreases by 22% due to an in-plane expansion of the lattice. The barrier height for vacancy diffusion within Si planes increases by 27% due to the epitaxial strain-in-plane Si vacancy diffusion is barely effected. The slower out-of-plane diffusivity, on the other hand, is enhanced by the strain but remains small.