Impact of strain and surface reconstruction on long-range diffusion of Ge atoms on Ge(111) surface
We investigate the effect of surface reconstruction and strain on diffusion of adsorbed Ge atoms on Ge$(111)\textrm{-}5\times5$ and Ge$(111)\textrm{-}7\times7$ surfaces by means of first principles calculations. Stable adsorption sites, their energies, diffusion paths, and corresponding activation barriers are reported. We demonstrate that the decisive migration path is located near the corner holes of surface structures, and they are associated with formation of weak bonds between the adsorbed Ge atom and surface dimers (within the $5\times5$ or $7\times7$ structures). The results show that Ge diffusion rates on $5\times5$ and $7\times7$ reconstructed Ge$(111)$ surfaces should be similar. Conversely, the diffusion barrier on a compressively strained Ge$(111)$ surface is considerably higher than that on a strain-free surface, thus explaining previous experimental results. Comparable diffusion rates on $5\times5$ and $7\times7$ reconstructed surfaces are explained by the identical local atomic arrangements of these structures. The increase of the migration barrier on a strained surface is explained by dimer bond strengthening upon surface compression, along with a weakening of bonds between the adsorbed Ge and dimer atoms.