Gold deposited on a Ge(0 0 1) surface: DFT calculations

The atomic geometry, stability and electronic properties of self-organized Au induced nanowires on a Ge(0 0 1) surface are investigated based on the density-functional theory in the generalized gradient approximation and the stoichiometry of Au. According to the formation energy and the simulated STM image, the Ge atoms substituted by the Au atoms have been confirmed as occurring at a Au coverage lower than 0.25 Ml. The STM image with single and double dimer vacancies looks like the Au atoms have penetrated the subsurface. The energetically favorable dimer-row arrayed structures at 0.50 Ml and 0.75 Ml Au coverages have a 4  ×  1, 4  ×  2 or c(8  ×  2) transition symmetry, which comprise a flat Au-Au homodimer row and an alternating various buckling phase Ge-Ge or Au-Ge dimer row. The c(8  ×  2) zigzag-shaped protruding chains of shallow-groove STM images are highly consistent with the observations, but a long-range order dimer-row arrayed structure formation requires sufficient mobile energy to complete mass transport of the substituted Ge atoms in order to avoid the re-adsorption of these atoms; otherwise a deep-groove structure reconstruction is sequentially formed. A quasi-1D electron-like energy trough aligns in the direction perpendicular to the nanowire of the dimer-row arrayed structure in the c(8  ×  2) phase on a 0.75 Ml Au/Ge(0 0 1) surface, which is contributed by the Au-Ge dimer rows and the subsurface Ge atoms below them. The bottom energy of the energy trough is consistent with angle-resolved photo-emission spectroscopy studies (Schäfer et al 2008 Phys. Rev. Lett. 101 236802, Meyer et al 2011 Phys. Rev. B 83 121411(R)).