First-principles description of atomic gold chains on Ge(001)

We have performed density-functional theory calculations, including the spin-orbit correction, to investigate atomic gold chains on Ge(001). A set of 26 possible configurations of the Au/Ge(001) system with $c\left(4\times 2\right)$ and $c\left(8\times 2\right)$ symmetries is studied. Our data show that the $c\left(4\times 2\right)$ order results in the lowest energy, which is not in direct agreement with recent experiments. Using total-energy calculations, we are able to explain these differences. We address the electronic band structure and apply the Tersoff-Hamann approach to correlate our data to scanning-tunneling microscopy (STM). We obtain two highly competitive structures of the atomic Au chains for which we report simulated STM images in order to clarify the composition of the experimental Au/Ge(001) surface.

Figure 1

(Color online) (a) Relaxed clean Ge(001) surface with the most likely Au positions for a coverage of 1/4 ML. Labels with tilde correspond to atoms in the second layer. (b) Adsorption sites of Au surface dimers. Ge surface atoms, second layer atoms, and third layer atoms are shown in blue (dark gray), black, and light gray, respectively.

Figure 2

(Color online) Top and side views of the relaxed clean Ge(001) surface and the 2–8 model. $\Delta z$ denotes the shift of the dimer atoms with respect to the clean surface. All values are given in $\text{Å}$.

Figure 3

Electronic band structures for the models (a) 1–5 and (b) 2–8. The zero energy is given by the Fermi level.

Figure 4

(Color online) STM images of a $2\times 2$ supercell simulated for the 1–5 model at $-0.2$ V. The constant-height images are calculated for planes 2, 1, and $0\text{Å}$ above the topmost Ge atoms and at the Au atoms. Au panel: Ge and Au atoms are marked blue (dark gray) and yellow (light gray), respectively.

Figure 5

(Color online) STM images of a $2\times 2$ supercell simulated for the 2–8 model between $-0.4$ and $+0.4$ V, analogous to Fig. 4. Positive voltages refer to unoccupied states.