Pt-induced nanowires on Ge(001): A density functional theory study

We study formation of the nanowires formed after deposition of Pt on a Ge(001) surface. The nanowires form spontaneously after high-temperature annealing. They are thermodynamically stable, only one atom wide and up to a few hundred atoms long. Ab initio density functional theory calculations are performed to identify possible structures of the Pt-Ge(001) surface with nanowires on top. A large number of structures are studied. With nanowires that are formed out of Pt or Ge dimers or mixed Pt-Ge dimers. By comparing simulated scanning tunneling microscopy images (STM) with experimental ones we model the formation of the nanowires and identify the geometries of the different phases in the formation process. We find that the formation of nanowires on a Pt-Ge(001) surface is a complex process based on increasing the Pt density in the top layers of the Ge(001) surface. Most remarkably we find the nanowires to consist of germanium dimers placed in troughs lined by mixed Pt-Ge dimer rows.

Figure 1

(Color online) Three typical experimental STM images (Refs. 31, 33, 34). (a) An empty state STM image of several NWs at 77 K using a bias of 0.15 V and a tunnel current of 0.437 nA (Ref. 31). [(b) and (c)] 2D and 3D filled-state STM images recorded at 4.7 K, using a bias voltage of $-1.5\text{V}$ and a tunneling current of 0.5 nA (Ref. 33). The ellipses indicate the symmetric bulges while the rectangles indicate two NW dimers showing $\left(4\times 1\right)$ periodicity. The dashed rectangles show the $\left(2\times 1\right)$ periodicity for edge NWs. Empty troughs are indicated with the arrows and have a width of 1.6 nm. In (b) and (c) also a QDR of the $\beta$ terrace is visible.

Figure 2

(Color online) The DB between an $\alpha$ and $\beta$ terrace (Ref. 34). Although many vacancies are present in the $\alpha$ terrace, the dimer rows can still be recognized. Lines show two neighboring QDRs on the $\beta$ terrace and two neighboring dimer rows on the $\alpha$ terrace.

Figure 3

Adsorption sites before relaxation. (a) Adsorption sites for Pt adatoms on the ${\beta }_6$ geometry (Ref. 24). (b) Adsorption sites of Pt addimers on the ${\beta }_6$ (shown here) and Ge(001) $b\left(2\times 1\right)$ surface geometry.

Figure 4

(Color online) Calculated STM images for a Pt dimer at the ${\text{T}}_{\text{d}1}$ site of the Ge(001) (a) and ${\beta }_6$ (b) geometries, after relaxation. For these filled-state images a simulated bias of $-1.5\text{V}$, and $z=3.0\text{Å}$ is used. Green/red (light/dark gray) disks indicate the locations of the Ge/Pt atoms in the two top layers. The yellow (white) disks in (b) indicate the position of the ejected Ge atom at position $2^{\prime }$ (cf. Fig. 3). Contours, separated $0.3\text{Å}$, are added to guide the eye.

Figure 5

(a) Possible position indices of Pt atoms in the top layer. (b) Adsorption sites of addimers, here shown on a surface containing Pt atoms at positions 2, 4, 6, and 7. Site A is positioned between two Pt atoms while site B is positioned between a Pt and a Ge atom.

Figure 6

(Color online) [(a) and (b)] Calculated STM images of a Ge NW, (c) Ge adatoms, (d) and a Pt NW on a surface containing Pt atoms at positions 2, 4, 6, and 7 (cf. Fig. 5). The green/red (light/dark gray) disks show the positions of Ge/Pt atoms in the surface, and [(a) and (b)] the yellow (white) disks show the positions of the Ge NW atoms, (c) Ge adatoms, or (d) Pt NW atoms. Contours are added to guide the eye. [(a), (c), and (d)] Calculated filled-state STM images, for $z=3.0\text{Å}$ and a simulated bias of $-1.50\text{V}$. (b) Calculated empty-state STM image, for $z=3.0\text{Å}$ and a simulated bias of $+1.50\text{V}$.

Figure 7

Schematic representation of the (a) ${\gamma }_c$- and (b) ${\gamma }_{as}$-surface geometries with the NW dimer adsorption site A.

Figure 8

(Color online) An experimental example of a trough flip observed at the boundary of two different NW patches (Ref. 35). Note that two NWs are spaced at least one empty trough in the lateral direction.

Figure 9

(Color online) Ball-and-stick model of the ${\gamma }_{as2}$-surface reconstruction after relaxation. The top left image shows a top view of the structure while the top-right and bottom images show side views along the $\left[1\overline{1}0\right]$ and [110] directions, respectively. Green and red balls show the positions of Ge and Pt atoms, respectively. The top-left figure shows $2\times 2$-surface unit cells with three troughs in the $x$ direction. The middle trough is lined with Pt atoms and is the location of NW adsorption in the calculations. The bottom image clearly shows the large tilting angles of some of the Pt-Ge surface dimers. It also shows the second-layer Ge atoms to be pushed up to positions higher than the Pt atoms in the substrate. If the third-layer Ge atoms are replaced with Pt atoms, the ${\gamma }_{as2}^{\star }$ surface is generated.

Figure 10

(Color online) (a) Geometric structure of the Ge NW on the ${\gamma }_{as}$ surface after relaxation. Pt atoms are shown in red and Ge atoms in green. (b) Contour plot of the total charge density of the adsorbed Ge NW, in the vertical plane along the NW. (c) Same as (b) but now for the partial charge density, for all energy levels from 0.7 eV below the Fermi level up to the Fermi level. Green triangles indicate the position of Ge atoms in the plane. The contours are separated $0.03\left(0.01\right)e/{\text{Å}}^3$ for the total (partial) charge-density plot. Major tics are separated $1\text{Å}$.

Figure 11

Schematic representation of the ${\gamma }_{as}^{\star }$ structure with adsorption sites discussed in the text.

Figure 12

(Color online) (a) Geometric structure of the Ge NW on the ${\gamma }_{as}^{\star }$ surface after relaxation. Pt atoms are shown in red and Ge atoms in green. (b) Contour plot of the total charge density of the adsorbed Ge NW, in the vertical plane along the NW. (c) Same as (b) but now for the partial charge density, for all energy levels going from 0.7 eV below the Fermi level up to the Fermi level. Green triangles (red squares) indicate the position of Ge (Pt) atoms in the plane. The contours are separated $0.1\left(0.01\right)e/{\text{Å}}^3$ for the total (partial) charge-density plot.

Figure 13

(Color online) Calculated STM images of a Ge NW adsorbed at the A [(a) and (b)] and C [(e) and (f)] site on a ${\gamma }_{as}^{\star }$ surface and on the A site of a ${\gamma }_{as2}^{\star }$ [(c) and (d)] surface, and calculated filled-state STM images of a Pt NW adsorbed at the A site of a ${\gamma }_{as}^{\star }$ (g) and ${\gamma }_{as2}^{\star }$ surface (h). The green/red (light/dark gray) disks show the positions of Ge/Pt atoms in the surface and the yellow (white) disks show the positions of the Ge/Pt NW atoms. Contours are added to guide the eye. [(a), (c), (e), (g), and (h)] Calculated filled-state STM images, for $z=3.0\text{Å}$ and a simulated bias of $-1.50\text{V}$. [(b), (d), and (f)] Calculated empty-state STM images, for $z=3.0\text{Å}$ and a simulated bias of $+1.50\text{V}$.

Figure 14

(Color online) Calculated STM images of a Ge NW adsorbed on a ${\gamma }_{as}^{\star }$ surface with extra Pt atoms adsorbed at the T sites of the trough. [(a) and (b)] Pt atoms are adsorbed at both T sites of the $\left(4\times 2\right)$-surface cell (2T), [(c) and (d)] only one T site is occupied (1T), and [(e) and (f)] only one T site per two surface-unit cells is occupied (0.5T). The green (light gray) disks show the positions of Ge atoms in the two top layers of the surface. The red (dark gray) disks show the positions of the Pt atoms in the top layer and the Pt atoms at the T sites in the trough, and the yellow (white) disks show the positions of the Ge NW atoms. Contours are added to guide the eye. [(a), (c) and (e)] Calculated filled-state STM images, for $z=3.0\text{Å}$ and a simulated bias of $-1.50\text{V}$. [(b), (d), and (f)] Calculated empty-state STM images, for $z=3.0\text{Å}$ and a simulated bias of $+1.50\text{V}$.

Figure 15

(Color online) (a) Geometric structure after relaxation of the Ge NW on the ${\gamma }_{as}^{\star }$ surface containing one extra Pt atom in the trough per two $\left(4\times 2\right)$ surface unit cells (NW2 structure). Pt atoms are shown in red and Ge atoms in green. Angles shown on the bonds are with regard to the $xy$ plane. (b) Contour plot of the total charge density of the adsorbed Ge NW, in the vertical plane along the NW. (c) Same as (b) but now for the partial charge density, for all energy levels going from 0.7 eV below the Fermi level up to the Fermi level. Green triangles (red squares) indicate the position of Ge (Pt) atoms in the plane. The contours are separated $0.1\left(0.01\right)e/{\text{Å}}^3$ for the total (partial) charge-density plot.

Figure 16

(Color online) Calculated STM images of a Ge NW adsorbed on a ${\beta }_3^{\star }$ surface. The green/red (light/dark gray) disks show the positions of Ge/Pt atoms in the top layers of the surface. The yellow (white) disks show the positions of the Ge NW atoms. Contours are added to guide the eye. (a) Calculated filled-state STM image, for $z=3.0\text{Å}$ and a simulated bias of $-1.50\text{V}$. (b) Calculated empty-state STM image, for $z=3.0\text{Å}$ and a simulated bias of $+1.50\text{V}$.

Figure 17

Schematic diagram of a possible formation path for NW arrays on Ge(001) with regard to increasing local Pt density, given from left to right in ML. Straight arrows indicate paths with increasing Pt density, curved arrows indicate possible relaxation paths during and after high temperature annealing. LDA formation energies are given in meV with regard to the Ge(001) $b\left(2\times 1\right)$ surface reconstruction. WT and NW indicate if the pseudo-STM pictures show WT-like images or NW-like images. Formation paths are discussed in the text.

Figure 18

Band structure of the NW1 model shown in Fig. 12. The energy zero is given by the Fermi level.

Figure 19

(Color online) Ball-and-stick representations of the relaxed (a) NW1 and (b) NW2 models indicating the (inequivalent) atoms of which the LDOS is shown in Figs. 20, 22.

Figure 20

(Color online) Total DOS of the NW1 structure and LDOS of the surface atoms as shown in Fig. 19a. The bold dashed green line shows the DOS of Bulk Ge, it was shifted to align the BG regions.

Figure 21

Band structure of the NW2 model shown in Fig. 15. The energy zero is given by the Fermi level.

Figure 22

(Color online) Total DOS of the NW2 structure and LDOS of the surface atoms as shown in Fig. 19b. The bold dashed green line shows the DOS of Bulk Ge, it was shifted to align the BG regions.

Figure 23

(Color online) Calculated filled state STM images of some WT geometries indicated in Fig. 17, for $z=3.0\text{Å}$ and a simulated bias of $-0.70\text{V}$. The green/red (light/dark gray) disks show the positions of Ge/Pt atoms in the two top layers of the surface and the adsorbed structure. Contours are added to guide the eye and are spaced $0.2\text{Å}$ in the $z$ direction. (a) ${\gamma }_{as2}+\text{Pt}$ NW, (b) ${\gamma }_{as2}^{\star }+\text{Ge}$ NW, (c) ${\gamma }_{as2}+3\text{Pt}$ atoms in the trough, and (d) ${\gamma }_{as2}^{\star }+1\text{Pt}$ at $\text{T}+\text{Ge}$ NW.

Figure 24

(Color online) (a) Calculated filled-state and (b) empty-state STM images of the Ge $b\left(2\times 1\right)$ ${\text{T}}_{1\text{d}}$ structure, for $z=3.0\text{Å}$ and a simulated bias of $\pm 1.50\text{V}$. The green/red (light/dark gray) disks show the positions of Ge/Pt atoms in the top layers of the surface and the adsorbed structure. The five topmost contours are added to guide the eye. They are spaced $0.2\text{Å}$ in the $z$ direction. [(c) and (d)] Top and side view of the Ge $b\left(2\times 1\right)$ ${\text{T}}_{1\text{d}}$ structure after relaxation, for comparison to Fig. 9 in Ref. 47. $\mathbf{r}$ and $\mathbf{d}$ indicate the Ge atoms that need to dimerize or be removed to have the TDC structure proposed by Stekolnikov et al. Important bond lengths are shown for comparison.