Density functional theory study of Pt-induced Ge(001) reconstructions

Pt deposited on a Ge(001) surface spontaneously forms nanowire arrays. These nanowires are thermodynamically stable and can be hundreds of atoms long. The nanowires only occur on a reconstructed Pt-Ge-surface where they fill the troughs between the dimer rows on the surface. This unique connection between the nanowires and the underlying substrate make a thorough understanding of the latter necessary for understanding the growth of the nanowires. In this paper we study possible surface reconstructions containing 0.25 and 0.5 of a monolayer of Pt. Comparison of calculated scanning tunneling microscope (STM) images to experimental STM images of the surface reconstruction reveal that the Pt atoms are located in the top layer, creating a structure with rows of alternating Pt-Ge and Ge-Ge dimers in a $c\left(4\times 2\right)$ arrangement. Our results also show that Pt atoms in the second or third layer cannot be responsible for the experimentally observed STM images.

Figure 1

Top view of the Ge(001) surface with symmetric $\left(2\times 1\right)$ reconstruction. 0–7 are indexes for the surface dimer atoms and are used in the nomenclature of the geometries (see text).

Figure 2

(Color online) Pseudo-STM images showing filled (a), (c), (e) and empty (b), (d), (f) states of the ${\beta }_{2u}$ (a), (b), ${\beta }_{2d}$ (c), (d), and ${\beta }_{7ud}$ (e), (f) geometries. For the filled-state images $\epsilon ={\epsilon }_F-0.70\text{eV}$ and for the empty-state images $\epsilon ={\epsilon }_F+1.50\text{eV}$ is used. The constant density is chosen such that the maximum $z$ is at $3.0\text{Å}$ above the highest atom. The small dark gray (red) filled circles represent the Pt atoms in the top layer, the small light gray (green) circles represent the positions of the Ge atoms in the two top layers. Contours are added to indicate the main features discussed in the text.

Figure 3

(Color online) Pseudo-STM images showing (a) filled and (b) empty states of the ${\beta }_{7ud}$ geometry close to the Fermi level, with $\epsilon ={\epsilon }_F\pm 0.30\text{eV}$. The maximum $z$ is at $4\text{Å}$ above the highest atom. There is a clear difference between the dimer rows with the Pt atoms located between up-Ge atoms (middle zigzag row) and the dimer rows with the Pt atoms located between down-Ge atoms (top and bottom row). A notch (circle) in the constant density surface above the location of the Pt atoms is visible for both the filled- and empty-state image.

Figure 4

(Color online) Comparison of $\beta$ and $\gamma$ structures. Filled state pseudo-STM images of the ${\beta }_{4u}$ (a), ${\beta }_{5ud}$ (b), ${\gamma }_1$ (c), ${\gamma }_2$ (d), and ${\gamma }_3$ structure (e) with $\epsilon ={\epsilon }_F-0.70\text{eV}$ and an empty-state pseudo-STM image of the ${\gamma }_3$ structure (f) close to the Fermi level with $\epsilon ={\epsilon }_F+0.30\text{eV}$. The maximum $z$ is at $3\text{Å}$ above the highest atom. The green/red (light/dark gray) disks indicate the positions of the Ge (Pt) atoms in the two top layers of the system. Contours separated $0.2\text{Å}$ are added to guide the eye. The circles indicate the “notch,” while the ellipse shows the position of the “bridge.” The Ge dimer row in (a) and (b) show slightly broader and higher dimer images than the Pt-Ge dimer row.

Figure 5

(Color online) Comparison of the filled-state pseudo-STM image of the ${\beta }_{6u}$ geometry (gray scale overlay) with the corresponding experimental STM image of the $\beta$ terrace. The STM image is obtained using a sample bias of $-0.3\text{V}$, while the pseudo-STM image is generated using $\epsilon ={\epsilon }_F-0.70\text{eV}$ and a maximum $z$ of $4\text{Å}$ above the highest atom. The small red (dark gray) disks represent the positions of the Pt atoms in the top layer, while the green (light gray) disks represent the positions of the Ge atoms in the top two layers. The QDRs are clearly visible in both STM images, as is the presence of two different types of dimer.

Figure 6

(Color online) Same as Fig. 5 but now for the empty-state images. The sample bias used for the STM image is $+0.3\text{V}$ and $\epsilon ={\epsilon }_F+0.70\text{eV}$ is used for the pseudo-STM image. Note the triangular holes above the Pt atoms (red disks) which are present in both the theoretical and the experimental STM image. This is a unique feature for the ${\beta }_{6u}$ structure.

Figure 7

High symmetry lines and points of the surface Brillouin zone (left) for the $\beta$ structures. A surface unit cell is shown on the right, indicating the orientation of the dimer rows.

Figure 8

(Color online) Comparison of the band structure, along high-symmetry lines (cf. Fig. 7), of the Ge(001) $c\left(4\times 2\right)$ reconstruction (a) and the ${\beta }_{6u}$ geometry (b). The energy zero is set at the Fermi level.

Figure 9

(Color online) Total DOS of the ${\beta }_{6u}$ geometry and the LDOS of the surface atoms. The bold dashed green curve shows the DOS of bulk Ge, it is shifted to align the edges of the BG regions. The labeled peaks are discussed in the text.

Figure 10

Top: diagram showing a side view of a relaxed Ge-Ge dimer, including the labeling used for both Ge-Ge and Ge-Pt surface dimers. Bottom: top view schematic representation of the ${\beta }_{6u}$ reconstruction.

Figure 11

The diagrams show a top view of the upper row, as represented in the diagram of the ${\beta }_{6u}$ reconstruction in Fig. 10, of second and third layer Ge atoms in a $\text{Ge}\left(2\times 2\right)$, Ge $c\left(4\times 2\right)$, and ${\beta }_{6u}$ reconstruction. The adjacent top layer atoms, as represented in the bottom diagram of Fig. 10, are then from left to right: Ge $\left(2\times 2\right)$: Ge up-dimer atom, down-dimer atom, up-dimer atom and down-dimer atom. Ge $c\left(4\times 2\right)$: Ge down-dimer atom, up-dimer atom, up-dimer atom, and down-dimer atom. ${\beta }_{6u}$: Ge atom, Pt atom, Ge down-dimer atom, and Ge up-dimer atom. [Data for the Ge $\left(2\times 2\right)$ reconstruction is taken from Gay et al. (Ref. 22)].

Figure 12

Locations of Ge atoms substituted by Pt atoms in the second (capital) and third (small) layer. The second layer Ge atoms pushed to the surface by third layer Pt atoms are marked by the $k_{\text{x}}$.

Figure 13

(Color online) Pseudo-STM images showing filled- (left of each pair) and empty- (right of each pair) state images for the geometries containing Pt in the second and third layer. $\epsilon ={\epsilon }_F\pm 0.70\text{eV}$ is used in these simulations and the maximum $z$ is chosen at $4\text{Å}$ above the highest atom. The positions of the Pt atoms are indicated by the (green) disks and the (red) squares indicate the positions of second layer Ge atoms which are pushed up to the first layer level. “Present” and “removed” refers to these Ge atoms being present or having been removed ($\ast$ configurations of Table ). The bottom dimer row in each picture shows Ge dimers which are not (or barely) influenced by the Pt atoms present. The dimers at the top of each picture show a clear modification caused by the Pt atoms present underneath.