Nanoengineering with dynamic atomic force microscopy: Lateral interchange of adatoms on a $\text{Ge}\left(111\right)\text{−}c\left(2\times 8\right)$ surface

Ab initio techniques are used to elucidate the lateral noncontact AFM pair exchange of Sn and Ge adatoms on the $\text{Ge}\left(111\right)\text{−}c\left(2\times 8\right)$ surface both at low and room temperatures. Two different processes are considered: (a) tip-assisted surface diffusion and (b) active tip participation via adatom pick-up/deposition processes. The adatom diffusion profiles indicate fairly modest energy barriers between 0.6 and 0.8 eV, which can be further significantly reduced by the tip. However, the diffusion-mediated exchange mechanism is precluded by a large barrier $\left(>1\text{eV}\right)$ to the (Sn, Ge)-pair exchange. The experimental data are only consistent with a mechanism involving a simultaneous adatom pick-up/deposition and adatom diffusion processes. Simulation results show that, contrary to general belief, the tip apex modification due to the pick-up/deposition processes may not be experimentally noticeable.

Figure 1

(Color online) The experimental NC AFM image (Ref. 8) with superimposed ball-and-stick model before (left) and after (right) the (Sn, Ge)-pair exchange, see white arrows. Sn adatoms (green color) are imaged as brighter spots, and germanium adatoms are imaged as darker spots (red color). Rest atoms are shown in yellow. The two types of adatoms $\left(A_1,A_2\right)$ are indicated by black dashed lines. The calculated lowest-energy pathways for adatom diffusion (Ref. 21) along the directions where manipulation was observed experimentally (Ref. 8) are shown by blue arrows, △ labels ${\text{H}}_3$ sites, and ◆ labels the midpoint site between two neighboring $T_4$ sites.

Figure 2

(Color online) Schematics of the lateral manipulation processes. (a) indirect and (b) direct processes. The arrows (numbers) indicate the respective motions of the atoms during the exchange process. Color coding of atoms follows Fig. 1.

Figure 3

(Color online) Static energy profiles for the indirect process of (Sn, Ge)-pair exchange between two $T_4$ sites in $\left[1\overline{1}0\right]$ direction labeled by $\xi$. The PESs were computed with a 10 atom Ge tip (Ref. 9) positioned over a rest atom as shown in the lower panel. The light blue arrow indicates the line along which the PES was computed in the $\left[1\overline{1}0\right]$ direction. Process (i): Sn diffusion toward and exchange around a Ge adatom in a $T_4$ position (red: no tip; green: tip in equilibrium over a rest atom; blue: tip over rest atom in a $0.5\text{Å}$ compression; and magenta: tip over rest atom in $1.0\text{Å}$ compression). Process (ii): exchange around a ◆ site, with Sn adatom staring the diffusion (magenta: tip over rest atom in a $1.0\text{Å}$ compression; cyan: tip over rest atom in a $1.25\text{Å}$ compression; and orange: tip over rest atom in a $1.25\text{Å}$ compression but with the Ge atom diffusing first to the ◆ site). For more details see text and Ref. 21. Finite-temperature delocalization of Sn adatom is shown in the inset by projection of MD trajectory onto the surface plane (red trace). The simulation was done at 1800 K with a 10 atom Ge tip (Ref. 9) indenting a nearby rest atom by $1.25\text{Å}$; see the lower panel. Color coding of atoms follows Fig. 1.

Figure 4

(Color online) PESs for Sn adatom diffusion toward a nearby empty $T_4$ site without the presence of a tip (red) and with tip indenting the rest atom closest to the Sn adatom by $1.25\text{Å}$ (green). Adatom diffusion in the $\left[1\overline{1}0\right]$ direction (top) and in the $\left[11\overline{2}\right]$ direction (bottom). Both profiles were computed for geometries and tip position shown in the lower panel of Fig. 3. The diffusion paths are shown in the insets. The green/red numbers indicate the dominant barrier reduction upon rest atom indentation.

Figure 5

(Color online) Schematics of a spontaneous formation of a trimerized apex from a dimer-terminated tip (Ref. 28). Color coding of atoms follows Fig. 1.

Figure 6

(Color online) PESs for adatom extraction (top) and adatom deposition (bottom) with a trimerized apex. Dashed line: first oscillation of the tip, and black line with dots: second/successive tip oscillations. Green: tip approach; red: tip retraction. The insets show the configurations at the (a) beginning of the process and (b) end of the process. $d-d_0$ is the tip-surface distance (Ref. 9). Color coding of atoms follows Fig. 1.