Atomic-scale modeling of next-layer nucleation and step flow at the Ge(105) rebonded-step surface

Based on ab initio calculations, we propose an atomic-scale path leading to the growth of a new layer on the rebonded-step reconstructed Ge(105) surface. We show that the nucleation of (001)-like dimers triggers the formation of low-energy adtrimers within the surface unit cell. The presence of adjacent trimers and the arrival of a further adatom initiate a fast kinetic process, allowing the perfect rebonded-step structure to be rebuilt. After repeating some of the calculations under compressive-strain conditions, we discuss position-dependent nucleation in (105) Ge pyramid on Si(001), finding solid theoretical justification for the experimentally observed preferential nucleation at the top of Ge islands, followed by fast step flow.

Figure 1

a) Top view of the simulation cell. Substrate atoms are represented by white circles, and atoms of the U-shaped structures are painted in gray. Circles’ radii are proportional to the distance to the observer. The A-M and ${\mathrm{A}}^{\prime }\text{−}{\mathrm{M}}^{\prime }$ letters correspond to the isolated-adatom possible positions, following the nomenclature proposed in Ref. 19. On the Ge(105)RS unit cell, there are 26 adsorption minima. The dashed lines encircle the unitary cell for the Ge(105)RS surface. (b) Lateral view of the (105) surface with the RS reconstruction (left panel) and in the as-cut configuration (right panel). With $d=0.555\mathrm{\AA }$, the distance between two adjacent layers is indicated.

Figure 2

(a) Binding energy per adatom for various two-adatom geometries on the Ge(105)RS computed according to Eq. (1). The sampling has been performed on the smaller unit cell in order to search the most stable structures. The points indicated with the circles were also studied on the large simulation cell. (b) Total energy difference between various configurations and the lowest-energy one (CL dimer), for both the small and the larger simulation cell.

Figure 3

Configurations obtained with ab initio optimization for the four most stable structures, whose energy is reported in Fig. 2. The adatoms are painted in black to distinguish them from the substrate.

Figure 4

Top view of the most stable structure for $N_{\mathrm{ad}}$ adatoms on the Ge(105)RS surface. (a) The most stable adatom configuration according to Ref. 19. (b) CL ad-dimer. (c) The adtrimer obtained combining CL and AL [see Fig. 3d]. (d) Two adjacent adtrimers; the asterisk (*) indicates the position for another adatom which allows the further evolution of the growing surface. (e) Energy per adatom computed according to Eq. (1) for the structures reported in (a)–(d) panels.

Figure 5

Snapshots of the kinetic path leading to a Ge(105)RS patch one layer higher with respect to the substrate. Panels (a)–(d) represent local minima. The configuration in panel (a) [equivalent to Fig. 4d plus an adatom] displays the starting structure. The final geometry in panel (d) is characterized by an upper Ge(105)RS island (encircled by the dashed line) in which two Uss’s of the new higher layer are easily detectable. The energy profile is reported in panel (e).

Figure 6

Top view of Ge(105)RS. Atoms of the upper panel are in black, and atoms of the substrate in gray. (a) Perfect stripe of an upper Ge(105)RS layer. The two step edges are indicated by dashed lines: on the left there is a $T$ step, on the right an $H$ one. The boundaries of the two Uss crossing at the left edge, characterizing the lowest $T$ step, are traced with a black line. (b) Two ad-dimers are added on the lower Uss at the left edge. (c) After new adatom arrival, two adtrimers are present at the edge. (d) The $T$-step is grown along the [501] direction: a larger, perfectly reconstructed Ge(105)RS terrace is now present in the middle of the slab.