Effect of strain on the energetics and kinetics of dissociation of ${\text{Sb}}_4$ on Ge(001)

A comprehensive search for the precursor dissociation of antimony tetramers on Ge(001) with strain was carried out using first-principles calculations. In contrast to previous theoretical studies on Si(001) [Phys. Rev. Lett. 97, 046103 (2006)] and in agreement with recent experiments, we reveal a square intermediate anisotropy dissociation pathway across the surface dimer row, where the dissociation energetics and kinetics can be qualitatively altered by the strain and lead to divergent dissociation pathways and patterns with substrate-dimer-bond breaking due to the weak interactions between Ge-Ge and Sb-Ge bonds.

Figure 1

(Color online) (a) Optimized cluster configurations for ${\text{Sb}}_4$ on Ge(001) and Si(001). Large (red) and small (gray) circles represent Sb and top-two-layer Ge (or Si) atoms, respectively. Lines are drawn to indicate the chemical bonds. (b) The binding energy of these configurations defined as $E_n=E\left[n\right]-E\left[0\right]$, where $E\left[n\right]$ and $E\left[0\right]$ are the total energy of the system with and without $n$ Sb adatoms on the Ge(001) or $\text{Si}\left(001\right)\text{−}c\left(4\times 2\right)$ surface. The surface lattice parameters denoted in the figures are $4.00\text{Å}$ for Ge(001), $3.92\text{Å}$ for $\text{Ge}-2\%$, and $\text{Si}+2\%$, and $3.84\text{Å}$ for Si(001), respectively.

Figure 2

(Color online) Strain dependent first-stage (3D-to-2D flat tetramers) conversion pathways of ${\text{Sb}}_4$ on Ge(001). (a) Potential-energy surface for $T_A\to S$ and $T_B\to S$, generated by a $11\times 11$ grid mesh; (b) energy profiles for $T_A\to S$ compared to $T_A\to P$; (c) energy profiles for $T_B\to S$ compared to $T_B\to R$; and [(d) and (e)] illustration of the above dissociation pathways. The atoms labeled 1–4 correspond to the ${\text{Sb}}_4$ molecule and 5–10 correspond to Ge atoms on the surface.

Figure 3

(Color online) Strain dependent first-stage (3D-to-2D flat tetramers) conversion pathways of ${\text{Sb}}_4$ on Si(001). (a) Energy profiles for $T_A\to S$ compared to $T_A\to P$; (b) energy profiles for $T_B\to S$ compared to $T_B\to R$. For the corresponding pathways see Figs. 2d, 2e.

Figure 4

(Color online) Strain dependent second-stage (2D tetramer-to-dimer) conversion pathways of the square tetramer ${\text{Sb}}_4$ on Ge(001). (a) Energy profiles for $S\to AA$ compared to $S\to BB$; (b) illustration of the above dissociation pathways.

Figure 5

(Color online) Strain dependent second-stage conversion pathways of the rotated rhombus ${\text{Sb}}_4$ on Ge(001). (a) Energy profiles for $P\to S_A$ compared to $P\to AB$ on Ge(001); (b) illustration of the above reaction pathways.