  Although the clean Si(001) and Ge(001) surfaces are very similar, experiments
to date have shown that dimer-vacancy (DV) defects self-organize into vacancy
lines (VLs) on Si(001), but not on Ge(001). In this paper, we perform
empirical-potential calculations aimed at understanding the differences between
the vacancies on Si(001) and Ge(001). We identify three energetic parameters
that characterize the DVs on the two surfaces: the formation energy of a single
DV, the attraction between two DVs in adjacent dimer rows, and the strain
sensitivity of the formation energy of DVs and VLs. At the empirical level of
treatment of the atomic interactions (Tersoff potentials), all three parameters
are favorable for the self-assembly of DVs on the Si(001) surface rather than
on Ge(001). The most significant difference between the defects on Si(001) and
on Ge(001) concerns the formation energy of single DVs, which is three times
larger in the latter case. By calculating the strain-dependent formation
energies of DVs and VLs, we propose that the experimental observation of
self-assembly of vacancies on clean Ge(001) could be achieved by applying
compressive strains of the order of 2%.
