Comparative study of dimer vacancies and dimer-vacancy lines on Si(001) and Ge(001)

TL;DR

This study compares the atomic-scale properties of dimer vacancies on Si(001) and Ge(001) surfaces, revealing why vacancy lines form on Si but not on Ge, and suggests strain can induce vacancy self-assembly on Ge.

Contribution

It identifies key energetic parameters explaining the different vacancy behaviors on Si and Ge surfaces and proposes strain application to promote vacancy line formation on Ge.

Findings

Dimer vacancies are energetically more favorable on Si(001) than Ge(001).

Strain influences the formation energies of vacancies and vacancy lines.

Applying compressive strain may induce vacancy self-assembly on Ge(001).

Abstract

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%.