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

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 empiricalpotential calculations aimed at understanding the differences between the vacancies on Si(001) and Ge(001). We identify three energetic parameters which characterize the DVs on the two surfaces: the formation energy of single DVs, 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, but not 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 straindependent 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%.

Surface energetics and structure of the Ge wetting layer on Si(100)

“…Important insights into the nature and origin of Ge on Si(100) wetting layer structures may nonetheless be gathered from studies considering only various subsets of the observed reconstructions, as previously demonstrated. [26][27][28][29][30][31][32][33] Using a modified Keating model, Tersoff calculated 26 the chemical potential of Ge atoms in a dimer reconstructed Ge wetting layer on Si(100) as a function of thickness. Estimating the limits of the chemical potential of Ge atoms in established QD islands, he extracted a critical Ge wetting layer thickness of 3 ML.…”

“…The formation energy of isolated dimer vacancies has been calculated and is found to be negative for Ge on Si(100) given appropriate second layer atom rebonding. It has been established that interactions between individual dimer vacancies lead to an ordering into dimer vacancy lines, 28,29 and the selection of a regular DVL spacing. 30 Lagally and coworkers have demonstrated that experimental results for 2 ϫ N DVL reconstructed wetting layers are consistent with only limited Ge-Si intermixing.…”

“…32,33 A recent study using the Tersoff potential has examined the energetics of the 2 ϫ N DVL wetting layer surface as a function of thickness and N vacancy line spacing. 29 In the following we report the results of first-principles total energy calculations of the Ge wetting layer on Si(100) energetics as a function of wetting layer thickness and surface structure. These results are a direct parametrization of the wetting potential for a subset of the observed DVL reconstructions in the Ge on Si(100) system.…”

Strain effects and intermixing at the Si surface: Importance of long-range elastic corrections in first-principles calculations

“…3 The exact interval is controlled by the wetting layer thickness as well as the amount of intermixing, which also affects internal strain. A number of numerical descriptions of the 2 × N reconstruction have been reported, using empirical potentials , [5][6][7] tight-binding 8 and DFT description. [9][10][11][12] These studies find that DVLs are the favored arrangement for surface dimer vacancies, and predict small (a few hundred meV per vacant dimer) to negative DVL formation energies, even on unstrained Si(001).…”

Controlled Self-Organization of Atom Vacancies in Monatomic Gallium Layers

“…The straight line indicates that the repulsive interaction between VLs is elastic in nature [10]. Accordingly [11]:…”