Role of Strain-Dependent Surface Energies in $\mathrm{Ge}/\mathrm{Si}(100)$ Island Formation

Formation energies for $\mathrm{Ge}/\mathrm{Si}(100)$ pyramidal islands are computed combining continuum calculations of strain energy with first-principles-computed strain-dependent surface energies. The strain dependence of surface energy is critically impacted by the presence of strain-induced changes in the Ge $\{100\}$ surface reconstruction. The appreciable strain dependencies of rebonded-step $\{105\}$ and dimer-vacancy-line-reconstructed $\{100\}$ surface energies are estimated to give rise to a significant reduction in the surface contribution to island formation energies.

Figure 1

Isolated $\{105\}$ pyramidal hut island on Si(100), colored according to one-half the trace of the calculated in-plane surface strain fields (see text for discussion).

Figure 2

Ge (100) and (105) surface energies (per unit area of deformed surface) versus biaxial strain. Triangles denote (105) results from Ref. 5. Circles, squares, and diamonds are (100) results obtained in this work for $p(2\times 2)$ and $p(2\times 2)$ based $2\times 6$ and $2\times 8$ DVL reconstructions, respectively. Solid lines highlight the surface energy for the stable reconstruction of a given orientation.

Figure 3

Contributions to the formation energy of an isolated Ge $\{105\}$ pyramidal island versus size ($L$). (a) $\Delta E^{\mathrm{relax}}$ (dotted lines) and $\Delta E^{\mathrm{surf}}$ (solid line) along with the $\{100\}$ and $\{105\}$ contributions to $\Delta E^{\mathrm{surf}}$ (dashed lines); (b) $\Delta E^{\mathrm{form}}$ for various edge energies, ${\sigma }^{\mathrm{edge}}$, in $\mathrm{eV}/\AA$.