Epilayer thickness and strain dependence of Ge(113) surface energies

Abstract

The stability and growth of three-dimensional (3D) nanostructures in the Ge on Si system is controlled in part by the strain-and overlayer-thickness-dependent surface energies of the crystal facets involved. Here, we use density functional theory (DFT) with local-density approximation calculations to calculate the strain-and thickness-dependent energy of various Ge(113) and Si(113) surface reconstructions. Results of DFT calculations are compared to Tersoff potential calculations to assess the relative importance of stress-strain effects compared to electronic effects not captured by empirical atomistic potentials. We find that the self-interstitial-based 3 × 2 adatom-dimer-interstitial and 3 × 2 adatom-interstitial surface reconstructions are stable for Ge overlayer thicknesses from 0 to 4 monolayers and at applied biaxial strains from ∼−4% to 0%. We leverage calculated surface energies to determine net effective surface energies of various experimentally observed 3D Ge on Si nanostructures.

Formation of Self-Connected Si0.8Ge0.2 Lateral Nanowires and Pyramids on Rib-Patterned Si(1 1 10) Substrate

“…The surface energy density of Ge (001) is about 6.1 eV/nm 2 [37]. As for the {1 1 3} facets, the key parameters of Ge {1 1 3} surface energies are adopted from the recent progress in ab initio calculation [38]. It should be noted that although the strain energy calculations are done with the Ge concentration being set to 20%, surface parameters for pure Ge {1 0 5}, (0 0 1), and {1 1 3} facets are adopted due to the dominating Ge surface segregation observed in previous studies [9, 14, 39].…”

Beneficial defects: exploiting the intrinsic polishing-induced wafer roughness for the catalyst-free growth of Ge in-plane nanowires

“…C S  =  SV -2/3 and C B  =  BV -2/3 are shape-dependent factors which depend on the relative extension of the area of the lateral facets, S , and of the base area, B , of dots/wires. Previous results have shown that both the tensile strained Ge(113) [28] and the Ge(001) [29] surfaces have roughly the same surface energy value of about 65 meV/Å 2 ; therefore, for the sake of simplicity, we assume γ S  =  γ B  = 65 meV/Å 2 . Figure  10d shows the dependence of the total energy of dots/wires on the volume; in panel (e), their relative difference is plotted.…”

Understanding the effects of strain on morphological instabilities of a nanoscale island during heteroepitaxial growth

“…Because the system can be regarded as an axially symmetric problem, in the polar coordinate system, substituting Eqs. (18) and (19) into Eq. (20), one gets Then the elastic displacement can be solved as follows:…”

“…By using Eq. (18) and Eq. (19), we obtain the stress and strain components in the island and substrate as follows:…”

“…12,13 Besides the lattice mismatch, the origin of strain can also be external applied strain which has been achieved via surface engineering, including generating a surface strain field from buried dislocation networks, strained islands, or patterned topographic surface features. [14][15][16][17][18][19] Strain in nanomaterials is expected to be significantly enhanced relative to bulk materials, thus opening a fruitful direction for research. It is critical to characterize elastic deformation within nanoscale structures.…”