7 x 7 reconstruction of Ge(111) surfaces under compressive strain

Strain-induced structure transformations on Si(111) and Ge(111) surfaces: a combined density-functional and scanning tunneling microscopy study

Si(111) and Ge(111) surface formation energies were calculated using density functional theory for various biaxial strain states ranging from -0.04 to 0.04, and for a wide set of experimentally observed surface reconstructions: 3 × 3, 5 × 5, 7 × 7 dimer-adatom-stacking fault reconstructions and c(2 × 8), 2 × 2, and √3×√3 adatoms based surfaces. The calculations are compared with scanning tunneling microscopy data obtained on stepped Si(111) surfaces and on Ge islands grown on a Si(111) substrate. It is shown that the surface structure transformations observed in these strained systems are accounted for by a phase diagram that relates the equilibrium surface structure to the applied strain. The calculated formation energy of the unstrained Si(111)-9 × 9 dimer-adatom-stacking fault surface is reported for the first time and it is higher than corresponding energies of Si(111)-5 × 5 and Si(111)-7 × 7 dimer-adatom-stacking fault surfaces as expected. We predict that the Si(111) surface should adopt a c(2 × 8) reconstruction when tensile strain is above 0.03.

First Principles Calculations of Surface Stress

Only recently have there been fully quantum-mechanical calculations of two-dimensional surface stress tensors. We have calculated total energies and stresses of semiconductor surfaces within the Local Density Approximation, using norm-conserving pseudopotentials. In order to hasten convergence of the stress with respect to basis size, it is useful to remove a fictitious tensile stress. We have calculated surface stress for the relaxed Si (111) 1×1 and 2×2-adatom surfaces, as well as for the relaxed Ge (111) 1×1 and 2×2-adatom surfaces. We have also calculated the surface stress for several chemisorbed systems, including Ga, Ge and As chemisorbed onto Si. We find a dramatic correlation between the electronic structure and chemistry of the surface, and its elastic properties.

Temperature-Dependent Strain Relaxation and Islanding of Ge/Si(111)

In order to understand Ge island nucleation and evolution, we have studied strain relaxation and clustering of Ge grown on Si(111) by molecular beam epitaxy (MBE) with in situ reflection high energy electron diffraction (RHEED), atomic force microscopy (AFM), and Rutherford backscattering spectrometry (RBS). Our goal is to tailor the size and density of the nanocrystals by controlling thermodynamics and kinetics. At low temperature (∼ 450°C), we observe a sharp 2D-3D growth mode transition after 2.5ML ±0.1ML (we define a thickness of 1ML to be one-third the length of the body diagonal of the Ge conventional unit cell), when transmission diffraction features appear in RHEED and the surface lattice constant begins to relax. The mechanisms of island growth and strain relaxation change with growth temperature. At ∼ 700°C, transmission diffraction spots never appear in RHEED for Ge/Si(111) and strain relaxation occurs gradually. After 37ML of growth, the apparent in-plane lattice parameter increases only 1.5% over that of the Si substrate. This behavior is explained by the different manner in which islands initially nucleate and grow in the two temperature regimes. At low temperature, small islands nucleate and grow on a relatively rough wetting layer (which itself provides preferential sites for dislocation introduction). The areal density of the small islands is relatively high. At high temperature, a small number of islands grow very large from the outset. A general model indicates how, at low temperature, the relative difficulty of overcoming the barrier to dislocation formation actually results in an apparent larger degree of strain relief than at high temperature.

Origin of the different reconstructions of diamond, Si, and Ge(111) surfaces

Ab initio calculations of the 2x1, c(2x8), and 7x7 reconstructions of the diamond, Si, and Ge(111) surfaces are reported. The pi-bonded chain, adatom, and dimer-adatom-stacking fault models are studied to understand the driving forces for a certain reconstruction. The resulting energetics, geometries, and band structures are compared for the elemental semiconductors with different atomic sizes, and chemical trends are derived. We show why the lowest-energy reconstructions are different for the group-IV materials considered.