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Multiscale Model of Germanium Quantum Dots in Silicon



David T. Read, Vinod K. Tewary


Atomic displacements, strains and strain energies in the neighborhood of near-spherical, coherent germanium ¿quantum dots¿ (QD) in crystalline silicon and near a {001} Si surface have been predicted by multiscale modeling, using a combination of classical molecular dynamics (MD) and Green¿s function (GF) techniques. The smallest QDs nearest the surface produces a characteristic pattern of out-of-plane surface displacement, namely, a depression or indent at the center of the peak. This feature was absent in the largest dot. For dots that are large (e.g., 8 nm diameter), and perhaps even for smaller dots close to the surface, the patterns of surface displacement are of a magnitude sufficient to be observed by advanced scanned probe force microscopy. Iterative force matching over a ¿shell¿ region of thickness a few lattice parameters joined the GF and MD solutions. A modified-embedded-atom-model interatomic potential was used in both analysis methods. Dots of four sizes were analyzed, ranging in diameter from 1.1 to 8.6 nm. The supercell size was 34.2 nm. Calculations for strains and displacements in the infinite solid were extended to the {001} surface of the semi-infinite solid using the scheme described previously. Atomic displacements in the infinite solid showed trends generally similar to the early estimate of Mott and Nabarro, but differed in detail, especially for the smaller dots. Both our calculated strain in the quantum dot and our far-field atomic displacements were smaller than the Mott-Nabarro estimate. Surface displacements were broadly similar in magnitude and shape to the classic isotropic continuum solution of Mindlin and Cheng. Different surface displacements occur along the and directions because of crystalline anisotropy. For the smallest dot, the elastic energy density at the surface shows a pronounced minimum directly above the center of the dot, while for the largest dot an energy maximum occurs at the projected center position.
Physical Review B (Condensed Matter and Materials Physics)


continuum, displacement, Green's function, lattice statics, MEAM model, molecular dynamics, scanned probe microscopy, strain energy, stress, surface
Created March 1, 2007, Updated January 27, 2020