Multiscale model of near-spherical germanium quantum dots in silicon

Atomic displacements, strains and strain energies in the neighbourhood of near-spherical, coherent Ge 'quantum dots' (QD) in crystalline Si and near a {001} Si surface have been predicted by multiscale modelling, by use of a combination of classical molecular dynamics (MD) and Green's function (GF) techniques. The model includes the nonlinear effects at the GeSi interface and allows the boundary of the system to be placed outside the two million atom host crystallite. A modified-embedded-atom-model interatomic potential was used for both MD and GF calculations. Dots of four sizes were analysed, ranging in diameter from 1.1 to 6.5 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. Surface displacements were broadly similar in magnitude and shape to the classic isotropic continuum solution of Mindlin and Cheng. For large (e.g. 6.5 nm diameter) near-surface dots, the surface displacements are of a magnitude sufficient to be observed by advanced scanned probe microscopy