The growth of Si nanocrystals from a Si-rich, oxyde matrices, e.g. those obtained from thermal treatment of an amorphous or organic (sol-gel) silica-based glass, is a subject with both fundamental and applied science implications. In particular, nanocrystals can be precipitated from the Si-rich matrix with the simultaneous addition of foreign species, such as Er atoms, so as to exploit at the same time the effects of quantum confinement and active doping. Experiments have shown that the optical gain of such systems can be improved by orders of magnitude, therefore opening the way to all-silicon optoelectronics. However, the detailed thermodynamics and kinetics of the precipitation and aggregation is not understood up to date.
With the aim of elucidating the role of interfacial interactions on the Si nanocrystal final shape and size, we used molecular dynamics simulations based on empirical potentials to study the equilibrium structures of Si nanocrystals embedded in an amorphous glass.  Atoms at the nanocrystal-glass interface were allowed to interact via mixture of Stillinger-Weber and BKS potentials, while assigning an effective charge to surface Si atoms, adjusted so as to reproduce qualitative results from ab initio calculations.
We calculated the relaxed, minimum energy structures of free-standing Si clusters of different diameters, going from about 3 to 5 nm, and found them to be spherical up to the maximum sizes studied. Both the static structure factor and phonon spectra indicate that the surface layer of the spherical Si cluster is more mobile than the bulk, and tends to be rather disordered. Subsequently, clusters of similar volume, but with either spherical or faceted shapes, were inserted into the a-SiO2 matrix, and their free energies were calculated in the quasi-harmonic approximation. Such a calculation allows to assess the size limit above which the clusters prefer a faceted shape, under the constraint and stress of the surrounding matrix.

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