In recent technological developments Si-based nanostructures have been widely investigated and utilized in many advanced applications, i.e. in optoelectronics, photonics and nanomechanics: typically, crystalline nanograins are dispersed into a silicon matrix in order to obtain desired physical properties such as the optical response, the quantum efficiency and the effective elastic moduli of different systems. The typical sizes of such nanostructures can range from the microscale to the nanoscale, generating several difficulties in the applications of the standard continuum approach to analyze the physical system response. From the mechanical point of view, the classical Eshelby theory describing the behavior of an inhomogeneity embedded in a matrix, does not take into consideration the actual size of the system at all, being this continuum approach a scale-free theory. Therefore, the atomistic structure of the medium is not considered and the results of the elasticity theory are meaningful only for geometrical structures ranging from the mesoscale to the macroscale. When the size of the embedded particles is comparable with the inter-atomic distance of the crystal lattice such results lose their validity and the atomistic simulation can be used to investigate the response at the nanoscale. In the present work we draw a comparison among the continuum theory and molecular dynamics results for Si-based composite systems formed by crystalline (or amorphous) inclusions embedded in a crystalline (or amorphous) bulk matrix. We performed a large campaign of simulations with decreasing radius (starting from a quite macroscopic one) of the cylindrical (or spherical) inhomogeneity. In particular, we observed a characteristic size of the embedded inhomogeneity, which represents the threshold of applicability of the Eshelby theory predictions.  Moreover, we obtained the behavior of the elastic fields under such a scale threshold, for different properties of the involved phases.

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1. Defects in silicon nanocrystals embedded in amorphous silicon oxide
2. Growth phenomena and optoelectronic properties of mixed-phase amorphous-crystalline nanosystems