Stress and strain fields from an array of spherical inclusions in semi-infinite elastic media: Ge nanoinclusions in Si

Atomically resolved stress and strain fields from arrays of laterally ordered spherical Ge nanoinclusions in a semi-infinite Si(001) matrix are studied via atomistic simulations. We find that the hydrostatic stress and strain on the Si(001) matrix surface, induced by the inclusion buried at depth d, are tensile and follow the inverse cubic dependence for both small and intermediate d. The magnitudes of the stress and strain fields from inclusions of different volumes are found to be nearly proportional to the volume of the inclusion for large radii of inclusions, while for small radii the volume dependence overestimates the effect. Furthermore, we find that the magnitude of the stress and strain fields on the matrix surface is nearly proportional to the lattice mismatch between the inclusion and host material. The obtained simulation results are compared with the predictions of continuum-elasticity-based models and an overall good agreement is found.