Molecular-dynamics investigation of the surface stress distribution in a Ge/Si quantum dot superlattice

The surface stress distribution in an ordered quantum dot superlattice is investigated using classical molecular dynamics simulations. We find that the surface stress field induced by various numbers (from 1 to 9) of Ge islands embedded in a Si(001) substrate is in good agreement with analytical expressions based on pointlike embedded force dipoles, explaining the tendency of layered arrays to form vertically aligned columns. The short-ranged nature of this stress field implies that only the uppermost layers affect the surface growth and that their influence decreases rapidly with layer depth.