Incorporating Surface Stress in Computations of Heteroepitaxial Quantum Dot Morphology

Abstract

Surface stress, which is an inherent property of several crystals, is expected to play a role in morphology of nanostructures. Here the authors describe how surface stress effects can be explicitly incorporated in the computation of quantum dot structure and evolution in coherent heteroepitaxial thin films. In the usual continuum formulation for surface evolution, surface stress enters as an additional contribution to the local chemical potential. Additionally, it modifies the film-vacuum interface boundary condition for the set-up of the elastic problem. The authors show how the resulting evolution can be computed order-by-order in the surface slope. The sign of the surface stress with respect to the mismatch affects the stability of the film to surface undulations. For the case of a positive-mismatched heteroepitaxial system, a tensile surface stress leads to film stabilization and increases the critical thickness for quantum dot formation in Stranski-Krastanov growth.