Elastic energy release rate of quantum islands in Stranski–Krastanow growth

Abstract

When constrained by a lattice-misfit substrate, a sufficiently thick epitaxial layer develops surface quantum islands (QIs) via mass transport as a thermodynamic process for energy minimization. By this process, the misfit strain energy is partially released, which serves as the driving force for island formation. In this work, we examine the elastic energy release rate (EERR, i.e., elastic relaxation energy per unit volume) of QI growth in multilayered heteroepitaxial structures under the condition of mass conservation. The analysis is based on a two-dimensional isotropic linear elastic continuum approach. A parametric study first is carried out to investigate the effects of various parameters on the variation of EERR of QI formation in an epilayer-substrate system. Furthermore, the EERR, which represents the energetics of global equilibrium, is applied to investigate the correlation of surface islands to buried seed islands in a multilayered heterostructure. The variation of EERR during nucleation of new surface islands shows a tendency of vertical correlation to buried seed islands in the isotropic heterogeneous system. This relationship of correlation does not alter with changing vertical distance between the surface and seed islands in the range examined.