Surface energy effects on the self-assembly of epitaxial quantum dots

Epitaxial self-assembled quantum dots (SAQDs) result from Stranski-Krastanow growth whereby epitaxial 3D islands form spontaneously on a planar thin film. Common systems are GexSi1−x/Si and InxGa1−xAs/GaAs. SAQDs are typically grown on a (001) surface. The formation and evolution of SAQDs is governed in large part by the interaction of surface energy and elastic strain; however, the surface energy density is quite complicated and not well understood. Many growth processes take place at high temperature where stress and entropy effects can have a profound effect on the surface free energy. There are three competing theories of the nature of the planar (001) surface: I. It is a stable crystal facet. II. It is a stable non-faceted surface. III. It is an unstable crystal antifacet. Each leads to a different theory of the SAQD formation process. The first theory appears most often in modeling literature, but the second two theories take explicit account of the discrete nature of a crystal surface. Existing observational and theoretical evidence in support of and against these theories is reviewed. Then a simple statistical mechanics model is presented that yields a phase-diagram depicting when each of the three theories is valid. Finally, the Solid-on-Solid model of crystal surfaces is used to validate the proposed phase diagram and to calculate the orientation and height dependence of the surface free energy that is expressed as a wetting chemical potential, a wetting modulus and surface tilt moduli.