Tuning and breakdown of faceting under externally applied stress

Abstract

The theory of thermodynamic faceting is developed for an epitaxial film grown coherently on a lattice-mismatched substrate. The situation is considered where the planar top surface of the epitaxial film in the absence of the lattice mismatch (Δa=0) is unstable against faceting, and the stable state of the surface is a periodic array of facets. It is shown that, for a finite lattice mismatch (Δa≠0), the continuous epitaxial film with a periodically faceted top surface is a metastable state of the heterophase system. The global energy minimum corresponds then to a periodic system of coherent strained islands. If attaining the global energy minimum is kinetically forbidden, the metastable continuous epitaxial film with a periodically faceted top surface is formed. In the case where the period of the faceted structure without external stress ${\mathit{L}}_0$ exceeds the order of ≊50 Å, the dependence of the period L on the lattice mismatch is determined by the linear theory of elasticity. The period L of the metastable faceted structure increases with ‖Δa‖ for both tensile and compressive mismatch-induced strain. The dependence of L on Δa gives a possibility of controlling the period of faceting by varying Δa. If the lattice mismatch exceeds a certain critical value [‖Δa‖>(Δa${)}_{\mathit{c}}$], the breakdown of formation of metastable faceted structures occurs; the metastable state disappears, and the surface shape is governed by kinetic mechanism.