Tuning and breakdown of faceting under externally applied stress

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 ({Δ}a=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 ({Δ}a{≠}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 L₀ exceeds the order of {}50 {}, 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 {}{Δ}a{} for both tensile and compressive mismatch-induced strain. The dependence of L on {Δ}a gives a possibility of controlling the period of faceting by varying {Δ}a. If the lattice mismatch exceeds a certain critical value [{}{Δ}a{}>({Δ}a)c], the breakdown of formation of metastable faceted structures occurs; the metastable state disappears, and the surface shape is governed by kinetic mechanism.In the case where the period of the faceted structure without external stress is L₀{}50 {}, the dependence of L on {Δ}a is determined by nonlinear elastic effects. The period L increases for one sign of {Δ}a up to the breakdown of formation of metastable faceted structures and decreases for the other sign of {Δ}a, where the macroscopic faceting transforms gradually into a microscopic surface reconstruction and the surface becomes apparently flat. The typical critical value of the lattice mismatch for nanometer-scale faceting varies from ({Δ}a/a)c{~}10^-4 for L{~}10³ {} to ({Δ}a/a)c{~}10^-2 {} for L{~}10 {}. A similar dependence of faceting on externally applied stress occurs for a loaded sample.