Phase equilibrium and stability of elastically stressed heteroepitaxial thin films

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Abstract
The thermodynamic description and stability of constrained lattice-mismatched heteroepitaxial thin-film systems, in which the lattice parameter in the plane of the film is essentially fixed by that of the substrate, are examined for binary alloys and ternary III-V systems. It is shown that the crystallographic orientation of the substrate and the difference in the lattice parameter between the substrate and the thin films may significantly affect equilibrium phase compositions and volume fraction, and the relative stability of phases in two- and three-phase heteroepitaxial systems. Unlike the elastic effects usually associated with bulk coherent solids, stresses introduced by the substrate can shift the solvus line towards either the single-phase or two-phase regions, the magnitude of the shift depending strongly on both the crystallographic orientation and state of stress. Constrained thin-film heteroepitaxial systems are shown to comprise a special subset of coherent stressed solid systems for which the Gibbs phase rule governing the coexistence of phases is recovered and for which the common tangent construction to appropriate free-energy curves may be used to determine equilibrium phase compositions and stability.