Coupling of the morphological and compositional instabilities in a stressed alloy with a free surface

We give a unified thermodynamic treatment of the morphological and compositional instabilities of a nonhydrostatically stressed alloy with a free surface, applying in particular to lattice-mismatched semiconductor epitaxial films. Provided its stress free unit cell volume depends on composition, any such alloy is unstable with respect to a range of joint surface undulations and composition modulations. The modulations of lowest energy are exponentially attenuated normally to the free surface. The domain of existence of the MC instability is determined as a function of temperature and modulation wavenumber. The critical temperature for decomposition becomes infinite. The critical wavenumber is larger than for the pure morphological instability. Quantitative predictions are given for various semiconductor alloys.