Morphological instability theory for strained alloy film growth: The effect of compositional stresses and species-dependent surface mobilities on ripple formation during epitaxial film deposition

Abstract

We develop a continuum model for the deposition of strained alloy films. The model includes the effect of stresses due to misfit and stresses due to composition gradients when the alloy components have different sizes. Two key features of our treatment are the derivation of chemical potentials for each alloy component on the surface, and the description of the surface diffusion of each species. From a linear stability analysis we characterize the effect of misfit strain, compositional strains, and different mobilities of the alloy components on the morphological stability of strained alloy film growth. We describe six basic cases, identifying general trends and physical mechanisms. In the most general case, we find that the interaction of misfit strains, solute strains, and mobility difference can lead to a complete suppression of the linear instability. This stabilization occurs for compressive misfits when one component is large and slow relative to the other; and for tensile misfits when one component is large and fast relative to the other. We apply our predictions to the growth of strained SiGe films and find that many of the observed trends can be explained by considering the limit that the diffusivity of Ge is much larger than that of Si. In particular, our results include a direct prediction of the wavelength of the instability (scaling inversely with film composition), an asymmetry of the instability with respect to the sign of the misfit for Si0.5Ge0.5 films, and an approximate (misfit) -4 scaling of the kinetic critical thickness for SiGe films on Si substrates.