Kinetic instability of semiconductor alloy growth

A kinetic theory of the instability of homogeneous alloy growth with respect to fluctuations of alloy composition is developed. The growth mechanism studied is the step-flow growth of an alloy from the vapor on a surface vicinal to the (001) surface of a cubic substrate. The epitaxial growth implies that the adsorbed atoms migrate on the surface during the growth of each monolayer, and that their motion is “frozen” after the completion of the monolayer. “Frozen” fluctuations of alloy composition in all completed monolayers create, via a composition-dependent lattice parameter, an elastic strain that influences the migration of adatoms of the growing monolayer. The migration consists of diffusion- and strain-induced drift in an effective potential. For temperatures lower than a certain critical temperature $T_c,$ strain-induced drift dominates diffusion and results in the kinetic instability of the homogeneous alloy growth. In an approximation linear in the fluctuation amplitude, the instability means the exponential increase of the fluctuation amplitude with the thickness of the epitaxial film. It is shown that the critical temperature of the kinetic instability $T_c$ increases with the increase of elastic effects. The wave vector ${\mathbf{k}}_c$ of the most unstable mode of composition fluctuations is determined by the interplay of the anisotropic elastic interaction and the anisotropic diffusion of the adatoms on a stepped vicinal surface. The direction of the wave vector ${\mathbf{k}}_c$ differs from the lowest-stiffness direction of the crystal. Regions in k space of both stable and unstable modes are found by model calculations.