Nonlinear theory for epitaxial growth of semiconductor alloys on vicinal surfaces

A set of coupled nonlinear diffusion equations is derived for describing the epitaxial growth of semiconductor alloys on vicinal surfaces. The equations include diffusion and a quadratic interaction term to account for incipient island formation. A criterion is obtained for determining the temperature T_c at which growth becomes dominated by step advancement as a function of alloy composition, substrate temperature, and growth rate. The sensitivity of T_c to variations in the interaction parameters is briefly discussed.