Aspect-ratio-dependent driving force for nonuniform alloying in Stranski-Krastanow islands

A semianalytical iterative method for determining the three-dimensional concentration profile minimizing the elastic energy in alloyed heteroepitaxial islands is developed. The method is shown to converge after only a few iterations (solutions of the elastic problem). Exploiting the reduced computational effort, easpect-ratio-dependent and average-concentration-dependent Si/Ge intermixing in alloyed SiGe/Si(001) islands is systematically investigated, considering realistic shapes. Islands providing the better elastic relaxation are also the ones able to lower the elastic load through nonuniform alloying more significantly. Universal behavior in terms of relaxation vs average concentration is demonstrated.