Composition evolution of quantum dots during the growth of solid films

This paper describes a simple mathematical model for the development of non-uniform composition during the growth of quantum dot (QD) islands (solid drops) on a substrate. The purpose of the model is to quantify a known phenomenon in such systems: deposition of pure germanium onto a silicon substrate results in a QD, which is not pure germanium. The intermixing is due to the interdiffusion between the wetting layer surrounding the island and the underlying substrate. Growth of the island occurs by surface diffusion of the intermixed wetting layer to the island surface, resulting in the growth of compositionally non-uniform islands. In this paper, we develop a simple model for the time evolution of composition in the wetting layer, which can then be used to determine the island composition. The resulting system is a history-dependent integrodifferential equation for the composition of the wetting layer. Numerical solutions were found and verified to be in good qualitative agreement with experimental results.