Kinetic Monte Carlo model of self-organized quantum dot superlattices

We study a model of self-organized growth of quantum dot superlattices using spacer layers of Si with Ge islands buried inside. At each new spacer layer, Ge atoms are deposited on the new Si surface with a flux F. These atoms diffuse on the Si surface with diffusion constant D. But the diffusion of these Ge atoms is biased due to the strain field of the buried Ge islands in the previous layer. When these diffusing atoms meet one another they nucleate into islands which grow by capturing other adatoms. When the Ge coverage reaches a fixed value Θ, these islands are buried under Si up to a thickness L to complete a new spacer layer. We find that after many successive spacer layers both the island size distribution and the island spacing become more uniform. However, the island spacing is controlled by the ratio $D/F$ rather than by the spacer thickness L. Also the island density ${\mathit{\rho }\mathit{\sim }\mathrm{}(\mathit{D}/\mathit{F})\mathrm{}}^{1/4},$ as in the case without strain, but with a different prefactor.