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Research Activities > Programs > Nonequilibrium Interface and Surface Dynamics 2007

A Level-Set Method for Self-Organized Pattern Formation during heteroepitaxial growth

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A Level-Set Method for Self-Organized Pattern Formation during heteroepitaxial growth

Professor Christian Ratsch


Abstract:   We have developed an island dynamics model for heteroepitaxial growth that employs an island dynamics model with the level-set technique in combination with a fully self-consistent elastic model. At every timestep in the simulation, we solve the elastic equations for the entire system. This is possible within our approach because the numerical timestep can be chosen much larger than in an atomistic simulation. At every lattice site strain then changes the local bonding, and thus the potential energy surface for adatoms and the microscopic parameters of the simulation. In particular, strain changes the diffusivity of adatoms and enhances the rate of detachment from island edges. We show that the island size distribution becomes more regular when strain increases. The reason is that bigger islands are typically more strained than smaller islands, and thus their growth is slowed down. We also present results that show how strain induced by buried islands influences the nucleation of new islands in higher layers, and in fact leads to a regularization of stacked islands or quantum dots. Our results indicate that for stacked quantum dots that are separated by a buffer layer, there exists an optimal thickness of the buffer layer for best regularization of the stacked dots.

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