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The morphology of the InAs/GaAs(001) system has been imaged by atomic force microscopy (AFM) at different stages of the epitaxial growth from the initial formation of a pseudomorphic two-dimensional (2D) interace up to the self-aggregation of InAs quantum dots (QDs). The substrate texture and the dependence of the cation diffusion on the elastic strain field fully control the lateral ordering of the nanoparticles in the self assembling process and determine the final morphology of multistacked InAs QD arrays. © 2002 American Institute of Physics.