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Based on first-principles density-functional pseudopotential calculations, the growth of InAs on the GaAs(001) surface has been studied. By analyzing the free energies of the surfaces with different thicknesses of the InAs coverages, the critical thickness of the layer-by-layer (2D) to island (3D) growth mode transition is predicted to be around 1.5 ML. Comparing the total energy differences between layer-by-layer growth models and 3D island models, the mechanism of the 2D-3D growth mode transition near the critical thickness (theta(crit)) is studied which indicates that at the initial stage of InAs quantum dots formation, small 3D islands are formed randomly. (c) 2006 Elsevier B.V. All rights reserved.