We show that the role played by surface energy in the total-energy balance between the initial twodimensional ͑2D͒ state and the final three-dimensional ͑3D͒ state is of prime importance to explain morphologies observed during the molecular-beam epitaxy growth of strained materials. This was established by analyzing differences in 2D-3D transition onsets for 2% mismatched In x Ga 1Ϫx As films grown on InP͑001͒ substrates when changing the mismatch sign ͑compression or tension͒, the film doping, and the type of surface stabilization ͑anion or cation͒. The 2D-3D onsets were measured by reflection high-energy electron diffraction and the corresponding surface morphologies characterized by scanning tunneling microscopy.

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Strained In 1Ϫx Ga x As epilayers have been grown on InP͑001͒ by molecular-beam epitaxy both for 2% compressive strain (xϭ0.18) and 2% tensile strain (xϭ0.75). After an initial stage of layer-by-layer growth, coherent three-dimensional structures were observed by scanning tunneling microscopy in both cases. The shape of these three-dimensional structures is determined by elastic relaxation of the strained layers: while compressive strain favors convex step curvatures leading to three-dimensional islands, a tensile strain favors concave curvatures leading to three-dimensional holes. It is shown using a two-dimensional Laplace-Young relationship that a tensile-step specific stress stabilizes the step curvature.