Shape transition during epitaxial growth of InAs quantum dots on GaAs 001 Theory and experiment

For heteroepitaxial growth of InAs islands on GaAs 001 , a transition of shapes is observed experimentally by scanning tunnelling microscopy and analyzed theoretically in terms of the thermodynamic stability of the islands.The experiments show the co existence of small islands bounded predominantly by shallow facets of the 137 family and large islands that show a variety of steeper facets, among them the 101 , 111 , and bar 1 bar 1 bar 1 orientations. The calculations of island stability employ a hybrid approach where the elastic strain relief in the islands is calculated by continuum elasticity theory, while surface energies and surface stresses are taken from density functional theory calculations that take into account the atomic structure of the various side facets, as well as of the InAs wetting layer on GaAs 001 . With the help of the theoretical analysis, we show that the flat pyramids dominated by 137 facets are energetically favorable for small island sizes. Density functional calculations of the surface energy and surface stress of these facets show that their appearance is favored by the pronounced lowering of the 137 surface energy on the compressively strained side facets of the InAs QDs. For larger islands, a higher aspect ratio of about 0.3 is found to be preferable due to more efficient strain relaxation in the steep part of the island which acts as a thermodynamic driving force for the shape transition. Furthermore, our theoretical analysis shows that the change of island shape can be understood in analogy to a phase transition with an abrupt drop of chemical potential at the transition point, with important consequences for the growth kinetics of the island ensemble