Islanding mechanism and band edges in InAs/GaAs (11n) nanostructures

Within the continuum elasticity theory, we investigate the substrate orientation effects on the Stranski-Krastanov (SK) growth mode and the band edges in InAs/GaAs (11n) nanostructures. Attending to the first part of the study, we estimate the transition thickness and the accumulated stress for substrate orientations (1 1 3) and (1 1 5) and we compare with the values obtained previously in InAs/GaAs (0 0 1) nanostructures. Assuming a coherent behavior at the substrate/film interface in the investigated substrate orientations, we consider a sigmoidal-type function for the dependence of the lattice parameter on the height. To evaluate the transition thickness, a minimization of the total free energy density with the slope is made. Similar to the orientation (0 0 1), in (1 1 3) and (1 1 5)-oriented substrates, two different stability regimes for the total free-energy density as well as for the accumulated stress are obtained. These regimes are directly related to the two stages of the SK growth mode. Although the relief strain mechanisms seem similar in all orientations, a delay in the 2D-3D phase transition is induced for high Miller indexes of the substrate. The non-rigid substrate approximation applied in InAs/GaAs (11n) nanostructures yields successful results for the transition thicknesses; the fraction of strained substrate being greater in InAs/GaAs (1 1 3). On the other hand, within our model, quantum dots formation is predicted for InAs/GaAs (1 1 1) heterostructures. Attending to the second, we find for all substrate orientations investigated, the strain-induced shifts lower the energies of the conduction band edges, while they raise the energies of the heavy- and light-holes band edges. In addition, the energy shifts are less significant for orientation (1 1 3), where the compressive stresses are smaller.