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Abstract:
Semiconductor nanostructures, and particularly quantum dots (QDs), have promising potential for technical applications such as light-emitting diodes, lasers, new devices, and quantum computers. But the big number of QDs needed, less than billions are hardly useful, is far beyond the means of normal manufacturing methods. For this nanotechnology to prevail, the QDs have to build themselves by self-assembly and self-organization. In this work, we study the growth of InAs QDs on GaAs substrates.
For this purpose we developed a many-body potential of the Abell-Tersoff type that is able to account for the energetic balance of strain relief and QD side-facet formation during QD growth. It simultaneously captures many microscopic quantities of In, Ga, As, GaAs, and InAs bulk phases, as well as GaAs and InAs surface structures as obtained from experiment and density-functional theory (DFT) calculations with good overall accuracy. Its predictions for biaxial strained GaAs and InAs are in good agreement with DFT calculations and analytic results of continuum-elasticity theory. Based on recent STM results, we set up detailed atomic structures of InAs QDs with In-As wetting layers and homogenous InAs films on GaAs, relax them with our potential, and compare the resulting total energies. We show that the lateral elastic interaction of `hut'-like QDs dominated by {317} facets is significantly larger than that of `dome'-like QDs dominated by {101} facets. A strain-tensor analysis suggests that this effect is due to the relative orientations of the QD side facets to the elastic principal axes. Our calculated onset of the Stranski-Krastanov growth mode with respect to the InAs coverage is in good agreement with experimentally deduced values. The critical nucleus for QD formation is approximately 70 In atoms in size and poses an energy barrier of 5.3 eV. Furthermore, we can explain the experimentally observed shape sequence of `hut'-like QDs and `dome'-like QDs through the finding of distinct stability regimes. The regime separation depends strongly on the chemical potentials and the QD density. The experimental finding of vertical growth correlation in QD stacks can be explained by a distinct minimum in the potential-energy-surface (PES) of freestanding QDs in different lateral positions above overgrown QDs. This effect vanishes with increasing distance between the stacked QDs. The energy gain observed in our calculations can lower the energy barrier for QD formation to 3.5 eV and the size of the critical nucleus to only 25 In atoms.
Additionally, we calculated the PES for In adsorption on surfaces that correspond to major side facets of `hut'- and `dome'-like QDs by means of DFT to study possible kinetic effects. The dominating diffusion paths are perpendicular and parallel to the QD contour lines on {317} facets, but only perpendicular on {101} facets. The In incorporation on {317} facets could be kinetically limited due to the high barrier of approximately 1 eV for breaking As dimers. The diffusion barriers on {101} facets are lowered near the bottom of `dome'-like QDs, which supports the interpretation of the {317} facets on top as kinetic effect.
