Comprehensive computational studies of the properties of semiconductor nanostructures such as InAs quantum dots on GaAs call for a combination of methods in order to cover all relevant aspects. It is our goal to investigate both the growth and atomic structure of InAs quantum dots, as well as their related electronic and optical properties.
The self-assembled quantum dot formation in the Stranski-Krastanov growth mode is governed by the energetic balance between strain relief and the energy cost due to formation of quantum dot side facets and edges. One way to investigate theoretically the energetics associated with island formation employs a hybrid approach [1,2]: surface energies and surface stress are calculated using density functional theory (DFT), taking into account the specific surface reconstructions. The bulk elastic energy in both the islands and the substrate is calculated within continuum elasticity theory, using the finite-element method. Both energy contributions are then combined in a scaling expression for the stability of islands of various shapes as a function of their size. Alternatively, a fully atomistic description can be achieved using carefully parameterized bond-order potentials [3]. In advantage over the hybrid approach, this atomistic approach also includes the energy cost due to dangling bonds at the edges of islands. Comparing the total energies of various island shapes, we find that a flat island shape with {137} facets is energetically preferable for small island volumes, while a steeper shape becomes energetically lower for larger islands, in agreement with recent experimental work.
Employing these bond-order potentials, the strain built up after overgrowth of the InAs islands with a GaAs capping layer can be described as well. In order to calculate the electronic states in such a system (consisting of more than 100.000 atoms), we fit the known band structures of GaAs and InAs to a sp3s* tight-binding description with interactions up to seconnd-nearest neighbors, which also accounts for the effect spin-orbit coupling. We analyse how the bond length and bond angle deviations from the ideal InAs and GaAs zinc-blende structure affect the bound state energies and the electron and hole wave functions confined in the quantum dot [4]. Moreover, we study the effect of post-growth annealing on the electronic and optical properties by modelling interdiffusion of Ga and In between the QD and the surrounding GaAs matrix. We find that the resulting blue-shift of the photoluminescence results partly from strain relief inside the QD, and partly from the chemical effect of exchanging In with Ga atoms [5]. Moreover, interdiffusion is predicted to strongly reduce the in-plane polarization asymmetry of the emitted light.
Through the combination of the methods described above, we get the complete view of the physics of self-assembled quantum dots, interrelating their electronic and optical properties with the conditions of their preparation.
[1] E. Pehlke, N. Moll, and M. Scheffler, Appl. Phys. A 65, (1997) 525.
[2] P. Kratzer and M. Scheffler, Comp. Sci. Eng. 3 (6), 16 (2001).
[3] T. Hammerschmidt, P. Kratzer, and M. Scheffler, in preparation
[4] R. Santoprete, B. Koiller, R.B. Capaz, P. Kratzer, Q.K.K. Liu, and M. Scheffler, Phys.
Rev. B 68, 235311 (2003).
[5] R. Santoprete, P. Kratzer, M. Scheffler, R.B. Capaz, and B. Koiller, Phys. Rev. B, submitt
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