Self-consistent calculation of the electronic structure and electron-electron interaction in self-assembled InAs-GaAs quantum dot structures

We have performed a detailed self-consistent calculation of the electronic structure and electron-electron interaction energy in pyramidal self-assembled InAs-GaAs quantum dot structures. Our model is general for three-dimensional quantum devices without simplifying assumptions on the shape of the confining potential nor fitting parameters. We have used a continuum model for the strain, from which the position-dependent effective mass and band diagram are calculated. The number of electrons in the dot is controlled by applying an external voltage to a metal gate on the top of a complete multilayer device containing a single dot. In order to determine the electron occupation number in the dot that minimizes the total energy of the system, we have adopted the concept of transition state as defined by Slater for shell filling in atoms. We have calculated the exchange and correlation terms of the many-body Hamiltonian using the local (-spin) -density approximation. By accounting for spins we have been able to determine the shell structure in the pyramid and to calculate the energy differences between the various spin configurations. We have also calculated the different contributions to the total electronic energy in the dot, i.e., the single-particle energies, the exchange-correlation energy, and the classical electrostatic electron-electron repulsion energy as a function of the gate voltage and number of electrons in the dot. Comparison with recent experimental data of Fricke et al. [Europhys. Lett. 36, 197 (1996)] shows good agreement.