Geometrical Effects on the properties of 1D, 2D and 3D Quantum Dots Supercrystals

The breakthrough in the experimental techniques by the formation of artificial crystals based on quantum dots (QD) has generated the need of having theoretical calculations as feedback for pre-design the physical properties of new materials. We focus on the specific geometry of the III-V and II-VI isolated quantum dots by accurately calculating their eigen-energies and wave functions taking into account the finite confinement. In this way, we obtain the on site parameters for the tight binding band structure. In addition, the hopping parameters are taking from the electron wave functions overlap between next nearing neighbors by using the extended Hueckel method. We present the electronic band-structure for three geometries of the QD's in two crystalline structures. The optical behavior is accounted in two ways: first, by EELS describing the energy loss due to interaction between an electron beam and 2D quantum dots arrays and second through the microscopic calculation of the optical absorption of quantum dot chains. We analyze the optical properties of surfaces and chains. We found an interesting anomaly in the electronic structure of the arrays of conical QD's, which is due to their lower symmetry and it could be detected in IR optical experiments.