Electron states in a quantum dot in an effective-bond-orbital model

The electronic-level structure in semiconductor quantum dots is investigated in a tight-binding framework. The energy levels and wave functions of GaAs and CdS crystallites containing up to ∼4000 atoms are calculated using an effective-bond-orbital model. The results obtained for GaAs crystallites by using parameters that accurately reproduce the band structure near the Γ point are compared with those obtained by calculations based on a multiband effective-mass theory. The effective-mass approximation (EMA) is found to correctly describe the qualitative features of the level structure, such as the bunching of levels and the spatial dependence of the wave functions. However, for very small particles the EMA grossly overestimates the confinement energies mainly because of the deviation of the bulk band structure from parabolic dispersion at high energies. For CdS crystallites we use a parametrization scheme that reproduces the main features of the bulk band structure throughout the Brillouin zone, and compare the results with those obtained by the multiband EMA, as well as with experimental data on interband transitions.