Complete minigaps for effective-mass carriers in three-dimensional semiconductor superlattices

This paper examines the possibility of obtaining complete gaps in the density of states of effective-mass carriers in a semiconductor, at the conduction or valence band fundamental edge. The dispersion relations are defined for waves associated with the effective-mass electrons or holes in a direct-gap material periodically modulated on a length scale significantly larger than the base crystal interatomic spacing. The specific case of cubic interacting quantum dots of ${\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\mathrm{As}$ in a GaAs matrix is considered. A striking similarity between the effective-mass spectral density and the atomic gallium arsenide host electronic structure is found for an effective-mass superstructure derived from the zinc-blende crystal atomic arrangement. The charge carrier density has also been examined in order to shed some light on this strong similarity with atomic GaAs.