On the existence of localized states in quantum pillars

Abstract

We have investigated the localization of electrons in quantum pillars, i.e. in nanometric structures in which electrons are confined by 5 sides, but are free to communicate with a bulk substrate of the same material through the 6th side and hence can be considered as open from this side. All nanopillars produced by an etching top-down process conform to this physical model. At first sight, electrons in such structures should have an equal probability of being everywhere, so confinement effects and consequently band-gap changes should not be present. However, experimentally, confinement effects are observed. We show, by a proper effective mass equation analysis of the combined pillars and substrate system, that eigenstates with a high degree of localization exist in the pillars – irrespective of the height of the pillar. Moreover, the eigenenergies of these states are extremely close to the energies of the quantum boxes that would be produced if the pillars were closed by all six sides. This analysis provides the justification for the previous application of effective mass calculations on the pillars alone.