My answer is not very different from John's and maybe a little tangential, but just offering my take. Electrons are confined in any system,e.g., a packet of liquid, solid etc. Just the fact that there is phase boundary or a system boundary that confines the electron (think electron in some potential well) the energy levels become discretized. Depending on the number of atoms in the phase/system the number of energy levels becomes huge and the energy-level gap very small. In crystalline systems the periodic potential allows bands (groups of energy level) with large gaps in between that has attractive implications. Anyway going back, the quantum dots is just an idea to shrink the size of the phase, therefore increasing the separation between energy levels, as though you were approaching a single atom (probably the best quantum dot). If your quantum dots were 20 atoms the levels will be more separated than if your dot had 100 atoms. Remember also that the elementary band theory is based on single non-interacting electrons. There are other effects (electron-electron, electron-phonon) that one might need to account for. But in any case this confinement is not special to systems that have an underlying crystalline periodicity. That just allows more interesting features.