Three-dimensional quantum-dot superlattices can be considered as nanocrystals. Spherical nanoparticles consisting of a big enough number (from 10 to 1000) of atoms or ions, which are connected with each other and are ordered in a certain fashion, can be considered as the structural units of such nanocrystals. Examples of nanocrystals that are of natural origin are the crystalline modifications of boron and carbon which have as their structural units the molecules B12 and C60. The boron molecule B12 consists of 12 boron atoms, and the carbon molecule C60, which is called fullerene, consists of 60 carbon atoms. The fullerene molecule resembles a soccer ball, i.e., it consists of 12 pentagons and 20 hexagons, with carbon atoms at their corners. These nanoparticles form face-centered superlattices with a period of about 1−10 nm. At these distances between molecules of C60 weak molecular forces, which provide the crystalline state of fullerene, act.

In addition to nanocrystals of natural origin, numerous artificial three-dimensional superlattices consisting of various types of nanoparticles have been fabricated. The variety of nanocrystalline structures as well as of conventional crystals is defined by the differences in the distribution of electrons over the quantum states of atoms. The most significant role in the formation of individual nanoparticles as well as of crystals is played by the electrons in the outer shells of atoms.