The energy spectrum of electrons in a solid differs significantly from the energy spectrum of free electrons (which is continuous) as well as from the spectrum of electrons that belong to individual isolated atoms (which is discrete with a set of available levels); it consists of individual allowed energy bands separated by forbidden energy bands.

According to quantum-mechanical Bohr postulates, the energy of an electron can have strictly discrete values in an isolated atom (i.e. the electron may occupy one of the orbitals). In the case of a system containing several chemically bonded atoms, the electronic orbitals are split into a number in proportion to the quantity of atoms, thus forming the so-called molecular orbitals. With further growth of the system to the macroscopic level, the number of orbitals becomes exceedingly large, and the difference in energy between the electrons in the neighbouring orbitals becomes very small; thus, the energy levels form two sets of nearly continuous sets: energy bands.

The highest allowed energy band in semiconductors and insulators in which all energy states are occupied by electrons at 0 K, is called the valence band; the following band is called the conduction band. The conduction band of conductors is the highest allowed band occupied by electrons at the temperature of 0 K. It is by the relative positions of these bands that all solids are divided into the three major groups (see Fig.):

- conductors are materials in which the conduction band and the valence band are overlapped (there is no energy gap) to form a band called the conduction band (thus, the electron that receives any acceptable low energy can move freely between the bands);

- dielectrics are materials in which the bands are not overlapped and the distance between them exceeds 3 eV (an electron transfer from the valence band into the conduction band requires more power, so insulators conduct practically no electric current);

- semiconductors are materials in which the bands are not overlapped and the distance between them (the band gap) is in the range from 0.1 to 3 eV (an electron transfer from the valence band into the conduction band requires less energy than in dielectrics, so pure semiconductors conduct poorly).

The band theory is the foundation of the modern theory of solids. It led to understanding of the nature and explained the important properties of metals, semiconductors and insulators. The width of the “forbidden” band (the energy gap between the valence and conduction bands) is the key variable in the band theory; it defines the electrical and optical properties of the material. For example, in semiconductors, the conductivity can be increased by creating an allowed energy level in the band gap by doping, i.e. introducing additives into the base material to alter its physical and chemical properties. Such semiconductors are referred to as “impurity semiconductors”. This principle is used in production of all semiconductor devices: solar cells, diodes, transistors, solid-state lasers, etc. The transition of an electron from the valence band into the conduction band is called the charge carrier generation process (carriers of a negative charge are electrons and carriers of a positive charge are holes), and the reverse transition is called the recombination process.

The applicability of the band theory is limited due to the three main assumptions: a) the potential of the crystal lattice is strictly periodic; b) the interaction between the free electrons is limited to one-electron self-consistent potential (and corrections are described by means of the perturbation theory); c) the interaction with phonons is weak (and can be considered by the perturbation theory).