Band Theory of Solids The presence of periodic potential in a crystal leads to energy bands, which are essentially energy intervals between which energy levels are nearly continuous. In fig1b the resulting potential energy function for a row of atoms is shown. The inner electrons have allowed energy that are localized in the vicinity of the nuclei. By comparison the 3s electrons are not localized to any particular atom. This happens in a metal like sodium, where 3s energy levels (or wave functions) overlap to such an extent that allowed energy values of these electrons are virtually independent of position in the crystal and constitute a continuous band extending through the entire crystal.

Fig b1

In nonmetals, the broad bands that lie above the inner electron bands can be divided into two groups: the valance band, whose available states are occupied by valance electrons, and the conduction band, whose available states are occupied by electrons that can participate in electric conduction. These bands are separated; the difference between the lowest possible energy value of conduction band and the highest possible energy value of valance band is called band gap (see fig b2).

At absolute zero temperature, the available states in the valance band of a nonmetal are completely filled, while in the conduction band they are completely empty. At a higher temperature, the electrons that are sufficiently energetic overcome the gap. This happens in a semiconductor where the gap is small (~ 1 eV). Thus in a semiconductor, electrons are available for conduction at room temperatures. In an insulator the band gap is so large ( >3 eV) that no electron can overcome this gap at normal room temperatures.

In a metal either the valance band and conduction band overlap or it has partially filled valance band. Hence electrons in large number are available for conduction.