What Is Energy Band Theory?

Electrons of an isolated atom are bound to the nucleus, and can only have distinct energy levels. How ever, when a large number of atoms, say, are brought close to one another to form a solid, each energy level of the isolated atom splits into N sub-levels, called states, under the action of the forces exerted by other atoms in the solid. These permissible energy states are discrete but so closely spaced that they appear to form a continuous energy band. In between two consecutive permissible energy bands, there is arrange of energy states which cannot be occupied by electrons. These are called forbidden energy states, and its range is termed as forbidden energy gap.

The electrons in the outermost shell of an atom are called valence electrons and the energy band occupying these electrons is known as valence band. It is obviously the highest occupied band. It may be either completely filled or partially filled with electrons and can never be empty. The band above the valence band is called conducting band. In conducting band, electrons move freely and conduct electric current through solids. That is why the electrons occupying this band are known as conductive electrons or free electrons. Any electron leaving the valence band is accommodated by this band. It may be either empty or partially filled with electrons. The bands below the valence band are normally completely filled and as such play no part in the conduction process.

Thus, while discussing the electrical conductivity we will consider only the valence and conductive bands.Insulators are those materials in which valence electrons are bound very tightly to their atoms and are not free. In terms of energy bands, it means that an insulator has an empty conductional band, a full valence band and a large energy gap between them.
Conductors are those which have plenty of free electrons for electrical conduction. In terms of energy bands, it means that conductors are those materials in which valence and conduction bands largely overlap each other.

According to the energy band theory, the energy levels split into many closely-spaced levels which they define a band. There are various bands, but most are completely filled or empty. The two at the boundary between filled and empty, determine behaviors of insulators, metals and semiconductors.

At zero temperature, the levels are filled by electrons up to Fermi energy, above which all levels are vacant. If the Fermi level is at the top of a band, the material is an insulator and filled bands are called valence bands. If that level is above the bottom of a band, it narrates a "conduction band" which is populated by electrons which are free to move.