Band Theory of Metals

What is Band Theory of Metals?

Metals conduct electricity with the help of valence electrons present in them. The atomic orbitals of the metals having the same energy combine to form molecular orbitals which are close in energy to each other so as to form a band. In case, the band is partially filled or it overlaps with another higher energy unoccupied conduction band, electrons can easily flow under an applied electric field showing high conductivity.

Let us take the example of sodium.

Sodium has an atomic configuration of 1s², 2s², 2p⁶, 3s¹. It has one unpaired electron in the 3s orbital. The 3s valence atomic orbital of sodium overlaps with another such orbital of the same energy to form molecular orbitals. The atomic orbitals continue to combine in same fashion forming a band. The energy spread of this band is calculated as the difference in energy between the most strongly bound “bonding orbital” and the highest energy “antibonding orbital”.

In other cases when the gap between the valence band and the conduction band (next higher unoccupied band) is quite high, electrons fail to jump from valence band to the conduction band. Such compounds show very less or no conductivity.

For example glass. When the gap between the valence band and conduction band is small, some electrons may jump from valence band to conduction band and thus show some conductivity. Such substances are known as semiconductors. For example silicon, germanium.

It is evident from the figure, in case of metal, there is no separation between the bands. This helps the incited electrons to easily move from one orbital to another and hence metals are good conductors of electricity. In the case of semiconductors, there is a small gap between the valence band and the conduction band.

Hence, only a small fraction of electrons (having sufficient energy) jumps when incited. However, we can increase the conductivity of such substances by increasing the temperature or doping. In insulators, the difference between the valence band and conduction band is very high. Hence, no conductivity is shown by such substances.