Band Theory of Conduction in Solids

Band Theory of Conduction in Solids
In this theory, all materials have two bands, the valency band and the conduction band separated by a gap called the forbidden gap. The conduction band is a high energy band while the valency band is a low energy band where electrons are easily found. As the name suggests, the forbidden gap cannot have electrons- electrons can only be found in the valency or conduction band. 

The conductivity of a material depends on the availability of electrons in the conduction band. This means that a material only conducts if there are electrons in the conduction band. However, it should be understood that electron would always occupy the low energy valency band-naturally.

Therefore, materials can be classified as conductors, insulators and semiconductors depending on the distance separating the bands (the forbidden gap) and the possibility of getting free electron in the conduction band.

In insulators the electrons in the valence band are separated by a large gap from the conduction band, in conductors like metals the valence band overlaps the conduction band, and in semiconductors there is a small enough gap between the valence and conduction bands that thermal or other excitations can bridge the gap. With such a small gap, the presence of a small percentage of a doping material can increase conductivity dramatically.

Band theory in Conductors 

In conductors, the forbidden gap is so small that the gaps overlap.  Since the gaps overlap, the electron in the valency band can easily move into the conduction band and are free and mobile to conduct electric current. No energy is required to overcome the forbidden gap. Hence, in terms of the band theory of solids, metals are unique as good conductors of electricity.

One unique property of conductors is that their conductivity decreases with increase in temperature. When conductors are heated, the present free electrons gain more kinetic energy increasing their collision with each other. These collisions instead increase the materials resistivity to electric current flow which requires that the available free electron flow in one specific direction.

Band theory Insulators

In insulators, there is a large forbidden gap between the valency band and the conduction band. All electrons are in the valenvy band and a large energy would be required to overcome the wide forbidden gap.  This way, insulators cannot conduct electric current.

The only way to help push electrons into the conduction band would be increasing temperature for the electrons to overcome the forbidden gap, but however, insulators will break (burn out) before the this happens- no condition will move electrons in valency band into the conduction band hence remains insulators at any given temperature.

Band theory Semiconductor 

 In semiconductors, the forbidden gap is bigger than that in conductors. When the bands are separated, electrons-under normal conditions- are found in the valency band. With absence of electrons in the conduction and at low temperatures, semiconductors are insulators; their resistance is very high.

When the temperature is increased, the electrons in the valency band gains kinetic energy. If the gained energy is large enough to overcome the forbidden gap, the electrons move into the conduction band increasing its electrical conductivity.(See how semiconductors conduct by doping)