# Electrical conduction using band theory

The often told cause of conductor conducting electricity is their valence band and conduction band overlap and when an electric field is applied the electrons jumps into conduction band and electricity flows.I don' t get this how the jump of electrons from valence band to conduction band i.e,the next available energy band cause current to flow.I learnt electrodynamics using free electron sea model and now I am unable to harmonise the two.For example, Suppose we have sodium crystal which is a conductor.The valence band in this case will be the one due to 3s and conduction band 3p.How can a jump from 3s to 3p cause current flow?

• The jump doesn't cause the flow of current, rather it causes flow of current to be possible. Also isn't 3s the half-filled conduction band in sodium? – aditya_stack Jan 29 '20 at 17:23
• @aditya_stack Can you please elaborate?Actually I am not able to combine free electron theory with this band theory. – Sharad1 Jan 29 '20 at 18:36

In your example of a sodium crystal the 3s electrons are delocalised and their orbitals can be thought of as forming a, half filled, band. This is a case of metallic binding so there is not really a distinction between valence and conduction band and certainly there is no gap. Such a crystal conducts in the ground state.

The reason the conduction band can't contribute to conduction in the ground state is because all its states are empty. Since there are no carriers in those states, the total charge is 0, and so of course there can't be any current associated with it.

The reason the valence band can't contribute to conduction in the ground state is because all its states are occupied. For every electron moving in direction +x there is another electron moving in direction -x. So the net current is 0.

I don' t get this how the jump of electrons from valence band to conduction band i.e,the next available energy band cause current to flow.

If an electron is promoted from the valence band to the conduction band, then neither of those conditions is true any more.

The conduction band is no longer empty. The single carrier now found in the conduction band has free choice of what state to occupy and can move in essentially any direction it likes. If there's an applied electric field, that will tend to "push" it to drift in one direction (opposite the direction of $$\vec{E}$$, meaning current is in the same direction as $$\vec{E}$$, since it's a negative carrier) more than in others.

The valence band is no longer completely full. I won't go into the subtleties of the behavior of electron holes, but in a simplified view we can say that there's no longer a perfect balance between electrons with momentum in one direction and electrons with momentum in the opposite direction, and so the net current is no longer always 0. Again, if there's an applied electric field, the net current will tend to be in the direction of $$\vec{E}$$.

In the conduction band the electronic state is such that the electron can hop from one atom to another with non-negligible probability. Unlike an electron in the valance band which is more or less localised to a particular atom.

This is why electrons in the conduction band are more free and can have a net momentum in the direction of applied electric field.