General
The bands of insulators are such that there
are two bands separated by a huge band gap: the lower one is the valence
band and the upper one is the conduction band. When each atom provides two
electrons per orbital, the lower band of orbitals is found to be full. The
result is that there is a band gap that separates the valence band from
the conduction band. Therefore, in order for conduction to occur, the
electrons must have enough energy to cross this band gap and most don't.
Therefore insulators have very poor conductivity.
The Band Theory Part of It!
In the above diagram is shown the schematic for the bands of an insulator. In insulators, the occupation of the bands is also controlled by the Fermi-Dirac distribution. The main difference here in comparison to metals is that the Fermi-Level is found in the middle of the band gap. If one observes the band gap, it is generally found that it is very large and hard for electrons to cross it. However, if one studies conductivity in insulators, it is observed that as temperature increases, the conductivity increases. This is a direct result of the electrons being thermally excited and being able to jump the band gap to get to the conduction band. However, even though some electrons make it to the conduction band with thermal excitation, these are few in number, which results in the poor conductivity in general. The figure below shows the thermal excitation that takes place with the result being that there is some occupation of the conduction band. An example of a semi-conductor is diamond.
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