Insulators, semi-conductors, conductors

As discussed in card7, conduction and valence bands form in some materials. The figure above shows the configuration for insulators, semi-conductors and metals. In insulators, the band gap Eg is to the tune of 6 eV, which is quite large in comparison with the kind of energy that an electron may pick up from the random thermal fluctuation. So the electrons stay put in the valence band. Now, since there are no empty states of higher energy available in the valence band, and since the Pauli exclusion principle does not allow crowding of electrons into the higher energy states from the band, it is not possible for an electron to gain some K.E. and start moving (in order to move, the electron has to have higher energy than at rest, and it can get that energy only if it goes to a higher energy state, which is already filled in this case.) So we have an insulator as the conduction band is completely empty.

If the gap becomes about 1 eV, we have an insulator at zero Kelvin, which, however, can collect some thermal energy at normal ambient temperatures and hop across the gap into the conduction band. This creates and electron-hole pair, both of which can conduct current. This is a semi-conductor. When electrons in the valence band hop from atom to atom, the collective process, where a neighbouring atom gives up an electron which falls into the void left by the promoted electron and this continues like a chain, is called hole conduction. These are the intrinsic semiconductors and the electron and hole concentrations are the same.
In Ge, Eg ~ 0.785 eV and in Si, it is ~ 1.21 eV.

If the configuration is such that there is no gap between the valence and conduction bands, or an overlap, the electrons have plenty of near-lying available empty states at slightly higher energies and can conduct current. This is a conductor.

The band gap Eg has some temperature dependence because the inter-atomic spacing is a function of temperature due to the assymmetry of the pseudo-potential (where we try to mimic the effect of the Pauli exclusion principle by introducing artificial forces which try to prevent electrons from occupying the same state) in the crystal.