Let us take a system of N electrons with a distance a between the atoms and a total length of L. We can calculate that if each atom has Z electrons contributing to the gas of electrons, then there are N=Z(L/a) electrons. The momentum, PF, at the Fermi Energy EF is equal to (pi/2a)Z. In a metal with one free electron per atom PF =(pi/2a) and the band would be partly filled and so conduction could easily occur and would be strongest at a low temperature.
In another solid, possibly a semiconductor that has 2 electrons in the external shell, the momentum at the Fermi Energy would be PF =(pi/a). There would be a gap, Delta, between the end of this band and the next level, but if this was small then there would be the possibility that as the temperature was increased, some electrons would jump up over the gap. Conduction here increases as the temperature increases because hot electrons move around more than cold ones do.
The bands introduced above have names that describe their functions:
The energy gap of an insulator is at least 5eV and aften more like 10eV. Band gaps in intrinsic semiconductors are of the order of 1eV and can reach up to 4eV or thereabouts.
PHYSICS 3H- HOMEPAGE