Formation of the band gap

The figure shown above is the same as that of card6, but extended to even lower spacing. At these distances, the energy band structure depends on the relative positions of the atoms (the lattice and basis structure) and th atomic number, which determines the electronic contribution of each atom. Here, the actual structure of the bands has to be found by numerical/approximate solutions of the Schrodinger equation. As we can see, the combined s-p system shows forbidden gaps at some distances. If now the actual interatomic spacing happens to be as shown in the figure, the nearly continuous energy levels will develop a band gap, with two arms containing 4N states each. The lower arm (B) with 4N electrons occupying 4N states is called the valence band and the upper one 4N empty states, the conduction band.

Thus we find tht the single band that is formed appears to be two bands with a forbidden gap Eg as viewed around the lattice spacing that actually obtains in these crystals. The complete filling and completely empty states occur only at absolute zero temperature.