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.