Elements of Modern Physics
268
are applicable in different situations but lead to qualitatively similar results.
Brief descriptions of these approximations are given here.
Tight Binding Approximation
In this approximation, the crystal is formed by bringing together N atoms. When
the atoms are separated by a large distance, their energy levels are the same i.e.
degenerate. As they come close together, these levels are perturbed by
interactions between the atoms and the degeneracy is removed. Thus, there will
E
0
5
1 0
3p
3s
Interatomic separation in Å
(a)
– 2 /a
p
– /a
p
p /a
2 /a
p
2nd Brillouin
zone
1st Brillouin zone
2nd Brillouin
zone
(b)
Energy gap
10
20
30
E in eV
Fig. 8.6 (a) Energy bands in the tight binding approximation, (b) Brillouin
zones and energy bands in the nearly free electron approximation.
a = 2Å, V 1 = 1 eV.
be 2N levels for an s state and 6N levels for a p state (two spin states for each
electron). Since N is very large, one gets bands of closely-spaced energy levels,