Energy Band Theory of Solids

ENERGY BAND THEORY OF SOLIDS

Energy band theory of solids plays a very important role in determining whether a solid is a conductor, insulator or a semiconductor. This theory explains how an energy band occurs in a solid.

(i) Free and bound electrons

In an isolated atom all the electrons are tightly bounded with the central positive nucleus and revolves around various orbits. The number of electrons at the outermost orbit are called valence electrons. In the outermost orbits, the attractive force between the nucleus and electrons will be very less, so that the electrons can be easily detached from the nucleus. These detached electrons from the outer most orbits are called free electrons. But as far as the innermost orbits are concerned, the electrons are tightly bounded with positive nucleus, and hence they are termed as bound electrons. The free and bounded electrons are shown in Fig. 1.29.

(ii) Energy levels

We know that each orbit of an atom has fixed amount of energy associated with it. The electrons moving in a particular orbit possess the energy of that orbit. The larger the orbit, the greater is its energy. So, the outermost orbit electrons possess more energy than the inner orbit electrons.

A convenient way of representing the energy of different orbits are called energy levels, as shown in Fig. 1.30. Let E₁ be the energy level of the K- shell, E₂ be the energy level of the M-shell, E₃ be the energy level of the L-shell and so on. The larger the orbit of an electron, the greater is its energy and higher is the energy level.

From the Fig. 1.30 it is clear that the electrons can revolve only in certain permitted orbits of radii r₁, r₂, r₃ ... and not in any arbitrary orbit. Since the electrons are not allowed inbetween the radii r₁ and r₂ or between the radii r₂ and r₃, etc., there won't be any electronic energy levels inbetween those radii, so called forbidden radii. These unallowed energy levels are called forbidden energy levels.

 (iii) Energy bands

It has to be noted that as long as the atoms are widely separated, they have identical energy levels. But, once the atoms are brought together the interatomic force of attraction between the atoms in the solid may modify the energy levels of a solid as energy bands.

Now let us discuss how energy levels of single free atom becomes energy bands in solids.

Let us consider two identical atoms of diameter(d) separated at a distance (r), so that the electronic energy levels of one atom [E₁¹ (K-shell) and E₂¹ (L – shell)] do not affect the electronic energy levels of the other atom [E₁² (K – shell) and E₂² (L-shell)] as shown in Fig. 1.31.

Note: In E₁¹, E₂¹, E₁², E₂²..., The subscript represents the Energy levels E₁, E₂, etc and superscript represents the atom- 1, atom- 2 etc.

Now, when we bring the atoms closer together, some force of attraction occurs between them and according to Quantum mechanics, their wave functions will start overlapping, Therefore when two atoms are brought closer, it does not remain as two independent atoms, rather it forms a single two-atom system with two different energy levels to form energy band as shown in Fig. 1.32.