Electron in periodic potential

ELECTRON IN PERIODIC POTENTIAL

Band theory of solids (Zone theory)

The free electron theory explains the properties like thermal conductivity, electrical conductivity and specific heat of most of the metals.

But, it fails to explain why some solids are conductors, some are insulators and others are semiconductors.

A solution to this problem was given by band theory of solids and is called zone theory.

According to free electron theory, the potential energy of the electron inside the crystal through which an electron moves is supposed to be constant (zero). So it is completely free to move about in the crystal, restrained only by the surface of the crystal.

Postulates

1. According to band theory, potential energy of electron within the crystal is periodic due to periodicity of the crystal i.e., free electrons move inside periodic lattice field.

2. The potential energy of the solid varies periodically with the periodicity of space lattice 'a' which is nothing but interatomic spacing.

Inside a real crystal, the electrons (-) move through periodic arrangement of positively charged holes (+) as shown in the fig.(2.13a)

Fig. (2.13b) shows one dimensional periodic potential distribution for a crystal. It is assumed that the potential energy of the electron at the positive ion site is zero and is maximum when it is half way between the adjacent nuclei.