Electron in Periodic Potential

ELECTRON IN PERIODIC POTENTIAL

In quantum free electron theory of metals the electrons were assumed to be moving in a region of constant potential and hence it moves freely about the crystal. But it fails to explain why some solids behaves as conductors, some as insulators and some an semiconductors etc.

Therefore instead of considering an electron to move in a constant potential, In Zone theory of solids the electrons are assumed to move in a field of periodic potential.

In a metal piece, the positive ions are arranged in a regular and proper order, therefore a periodic potential (i.e) the potential field which varies periodically with the same period as the lattice, exists in the metal. Also the potential is minimum near the centre of positive ions and is maximum between the centres of ions as shown in Fig. 1.13.

Therefore the potential energy of the electron near by the centre of positive ion is maximum and will not be able to move freely, but the electrons which are above these potential peaks are free to move inside the metal and hence they are termed as free electrons.