Question

Solid-state physics, Band gap

a, How does the size of the band gap depend on the strength of the periodic potential?

b, Which type of material would you expect to have the stronger periodic potential, a metal or an insulator? Why?

Please explain thoroughly

Answer 1

The concept of periodic potential in solid state physics is used to determine the conductivity in semi conductors and insulators.

This is done using a model called Kroning Penney model.

The electrons are considered to be free particles trapped inside a potential well. This potential well is the space between the two atoms. It is the atoms (ions) that provide the potential. The derivation of the model is very complicated and long.

a) According to the model, the width of the allowed energy band increases and forbidden energy band decreases with an increase in the strength of the periodic potential P.

The size of the band gap is the width of the forbidden band. So, as P increases, band gap decreases.

b) The strength of the periodic potential is provided by the ions. In metals, there are a lot of free electrons, meaning that there are a lot of positive ions. In other words, the strength of periodic potential is high.

For insulators, the no of free electrons is very less. So, the no of ions and consequently the strength of the periodic potential will be less.