Chapter 29, Problem 76A

To determine

To Explain:Pauli’s exclusion principle, Wolfgang Pauli’s life and his contribution to science, and the application of exclusion principle to the band theory of conductors, especially in semiconductors.

Explanation of Solution

Introduction:

According to Pauli’s exclusion principle, two or more indistinguishable fermionscannot simultaneously have the same quantum state within a quantum system.

Wolfgang Ernst Pauli was an Austrian physicist and was also one of the pioneers of quantum physics. In 1945, he was nominated by Albert Einstein himself for the conclusive contribution through the discovery of a new law-the exclusion principle. Wolfgang Pauli received the Noble Prize in Physics. The principle involved spin theory, which is the basis of a theory of the structure of matter.

Because of Pauli’s exclusion principle, no two electrons of the same spin can occupy the same quantum state. Electrons want to be in the lowest energy state possible, so they first fill-up the valence band (filing the lower states first) and then the conduction band.

For the electrons to enter the conduction band from the valence band, they should have enough energy to jump the energy gap.

In case of conductors, the conduction band and valence band overlap. Thus, there is free motion of electrons of valence band in partially filled conduction band.

In case of insulators, the conduction band is completely empty and the energy gap between the valence band and conduction band is of about $6\text{ eV}$ . Due to large energy gap, no electrons are promoted to the conduction band and the valence remains completely filed.

In case of semiconductors, there is energy gap of $\text{1 eV}$ approximately between the empty conduction band and the valence band.On gaining energy, the electrons cross over to the conduction band. The electrons leaving the valence band leave behind equal number of vacant sites called holes, which have positive charge.