Chapter 29, Problem 77A

To determine

To Explain:The fermi energy level as it applies to energy-band diagrams for semi-conductors.

Explanation of Solution

Introduction:

As the temperature of a material is increased, electrons start to exist in higher energy states.Fermi energy level is the uppermost energy state which is occupied by electrons at absolute zero temperature in a material.

In pure or intrinsic semiconductors, the number of holes in the valence band is equal to the number of electrons in the conduction band. Thus, there is equal probability of occupation of energy levels in valence band and in conduction band. Therefore, the fermi level lies in the middle of the forbidden band. The fermi level in the middle indicates equal concentration of free electrons and holes.

  

In extrinsic semiconductors, the number of holes in the valence band is not equal to the number of electrons in the conduction band.Thus, there is unequal probability of occupation of energy levels in valence band and conduction band.Therefore, the fermi level lies close to the conduction band or valence band depending on the concentration of the electrons and holes.

In n-type semi-conductor, doped with a pentavalent impurity, more free electrons exists. Hence, the fermi level is close to the conduction band, whereas in p-type semiconductor, doped with trivalent impurity, number of holes in the valence band is more, so the fermi level is near the valence band.

  

Conclusion:

The position of the fermi level indicates whether the concentration of electron or hole is higher.