STATISTICS OF CHARGE CARRIERS IN A DEGENERATE AND NON-DEGENERATE SEMICONDUCTOR

Abstract

Electrons in the conduction band and holes in the valence band can be considered as an ideal Fermi gas. In semiconductors at not very low temperatures, the kinetic energy of electrons is greater than the Coulomb energy, so electrons can be considered as free. For an ideal Fermi gas, the probability of filling a state with energy E at temperature T is found using the Fermi distribution.
For a degenerate and non-degenerate semiconductor, expressions have been found for calculating the concentrations of charge carriers, electrons in the conduction band, and holes in the valence band, when the position of the Fermi level is known. The expressions for the concentrations of electrons and holes are greatly simplified if the semiconductor is non-degenerate.