The Fermi level in a semiconductor is the probability that energy levels in a valence band and conduction band in the atoms are occupied. At absolute zero temperature, a semiconductor acts as a perfect insulator. As the temperature increases, free electrons are made available. An intrinsic semiconductor is a pure crystal with no impurities or defect atoms. In an intrinsic semiconductor, the probability of occupation of energy levels in either the conduction band or the valence band are equal. The Fermi level of an intrinsic semiconductor lies between the valence band and the conduction band. This area between both bands is known as the forbidden band.
Where KB is the Boltzmann constant (1.3806503 × 10-23 m2 kg s-2 K-1), T is the absolute temperature of the intrinsic semiconductor, Nv is the density of states in the valence band, the hole concentration in the valence band is:
Where Nc is the density of states in the conduction band, the electron concentration in the conduction band is calculated:
The Fermi level for an intrinsic semiconductor is given as the average of the conduction band level and the valence band level.
A intrinsic semiconductor may be altered by adding controlled amounts of specific atoms, called dopants to the crystal. This alters the number of electrons in the conduction bands or electron holes in the valence bands.