Explain the Fermi level in semiconductor in case of intrinsic and extrinsic?

The Fermi level is a concept used to describe the energy level at which electrons in a material are distributed at a given temperature. It is named after the Italian physicist Enrico Fermi.

In the case of an intrinsic semiconductor, which is a pure semiconductor material with no impurities, the Fermi level lies in the middle of the energy band gap between the valence band (which contains electrons) and the conduction band (which is empty). At absolute zero temperature, the Fermi level is at the midpoint of the band gap. As the temperature increases, some electrons gain enough energy to move from the valence band to the conduction band, leaving behind holes in the valence band. This causes the Fermi level to shift towards the conduction band, but it still remains in the middle of the band gap.

In the case of an extrinsic semiconductor, which is a semiconductor material doped with impurities, the Fermi level is affected by the presence of these impurities. Doping introduces additional energy levels within the band gap, either above the valence band (for p-type doping) or below the conduction band (for n-type doping). These energy levels are associated with the impurity atoms and are called donor levels (for n-type doping) or acceptor levels (for p-type doping). The Fermi level now aligns itself with these impurity levels, depending on the type of doping. In n-type doping, the Fermi level is closer to the conduction band due to the presence of extra electrons from the donor impurities. In p-type doping, the Fermi level is closer to the valence band due to the presence of extra holes from the acceptor impurities.

In summary, the Fermi level in a semiconductor is a measure of the energy distribution of electrons at a given temperature. In intrinsic semiconductors, it lies in the middle of the band gap, while in extrinsic semiconductors, it aligns itself with the impurity levels introduced by doping.