Explain the variation of Fermi level with temperature in an extrinsic semiconductors

In an extrinsic semiconductor, the Fermi level varies with temperature in the following way:

1. At Absolute Zero Temperature (0K): At this temperature, all the electrons are in the valence band and the Fermi level is near the donor energy level for n-type semiconductors and near the acceptor energy level for p-type semiconductors.

2. At Room Temperature: At this temperature, the electrons have enough thermal energy to jump from the donor energy level to the conduction band in n-type semiconductors and from the valence band to the acceptor energy level in p-type semiconductors. This causes the Fermi level to move closer to the conduction band in n-type semiconductors and closer to the valence band in p-type semiconductors.

3. At High Temperatures: At high temperatures, the semiconductor behaves like an intrinsic semiconductor as the number of thermally generated electron-hole pairs is much larger than the number of impurity atoms. The Fermi level moves towards the middle of the band gap.

In summary, the Fermi level in an extrinsic semiconductor moves from near the donor or acceptor energy level at absolute zero temperature to near the conduction band for n-type and near the valence band for p-type at room temperature, and towards the middle of the band gap at high temperatures.