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What is Fermi level

As discussed in energy band theory of crystals, we know that N energy levels exist for an intrinsic semiconductor. Out of which 4N energy levels (or energy states) lie in the valence band and remaining 4N states lie in the conduction band. At 0°K, all 4N states of valence band are completely filled while 4N energy levels of conduction band are completely empty. Therefore, out of allowed 8N energy levels, only 4N energy levels are filled. Thus, the probability of energy levels being filled is 50% (4N/8N-05) This probability is shown in the energy band diagram by a new imaginary energy level called Fermi level' (Ep). 

Since probability is 50% for intrinsic semiconductor at 0°K, therefore, level (EF) is located in the Centre is forbidden energy gap [Figure 1.21 (a)] For a probability of 70% and 30% the Fermi levels will be located as shown in figure 1.21(b) and figure 1.21(c) respectively.

Fermi Level In Extrinsic Semiconductors

(A) N-type semiconductor

Consider An N-type semiconductor. At room temperature, donor atoms ionize. These additional electron jump conduction band, thereby, filling some of the energy levels of the conduction band, which were otherwise completely empty. Since 4N energy levels of valence band are already filled and some energy levels out of 4N energy levels of conduction band will be filled by donor electrons, therefore, a total number of filled energy states will be more than 4N.

Thus for N-type semiconductor, out of 8N energy states, more than 4N energy levels are filled, therefore, the probability is more than 50% and Fermi level shifts towards conduction band [Figure 1.22(a)]. Amount of shift depends upon the level of doping.

(B) P-type semiconductor

For intrinsic semiconductor, all 4N states of valence band are completely filled by electrons. Addition of P-type impurity aids up acceptor atoms. These acceptor atoms absorb electrons from valence band and make it partially empty. Therefore, filled energy levels fall below 4N and probability of filled states decreases below 50% and Fermi level shifts downward and towards valence band Figure 1.22(b) Amount of shift depends upon the concentration of doping.

Salient features of Fermi level

1. Fermi level is a measure of the probability of occupancy of the allowed energy states by electrons.
2. Fermi level is the highest energy level that an electron can occupy at 0° K.
3. Fermi level is the energy level at which the chances of finding an electron is 50 %.
4. Doping the semiconductor with pentavalent impurity shifts the Fermi level towards conduction band.
5. Doping with trivalent impurity shifts the Fermi level towards valence band.