# What is the Fermi level?

As discussed in the 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 the remaining 4N states lie in the conduction band. At 0°K, all 4N states of the valence band are completely filled while 4N energy levels of the conduction band are entirely empty.

Therefore, out of the 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 the Fermi level' (Ep).

Since the probability is 50% for intrinsic semiconductors at 0°K, therefore, level (EF) located in the Centre is a 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 bands, thereby, fill some of the energy levels of the conduction band, which were otherwise completely empty.

Since 4N energy levels of the valence band are already filled and some energy levels out of 4N energy levels of the conduction band will be filled by donor electrons, therefore, the total number of filled energy states will be more than 4N.

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

### (B) P-type semiconductor

For intrinsic semiconductors, all 4N states of the valence band are completely filled by electrons. The addition of P-type impurity aids up acceptor atoms. These acceptor atoms absorb electrons from the valence band and make it partially empty.

Therefore, filled energy levels fall below 4N and the probability of filled states decreases below 50% and the Fermi level shifts downward and towards the valence band, Figure 1.22(b) Amount of shift depends upon the doping concentration.

## Salient features of Fermi level

1. Fermi level measures 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 chance of finding an electron is 50 %.
4. Doping the semiconductor with pentavalent impurity shifts the Fermi level towards the conduction band.
5. Doping with trivalent impurity shifts the Fermi level towards the valence band.

### Limitations of Terzaghi Theory

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