Question

the fermi energy of an intrinsic semiconductor is closer to the valence band than the conduction band true and false ?

Answer 1

Fermi level :

The probability of occupation of energy levels in valence and conduction band.

At absolute zero temperature, the intrinsic semiconductor is a perfect insulator.

However as temperature increases holes and electrons are generated.

In intrinsic semiconductor, the number of holes in valence band equals the number of electrons in conduction band.

Therefore the probability of occupation of energy levels in valence band and conduction band are equal.

The fermi energy therefore lies at the middle of the forbidden gap and hence it is equidistant from the valence band and conduction band.

Answer 2

Before coming into any conclusion, first we have to understand Fermi energy.

From statistical mechanics we know that-

                           $f(E)= \frac{1}{1+e^(E-E_{f})/kT}$

Here f(E) is called the probability of occupancy of the state with energy E.

$E_{f}$ is called as the Fermi level.

T stands for absolute temperature and k stands for Boltzmann's constant.

From above we see that at absolute zero temperature , the probability is 1 for E < $E_{f}$ and 0 for E> $E_{f}$

For T > 0 K, f(e) = 0.5 for $E=E_{f}$.  Hence, the Fermi level is defined as the level for which the probability of occupancy is half for a finite non zero temperature .

In an intrinsic semi conductor, the hole concentration is equal to the electron concentration.Hence, the number of electrons in conduction band is equal to number of holes in valence band.

Hence, the Fermi level will lie near the middle of the forbidden energy gap i.e the Fermi level will be just at the middle of valence band and conduction band.