Question

Fermi level for intrinsic semiconductors lies at :
A) The middle of the conduction band and valence band.
B) Near the valence band
C) Near the conduction band
D) None of the above

Answer 1

Hint:
In intrinsic semiconductor or which is also called a pure semiconductor , the number of holes in the valence band is equal to the number of electrons in the conduction band. Hence the probability of finding an energy level in the conduction band and valence band are equal .

Complete step by step solution:
     

Intrinsic semiconductors: also called an un doped semiconductor ,it is a pure semiconductor without any significant impurities present .The number of charge carriers is therefore determined by the properties of the semiconductor itself instead of the amount of impurities .
In the language of science we can say that , holes in the valence band are vacancies created by electrons that have been thermally excited to the conduction band, as compared to doped semiconductors where holes or electrons are supplied by an outside atom acting as an impurity.

In the given figure , we have tried to show the conduction band ,valence band and the position of Fermi level in an intrinsic semiconductor.
Position of the Fermi level lies in the middle of the conduction band and valence band because the number of holes and electrons are almost equal in numbers in intrinsic semiconductors .

Therefore , option 1 is correct.

Note:At exact zero temperature intrinsic semiconductor acts as a perfect insulator, which does not show any conduction .However, as the temperature increases free electrons and holes get created.
Mathematically we can write ;
\[{E_F} = {\dfrac{{{E_C} + {E_V}}}{2}_{}}\]
${E_F}$ ,is the fermi level ,${E_C}$ is the conduction band,${E_V}$ is the valence band .