Question

In an intrinsic semiconductor, the number of free electrons,
A. Equals the number of holes
B. Is greater than the number of holes
C. Is less than the number of holes
D. None of the above

Answer 1

Hint: The quantity of charge carriers is thus dictated by the material's characteristics rather than the number of impurities. The number of excited electrons and holes in intrinsic semiconductors is equal: \[n = p\] . This may be true even after the semiconductor has been doped, but only if both donors and acceptors have been equally doped. This scenario \[n = p\] holds true, and the semiconductor is intrinsic, despite being doped.

Complete step by step solution:
An intrinsic semiconductor has not been doped with any other material (similar to mixing). For instance, Si and Ge. At absolute zero, it acts as an insulator. Thermodynamic energy excites electrons. They differ from pure semiconductors in that they may include certain impurities. Because impurities offer a few energy levels in the bandgap, intrinsic semiconductors have higher conductivity than pure semiconductors.
The potential difference is given to an intrinsic semiconductor means, the electron from one of the bonds is free, and at the same place, the vacancy was generated. So the only equal number of holes and electrons are generated in the intrinsic semiconductor.
So the option (A) is correct.

Additional Information:
Let us consider the another options:
Option (B)
If we apply power or increase a temperature to an intrinsic semiconductor, the electron bond will be broken, and the electron will generate. At the same time, the place where electrons get free, the vacancy was generated, it is called holes. So there is no chance to generate greater holes. So the option (B) is wrong.
Option (C)
If we apply a potential difference to an intrinsic semiconductor means, the electron bond will be broken, at the same place, the holes will be generated. So there is no chance to generate high electrons compared to a-holes. So the option (C) was wrong.

Note:
Pure semiconductors are those that are free of impurities. In an ideal world, no semiconductor exists in nature that is completely pure. In a semiconductor, holes do not truly move. The movement of holes can be thought of as electrons moving from the valence band to the conduction band and from one atom to the next.