Question

For pure semiconductor

• A. No. of electrons = number of holes
• B. No. of electrons>number of holes
• C. No. of electrons<number of holes
• D. None of these

Hint:

- Intrinsic (pure): $n_e = n_h$
- n-type (doped with pentavalent): $n_e \gg n_h$
- p-type (doped with trivalent): $n_h \gg n_e$

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
A pure semiconductor, also known as an intrinsic semiconductor, is one without any significant dopant atoms present. Its electrical conductivity is determined solely by its inherent properties.
Step 2: Key Formula or Approach:
In an intrinsic semiconductor, charge carriers are generated through thermal excitation.
Step 3: Detailed Explanation:
At absolute zero temperature (0 K), the valence band is completely full and the conduction band is completely empty. The material behaves as a perfect insulator.
As temperature increases, thermal energy breaks some covalent bonds. When an electron is freed and jumps from the valence band to the conduction band, it leaves behind a vacancy in the valence band. This vacancy behaves as a positively charged particle and is called a 'hole'.
Because every free electron in the conduction band was created by leaving exactly one hole in the valence band, the generation of charge carriers always occurs in pairs (electron-hole pairs).
Therefore, in a pure (intrinsic) semiconductor, the number density of intrinsic electrons (\(n_e\)) is strictly equal to the number density of intrinsic holes (\(n_h\)).
\[ n_e = n_h = n_i \]
Where \(n_i\) is the intrinsic carrier concentration.
Step 4: Final Answer:
For a pure semiconductor, the number of electrons equals the number of holes.