Question

The product of electron and hole concentration in an extrinsic semiconductor is?

• A. Infinity
• B. Dependent of impurity concentration
• C. Independent of impurity concentration
• D. Zero

Hint:

In extrinsic semiconductors, the product of electron and hole concentrations is always equal to the square of the intrinsic carrier concentration (\(n \cdot p = n_i^2\)) and does not depend on impurity levels.

Answer 1

The Correct Option is C

In an extrinsic semiconductor, the electron and hole concentrations are primarily controlled by the impurities (dopants) introduced into the semiconductor material. However, the product of the electron concentration (\(n\)) and hole concentration (\(p\)) in such a material is constant and is given by the intrinsic carrier concentration (\(n_i\)) squared. This is a fundamental property of semiconductors, as described by the relation: \[ n \cdot p = n_i^2 \] This product is independent of the concentration of dopants (impurities) because the intrinsic carrier concentration \(n_i\) is determined by the material properties, not by the doping level.
- Infinity is not correct, as the product of electron and hole concentration is finite in a semiconductor.
- Dependent of impurity concentration is incorrect because, as explained, the product is constant for a given material.
- Zero is incorrect because the product of the electron and hole concentrations is never zero in an intrinsic or extrinsic semiconductor, unless the material is completely depleted of carriers (which does not occur in typical extrinsic semiconductors).
Thus, the product of the electron and hole concentrations in an extrinsic semiconductor is independent of impurity concentration.