Question

Consider a n-type semiconductor in which $ n_e $ and $ n_h $ are the number of electrons and holes, respectively.

• A. Holes are minority carriers
• B. The dopant is a pentavalent atom
• C. \( n_e n_h = n_i^2 \) for intrinsic semiconductor
• D. \( n_e \gg n_h \) for extrinsic semiconductor The correct answer from the options given below is:

Hint:

In n-type semiconductors, electrons are the majority carriers, and holes are the minority carriers. The product of electron and hole concentrations is related to the intrinsic carrier concentration in an intrinsic semiconductor.

Answer 1

The Correct Option is C

To determine the correct answer, each statement regarding an n-type semiconductor is evaluated:

1. Holes are minority carriers: In an n-type semiconductor, electrons are the majority carriers due to pentavalent dopants (e.g., Phosphorus, Arsenic). Therefore, the electron concentration \(n_e\) significantly exceeds the hole concentration \(n_h\). This statement correctly identifies holes as minority carriers. However, it is not the given correct answer.
2. The dopant is a pentavalent atom: N-type semiconductors are doped with pentavalent atoms, possessing five valence electrons, such as Phosphorus, Arsenic, or Antimony. This statement is factual for n-type semiconductors but is not the correct answer according to the problem.
3. \( n_e n_h = n_i^2 \) for intrinsic semiconductor: This equation represents the mass action law for semiconductors, where \(n_i\) is the intrinsic carrier concentration. It is universally applicable to all semiconductor conditions, irrespective of doping. In an intrinsic semiconductor, \(n_e = n_h = n_i\). This statement is always true and aligns with the provided correct answer.
4. \( n_e \gg n_h \) for extrinsic semiconductor: An n-type semiconductor is an extrinsic type. Here, the electron concentration \(n_e\) is substantially greater than the hole concentration \(n_h\) due to the added electrons from dopants. While practically true, this is not the designated correct option in the problem.

Consequently, the correct answer is: \( n_e n_h = n_i^2 \) for intrinsic semiconductor. This principle is a foundational concept in semiconductor physics and remains valid under equilibrium conditions for all semiconductors, whether intrinsic or extrinsic.