JEE Physics 2025 Question with Solution

Given: An $n$-type semiconductor with electron concentration $n_e$ and hole concentration $n_h$.

Find: Which combination of statements is correct.

Evaluate each statement:

1. (A) Holes are minority carriers — In an $n$-type semiconductor, electrons are the majority carriers, so holes are minority carriers. Hence (A) is true.

2. (B) The dopant is a pentavalent atom — $n$-type semiconductors are formed by doping with pentavalent impurities, so (B) is true.

3. (C) $n_e n_h = n_i^2$ for intrinsic semiconductor — The mass action law is

For an intrinsic semiconductor, $n_e = n_h = n_i$, so the relation is valid. Hence (C) is true.

4. (D) $n_e \gg n_h$ for extrinsic semiconductor — This is not true for all extrinsic semiconductors, because in a $p$-type semiconductor holes are the majority carriers. So as stated for extrinsic semiconductor in general, (D) is false.

Therefore, the correct combination is (A), (B) and (C) only, so the correct option is C.

Note: The first solution block in the source contains an internal inconsistency in its explanation, but the marked correct option and the second approach both support option C.

Given: Statements about an $n$-type semiconductor.

Find: The correct option by checking the truth value of each statement.

For $n$-type semiconductor:

• Majority carriers are electrons.
• Minority carriers are holes.
• Dopants are usually pentavalent atoms.

Also, under equilibrium,

This relation holds for semiconductors, and for an intrinsic semiconductor specifically, $n_e = n_h = n_i$.

Now check the options:

• (A) True
• (B) True
• (C) True
• (D) As written for extrinsic semiconductor in general, false

Hence the correct set is (A), (B) and (C) only.

Therefore, the correct option is C.