Assertion–Reason: (A) The conductivity of a p-type semiconductor is higher than that of an intrinsic semiconductor. (R) Adding donor impurities creates extra energy levels just below the conduction band.

Difficulty: Medium

Correct Answer: A is true but R is false

Explanation:


Introduction / Context:
Assertion–Reason questions evaluate not only factual correctness but also causal linkage. Here we compare conductivity of p-type versus intrinsic material and examine whether the stated reason logically supports the assertion.


Given Data / Assumptions:

  • Intrinsic semiconductor: n = p = ni; conductivity σi = q ni (μn + μp).
  • p-type semiconductor: majority holes with p ≫ n; conductivity σp ≈ q p μp with p set by acceptor doping.
  • Donor impurities (n-type) introduce energy levels near the conduction band; acceptor impurities (p-type) introduce levels near the valence band.


Concept / Approach:
The assertion states p-type conductivity exceeds intrinsic conductivity—usually true, because doping greatly increases majority carrier concentration compared to ni at room temperature. The reason, however, mentions donor impurities (n-type mechanism) rather than acceptors, so it does not explain the improved conductivity of a p-type semiconductor. Thus A is true, R is false in this context.


Step-by-Step Solution:

Assess A: Doping (acceptors) raises hole concentration well above ni → σ increases → A is true.Assess R: Donor levels below conduction band correspond to n-type doping, irrelevant to p-type improvement → R is false as an explanation for A.Therefore, correct choice: A true, R false.


Verification / Alternative check:

If R had referred to acceptor levels near the valence band (promoting holes), it could have explained A. Since it does not, the pairing fails.


Why Other Options Are Wrong:

(a) Incorrect because R does not support A.(b) R is not even true in the p-type context used to explain A.(d) A is not false; p-type typically has higher σ than intrinsic.


Common Pitfalls:

Overlooking the specific impurity type (donor vs acceptor) in reason statements.


Final Answer:

A is true but R is false

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