Assertion–Reason on acceptor (p-type) semiconductors and conductivity Assertion (A): An acceptor-doped (p-type) extrinsic semiconductor has higher conductivity than the intrinsic semiconductor at the same temperature. Reason (R): Adding a p-type impurity introduces an allowable discrete acceptor energy level just above the valence band, enabling easier hole formation.
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ABoth A and R are true and R is correct explanation of A
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BBoth A and R are true but R is not correct explanation of A
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CA is true but R is false
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DA is false but R is true
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EBoth A and R are false
Answer
Correct Answer: Both A and R are true and R is correct explanation of A
Explanation
Introduction / Context:Doping dramatically increases semiconductor conductivity by creating majority carriers. In p-type materials, acceptor dopants facilitate hole generation with far less thermal energy than intrinsic excitation requires. This question examines whether the microscopic band-structure explanation correctly justifies the macroscopic increase in conductivity.
Given Data / Assumptions:
- Intrinsic semiconductor at a given temperature has limited carrier concentration n = p = ni.
- Acceptor doping (e.g., boron in Si) introduces energy levels slightly above the valence band edge.
- Conductivity σ = q (n μn + p μp).
Concept / Approach:
With acceptor levels present, electrons from the valence band can be thermally promoted into these levels with a small energy, leaving behind holes in the valence band. The hole concentration increases greatly compared to intrinsic, so σ rises even if mobility changes modestly. Therefore A is true. The reason R correctly states the band-structure mechanism (acceptor level just above the valence band), which directly explains the rise in hole population and thus conductivity, so R also is true and explains A.
Step-by-Step Solution:
Write σ = q (n μn + p μp).In intrinsic: n = p = ni → relatively small.In p-type: p ≈ N_A (for moderate doping, full ionization) >> ni → σ increases.Mechanism: acceptor level above valence band allows easy electron capture → holes left in valence band.Verification / Alternative check:
Hall measurements show positive Hall coefficients and higher conductivity in p-type samples compared to intrinsic wafers at room temperature, validating the explanation.
Why Other Options Are Wrong:
If R were false, the main microscopic justification for increased hole concentration would be missing. Claims that R does not explain A ignore the direct causal link between acceptor levels and hole generation.
Common Pitfalls:
Confusing the position of donor versus acceptor levels; assuming conductivity depends only on mobility rather than carrier concentration.
Final Answer:
Both A and R are true and R is correct explanation of A