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.

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:

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