Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Silicon doped with arsenic has a smaller hole concentration than pure silicon at the same temperature.
Reason (R): In the doped crystal, the large number of free electrons gives the thermally generated holes a greater chance of meeting electrons and recombining.
In the light of the above statements, choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Both (A) and (R) are true and (R) is the correct explanation of (A).
Arsenic is a pentavalent donor, so arsenic-doped silicon is n-type. Free electrons are its majority carriers and holes its minority carriers.
Assertion (A) Silicon doped with arsenic has a smaller hole concentration than pure silicon at the same temperature. — True. In pure silicon \( n_h=n_i \). In the doped crystal \( n_h=n_i^{2}/n_e \). Since \( n_e\gg n_i \), the hole concentration falls well below \( n_i \).
Reason (R) In the doped crystal, the large number of free electrons gives the thermally generated holes a greater chance of meeting electrons and recombining. — True. Around each hole made by thermal energy there are very many free electrons from the donors. So the hole meets an electron and recombines much sooner than in pure silicon.
Why R explains A?
Holes are still produced thermally in the doped crystal. But each one is soon destroyed when it recombines with one of the many free electrons.
So fewer holes survive at any moment, and the hole concentration drops below its intrinsic value. Hence (R) is the correct explanation of (A).
NCERT (2026-27):
Extrinsic Semiconductor – “… In extrinsic semiconductors, because of the abundance of majority current carriers, the minority carriers produced thermally have more chance of meeting majority carriers and thus getting destroyed. Hence, the dopant, by adding a large number of current carriers of one type, which become the majority carriers, indirectly helps to reduce the intrinsic concentration of minority carriers.”