Question

Assertion (A) : The conductivity of an n-type semiconductor is higher than that of a p-type semiconductor at a given temperature.
Reason (R) : The electrons being in the conduction band in n-type semiconductor are more mobile than the holes in the valence band in p-type semiconductor.

• A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
• B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
• C. Assertion (A) is true, but Reason (R) is false.
• D. Both Assertion (A) and Reason (R) are false.

Hint:

Electrons in the conduction band have lower effective mass and move in empty states, making $\mu_e > \mu_h$. Because conductivity $\sigma \propto \mu$, n-type semiconductors are preferred for high-frequency operations.\

Answer 1

The Correct Option is A

Concept:
• Electrical conductivity of an extrinsic semiconductor is determined by the concentration and mobility of charge carriers, given by $\sigma = e(n_e \mu_e + n_h \mu_h)$.
• In an n-type semiconductor, majority carriers are electrons in the conduction band, while in a p-type semiconductor, majority carriers are holes in the valence band.
• Mobility refers to the magnitude of the drift velocity acquired by a charge carrier per unit applied electric field ($\mu = \frac{v_d}{E}$).

Step 1: Analyze the Assertion (A)
For semiconductors with identical doping levels ($N_d \approx N_a$), the majority carrier density in n-type semiconductor ($n_e$) is equal to that in p-type semiconductor ($n_h$).
The conductivity of an n-type semiconductor is dominated by electrons: $\sigma_n \approx e n_e \mu_e = e N_d \mu_e$.
The conductivity of a p-type semiconductor is dominated by holes: $\sigma_p \approx e n_h \mu_h = e N_a \mu_h$.
Because electron mobility $\mu_e$ is substantially higher than hole mobility $\mu_h$, the resulting conductivity $\sigma_n$ of n-type semiconductor is greater than $\sigma_p$ of p-type semiconductor.
Therefore, Assertion (A) is true.

Step 2: Analyze the Reason (R)
Electrons move freely in the conduction band where available energy states are largely vacant and inter-atomic binding is negligible.
Holes move in the valence band through a process of bound electrons jumping into adjacent vacancies, encountering significantly more resistance and scattering from the crystal lattice.
Consequently, the mobility of electrons ($\mu_e$) in the conduction band is inherently greater than the mobility of holes ($\mu_h$) in the valence band.
Therefore, Reason (R) is true and correctly explains why n-type semiconductors have higher conductivity.

Step 3: Conclusion
Both Assertion (A) and Reason (R) are correct, and Reason (R) provides the accurate physical justification for Assertion (A). Hence, option (A) is the correct choice.