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.
Step 1 (Governing Law & Definition): [0.25 Mark]
The conductivity ($\sigma$) of a semiconductor is given by the relation:
$$\sigma = e(n_e \mu_e + n_h \mu_h)$$Where $n_e$ and $n_h$ are the concentrations of electrons and holes, and $\mu_e$ and $\mu_h$ are their respective mobilities.
Step 2 (Step-by-Step Logical Analysis): [0.50 Mark]
- In an n-type semiconductor, the majority charge carriers are electrons, and in a p-type semiconductor, the majority charge carriers are holes.
- The mobility of electrons ($\mu_e$) is significantly higher than the mobility of holes ($\mu_h$) because electrons move in the conduction band, whereas holes move in the valence band, where they experience more scattering and restricted motion.
- Since $\mu_e > \mu_h$, for the same doping concentration, the conductivity of an n-type semiconductor is higher than that of a p-type semiconductor.
- Therefore, both the Assertion (A) and the Reason (R) are true, and the Reason (R) is the correct explanation for the Assertion (A).
Step 3 (Final Concluded Answer): [0.25 Mark]
Correct Option: Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
💡 EL10 Concept Insight: Think of electrons as runners on a smooth track (conduction band) and holes as people trying to move through a crowded room (valence band); because the electrons have a much clearer path, they move faster, making n-type materials better conductors.