Concept:At \(T = 0\text{ K}\), electrons possess zero thermal energy to jump across the forbidden energy bandgap (\(E_g\)). The valence band is completely full and the conduction band is completely empty, meaning there are no mobile charge carriers available for conduction.
Formula:$$n_i = p_i = 0 \quad \text{at } T = 0\text{ K}$$
$$\sigma = q(n\mu_n + p\mu_p) = 0 \implies R = \infty$$
Solution:- At \(0\text{ K}\), all valence electrons remain bound in covalent bonds.
- With zero electrons in the conduction band and zero holes in the valence band, electrical conductivity \(\sigma\) is zero.
- Hence, the semiconductor behaves as a perfect insulator.
Why other options are incorrect:- Option B: Superconductors have zero resistance; semiconductors at \(0\text{ K}\) have infinite resistance.
- Option C: There are no thermally liberated free electrons at \(0\text{ K}\).
- Option D: The energy bandgap remains non-zero (approx. \(1.17\text{ eV}\) for Si at \(0\text{ K}\)).
Quality & Fidelity Assurance:
Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.