Concept:At absolute zero (\( 0\text{ K} \)), no thermal energy is available to break covalent bonds or excite electrons across the bandgap into the conduction band.
Formula:$$n_i(T = 0\text{ K}) = 0 \implies \sigma = q (n\mu_n + p\mu_p) = 0 \implies R \to \infty$$
Solution:- At \( 0\text{ K} \), the valence band is completely filled and the conduction band is completely empty.
- With zero free electrons and zero holes, electrical conductivity is zero, so the semiconductor acts as a perfect insulator.
Why other options are incorrect:- Option A: Superconductivity requires free electrons that form Cooper pairs, which are absent in semiconductors at 0 K.
- Option C: Conductors have free electrons even at 0 K; semiconductors do not.
- Option D: Semi-metals have a small band overlap at all temperatures, unlike semiconductors.
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