Concept:At \( 0\text{ K} \), no thermal energy is available to promote electrons across the energy bandgap into the conduction band.
Formula:$$n_i(0\text{ K}) = 0 \implies \sigma = e(n\mu_n + p\mu_p) = 0\text{ S/m}$$
Solution:- At \( 0\text{ K} \), all valence electrons are bound in covalent bonds, leaving the valence band full.
- The conduction band is completely empty, and no electron-hole pairs are thermally generated.
- Without mobile charge carriers, electrical conductivity is zero (\( \sigma = 0 \)), and intrinsic silicon behaves as an insulator.
Why other options are incorrect:- Option A: Silicon is a semiconductor and does not exhibit superconductivity at \( 0\text{ K} \).
- Option B: Metallic conduction requires partially filled bands or overlapping band structures, which are not present in pure silicon.
- Option C: Plasma conduction requires ionized gas states, which do not apply to solid-state semiconductors.
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