Concept:At \( 0\text{ K} \), there is no thermal energy to break covalent bonds. The valence band is completely full and the conduction band is completely empty, leaving zero charge carriers to conduct current.
Formula:$$\sigma(T = 0\text{ K}) = q (n \mu_n + p \mu_p) = 0 \implies I = 0$$
Solution:- At \( 0\text{ K} \), \( n = 0 \) and \( p = 0 \).
- With no free electrons or holes available, the material has zero electrical conductivity and acts as a perfect insulator.
Why other options are incorrect:- Option B: Even without lattice scattering, current cannot flow without mobile charge carriers.
- Option C: Hole generation requires electrons to be excited out of the valence band, which cannot occur at 0 K.
- Option D: Pure semiconductors do not form Cooper pairs or exhibit superconductivity at 0 K.
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